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Sample records for two-equation closure modelling

  1. Flow and transport simulation of Madeira River using three depth-averaged two-equation turbulence closure models

    Directory of Open Access Journals (Sweden)

    Li-ren Yu

    2012-03-01

    Full Text Available This paper describes a numerical simulation in the Amazon water system, aiming to develop a quasi-three-dimensional numerical tool for refined modeling of turbulent flow and passive transport of mass in natural waters. Three depth-averaged two-equation turbulence closure models, k˜−ε˜,k˜−w˜, and k˜−ω˜ , were used to close the non-simplified quasi-three dimensional hydrodynamic fundamental governing equations. The discretized equations were solved with the advanced multi-grid iterative method using non-orthogonal body-fitted coarse and fine grids with collocated variable arrangement. Except for steady flow computation, the processes of contaminant inpouring and plume development at the beginning of discharge, caused by a side-discharge of a tributary, have also been numerically investigated. The three depth-averaged two-equation closure models are all suitable for modeling strong mixing turbulence. The newly established turbulence models such as the k˜−ω˜ model, with a higher order of magnitude of the turbulence parameter, provide a possibility for improving computational precision.

  2. An upscaled two-equation model of transport in porous media through unsteady-state closure of volume averaged formulations

    Science.gov (United States)

    Chaynikov, S.; Porta, G.; Riva, M.; Guadagnini, A.

    2012-04-01

    . Consistently with the two-region model working hypotheses, we subdivide the pore space into two volumes, which we select according to the features of the local micro-scale velocity field. Assuming separation of the scales, the mathematical development associated with the averaging method in the two volumes leads to a generalized two-equation model. The final (upscaled) formulation includes the standard first order mass exchange term together with additional terms, which we discuss. Our developments allow to identify the assumptions which are usually implicitly embedded in the usual adoption of a two region mobile-mobile model. All macro-scale properties introduced in this model can be determined explicitly from the pore-scale geometry and hydrodynamics through the solution of a set of closure equations. We pursue here an unsteady closure of the problem, leading to the occurrence of nonlocal (in time) terms in the upscaled system of equations. We provide the solution of the closure problems for a simple application documenting the time dependent and the asymptotic behavior of the system.

  3. Non-Equilibrium Turbulence and Two-Equation Modeling

    Science.gov (United States)

    Rubinstein, Robert

    2011-01-01

    Two-equation turbulence models are analyzed from the perspective of spectral closure theories. Kolmogorov theory provides useful information for models, but it is limited to equilibrium conditions in which the energy spectrum has relaxed to a steady state consistent with the forcing at large scales; it does not describe transient evolution between such states. Transient evolution is necessarily through nonequilibrium states, which can only be found from a theory of turbulence evolution, such as one provided by a spectral closure. When the departure from equilibrium is small, perturbation theory can be used to approximate the evolution by a two-equation model. The perturbation theory also gives explicit conditions under which this model can be valid, and when it will fail. Implications of the non-equilibrium corrections for the classic Tennekes-Lumley balance in the dissipation rate equation are drawn: it is possible to establish both the cancellation of the leading order Re1/2 divergent contributions to vortex stretching and enstrophy destruction, and the existence of a nonzero difference which is finite in the limit of infinite Reynolds number.

  4. Assessment of consistent two-equation closure for forest flows

    DEFF Research Database (Denmark)

    Sogachev, Andrey; Cavar, Dalibor; Bechmann, Andreas

    of grid turbulence and wall-bounded flow, the closure suggested is also valid for homogeneous shear flows commonly observed inside tall vegetative canopies. The present work assess the plant drag closure by comparing results of two different CFD models against observations derived over the forested area...... and can be applied for any twoequation closure. Results derived by different CFD models with k-epsilon and k-omega closure are similar and in good comparison with observations. Overall, numerical results show that the closure performs well, opening new possibilities for application to tasks related...... to the atmospheric boundary layer—where it is important to adequately account for the influences of vegetation....

  5. Numerical approximation of the Boltzmann equation : moment closure

    NARCIS (Netherlands)

    Abdel Malik, M.R.A.; Brummelen, van E.H.

    2012-01-01

    This work applies the moment method onto a generic form of kinetic equations to simplify kinetic models of particle systems. This leads to the moment closure problem which is addressed using entropy-based moment closure techniques utilizing entropy minimization. The resulting moment closure system

  6. Some Recent Developments in Turbulence Closure Modeling

    Science.gov (United States)

    Durbin, Paul A.

    2018-01-01

    Turbulence closure models are central to a good deal of applied computational fluid dynamical analysis. Closure modeling endures as a productive area of research. This review covers recent developments in elliptic relaxation and elliptic blending models, unified rotation and curvature corrections, transition prediction, hybrid simulation, and data-driven methods. The focus is on closure models in which transport equations are solved for scalar variables, such as the turbulent kinetic energy, a timescale, or a measure of anisotropy. Algebraic constitutive representations are reviewed for their role in relating scalar closures to the Reynolds stress tensor. Seamless and nonzonal methods, which invoke a single closure model, are reviewed, especially detached eddy simulation (DES) and adaptive DES. Other topics surveyed include data-driven modeling and intermittency and laminar fluctuation models for transition prediction. The review concludes with an outlook.

  7. Formal derivation of a 6 equation macro scale model for two-phase flows - link with the 4 equation macro scale model implemented in Flica 4; Etablissement formel d'un modele diphasique macroscopique a 6 equations - lien avec le modele macroscopique a 4 equations flica 4

    Energy Technology Data Exchange (ETDEWEB)

    Gregoire, O

    2008-07-01

    In order to simulate nuclear reactor cores, we presently use the 4 equation model implemented within FLICA4 code. This model is complemented with 2 algebraic closures for thermal disequilibrium and relative velocity between phases. Using such closures, means an 'a priori' knowledge of flows calculated in order to ensure that modelling assumptions apply. In order to improve the degree of universality to our macroscopic modelling, we propose in the report to derive a more general 6 equation model (balance equations for mass, momentum and enthalpy for each phase) for 2-phase flows. We apply the up-scaling procedure (Whitaker, 1999) classically used in porous media analysis to the statistically averaged equations (Aniel-Buchheit et al., 2003). By doing this, we apply the double-averaging procedure (Pedras and De Lemos, 2001 and Pinson et al. 2006): statistical and spatial averages. Then, using weighted averages (analogous to Favre's average) we extend the spatial averaging concept to variable density and 2-phase flows. This approach allows the global recovering of the structure of the systems of equations implemented in industrial codes. Supplementary contributions, such as dispersion, are also highlighted. Mechanical and thermal exchanges between solids and fluid are formally derived. Then, thanks to realistic simplifying assumptions, we show how it is possible to derive the original 4 equation model from the full 6 equation model. (author)

  8. Mathematical modeling and the two-phase constitutive equations

    International Nuclear Information System (INIS)

    Boure, J.A.

    1975-01-01

    The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

  9. Hamiltonian closures in fluid models for plasmas

    Science.gov (United States)

    Tassi, Emanuele

    2017-11-01

    This article reviews recent activity on the Hamiltonian formulation of fluid models for plasmas in the non-dissipative limit, with emphasis on the relations between the fluid closures adopted for the different models and the Hamiltonian structures. The review focuses on results obtained during the last decade, but a few classical results are also described, in order to illustrate connections with the most recent developments. With the hope of making the review accessible not only to specialists in the field, an introduction to the mathematical tools applied in the Hamiltonian formalism for continuum models is provided. Subsequently, we review the Hamiltonian formulation of models based on the magnetohydrodynamics description, including those based on the adiabatic and double adiabatic closure. It is shown how Dirac's theory of constrained Hamiltonian systems can be applied to impose the incompressibility closure on a magnetohydrodynamic model and how an extended version of barotropic magnetohydrodynamics, accounting for two-fluid effects, is amenable to a Hamiltonian formulation. Hamiltonian reduced fluid models, valid in the presence of a strong magnetic field, are also reviewed. In particular, reduced magnetohydrodynamics and models assuming cold ions and different closures for the electron fluid are discussed. Hamiltonian models relaxing the cold-ion assumption are then introduced. These include models where finite Larmor radius effects are added by means of the gyromap technique, and gyrofluid models. Numerical simulations of Hamiltonian reduced fluid models investigating the phenomenon of magnetic reconnection are illustrated. The last part of the review concerns recent results based on the derivation of closures preserving a Hamiltonian structure, based on the Hamiltonian structure of parent kinetic models. Identification of such closures for fluid models derived from kinetic systems based on the Vlasov and drift-kinetic equations are presented, and

  10. Gravitational closure of matter field equations

    Science.gov (United States)

    Düll, Maximilian; Schuller, Frederic P.; Stritzelberger, Nadine; Wolz, Florian

    2018-04-01

    The requirement that both the matter and the geometry of a spacetime canonically evolve together, starting and ending on shared Cauchy surfaces and independently of the intermediate foliation, leaves one with little choice for diffeomorphism-invariant gravitational dynamics that can equip the coefficients of a given system of matter field equations with causally compatible canonical dynamics. Concretely, we show how starting from any linear local matter field equations whose principal polynomial satisfies three physicality conditions, one may calculate coefficient functions which then enter an otherwise immutable set of countably many linear homogeneous partial differential equations. Any solution of these so-called gravitational closure equations then provides a Lagrangian density for any type of tensorial geometry that features ultralocally in the initially specified matter Lagrangian density. Thus the given system of matter field equations is indeed closed by the so obtained gravitational equations. In contrast to previous work, we build the theory on a suitable associated bundle encoding the canonical configuration degrees of freedom, which allows one to include necessary constraints on the geometry in practically tractable fashion. By virtue of the presented mechanism, one thus can practically calculate, rather than having to postulate, the gravitational theory that is required by specific matter field dynamics. For the special case of standard model matter one obtains general relativity.

  11. Data-driven non-Markovian closure models

    Science.gov (United States)

    Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael

    2015-03-01

    This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model's parameter

  12. Modelling turbulence around and inside porous media based on the second moment closure

    International Nuclear Information System (INIS)

    Kuwata, Yusuke; Suga, Kazuhiko

    2013-01-01

    Highlights: • A novel turbulence model for flows in porous media is proposed. • Three stress tensors emerging in double averaging N–S are individually modelled. • The most advanced second moment closure is applied for the macro-scale stress. • A one equation and the Smagorinsky models are applied to the other stresses. • Promising results are obtained in test flows around and inside porous media. -- Abstract: To predict turbulence in porous media, a new approach is discussed. By double (both volume and Reynolds) averaging Navier–Stokes equations, there appear three unknown covariant terms in the momentum equation. They are namely the dispersive covariance, the macro-scale and the micro-scale Reynolds stresses, in the present study. For the macro-scale Reynolds stress, the TCL (two-component-limit) second moment closure is applied whereas the eddy viscosity models are applied to the other covariant terms: the Smagorinsky model and the one-equation eddy viscosity model, respectively for the dispersive covariance and the micro-scale Reynolds stress. The presently proposed model is evaluated in square rib array flows and porous wall channel flows with reasonable accuracy though further development is required

  13. Macroscopic balance equations for two-phase flow models

    International Nuclear Information System (INIS)

    Hughes, E.D.

    1979-01-01

    The macroscopic, or overall, balance equations of mass, momentum, and energy are derived for a two-fluid model of two-phase flows in complex geometries. These equations provide a base for investigating methods of incorporating improved analysis methods into computer programs, such as RETRAN, which are used for transient and steady-state thermal-hydraulic analyses of nuclear steam supply systems. The equations are derived in a very general manner so that three-dimensional, compressible flows can be analysed. The equations obtained supplement the various partial differential equation two-fluid models of two-phase flow which have recently appeared in the literature. The primary objective of the investigation is the macroscopic balance equations. (Auth.)

  14. Modified two-fluid model for the two-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.

    2003-01-01

    This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

  15. Geometric analysis of the solutions of two-phase flows: two-fluid model

    International Nuclear Information System (INIS)

    Kestin, J.; Zeng, D.L.

    1984-01-01

    This report contains a lightly edited draft of a study of the two-fluid model in two-phase flow. The motivation for the study stems from the authors' conviction that the construction of a computer code for any model should be preceded by a geometrical analysis of the pattern of trajectories in the phase space appropriate for the model. Such a study greatly facilitates the understanding of the phenomenon of choking and anticipates the computational difficulties which arise from the existence of singularities. The report contains a derivation of the six conservation equations of the model which includes a consideration of the simplifications imposed on a one-dimensional treatment by the presence of boundary layers at the wall and between the phases. The model is restricted to one-dimensional adiabatic flows of a single substance present in two phases, but thermodynamic equilibrium between the phases is not assumed. The role of closure conditions is defined but no specific closure conditions, or explicit equations of state, are introduced

  16. Eight equation model for arbitrary shaped pipe conveying fluid

    International Nuclear Information System (INIS)

    Gale, J.; Tiselj, I.

    2006-01-01

    Linear eight-equation system for two-way coupling of single-phase fluid transient and arbitrary shaped one-dimensional pipeline movement is described and discussed. The governing phenomenon described with this system is also known as Fluid-Structure Interaction. Standard Skalak's four-equation model for axial coupling was improved with additional four Timoshenko's beam equations for description of flexural displacements and rotations. In addition to the conventional eight-equation system that enables coupling of straight sections, the applied mathematical model was improved for description of the arbitrary shaped pipeline located in two-dimensional plane. The applied model was solved with second-order accurate numerical method that is based on Godounov's characteristic upwind schemes. The model was successfully used for simulation of the rod impact induced transient and conventional instantaneous valve closure induced transient in the tank-pipe-valve system. (author)

  17. Revisit to Grad's Closure and Development of Physically Motivated Closure for Phenomenological High-Order Moment Model

    International Nuclear Information System (INIS)

    Myong, R. S.; Nagdewe, S. P.

    2011-01-01

    The Grad's closure for the high-order moment equation is revisited and, by extending his theory, a physically motivated closure is developed for the one-dimensional velocity shear gas flow. The closure is based on the physical argument of the relative importance of various terms appearing in the moment equation. Also, the closure is derived such that the resulting theory may be inclusive of the well established linear theory (Navier-Stokes-Fourier) as limiting case near local thermal equilibrium.

  18. Structure of highly asymmetric hard-sphere mixtures: an efficient closure of the Ornstein-Zernike equations.

    Science.gov (United States)

    Amokrane, S; Ayadim, A; Malherbe, J G

    2005-11-01

    A simple modification of the reference hypernetted chain (RHNC) closure of the multicomponent Ornstein-Zernike equations with bridge functions taken from Rosenfeld's hard-sphere bridge functional is proposed. Its main effect is to remedy the major limitation of the RHNC closure in the case of highly asymmetric mixtures--the wide domain of packing fractions in which it has no solution. The modified closure is also much faster, while being of similar complexity. This is achieved with a limited loss of accuracy, mainly for the contact value of the big sphere correlation functions. Comparison with simulation shows that inside the RHNC no-solution domain, it provides a good description of the structure, while being clearly superior to all the other closures used so far to study highly asymmetric mixtures. The generic nature of this closure and its good accuracy combined with a reduced no-solution domain open up the possibility to study the phase diagram of complex fluids beyond the hard-sphere model.

  19. Development of a three-dimensional local scale atmospheric model with turbulence closure model

    International Nuclear Information System (INIS)

    Yamazawa, Hiromi

    1989-05-01

    Through the study to improve SPEEDI's capability, a three-dimensional numerical atmospheric model PHYSIC (Prognostic HYdroStatic model Including turbulence Closure model) was developed to apply it to the transport and diffusion evaluation over complex terrains. The detailed description of the atmospheric model was given. This model consists of five prognostic equations; the momentum equations of horizontal components with the so-called Boussinesq and hydrostatic assumptions, the conservation equations of heat, turbulence kinetic energy and turbulence length scale. The coordinate system used is the terrain following z * coordinate system which allows the existence of complex terrain. The minute formula of the turbulence closure calculation, the surface layer process, the ground surface heat budget, and the atmospheric and solar radiation were also presented. The time integration method used in this model is the Alternating Direction Implicit (A.D.I.) method with a vertically and horizontally staggered grid system. The memory storage needed to execute this model with 31 x 31 x 16 grid points, five layers in soil and double precision variables is about 5.3 MBytes. The CPU time is about 2.2 x 10 -5 s per one step per one grid point with a vector processor FACOM VP-100. (author)

  20. A modified two-fluid model for the application of two-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Sun, X.; Ishii, M.; Kelly, J.

    2003-01-01

    This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

  1. Hamiltonian fluid closures of the Vlasov-Ampère equations: From water-bags to N moment models

    Energy Technology Data Exchange (ETDEWEB)

    Perin, M.; Chandre, C.; Tassi, E. [Aix-Marseille Université, Université de Toulon, CNRS, CPT UMR 7332, 13288 Marseille (France); Morrison, P. J. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712-1060 (United States)

    2015-09-15

    Moment closures of the Vlasov-Ampère system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two, and three water-bags are treated and their Hamiltonian structures are provided. In each case, we give the associated fluid closures and we discuss their Casimir invariants. We show how the method can be extended to an arbitrary number of fields, i.e., an arbitrary number of water-bags and associated moments. The thermodynamic interpretation of the resulting models is discussed. Finally, a general procedure to derive Hamiltonian N-field fluid models is proposed.

  2. RELAP-7 Closure Correlations

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Ling [Idaho National Lab. (INL), Idaho Falls, ID (United States); Berry, R. A. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Martineau, R. C. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Andrs, D. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, H. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Hansel, J. E. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Sharpe, J. P. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Johns, Russell C. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2017-04-01

    The RELAP-7 code is the next generation nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). The code is based on the INL’s modern scientific software development framework, MOOSE (Multi-Physics Object Oriented Simulation Environment). The overall design goal of RELAP-7 is to take advantage of the previous thirty years of advancements in computer architecture, software design, numerical integration methods, and physical models. The end result will be a reactor systems analysis capability that retains and improves upon RELAP5’s and TRACE’s capabilities and extends their analysis capabilities for all reactor system simulation scenarios. The RELAP-7 code utilizes the well-posed 7-equation two-phase flow model for compressible two-phase flow. Closure models used in the TRACE code has been reviewed and selected to reflect the progress made during the past decades and provide a basis for the colure correlations implemented in the RELAP-7 code. This document provides a summary on the closure correlations that are currently implemented in the RELAP-7 code. The closure correlations include sub-grid models that describe interactions between the fluids and the flow channel, and interactions between the two phases.

  3. Multigrid solution of incompressible turbulent flows by using two-equation turbulence models

    Energy Technology Data Exchange (ETDEWEB)

    Zheng, X.; Liu, C. [Front Range Scientific Computations, Inc., Denver, CO (United States); Sung, C.H. [David Taylor Model Basin, Bethesda, MD (United States)

    1996-12-31

    Most of practical flows are turbulent. From the interest of engineering applications, simulation of realistic flows is usually done through solution of Reynolds-averaged Navier-Stokes equations and turbulence model equations. It has been widely accepted that turbulence modeling plays a very important role in numerical simulation of practical flow problem, particularly when the accuracy is of great concern. Among the most used turbulence models today, two-equation models appear to be favored for the reason that they are more general than algebraic models and affordable with current available computer resources. However, investigators using two-equation models seem to have been more concerned with the solution of N-S equations. Less attention is paid to the solution method for the turbulence model equations. In most cases, the turbulence model equations are loosely coupled with N-S equations, multigrid acceleration is only applied to the solution of N-S equations due to perhaps the fact the turbulence model equations are source-term dominant and very stiff in sublayer region.

  4. A wavenumber-partitioning scheme for two-dimensional statistical closures

    International Nuclear Information System (INIS)

    Bowman, J.C.

    1994-11-01

    One of the principal advantages of statistical closure approximations for fluid turbulence is that they involve smoothly varying functions of wavenumber. This suggests the possibility of modeling a flow by following the evolution of only a few representative wavenumbers. This work presents two new techniques for the implementation of two-dimensional isotropic statistical closures that for the first time allows the inertial-range scalings of these approximation to be numerically demonstrated. A technique of wavenumber partitioning that conserves both energy and enstrophy is developed for two-dimensional statistical closures. Coupled with a new time-stepping scheme based on a variable integrating factor, this advance facilitates the computation of energy spectra over seven wavenumber decades, a task that will clearly remain outside the realm of conventional numerical simulations for the foreseeable future. Within the context of the test-field model, the method is used to demonstrate Kraichnan's logarithmically-corrected scaling for the enstrophy inertial range and to make a quantitative assessment of the effect of replacing the physical Laplacian viscosity with an enhanced hyperviscosity

  5. Relations between the kinetic equation and the Langevin models in two-phase flow modelling

    International Nuclear Information System (INIS)

    Minier, J.P.; Pozorski, J.

    1997-05-01

    The purpose of this paper is to discuss PDF and stochastic models which are used in two-phase flow modelling. The aim of the present analysis is essentially to try to determine relations and consistency between different models. It is first recalled that different approaches actually correspond to PDF models written either in terms of the process trajectories or in terms of the PDF itself. The main difference lies in the choice of the independent variables which are retained. Two particular models are studied, the Kinetic Equation and the Langevin Equation model. The latter uses a Langevin equation to model the fluid velocities seen along particle trajectories. The Langevin model is more general since it contains an additional variable. It is shown that, in certain cases, this variable can be summed up exactly to retrieve the Kinetic Equation model as a marginal PDF. A joint fluid and solid particle PDF which includes the characteristics of both phases is proposed at the end of the paper. (author)

  6. Continuum model of the two-component Becker-Döring equations

    Directory of Open Access Journals (Sweden)

    Ali Reza Soheili

    2004-01-01

    Full Text Available The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum model.

  7. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  8. Mathematical modeling of disperse two-phase flows

    CERN Document Server

    Morel, Christophe

    2015-01-01

    This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, a...

  9. Supersymmetric two-particle equations

    International Nuclear Information System (INIS)

    Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.

    1986-01-01

    In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found

  10. Dynamic modeling of interfacial structures via interfacial area transport equation

    International Nuclear Information System (INIS)

    Seungjin, Kim; Mamoru, Ishii

    2004-01-01

    Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

  11. Continuum model of the two-component Becker-Döring equations

    OpenAIRE

    Soheili, Ali Reza

    2004-01-01

    The process of collision between particles is a subject of interest in many fields of physics, astronomy, polymer physics, atmospheric physics, and colloid chemistry. If two types of particles are allowed to participate in the cluster coalescence, then the time evolution of the cluster distribution has been described by an infinite system of ordinary differential equations. In this paper, we describe the model with a second-order two-dimensional partial differential equation, as a continuum m...

  12. Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

    Science.gov (United States)

    Yuan, Ke-Hai; Hayashi, Kentaro

    2010-01-01

    This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

  13. A Two-Phase Solid/Fluid Model for Dense Granular Flows Including Dilatancy Effects

    Science.gov (United States)

    Mangeney, Anne; Bouchut, Francois; Fernandez-Nieto, Enrique; Narbona-Reina, Gladys

    2015-04-01

    We propose a thin layer depth-averaged two-phase model to describe solid-fluid mixtures such as debris flows. It describes the velocity of the two phases, the compression/dilatation of the granular media and its interaction with the pore fluid pressure, that itself modifies the friction within the granular phase (Iverson et al., 2010). The model is derived from a 3D two-phase model proposed by Jackson (2000) based on the 4 equations of mass and momentum conservation within the two phases. This system has 5 unknowns: the solid and fluid velocities, the solid and fluid pressures and the solid volume fraction. As a result, an additional equation inside the mixture is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson's work (Bouchut et al., 2014). In particular, Pitman and Le replaced this closure simply by imposing an extra boundary condition at the surface of the flow. When making a shallow expansion, this condition can be considered as a closure condition. However, the corresponding model cannot account for a dissipative energy balance. We propose here an approach to correctly deal with the thermodynamics of Jackson's equations. We close the mixture equations by a weak compressibility relation involving a critical density, or equivalently a critical pressure. Moreover, we relax one boundary condition, making it possible for the fluid to escape the granular media when compression of the granular mass occurs. Furthermore, we introduce second order terms in the equations making it possible to describe the evolution of the pore fluid pressure in response to the compression/dilatation of the granular mass without prescribing an extra ad-hoc equation for the pore pressure. We prove that the energy balance associated with this Jackson closure is dissipative, as well as its thin layer associated model. We present several numerical tests for the 1D case that are compared to the

  14. Review on improved seismic imaging with closure phase

    KAUST Repository

    Schuster, Gerard T.

    2014-08-13

    The timing and amplitudes of arrivals recorded in seismic traces are influenced by velocity variations all along the associated raypaths. Consequently, velocity errors far from the target can lead to blurred imaging of the target body. To partly remedy this problem, we comprehensively reviewed inverting differential traveltimes that satisfied the closure-phase condition. The result is that the source and receiver statics are completely eliminated in the data and velocities far from the target do not need to be known. We successfully used the phase closure equation for traveltime tomography, refraction statics, migration, refraction tomography, and earthquake location, all of which demonstrated the higher resolution achievable by processing data with differential traveltimes rather than absolute traveltimes. More generally, the stationary version of the closure-phase equation is equivalent to Fermat’s principle and can be derived from the equations of seismic interferometry. In summary, the general closure-phase equation is the mathematical foundation for approximately redatuming sources and/or receivers to the target of interest without the need to accurately know the statics or the velocity model away from the target.

  15. Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

    KAUST Repository

    Davit, Y.; Wood, B. D.; Debenest, G.; Quintard, M.

    2012-01-01

    In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time

  16. Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

    Science.gov (United States)

    Parish, Eric J.; Duraisamy, Karthik

    2017-01-01

    This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.

  17. Application of discontinuous Galerkin method for solving a compressible five-equation two-phase flow model

    Science.gov (United States)

    Saleem, M. Rehan; Ali, Ishtiaq; Qamar, Shamsul

    2018-03-01

    In this article, a reduced five-equation two-phase flow model is numerically investigated. The formulation of the model is based on the conservation and energy exchange laws. The model is non-conservative and the governing equations contain two equations for the mass conservation, one for the over all momentum and one for the total energy. The fifth equation is the energy equation for one of the two phases that includes a source term on the right hand side for incorporating energy exchange between the two fluids in the form of mechanical and thermodynamical works. A Runge-Kutta discontinuous Galerkin finite element method is applied to solve the model equations. The main attractive features of the proposed method include its formal higher order accuracy, its nonlinear stability, its ability to handle complicated geometries, and its ability to capture sharp discontinuities or strong gradients in the solutions without producing spurious oscillations. The proposed method is robust and well suited for large-scale time-dependent computational problems. Several case studies of two-phase flows are presented. For validation and comparison of the results, the same model equations are also solved by using a staggered central scheme. It was found that discontinuous Galerkin scheme produces better results as compared to the staggered central scheme.

  18. Anti-Transgender Prejudice: A Structural Equation Model of Associated Constructs

    Science.gov (United States)

    Tebbe, Esther N.; Moradi, Bonnie

    2012-01-01

    This study aimed to identify theoretically relevant key correlates of anti-transgender prejudice. Specifically, structural equation modeling was used to test the unique relations of anti-lesbian, gay, and bisexual (LGB) prejudice; traditional gender role attitudes; need for closure; and social dominance orientation with anti-transgender prejudice.…

  19. A Surface Temperature Initiated Closure (STIC) for surface energy balance fluxes

    DEFF Research Database (Denmark)

    Mallick, Kaniska; Jarvis, Andrew J.; Boegh, Eva

    2014-01-01

    The use of Penman–Monteith (PM) equation in thermal remote sensing based surface energy balance modeling is not prevalent due to the unavailability of any direct method to integrate thermal data into the PM equation and due to the lack of physical models expressing the surface (or stomatal......) and boundary layer conductances (gS and gB) as a function of surface temperature. Here we demonstrate a new method that physically integrates the radiometric surface temperature (TS) into the PM equation for estimating the terrestrial surface energy balance fluxes (sensible heat, H and latent heat, λ......E). The method combines satellite TS data with standard energy balance closure models in order to derive a hybrid closure that does not require the specification of surface to atmosphere conductance terms. We call this the Surface Temperature Initiated Closure (STIC), which is formed by the simultaneous solution...

  20. Water hammer caused by closure of turbine safety spherical valves

    Science.gov (United States)

    Karadžić, U.; Bergant, A.; Vukoslavčević, P.

    2010-08-01

    This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perućica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

  1. Water hammer caused by closure of turbine safety spherical valves

    International Nuclear Information System (INIS)

    Karadzic, U; Vukoslavcevic, P; Bergant, A

    2010-01-01

    This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perucica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

  2. Water hammer caused by closure of turbine safety spherical valves

    Energy Technology Data Exchange (ETDEWEB)

    Karadzic, U; Vukoslavcevic, P [Faculty of Mechanical Engineering, University of Montenegro Dzordza Vasingtona nn, Podgorica, 81000 (Montenegro); Bergant, A, E-mail: uros.karadzic@ac.m [LitostrojPower d.o.o., Litostrojska 50, Ljubljana, 1000 (Slovenia)

    2010-08-15

    This paper investigates water hammer effects caused by closure of spherical valves against the discharge. During the first phase of modernisation of Perucica high-head hydropower plant (HPP), Montenegro, safety spherical valves (inlet turbine valves) have been refurbished on the first two Pelton turbine units. The valve closure is controlled by the valve actuator (hydraulic servomotor). Because the torque acting on the valve body is dependent on flow conditions the valve closing time may vary significantly for different flow velocities (passive valve). For the passive valve the torques acting on the valve body should be considered in the valve model. The valve closing time results from numerical simulation. On the contrary, for the active valve the valve closing time is assumed prior to simulation. The spherical valve boundary condition is incorporated into the method of characteristics (MOC) algorithm. The staggered (diamond) grid in applying the MOC is used in this paper. The passive valve boundary condition is described by the water hammer equations, the valve equation that relates discharge to pressure head drop and the dynamic equation of the valve body motion (torque equation). The active valve boundary condition is described by the first two equations, respectively. Standard quasi-steady friction model is used for estimating friction losses in plant's tunnel and penstocks. Numerical results using both the active and the passive spherical valve models are compared with results of measurements. It has been found that the influence of flow conditions on the spherical valve closing time is minor for the cases considered. Computed and measured results agree reasonably well.

  3. MINI-TRAC code: a driver program for assessment of constitutive equations of two-fluid model

    International Nuclear Information System (INIS)

    Akimoto, Hajime; Abe, Yutaka; Ohnuki, Akira; Murao, Yoshio

    1991-05-01

    MINI-TRAC code, a driver program for assessment of constitutive equations of two-fluid model, has been developed to perform assessment and improvement of constitutive equations of two-fluid model widely and efficiently. The MINI-TRAC code uses one-dimensional conservation equations for mass, momentum and energy based on the two-fluid model. The code can work on a personal computer because it can be operated with a core memory size less than 640 KB. The MINI-TRAC code includes constitutive equations of TRAC-PF1/MOD1 code, TRAC-BF1 code and RELAP5/MOD2 code. The code is modulated so that one can easily change constitutive equations to perform a test calculation. This report is a manual of the MINI-TRAC code. The basic equations, numerics, constitutive, equations included in the MINI-TRAC code will be described. The user's manual such as input description will be presented. The program structure and contents of main variables will also be mentioned in this report. (author)

  4. Numerical Solutions of the Complete Navier-Stokes Equations

    Science.gov (United States)

    Robinson, David F.; Hassan, H. A.

    1997-01-01

    This report details the development of a new two-equation turbulence closure model based on the exact turbulent kinetic energy k and the variance of vorticity, zeta. The model, which is applicable to three dimensional flowfields, employs one set of model constants and does not use damping or wall functions, or geometric factors.

  5. Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

    Energy Technology Data Exchange (ETDEWEB)

    Yamagishi, Osamu, E-mail: yamagisi@nifs.ac.jp; Sugama, Hideo [National Institute for Fusion Science, Toki, Gifu 509-5292 (Japan)

    2016-03-15

    Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

  6. Fluid simulation of tokamak ion temperature gradient turbulence with zonal flow closure model

    Science.gov (United States)

    Yamagishi, Osamu; Sugama, Hideo

    2016-03-01

    Nonlinear fluid simulation of turbulence driven by ion temperature gradient modes in the tokamak fluxtube configuration is performed by combining two different closure models. One model is a gyrofluid model by Beer and Hammett [Phys. Plasmas 3, 4046 (1996)], and the other is a closure model to reproduce the kinetic zonal flow response [Sugama et al., Phys. Plasmas 14, 022502 (2007)]. By including the zonal flow closure, generation of zonal flows, significant reduction in energy transport, reproduction of the gyrokinetic transport level, and nonlinear upshift on the critical value of gradient scale length are observed.

  7. Evaluation of Two Energy Balance Closure Parametrizations

    Science.gov (United States)

    Eder, Fabian; De Roo, Frederik; Kohnert, Katrin; Desjardins, Raymond L.; Schmid, Hans Peter; Mauder, Matthias

    2014-05-01

    A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273-292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701-716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the "missing energy" between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios 1.

  8. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  9. Towards a collisionless fluid closure in plasma turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Dif Pradalier, G

    2005-07-01

    In this work 2 generic possible descriptions of a plasma have been compared namely the kinetic and the fluid approaches. The latter focuses on the successive moments (n, u, p, q,...) of the distribution function, whereas the former describes the time-evolution in phase space of this distribution function, both being based on the Vlasov equation. The fluid description is attractive for the Vlasov equation is tractable with great difficulties. Nevertheless it rests on a major difficulty: as the set of fluid equations constitute an infinite hierarchy, a closure equation must be chosen. The first chapter details physical characteristics of a fundamental kinetic interaction mechanism between waves and particles. In chapter 2 we propose a fluid closure that allows analytic comparison with a linear fully kinetic result, near an homogeneous, electrostatic, Maxwellian equilibrium. This approach consists in adjusting chosen parameters in order to minimize the discrepancies between fluid and kinetic linear response functions. In chapter 3 we present a general frame for a fluid closure in a magnetized plasma. This is attempted in a linear, simplified model with low dimensionality.

  10. Statistically derived conservation equations for fluid particle flows

    International Nuclear Information System (INIS)

    Reyes, J.N. Jr.

    1989-01-01

    The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior

  11. Development, implementation and assessment of specific closure laws for inverted-annular film-boiling in a two-fluid model

    International Nuclear Information System (INIS)

    Cachard, F. de

    1994-10-01

    Inverted-annular film-boiling (IAFB) is one of the post-burnout heat transfer modes taking place, in particular, during the reflooding phase of the loss-of-coolant accident, when the liquid at the quench front is subcooled. Under IAFB conditions, a continuous liquid core is separated from the wall by a superheated vapour film. The heat transfer rate in IAFB is influenced by the flooding rate, liquid subcooling, pressure, and the wall geometry and temperature. These influences can be accounted by a two-fluid model with physically sound closure laws for mass, momentum and heat transfer between the wall, the vapour film, the vapour-liquid interface, and the liquid core. The applicability of existing IAFB two-fluid models is limited. This is attributed to shortcomings in the description of heat transfer within the liquid core, to use of certain correlations outside their validity range, and to a limited use of experimental information on IAFB. The usual approach has been to develop models employing generally applicable closure laws including, however, adjustable parameters, and to adjust these using global experimental results. The present approach has been to develop IAFB-specific closure laws in such a form that they could be adjusted separately using detailed, IAFB-relevant, experimental result. Steady-state results, including heat flux, wall temperature and void fraction data have been used for the adjustment. A key issue in IAFB modeling is to predict how the heat flux reaching the vapour-liquid interface is split into a liquid heating term and a vaporization term. In the model proposed, convective liquid heating is related to the liquid velocity relative to the interface, and not to the absolute liquid velocity, as in previous models. This relative velocity is deduced from the interfacial shear stress, using the liquid-interface friction law. With this modification, the prediction of the experimental trends is greatly improved. (author) figs., tabs., refs

  12. Moment Closure for the Stochastic Logistic Model

    National Research Council Canada - National Science Library

    Singh, Abhyudai; Hespanha, Joao P

    2006-01-01

    ..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...

  13. The drift-flux asymptotic limit of baro-tropic two-phase two-pressure models

    International Nuclear Information System (INIS)

    Ambroso, A.; Galie, Th.; Chalons, Ch.; Coquel, F.; Godlewski, E.; Raviart, P.A.; Seguin, N.; Coquel, F.

    2008-01-01

    We study the asymptotic behavior of the solutions of baro-tropic two-phase two-pressure models, with pressure relaxation, drag force and external forces. Using Chapman-Enskog expansions close to the expected equilibrium, a drift-flux model with a Darcy type closure law is obtained. Also, restricting this closure law to permanent flows (defined as steady flows in some Lagrangian frame), we can obtain a drift-flux model with an algebraic closure law, in the spirit of Zuber-Findlay models. The example of a two-phase flow in a vertical pipe is described. (authors)

  14. Correspondence Between One- and Two-Equation Models for Solute Transport in Two-Region Heterogeneous Porous Media

    KAUST Repository

    Davit, Y.

    2012-07-26

    In this work, we study the transient behavior of homogenized models for solute transport in two-region porous media. We focus on the following three models: (1) a time non-local, two-equation model (2eq-nlt). This model does not rely on time constraints and, therefore, is particularly useful in the short-time regime, when the timescale of interest (t) is smaller than the characteristic time (τ 1) for the relaxation of the effective macroscale parameters (i. e., when t ≤ τ 1); (2) a time local, two-equation model (2eq). This model can be adopted when (t) is significantly larger than (τ 1) (i.e., when t≫τ 1); and (3) a one-equation, time-asymptotic formulation (1eq ∞). This model can be adopted when (t) is significantly larger than the timescale (τ 2) associated with exchange processes between the two regions (i. e., when t≫τ 2). In order to obtain insight into this transient behavior, we combine a theoretical approach based on the analysis of spatial moments with numerical and analytical results in several simple cases. The main result of this paper is to show that there is only a weak asymptotic convergence of the solution of (2eq) towards the solution of (1eq ∞) in terms of standardized moments but, interestingly, not in terms of centered moments. The physical interpretation of this result is that deviations from the Fickian situation persist in the limit of long times but that the spreading of the solute is eventually dominating these higher order effects. © 2012 Springer Science+Business Media B.V.

  15. Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

    International Nuclear Information System (INIS)

    Kataoka, Isao; Tomiyama, Akio

    2004-01-01

    The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

  16. Comparison of PDF and Moment Closure Methods in the Modeling of Turbulent Reacting Flows

    Science.gov (United States)

    Norris, Andrew T.; Hsu, Andrew T.

    1994-01-01

    In modeling turbulent reactive flows, Probability Density Function (PDF) methods have an advantage over the more traditional moment closure schemes in that the PDF formulation treats the chemical reaction source terms exactly, while moment closure methods are required to model the mean reaction rate. The common model used is the laminar chemistry approximation, where the effects of turbulence on the reaction are assumed negligible. For flows with low turbulence levels and fast chemistry, the difference between the two methods can be expected to be small. However for flows with finite rate chemistry and high turbulence levels, significant errors can be expected in the moment closure method. In this paper, the ability of the PDF method and the moment closure scheme to accurately model a turbulent reacting flow is tested. To accomplish this, both schemes were used to model a CO/H2/N2- air piloted diffusion flame near extinction. Identical thermochemistry, turbulence models, initial conditions and boundary conditions are employed to ensure a consistent comparison can be made. The results of the two methods are compared to experimental data as well as to each other. The comparison reveals that the PDF method provides good agreement with the experimental data, while the moment closure scheme incorrectly shows a broad, laminar-like flame structure.

  17. Analysis of the two-fluid model and the drift-flux model for numerical calculation of two-phase flow

    Energy Technology Data Exchange (ETDEWEB)

    Munkejord, Svend Tollak

    2006-05-11

    This thesis analyses models for two-phase flows and methods for the numerical resolution of these models. It is therefore one contribution to the development of reliable design tools for multiphase applications. Such tools are needed and expected by engineers in a range of fields, including in the oil and gas industry. The approximate Riemann solver of Roe has been studied. Roe schemes for three different two-phase flow models have been implemented in the framework of a standard numerical algorithm for the solution of hyperbolic conservation laws. The schemes have been analysed by calculation of benchmark tests from the literature, and by comparison with each other. A Roe scheme for the four-equation one-pressure two-fluid model has been implemented, and a second-order extension based on wave decomposition and flux-difference splitting was shown to work well and to give improved results compared to the first-order scheme. The convergence properties of the scheme were tested on smooth and discontinuous solutions. A Roe scheme has been proposed for a five-equation two-pressure two-fluid model with pressure relaxation. The use of analogous numerical methods for the five-equation and four-equation models allowed for a direct comparison of a method with and without pressure relaxation. Numerical experiments demonstrated that the two approaches converged to the same results, but that the five-equation pressure-relaxation method was significantly more dissipative, particularly for contact discontinuities. Furthermore, even though the five-equation model with instantaneous pressure relaxation has real eigenvalues, the calculations showed that it produced oscillations for cases where the four-equation model had complex eigenvalues. A Roe scheme has been constructed for the drift-flux model with general closure laws. For the case of the Zuber-Findlay slip law describing bubbly flows, the Roe matrix is completely analytical. Hence the present Roe scheme is more efficient than

  18. An ordinary differential equation model for full thickness wounds and the effects of diabetes.

    Science.gov (United States)

    Bowden, L G; Maini, P K; Moulton, D E; Tang, J B; Wang, X T; Liu, P Y; Byrne, H M

    2014-11-21

    Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment. Copyright © 2014 Elsevier Ltd. All rights reserved.

  19. An evaluation of state-of-the-art two-velocity two-phase flow models and their applicability to nuclear reactor transient analysis. Volume 2. Theoretical bases. Final report

    International Nuclear Information System (INIS)

    Hughes, E.D.; Lyczkowski, R.W.; McFadden, J.H.

    1976-02-01

    A state-of-the-art review was conducted in order to provide the nuclear industry with a publicly available assessment of two velocity thermal-hydraulic models and their applicability to nuclear reactor technology. The two major objectives of this state-of-the-art evaluation were: (1) document the basic theory in a consistent self-contained report; and (2) apply a prototype 'two-velocity' code (UVUT) to a limited number of separate effect tests. The theoretical basis of the two-velocity models given in Volume 2 is divided into three parts; Part I is the derivation of the basic differential equations; Part II describes in detail, the constitutive models required for closure of the system of equations; and Part III presents the numerical solution schemes

  20. Magnetohydrodynamic motion of a two-fluid plasma

    Science.gov (United States)

    Burby, J. W.

    2017-08-01

    The two-fluid Maxwell system couples frictionless electrons and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from the two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-order closure may be obtained in the closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-order bracket gives explicit expressions for a number of the full closure's conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.

  1. ANALYTICAL MODELS OF EXOPLANETARY ATMOSPHERES. II. RADIATIVE TRANSFER VIA THE TWO-STREAM APPROXIMATION

    Energy Technology Data Exchange (ETDEWEB)

    Heng, Kevin; Mendonça, João M.; Lee, Jae-Min, E-mail: kevin.heng@csh.unibe.ch, E-mail: joao.mendonca@csh.unibe.ch, E-mail: lee@physik.uzh.ch [University of Bern, Center for Space and Habitability, Sidlerstrasse 5, CH-3012 Bern (Switzerland)

    2014-11-01

    We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and solutions describing two-stream radiative transfer (which approximates the passage of radiation as a pair of outgoing and incoming fluxes), flux-limited diffusion (which describes radiative transfer in the deep interior), and solutions for the temperature-pressure profiles. Generally, the problem is mathematically underdetermined unless a set of closures (Eddington coefficients) is specified. We demonstrate that the hemispheric (or hemi-isotropic) closure naturally derives from the radiative transfer equation if energy conservation is obeyed, while the Eddington closure produces spurious enhancements of both reflected light and thermal emission. We concoct recipes for implementing two-stream radiative transfer in stand-alone numerical calculations and general circulation models. We use our two-stream solutions to construct toy models of the runaway greenhouse effect. We present a new solution for temperature-pressure profiles with a non-constant optical opacity and elucidate the effects of non-isotropic scattering in the optical and infrared. We derive generalized expressions for the spherical and Bond albedos and the photon deposition depth. We demonstrate that the value of the optical depth corresponding to the photosphere is not always 2/3 (Milne's solution) and depends on a combination of stellar irradiation, internal heat, and the properties of scattering in both the optical and infrared. Finally, we derive generalized expressions for the total, net, outgoing, and incoming fluxes in the convective regime.

  2. Eigenspace perturbations for structural uncertainty estimation of turbulence closure models

    Science.gov (United States)

    Jofre, Lluis; Mishra, Aashwin; Iaccarino, Gianluca

    2017-11-01

    With the present state of computational resources, a purely numerical resolution of turbulent flows encountered in engineering applications is not viable. Consequently, investigations into turbulence rely on various degrees of modeling. Archetypal amongst these variable resolution approaches would be RANS models in two-equation closures, and subgrid-scale models in LES. However, owing to the simplifications introduced during model formulation, the fidelity of all such models is limited, and therefore the explicit quantification of the predictive uncertainty is essential. In such scenario, the ideal uncertainty estimation procedure must be agnostic to modeling resolution, methodology, and the nature or level of the model filter. The procedure should be able to give reliable prediction intervals for different Quantities of Interest, over varied flows and flow conditions, and at diametric levels of modeling resolution. In this talk, we present and substantiate the Eigenspace perturbation framework as an uncertainty estimation paradigm that meets these criteria. Commencing from a broad overview, we outline the details of this framework at different modeling resolution. Thence, using benchmark flows, along with engineering problems, the efficacy of this procedure is established. This research was partially supported by NNSA under the Predictive Science Academic Alliance Program (PSAAP) II, and by DARPA under the Enabling Quantification of Uncertainty in Physical Systems (EQUiPS) project (technical monitor: Dr Fariba Fahroo).

  3. Modeling and Simulating Passenger Behavior for a Station Closure in a Rail Transit Network

    Science.gov (United States)

    Yin, Haodong; Han, Baoming; Li, Dewei; Wu, Jianjun; Sun, Huijun

    2016-01-01

    A station closure is an abnormal operational situation in which the entrances or exits of a rail transit station have to be closed for some time due to an unexpected incident. A novel approach is developed to estimate the impacts of the alternative station closure scenarios on both passenger behavioral choices at the individual level and passenger demand at the disaggregate level in a rail transit network. Therefore, the contributions of this study are two-fold: (1) A basic passenger behavior optimization model is mathematically constructed based on 0–1 integer programming to describe passengers’ responses to alternative origin station closure scenarios and destination station closure scenarios; this model also considers the availability of multi-mode transportation and the uncertain duration of the station closure; (2) An integrated solution algorithm based on the passenger simulation is developed to solve the proposed model and to estimate the effects of a station closure on passenger demand in a rail transit network. Furthermore, 13 groups of numerical experiments based on the Beijing rail transit network are performed as case studies with 2,074,267 records of smart card data. The comparisons of the model outputs and the manual survey show that the accuracy of our proposed behavior optimization model is approximately 80%. The results also show that our model can be used to capture the passenger behavior and to quantitatively estimate the effects of alternative closure scenarios on passenger flow demand for the rail transit network. Moreover, the closure duration and its overestimation greatly influence the individual behavioral choices of the affected passengers and the passenger demand. Furthermore, if the rail transit operator can more accurately estimate the closure duration (namely, as g approaches 1), the impact of the closure can be somewhat mitigated. PMID:27935963

  4. Modeling and Simulating Passenger Behavior for a Station Closure in a Rail Transit Network.

    Directory of Open Access Journals (Sweden)

    Haodong Yin

    Full Text Available A station closure is an abnormal operational situation in which the entrances or exits of a rail transit station have to be closed for some time due to an unexpected incident. A novel approach is developed to estimate the impacts of the alternative station closure scenarios on both passenger behavioral choices at the individual level and passenger demand at the disaggregate level in a rail transit network. Therefore, the contributions of this study are two-fold: (1 A basic passenger behavior optimization model is mathematically constructed based on 0-1 integer programming to describe passengers' responses to alternative origin station closure scenarios and destination station closure scenarios; this model also considers the availability of multi-mode transportation and the uncertain duration of the station closure; (2 An integrated solution algorithm based on the passenger simulation is developed to solve the proposed model and to estimate the effects of a station closure on passenger demand in a rail transit network. Furthermore, 13 groups of numerical experiments based on the Beijing rail transit network are performed as case studies with 2,074,267 records of smart card data. The comparisons of the model outputs and the manual survey show that the accuracy of our proposed behavior optimization model is approximately 80%. The results also show that our model can be used to capture the passenger behavior and to quantitatively estimate the effects of alternative closure scenarios on passenger flow demand for the rail transit network. Moreover, the closure duration and its overestimation greatly influence the individual behavioral choices of the affected passengers and the passenger demand. Furthermore, if the rail transit operator can more accurately estimate the closure duration (namely, as g approaches 1, the impact of the closure can be somewhat mitigated.

  5. Modeling and Simulating Passenger Behavior for a Station Closure in a Rail Transit Network.

    Science.gov (United States)

    Yin, Haodong; Han, Baoming; Li, Dewei; Wu, Jianjun; Sun, Huijun

    2016-01-01

    A station closure is an abnormal operational situation in which the entrances or exits of a rail transit station have to be closed for some time due to an unexpected incident. A novel approach is developed to estimate the impacts of the alternative station closure scenarios on both passenger behavioral choices at the individual level and passenger demand at the disaggregate level in a rail transit network. Therefore, the contributions of this study are two-fold: (1) A basic passenger behavior optimization model is mathematically constructed based on 0-1 integer programming to describe passengers' responses to alternative origin station closure scenarios and destination station closure scenarios; this model also considers the availability of multi-mode transportation and the uncertain duration of the station closure; (2) An integrated solution algorithm based on the passenger simulation is developed to solve the proposed model and to estimate the effects of a station closure on passenger demand in a rail transit network. Furthermore, 13 groups of numerical experiments based on the Beijing rail transit network are performed as case studies with 2,074,267 records of smart card data. The comparisons of the model outputs and the manual survey show that the accuracy of our proposed behavior optimization model is approximately 80%. The results also show that our model can be used to capture the passenger behavior and to quantitatively estimate the effects of alternative closure scenarios on passenger flow demand for the rail transit network. Moreover, the closure duration and its overestimation greatly influence the individual behavioral choices of the affected passengers and the passenger demand. Furthermore, if the rail transit operator can more accurately estimate the closure duration (namely, as g approaches 1), the impact of the closure can be somewhat mitigated.

  6. A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations

    Science.gov (United States)

    Guinot, Vincent

    2017-11-01

    The validity of flux and source term formulae used in shallow water models with porosity for urban flood simulations is assessed by solving the two-dimensional shallow water equations over computational domains representing periodic building layouts. The models under assessment are the Single Porosity (SP), the Integral Porosity (IP) and the Dual Integral Porosity (DIP) models. 9 different geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are defined. This results in a set of 96 fine grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP flux and source term models outperform those of the SP and IP models when the Riemann problem is aligned with the main street directions, (ii) all models give erroneous flux closures when is the Riemann problem is not aligned with one of the main street directions or when the main street directions are not orthogonal, (iii) the solution of the Riemann problem is self-similar in space-time when the street directions are orthogonal and the Riemann problem is aligned with one of them, (iv) a momentum balance confirms the existence of the transient momentum dissipation model presented in the DIP model, (v) none of the source term models presented so far in the literature allows all flow configurations to be accounted for(vi) future laboratory experiments aiming at the validation of flux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and flow velocity fields.

  7. Development of two-group interfacial area transport equation for confined flow-1. Modeling of bubble interactions

    International Nuclear Information System (INIS)

    Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

    2003-01-01

    This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equations based on certain assumptions for the confined flow. These models include both intra-group (within a certain group) and inter-group (between two groups) bubble interactions. The comparisons of the prediction by the one-dimensional two-group IATE with experimental data are presented in the second paper of this series. (author)

  8. A short summary on finite element modelling of fatigue crack closure

    Energy Technology Data Exchange (ETDEWEB)

    Singh, Konjengbam Darunkumar [Indian Institute of Technology, Guwahati (India); Parry, Matthew Roger [Airbus Operations Ltd, Bristol(United Kingdom); Sinclair, Ian [University of Southampton, Southampton (United Kingdom)

    2011-12-15

    This paper presents a short summary pertaining to the finite element modelling of fatigue crack closure. Several key issues related to finite element modelling of fatigue crack closure are highlighted: element type, mesh refinement, stabilization of crack closure, crack-tip node release scheme, constitutive model, specimen geometry, stress-states (i.e., plane stress, plane strain), crack closure monitoring. Reviews are presented for both straight and deflected cracks.

  9. Stability equation and two-component Eigenmode for domain walls in scalar potential model

    International Nuclear Information System (INIS)

    Dias, G.S.; Graca, E.L.; Rodrigues, R. de Lima

    2002-08-01

    Supersymmetric quantum mechanics involving a two-component representation and two-component eigenfunctions is applied to obtain the stability equation associated to a potential model formulated in terms of two coupled real scalar fields. We investigate the question of stability by introducing an operator technique for the Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS states on two domain walls in a scalar potential model with minimal N 1-supersymmetry. (author)

  10. NASA Trapezoidal Wing Simulation Using Stress-w and One- and Two-Equation Turbulence Models

    Science.gov (United States)

    Rodio, J. J.; Xiao, X; Hassan, H. A.; Rumsey, C. L.

    2014-01-01

    The Wilcox 2006 stress-omega model (also referred to as WilcoxRSM-w2006) has been implemented in the NASA Langley code CFL3D and used to study a variety of 2-D and 3-D configurations. It predicted a variety of basic cases reasonably well, including secondary flow in a supersonic rectangular duct. One- and two-equation turbulence models that employ the Boussinesq constitutive relation were unable to predict this secondary flow accurately because it is driven by normal turbulent stress differences. For the NASA trapezoidal wing at high angles of attack, the WilcoxRSM-w2006 model predicted lower maximum lift than experiment, similar to results of a two-equation model.

  11. Interfacial area and interfacial transfer in two-phase systems. DOE final report

    Energy Technology Data Exchange (ETDEWEB)

    Ishii, Mamoru; Hibiki, T.; Revankar, S.T.; Kim, S.; Le Corre, J.M.

    2002-07-01

    In the two-fluid model, the field equations are expressed by the six conservation equations consisting of mass, momentum and energy equations for each phase. The existence of the interfacial transfer terms is one of the most important characteristics of the two-fluid model formulation. The interfacial transfer terms are strongly related to the interfacial area concentration and to the local transfer mechanisms such as the degree of turbulence near interfaces. This study focuses on the development of a closure relation for the interfacial area concentration. A brief summary of several problems of the current closure relation for the interfacial area concentration and a new concept to overcome the problem are given.

  12. Closure of the squared Zakharov--Shabat eigenstates

    International Nuclear Information System (INIS)

    Kaup, D.J.

    1976-01-01

    By solution of the inverse scattering problem for a third-order (degenerate) eigenvalue problem, the closure of the squared eigenfunctions of the Zakharov--Shabat equations is found. The question of the completeness of squared eigenstates occurs in many aspects of ''inverse scattering transforms'' (solving nonlinear evolution equations exactly by inverse scattering techniques), as well as in various aspects of the inverse scattering problem. The method used here is quite suggestive as to how one might find the closure of the squared eigenfunctions of other eigenvalue equations, and the strong analogy between these results and the problem of finding the closure of the eigenvectors of a nonself-adjoint matrix is pointed out

  13. Superresolving Black Hole Images with Full-Closure Sparse Modeling

    Science.gov (United States)

    Crowley, Chelsea; Akiyama, Kazunori; Fish, Vincent

    2018-01-01

    It is believed that almost all galaxies have black holes at their centers. Imaging a black hole is a primary objective to answer scientific questions relating to relativistic accretion and jet formation. The Event Horizon Telescope (EHT) is set to capture images of two nearby black holes, Sagittarius A* at the center of the Milky Way galaxy roughly 26,000 light years away and the other M87 which is in Virgo A, a large elliptical galaxy that is 50 million light years away. Sparse imaging techniques have shown great promise for reconstructing high-fidelity superresolved images of black holes from simulated data. Previous work has included the effects of atmospheric phase errors and thermal noise, but not systematic amplitude errors that arise due to miscalibration. We explore a full-closure imaging technique with sparse modeling that uses closure amplitudes and closure phases to improve the imaging process. This new technique can successfully handle data with systematic amplitude errors. Applying our technique to synthetic EHT data of M87, we find that full-closure sparse modeling can reconstruct images better than traditional methods and recover key structural information on the source, such as the shape and size of the predicted photon ring. These results suggest that our new approach will provide superior imaging performance for data from the EHT and other interferometric arrays.

  14. Multivariate moment closure techniques for stochastic kinetic models

    International Nuclear Information System (INIS)

    Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.

    2015-01-01

    Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

  15. Multivariate moment closure techniques for stochastic kinetic models

    Energy Technology Data Exchange (ETDEWEB)

    Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)

    2015-09-07

    Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

  16. Development, implementation and assessment of specific, two-fluid closure laws for inverted-annular film-boiling

    Energy Technology Data Exchange (ETDEWEB)

    Cachard, F. de [Laboratory for Thermal Hydraulics, Villigen (Switzerland)

    1995-09-01

    Inverted-Annular Film-Boiling (IAFB) is one of the post-burnout heat transfer modes taking place during the reflooding phase of the loss-of-coolant accident, when the liquid at the quench front is subcooled. Under IAFB conditions, a continuous, liquid core is separated from the wall by a superheated vapour film. the heat transfer rate in IAFB is influenced by the flooding rate, liquid subcooling, pressure, and the wall geometry and temperature. These influences can be accounted by a two-fluid model with physically sound closure laws for mass, momentum and heat transfers between the wall, the vapour film, the vapour-liquid interface, and the liquid core. Such closure laws have been developed and adjusted using IAFB-relevant experimental results, including heat flux, wall temperature and void fraction data. The model is extensively assessed against data from three independent sources. A total of 46 experiments have been analyzed. The overall predictions are good. The IAFB-specific closure laws proposed have also intrinsic value, and may be used in other two-fluid models. They should allow to improve the description of post-dryout, low quality heat transfer by the safety codes.

  17. Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure

    Science.gov (United States)

    Sen, O.; Gaul, N. J.; Davis, S.; Choi, K. K.; Jacobs, G.; Udaykumar, H. S.

    2018-05-01

    Macroscale models of shock-particle interactions require closure terms for unresolved solid-fluid momentum and energy transfer. These comprise the effects of mean as well as fluctuating fluid-phase velocity fields in the particle cloud. Mean drag and Reynolds stress equivalent terms (also known as pseudo-turbulent terms) appear in the macroscale equations. Closure laws for the pseudo-turbulent terms are constructed in this work from ensembles of high-fidelity mesoscale simulations. The computations are performed over a wide range of Mach numbers ( M) and particle volume fractions (φ ) and are used to explicitly compute the pseudo-turbulent stresses from the Favre average of the velocity fluctuations in the flow field. The computed stresses are then used as inputs to a Modified Bayesian Kriging method to generate surrogate models. The surrogates can be used as closure models for the pseudo-turbulent terms in macroscale computations of shock-particle interactions. It is found that the kinetic energy associated with the velocity fluctuations is comparable to that of the mean flow—especially for increasing M and φ . This work is a first attempt to quantify and evaluate the effect of velocity fluctuations for problems of shock-particle interactions.

  18. On some issues of the modeling and analysis of two phase flow systems

    International Nuclear Information System (INIS)

    Ndjinga, M.

    2007-04-01

    Two-fluid and multi-field models are commonly used in the modeling and numerical simulation of two phase flows. They however present several mathematical and numerical difficulties, such as their lack of hyperbolicity or their non trivial Eigen-structure. It is important to understand the well-posedness of such possibly non hyperbolic systems before solving them numerically. For this reason, we study the solutions of systems of first order partial differential equations having a possibly complex Eigen-structure. We then characterise the hyperbolicity of the six equations two-fluid model with interfacial forces having differential expressions such as the interfacial pressure term, virtual mass and lift forces. The study of the characteristic polynomial leads to a diagram representing the location and topology of the non hyperbolic regions. We eventually propose numerous closure laws that make the two-fluid and multi-field models unconditionally hyperbolic. In order to numerically solve the two-fluid and multi-field models equations in a finite volume approach using a Roe type scheme, we propose two new algorithms designed for an efficient computation of the matrix absolute value function. These algorithms are robust as they avoid the computation of the eigenvectors of the argument matrix. The first is based on an iterative approach and converges in a finite number of steps if the eigenvalues are real. The second is faster, and besides can handle the case of complex eigenvalues. Thanks to these new algorithms, it is now possible to solve efficiently the six equations two-fluid model with differential interfacial terms, or the multi-field model with an arbitrary number of fields. We finally show the results of some recent numerical simulations of the six equations two-fluid model and the multi-field model with interfacial forces having a differential expression. (author)

  19. Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations

    Science.gov (United States)

    Foucart, Francois

    2018-04-01

    General relativistic radiation hydrodynamic simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion discs, while neutrino transport is critical to core-collapse supernovae and to the modelling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SPEC code of a cheaper radiation hydrodynamic method that theoretically converges to a solution of Boltzmann's equation in the limit of infinite numerical resources. The algorithm is based on a grey two-moment scheme, in which we evolve the energy density and momentum density of the radiation. Two-moment schemes require a closure that fills in missing information about the energy spectrum and higher order moments of the radiation. Instead of the approximate analytical closure currently used in core-collapse and merger simulations, we complement the two-moment scheme with a low-accuracy Monte Carlo evolution. The Monte Carlo results can provide any or all of the missing information in the evolution of the moments, as desired by the user. As a first test of our methods, we study a set of idealized problems demonstrating that our algorithm performs significantly better than existing analytical closures. We also discuss the current limitations of our method, in particular open questions regarding the stability of the fully coupled scheme.

  20. Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model

    CERN Document Server

    Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix

    2012-01-01

    We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.

  1. Modeling strategy of the source and sink terms in the two-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Ishii, Mamoru; Sun Xiaodong; Kim, Seungjin

    2003-01-01

    This paper presents the general strategy for modeling the source and sink terms in the two-group interfacial area transport equation. The two-group transport equation is applicable in bubbly, cap bubbly, slug, and churn-turbulent flow regimes to predict the change of the interfacial area concentration. This dynamic approach has an advantage of flow regime-independence over the conventional empirical correlation approach for the interfacial area concentration in the applications with the two-fluid model. In the two-group interfacial area transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Based upon a detailed literature review of the research on the bubble interactions, five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest. A systematic integral approach, in which the significant variations of bubble volume and shape are accounted for, is suggested for the modeling of two-group bubble interactions. To obtain analytical forms for the various bubble interactions, a simplification is made for the bubble number density distribution function

  2. Balance of liquid-phase turbulence kinetic energy equation for bubble-train flow

    International Nuclear Information System (INIS)

    Ilic, Milica; Woerner, Martin; Cacuci, Dan Gabriel

    2004-01-01

    In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k-ε and the two-phase k-l model is evaluated. (author)

  3. Two-body Dirac equations for nucleon-nucleon scattering

    International Nuclear Information System (INIS)

    Liu Bin; Crater, Horace

    2003-01-01

    We investigate the nucleon-nucleon interaction by using the meson exchange model and the two-body Dirac equations of constraint dynamics. This approach to the two-body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two-body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two-body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve them already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this, we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our equations gives a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involve seven angular momentum states including the singlet states 1 S 0 , 1 P 1 , 1 D 2 and the triplet states 3 P 0 , 3 P 1 , 3 S 1 , 3 D 1 . Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the singlet states 1 S 0 , 1 D 2 and triplet states 3 P 0 , 3 P 1 ). Thus the two-body Dirac equations of constraint dynamics present us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit

  4. Comparison of two spectral domain optical coherence tomography devices for angle-closure assessment.

    Science.gov (United States)

    Quek, Desmond T; Narayanaswamy, Arun K; Tun, Tin A; Htoon, Hla M; Baskaran, Mani; Perera, Shamira A; Aung, Tin

    2012-08-03

    To compare two spectral domain optical coherence tomography (SD-OCT) devices for the identification of angle structures and the presence of angle closure. This was a prospective comparative study. Consecutive patients underwent gonioscopy and anterior segment imaging using two SD-OCT devices (iVue and Cirrus). Images were evaluated for the ability to detect angle structures such as Schwalbe's line (SL), trabecular meshwork (TM), Schlemm's canal (SC), and scleral spur (SS), and the presence of angle closure. Angle closure was defined as iris contact with the angle wall anterior to the SS on SD-OCT, and nonvisibility of the posterior TM on gonioscopy. Angle closure in an eye was defined as ≥two quadrants of closed angles. AC1 statistic was used to assess the agreement between devices. Of the 69 subjects studied (46.4% male, 84.1% Chinese, mean age 64.0 ± 10.5 years), 40 subjects (40 eyes, 58.0%) had angle closure on gonioscopy. The most identifiable structure on Cirrus SD-OCT was the SS (82.2%) and SL on iVue SD-OCT (74.5%). Angle closure was indeterminable in 14.5% and 50.7% of Cirrus and iVue scans (P gonioscopy was only fair (AC1 = 0.35 and 0.50 for Cirrus and iVue, respectively). It was more difficult to determine angle closure status with iVue compared with Cirrus SD-OCT. There was fair agreement between both devices with gonioscopy for identifying angle closure.

  5. Flux-probability distributions from the master equation for radiation transport in stochastic media

    International Nuclear Information System (INIS)

    Franke, Brian C.; Prinja, Anil K.

    2011-01-01

    We present numerical investigations into the accuracy of approximations in the master equation for radiation transport in discrete binary random media. Our solutions of the master equation yield probability distributions of particle flux at each element of phase space. We employ the Levermore-Pomraning interface closure and evaluate the effectiveness of closures for the joint conditional flux distribution for estimating scattering integrals. We propose a parameterized model for this joint-pdf closure, varying between correlation neglect and a full-correlation model. The closure is evaluated for a variety of parameter settings. Comparisons are made with benchmark results obtained through suites of fixed-geometry realizations of random media in rod problems. All calculations are performed using Monte Carlo techniques. Accuracy of the approximations in the master equation is assessed by examining the probability distributions for reflection and transmission and by evaluating the moments of the pdfs. The results suggest the correlation-neglect setting in our model performs best and shows improved agreement in the atomic-mix limit. (author)

  6. Advancements in engineering turbulence modeling

    Science.gov (United States)

    Shih, T.-H.

    1991-01-01

    Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

  7. Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

    Energy Technology Data Exchange (ETDEWEB)

    Ohnuki, Akira; Akimoto, Hajime [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment; Kamo, Hideki

    1996-11-01

    In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A {kappa}-{epsilon} turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

  8. Development of multidimensional two-fluid model code ACE-3D for evaluation of constitutive equations

    International Nuclear Information System (INIS)

    Ohnuki, Akira; Akimoto, Hajime; Kamo, Hideki.

    1996-11-01

    In order to perform design calculations for a passive safety reactor with good accuracy by a multidimensional two-fluid model, we developed an analysis code, ACE-3D, which can apply for evaluation of constitutive equations. The developed code has the following features: 1. The basic equations are based on 3-dimensional two-fluid model and the orthogonal or the cylindrical coordinate system can be selected. The fluid system is air-water or steam-water. 2. The basic equations are formulated by the finite-difference scheme of staggered mesh. The convection term is formulated by an upwind scheme and the diffusion term by a center-difference scheme. 3. Semi-implicit numerical scheme is adopted and the mass and the energy equations are treated equally in convergent steps for Jacobi equations. 4. The interfacial stress term consists of drag force, life force, turbulent dispersion force, wall force and virtual mass force. 5. A κ-ε turbulent model for bubbly flow is incorporated as the turbulent model. The predictive capability of ACE-3D has been verified using a data-base for bubbly flow in a small-scale vertical pipe. In future, the constitutive equations will be improved with a data-base in a large vertical pipe developed in our laboratory and we have a plan to construct a reliable analytical tool through the improvement work, the progress of calculational speed with vector and parallel processing, the assessments for phase change terms and so on. This report describes the outline for the basic equations and the finite-difference equations in ACE-3D code and also the outline for the program structure. Besides, the results for the assessments of ACE-3D code for the small-scale pipe are summarized. (author)

  9. Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing

    International Nuclear Information System (INIS)

    Kokkinakis, I.W.; Drikakis, D.; Youngs, D.L.; Williams, R.J.R.

    2015-01-01

    Highlights: • We present a new improved version of the K–L model. • The improved K–L is found in good agreement with the multi-fluid model and ILES. • The study concerns Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. - Abstract: This paper presents a new, improved version of the K–L model, as well as a detailed investigation of K–L and multi-fluid models with reference to high-resolution implicit large eddy simulations of compressible Rayleigh–Taylor mixing. The accuracy of the models is examined for different interface pressures and specific heat ratios for Rayleigh–Taylor flows at initial density ratios 3:1 and 20:1. It is shown that the original version of the K–L model requires modifications in order to provide comparable results to the multi-fluid model. The modifications concern the addition of an enthalpy diffusion term to the energy equation; the formulation of the turbulent kinetic energy (source) term in the K equation; and the calculation of the local Atwood number. The proposed modifications significantly improve the results of the K–L model, which are found in good agreement with the multi-fluid model and implicit large eddy simulations with respect to the self-similar mixing width; peak turbulent kinetic energy growth rate, as well as volume fraction and turbulent kinetic energy profiles. However, a key advantage of the two-fluid model is that it can represent the degree of molecular mixing in a direct way, by transferring mass between the two phases. The limitations of the single-fluid K–L model as well as the merits of more advanced Reynolds-averaged Navier–Stokes models are also discussed throughout the paper.

  10. Modelling of Non-Premixed Turbulent Combustion of Hydrogen using Conditional Moment Closure Method

    International Nuclear Information System (INIS)

    Noor, M M; Hairuddin, A Aziz; Wandel, Andrew P; Yusaf, T F

    2012-01-01

    Most of the electricity generation and energy for transport is still generated by the conversion of chemical to mechanical energy by burning the fuels in the combustion chamber. Regulation for pollution and the demand for more fuel economy had driven worldwide researcher to focus on combustion efficiency. In order to reduce experimental cost, accurate modelling and simulation is very critical step. Taylor series expansion was utilised to reduce the error term for the discretization. FORTRAN code was used to execute the discretized partial differential equation. Hydrogen combustion was simulated using Conditional Moment Closure (CMC) model. Combustion of hydrogen with oxygen was successfully simulated and reported in this paper.

  11. Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux

    International Nuclear Information System (INIS)

    Kawamura, Hiroshi

    1978-01-01

    Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)

  12. Advances in engineering turbulence modeling. [computational fluid dynamics

    Science.gov (United States)

    Shih, T.-H.

    1992-01-01

    Some new developments in two equation models and second order closure models are presented. In this paper, modified two equation models are proposed to remove shortcomings such as computing flows over complex geometries and the ad hoc treatment near the separation and reattachment points. The calculations using various two equation models are compared with direct numerical solutions of channel flows and flat plate boundary layers. Development of second order closure models will also be discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All existing models poorly predict the normal stresses near the wall and fail to predict the three dimensional effect of mean flow on the turbulence. The newly developed second order near-wall turbulence model to be described in this paper is capable of capturing the near-wall behavior of turbulence as well as the effect of three dimension mean flow on the turbulence.

  13. Consistent three-equation model for thin films

    Science.gov (United States)

    Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

    2017-11-01

    Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

  14. Experimental determination and modelling of interface area concentration in horizontal stratified flow

    International Nuclear Information System (INIS)

    Junqua-Moullet, Alexandra

    2003-01-01

    This research thesis concerns the modelling and experimentation of biphasic liquid/gas flows (water/air) while using the two-fluid model, a six-equation model. The author first addresses the modelling of interfacial magnitudes for a known topology (problem of two-fluid model closure, closure relationships for some variables, equation for a given configuration). She reports the development of an equation system for interfacial magnitudes. The next parts deal with experiments and report the study of stratified flows in the THALC experiment, and more particularly the study of the interfacial area concentration and of the liquid velocities in such flows. Results are discussed, as well as their consistency

  15. Modelling biochemical reaction systems by stochastic differential equations with reflection.

    Science.gov (United States)

    Niu, Yuanling; Burrage, Kevin; Chen, Luonan

    2016-05-07

    In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.

  16. Implementation of two-equation soot flamelet models for laminar diffusion flames

    Energy Technology Data Exchange (ETDEWEB)

    Carbonell, D.; Oliva, A.; Perez-Segarra, C.D. [Centre Tecnologic de Transferencia de Calor (CTTC), Universitat Politecnica de Catalunya (UPC), ETSEIAT, Colom 11, E-08222, Terrassa (Barcelona) (Spain)

    2009-03-15

    The two-equation soot model proposed by Leung et al. [K.M. Leung, R.P. Lindstedt, W.P. Jones, Combust. Flame 87 (1991) 289-305] has been derived in the mixture fraction space. The model has been implemented using both Interactive and Non-Interactive flamelet strategies. An Extended Enthalpy Defect Flamelet Model (E-EDFM) which uses a flamelet library obtained neglecting the soot formation is proposed as a Non-Interactive method. The Lagrangian Flamelet Model (LFM) is used to represent the Interactive models. This model uses direct values of soot mass fraction from flamelet calculations. An Extended version (E-LFM) of this model is also suggested in which soot mass fraction reaction rates are used from flamelet calculations. Results presented in this work show that the E-EDFM predict acceptable results. However, it overpredicts the soot volume fraction due to the inability of this model to couple the soot and gas-phase mechanisms. It has been demonstrated that the LFM is not able to predict accurately the soot volume fraction. On the other hand, the extended version proposed here has been shown to be very accurate. The different flamelet mathematical formulations have been tested and compared using well verified reference calculations obtained solving the set of the Full Transport Equations (FTE) in the physical space. (author)

  17. Two-level schemes for the advection equation

    Science.gov (United States)

    Vabishchevich, Petr N.

    2018-06-01

    The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

  18. Lagrangian derivation of the two coupled field equations in the Janus cosmological model

    Science.gov (United States)

    Petit, Jean-Pierre; D'Agostini, G.

    2015-05-01

    After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.

  19. Development of two-group interfacial area transport equation for confined flow-2. Model evaluation

    International Nuclear Information System (INIS)

    Sun, Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

    2003-01-01

    The bubble interaction mechanisms have been analytically modeled in the first paper of this series to provide mechanistic constitutive relations for the two-group interfacial area transport equation (IATE), which was proposed to dynamically solve the interfacial area concentration in the two-fluid model. This paper presents the evaluation approach and results of the two-group IATE based on available experimental data obtained in confined flow, namely, 11 data sets in or near bubbly flow and 13 sets in cap-turbulent and churn-turbulent flow. The two-group IATE is evaluated in steady state, one-dimensional form. Also, since the experiments were performed under adiabatic, air-water two-phase flow conditions, the phase change effect is omitted in the evaluation. To account for the inter-group bubble transport, the void fraction transport equation for Group-2 bubbles is also used to predict the void fraction for Group-2 bubbles. Agreement between the data and the model predictions is reasonably good and the average relative difference for the total interfacial area concentration between the 24 data sets and predictions is within 7%. The model evaluation demonstrates the capability of the two-group IATE focused on the current confined flow to predict the interfacial area concentration over a wide range of flow regimes. (author)

  20. Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

    Science.gov (United States)

    Skinner, Thomas E.

    2018-01-01

    The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which

  1. The PDF method for Lagrangian two-phase flow simulations

    International Nuclear Information System (INIS)

    Minier, J.P.; Pozorski, J.

    1996-04-01

    A recent turbulence model put forward by Pope (1991) in the context of PDF modelling has been used. In this approach, the one-point joint velocity-dissipation pdf equation is solved by simulating the instantaneous behaviour of a large number of Lagrangian fluid particles. Closure of the evolution equations of these Lagrangian particles is based on stochastic models and more specifically on diffusion processes. Such models are of direct use for two-phase flow modelling where the so-called fluid seen by discrete inclusions has to be modelled. Full Lagrangian simulations have been performed for shear-flows. It is emphasized that this approach gives far more information than traditional turbulence closures (such as the K-ε model) and therefore can be very useful for situations involving complex physics. It is also believed that the present model represents the first step towards a complete Lagrangian-Lagrangian model for dispersed two-phase flow problems. (authors). 21 refs., 6 figs

  2. GCFR 1/20-scale PCRV central core cavity closure model test

    International Nuclear Information System (INIS)

    Robinson, G.C.; Dougan, J.R.

    1981-06-01

    Oak Ridge National Laboratory has been conducting structural response tests of the prestressed concrete reactor vessel (PCRV) closures for the 300-MW(e) gas-cooled fast reactor demonstration power plant. This report describes the third in a series of tests of small-scale closure plug models. The model represents a redesign of the central core cavity closure plug. The primary objective was to demonstrate structural performance and ultimate load capacity of the closure plug. Secondary objectives included obtaining data on crack development and propagation and on mode of failure of the composite structure

  3. Acoustic Wave Propagation Modeling by a Two-dimensional Finite-difference Summation-by-parts Algorithm

    Energy Technology Data Exchange (ETDEWEB)

    Kim, K. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Petersson, N. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rodgers, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

    2016-10-25

    Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examples and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.

  4. Dynamic modelling of costs and health consequences of school closure during an influenza pandemic

    Directory of Open Access Journals (Sweden)

    Xue Yiting

    2012-11-01

    Full Text Available Abstract Background The purpose of this article is to evaluate the cost-effectiveness of school closure during a potential influenza pandemic and to examine the trade-off between costs and health benefits for school closure involving different target groups and different closure durations. Methods We developed two models: a dynamic disease model capturing the spread of influenza and an economic model capturing the costs and benefits of school closure. Decisions were based on quality-adjusted life years gained using incremental cost-effectiveness ratios. The disease model is an age-structured SEIR compartmental model based on the population of Oslo. We studied the costs and benefits of school closure by varying the age targets (kindergarten, primary school, secondary school and closure durations (1–10 weeks, given pandemics with basic reproductive number of 1.5, 2.0 or 2.5. Results The cost-effectiveness of school closure varies depending on the target group, duration and whether indirect costs are considered. Using a case fatality rate (CFR of 0.1-0.2% and with current cost-effectiveness threshold for Norway, closing secondary school is the only cost-effective strategy, when indirect costs are included. The most cost-effective strategies would be closing secondary schools for 8 weeks if R0=1.5, 6 weeks if R0=2.0, and 4 weeks if R0= 2.5. For severe pandemics with case fatality rates of 1-2%, similar to the Spanish flu, or when indirect costs are disregarded, the optimal strategy is closing kindergarten, primary and secondary school for extended periods of time. For a pandemic with 2009 H1N1 characteristics (mild severity and low transmissibility, closing schools would not be cost-effective, regardless of the age target of school children. Conclusions School closure has moderate impact on the epidemic’s scope, but the resulting disruption to society imposes a potentially great cost in terms of lost productivity from parents’ work absenteeism.

  5. Treatment of severe refractory epistaxis in hereditary hemorrhagic telangiectasia using a two-flap nasal closure method

    Science.gov (United States)

    Timmins, Benjamin H.; Hunter, Benjamin N.; Wilson, Kevin F.; Ward, P. Daniel

    2016-01-01

    Background Nasal closure has been shown to effectively manage severe epistaxis refractory to other treatments in patients with hereditary hemorrhagic telangiectasia (HHT). The nasal closure procedure may be underutilized due to its surgical complexity and flap breakdown. Methods Retrospective review of thirteen HHT patients treated for severe epistaxis with nasal closure between 2005 and 2013. Operating room (OR) time, need for revision surgery, pre- and post-procedure epistaxis severity score (ESS), complete blood count values, and Glasgow Benefit Inventory (GBI) questionnaire results were collected for each patient. The technique is described. We characterize a typical nasal closure patient and compare outcomes based on our experience with the traditional three-flap closure and a simplified two-flap nasal closure procedure. Results The average candidate for nasal closure in this series had an ESS of 7.88, Hgb of 8.3 g/dL, and received multiple transfusions, iron therapy, and cautery/coagulation procedures. Average ESS subsequent to nasal closure using the two flap method is 0.92 and mean GBI score is 56.3. Comparison of five patients who underwent the traditional three-flap nasal closure procedure and eight patients receiving the two flap nasal closure showed no significant difference in post-op ESS or GBI metrics. Mean operating room times of the traditional and simplified methods were 3.12 hours and 1.44 hours (p=0.0001). Mean time to first revision for eight nasal closure patients is 21.5 months. Conclusion In short-term follow-up, the two-flap procedure has shown comparable effectiveness with significantly reduced complexity and operative time compared to the traditional nasal closure method. PMID:26751606

  6. Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells

    Directory of Open Access Journals (Sweden)

    Beguerisse-Dıaz Mariano

    2012-11-01

    Full Text Available Abstract Background Stomata are tiny pores in plant leaves that regulate gas and water exchange between the plant and its environment. Abscisic acid and ethylene are two well-known elicitors of stomatal closure when acting independently. However, when stomata are presented with a combination of both signals, they fail to close. Results Toshed light on this unexplained behaviour, we have collected time course measurements of stomatal aperture and hydrogen peroxide production in Arabidopsis thaliana guard cells treated with abscisic acid, ethylene, and a combination of both. Our experiments show that stomatal closure is linked to sustained high levels of hydrogen peroxide in guard cells. When treated with a combined dose of abscisic acid and ethylene, guard cells exhibit increased antioxidant activity that reduces hydrogen peroxide levels and precludes closure. We construct a simplified model of stomatal closure derived from known biochemical pathways that captures the experimentally observed behaviour. Conclusions Our experiments and modelling results suggest a distinct role for two antioxidant mechanisms during stomatal closure: a slower, delayed response activated by a single stimulus (abscisic acid ‘or’ ethylene and another more rapid ‘and’ mechanism that is only activated when both stimuli are present. Our model indicates that the presence of this rapid ‘and’ mechanism in the antioxidant response is key to explain the lack of closure under a combined stimulus.

  7. Gross-Pitaevskii equation for Bose particles in a double-well potential: Two-mode models and beyond

    International Nuclear Information System (INIS)

    Ananikian, D.; Bergeman, T.

    2006-01-01

    In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an 'improved two-mode model' (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled ''interaction tunneling,'' that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem

  8. Optimization of a Two-Fluid Hydrodynamic Model of Churn-Turbulent Flow

    Energy Technology Data Exchange (ETDEWEB)

    Donna Post Guillen

    2009-07-01

    A hydrodynamic model of two-phase, churn-turbulent flows is being developed using the computational multiphase fluid dynamics (CMFD) code, NPHASE-CMFD. The numerical solutions obtained by this model are compared with experimental data obtained at the TOPFLOW facility of the Institute of Safety Research at the Forschungszentrum Dresden-Rossendorf. The TOPFLOW data is a high quality experimental database of upward, co-current air-water flows in a vertical pipe suitable for validation of computational fluid dynamics (CFD) codes. A five-field CMFD model was developed for the continuous liquid phase and four bubble size groups using mechanistic closure models for the ensemble-averaged Navier-Stokes equations. Mechanistic models for the drag and non-drag interfacial forces are implemented to include the governing physics to describe the hydrodynamic forces controlling the gas distribution. The closure models provide the functional form of the interfacial forces, with user defined coefficients to adjust the force magnitude. An optimization strategy was devised for these coefficients using commercial design optimization software. This paper demonstrates an approach to optimizing CMFD model parameters using a design optimization approach. Computed radial void fraction profiles predicted by the NPHASE-CMFD code are compared to experimental data for four bubble size groups.

  9. Dynamical System Analysis of Reynolds Stress Closure Equations

    Science.gov (United States)

    Girimaji, Sharath S.

    1997-01-01

    In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

  10. Interfacial shear modeling in two-phase annular flow

    International Nuclear Information System (INIS)

    Kumar, R.; Edwards, D.P.

    1996-11-01

    A new interfacial shear stress model called the law of the interface model, based on the law of the wall approach in turbulent flows, has been developed and locally applied in a fully developed, adiabatic, two-phase annular flow in a duct. Numerical results have been obtained using this model in conjunction with other models available in the literature that are required for the closure of the continuity and momentum equations. These results have been compared with droplet velocity data (using laser Doppler velocimetry and hot film anemometry), void fraction data (using gamma densitometry) and pressure drop data obtained in a R-134A refrigerant test facility. Droplet velocity results match the experimental data well, however, the prediction of the void fraction is less accurate. The poor prediction of void fraction, especially for the low void fraction cases, appears to be due to the lack of a good mechanistic model for entrainment

  11. Interfacial shear modeling in two-phase annular flow

    International Nuclear Information System (INIS)

    Kumar, R.; Edwards, D.P.

    1996-07-01

    A new interfacial shear stress model called the law of the interface model, based on the law of the wall approach in turbulent flows, has been developed and locally applied in a fully developed, adiabatic, two-phase annular flow in a duct. Numerical results have been obtained using this model in conjunction with other models available in the literature that are required for the closure of the continuity and momentum equations. These results have been compared with droplet velocity data (using laser Doppler velocimetry and hot film anemometry), void fraction data (using gamma densitometry) and pressure drop data obtained in a R-134A refrigerant test facility. Droplet velocity results match the experimental data well, however, the prediction of the void fraction is less accurate. The poor prediction of void fraction, especially for the low void fraction cases, appears to be due to the lack of a good mechanistic model for entrainment

  12. Direct numerical simulation of natural convection in a vertical channel: a tool for second moment closure modeling

    International Nuclear Information System (INIS)

    Maupu, V.; Laurence, D.

    1996-01-01

    Natural turbulent convection in a differentially heated infinite vertical slot is computed with a mixed finite differences/Fourier code. At a Rayleigh number of 10 5 , in the case without mean stratification, periodic perturbations from the laminar solution develop and transition to a fully turbulent flow occurs. From then on, a database of one-point statistics is presented: mean velocity and temperature, Reynolds stress components, turbulent heat fluxes and variance of temperature, but also budgets of second moment equations. This database is then used for testing of a second moment closure based on the Launder-Reece-Rodi model on an elliptic relaxation for near wall effects on pressure redistribution. This level of modelling is required by the presence of counter gradient fluxes, which cannot be accounted for eddy viscosity and eddy diffusivity assumptions. Furthermore, an algebraic third order moment closure was found necessary because of counter gradient turbulent transport terms which appear to mainly originate from the mean velocity and temperature gradient terms usually neglected in conventional transport models, such as the standard Daly-Harlow or Hanjalic-Launder models. (authors)

  13. Occupancy estimation and the closure assumption

    Science.gov (United States)

    Rota, Christopher T.; Fletcher, Robert J.; Dorazio, Robert M.; Betts, Matthew G.

    2009-01-01

    1. Recent advances in occupancy estimation that adjust for imperfect detection have provided substantial improvements over traditional approaches and are receiving considerable use in applied ecology. To estimate and adjust for detectability, occupancy modelling requires multiple surveys at a site and requires the assumption of 'closure' between surveys, i.e. no changes in occupancy between surveys. Violations of this assumption could bias parameter estimates; however, little work has assessed model sensitivity to violations of this assumption or how commonly such violations occur in nature. 2. We apply a modelling procedure that can test for closure to two avian point-count data sets in Montana and New Hampshire, USA, that exemplify time-scales at which closure is often assumed. These data sets illustrate different sampling designs that allow testing for closure but are currently rarely employed in field investigations. Using a simulation study, we then evaluate the sensitivity of parameter estimates to changes in site occupancy and evaluate a power analysis developed for sampling designs that is aimed at limiting the likelihood of closure. 3. Application of our approach to point-count data indicates that habitats may frequently be open to changes in site occupancy at time-scales typical of many occupancy investigations, with 71% and 100% of species investigated in Montana and New Hampshire respectively, showing violation of closure across time periods of 3 weeks and 8 days respectively. 4. Simulations suggest that models assuming closure are sensitive to changes in occupancy. Power analyses further suggest that the modelling procedure we apply can effectively test for closure. 5. Synthesis and applications. Our demonstration that sites may be open to changes in site occupancy over time-scales typical of many occupancy investigations, combined with the sensitivity of models to violations of the closure assumption, highlights the importance of properly addressing

  14. Comparisons of Multilevel Modeling and Structural Equation Modeling Approaches to Actor-Partner Interdependence Model.

    Science.gov (United States)

    Hong, Sehee; Kim, Soyoung

    2018-01-01

    There are basically two modeling approaches applicable to analyzing an actor-partner interdependence model: the multilevel modeling (hierarchical linear model) and the structural equation modeling. This article explains how to use these two models in analyzing an actor-partner interdependence model and how these two approaches work differently. As an empirical example, marital conflict data were used to analyze an actor-partner interdependence model. The multilevel modeling and the structural equation modeling produced virtually identical estimates for a basic model. However, the structural equation modeling approach allowed more realistic assumptions on measurement errors and factor loadings, rendering better model fit indices.

  15. Unification of the Two-Parameter Equation of State and the Principle of Corresponding States

    DEFF Research Database (Denmark)

    Mollerup, Jørgen

    1998-01-01

    A two-parameter equation of state is a two-parameter corresponding states model. A two-parameter corresponding states model is composed of two scale factor correlations and a reference fluid equation of state. In a two-parameter equation of state the reference equation of state is the two-paramet...

  16. A Crack Closure Model and Its Application to Vibrothermography Nondestructive Evaluation

    Science.gov (United States)

    Schiefelbein, Bryan Edward

    saying that the effective crack tip is located where the stress singularity vanishes. If the closure stresses are unknown, the model provides an algorithm with which to solve for the distribution, given measurements of the effective crack length as a function of external load. Within literature, a number of heating mechanisms have been proposed as being dominant in vibrothermography. These include strain hysteresis, adhesion hysteresis, plastic flow, thermoelasticity, and sliding friction. Based on experimental observation and theory, this work eliminates strain hysteresis, thermoelasticity, and plastic flow as plausible heating mechanisms. This leaves friction and adhesion hysteresis as the only plausible mechanisms. Frictional heating is based on the classical Coulomb friction model, while adhesion hysteresis heating comes from irreversibility in surface adhesion. Adhesion hysteresis only satisfies the experimental observation that heating vanishes for high compressive loading if surface roughness and the instability of surface adhesion is considered. By understanding the fundamental behavior of a partially closed crack in response to non-uniform loading, and the link between crack surface motion and heat generation, we are one step closer to a fully predictive vibrothermography heat generation model. Future work is needed to extend the crack closure model to a two-dimensional semi-elliptical surface crack and better understand the distinction between frictional and adhesion heating.

  17. A summary of methods for approximating salt creep and disposal room closure in numerical models of multiphase flow

    Energy Technology Data Exchange (ETDEWEB)

    Freeze, G.A.; Larson, K.W. [INTERA, Inc., Albuquerque, NM (United States); Davies, P.B. [Sandia National Labs., Albuquerque, NM (United States)

    1995-10-01

    Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time.

  18. A summary of methods for approximating salt creep and disposal room closure in numerical models of multiphase flow

    International Nuclear Information System (INIS)

    Freeze, G.A.; Larson, K.W.; Davies, P.B.

    1995-10-01

    Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time

  19. Steady state conductance in a double quantum dot array: the nonequilibrium equation-of-motion Green function approach.

    Science.gov (United States)

    Levy, Tal J; Rabani, Eran

    2013-04-28

    We study steady state transport through a double quantum dot array using the equation-of-motion approach to the nonequilibrium Green functions formalism. This popular technique relies on uncontrolled approximations to obtain a closure for a hierarchy of equations; however, its accuracy is questioned. We focus on 4 different closures, 2 of which were previously proposed in the context of the single quantum dot system (Anderson impurity model) and were extended to the double quantum dot array, and develop 2 new closures. Results for the differential conductance are compared to those attained by a master equation approach known to be accurate for weak system-leads couplings and high temperatures. While all 4 closures provide an accurate description of the Coulomb blockade and other transport properties in the single quantum dot case, they differ in the case of the double quantum dot array, where only one of the developed closures provides satisfactory results. This is rationalized by comparing the poles of the Green functions to the exact many-particle energy differences for the isolate system. Our analysis provides means to extend the equation-of-motion technique to more elaborate models of large bridge systems with strong electronic interactions.

  20. Modeling Effects of Groundwater Basin Closure, and Reversal of Closure, on Groundwater Quality

    Science.gov (United States)

    Pauloo, R.; Guo, Z.; Fogg, G. E.

    2017-12-01

    Population growth, the expansion of agriculture, and climate uncertainties have accelerated groundwater pumping and overdraft in aquifers worldwide. In many agricultural basins, a water budget may be stable or not in overdraft, yet disconnected ground and surface water bodies can contribute to the formation of a "closed" basin, where water principally exits the basin as evapotranspiration. Although decreasing water quality associated with increases in Total Dissolved Solids (TDS) have been documented in aquifers across the United States in the past half century, connections between water quality declines and significant changes in hydrologic budgets leading to closed basin formation remain poorly understood. Preliminary results from an analysis with a regional-scale mixing model of the Tulare Lake Basin in California indicate that groundwater salinization resulting from open to closed basin conversion can operate on a decades-to-century long time scale. The only way to reverse groundwater salinization caused by basin closure is to refill the basin and change the hydrologic budget sufficiently for natural groundwater discharge to resume. 3D flow and transport modeling, including the effects of heterogeneity based on a hydrostratigraphic facies model, is used to explore rates and time scales of groundwater salinization and its reversal under different water and land management scenarios. The modeling is also used to ascertain the extent to which local and regional heterogeneity need to be included in order to appropriately upscale the advection-dispersion equation in a basin scale groundwater quality management model. Results imply that persistent managed aquifer recharge may slow groundwater salinization, and complete reversal may be possible at sufficiently high water tables.

  1. Zero singularities of codimension two and three in delay differential equations

    International Nuclear Information System (INIS)

    Campbell, Sue Ann; Yuan Yuan

    2008-01-01

    We give conditions under which a general class of delay differential equations has a point of Bogdanov–Takens or a triple zero bifurcation. We show how a centre manifold projection of the delay equations reduces the dynamics to two- or three-dimensional systems of ordinary differential equations. We put these equations in normal form and determine how the coefficients of the normal forms depend on the original parameters in the model. Finally we apply our results to two neural models and compare the predictions of the theory with numerical bifurcation analysis of the full equations. One model involves a transcritical bifurcation, hence we derive and analyse the appropriate unfoldings for this case

  2. Nickel titanium springs versus stainless steel springs: A randomized clinical trial of two methods of space closure.

    Science.gov (United States)

    Norman, Noraina Hafizan; Worthington, Helen; Chadwick, Stephen Mark

    2016-09-01

    To compare the clinical performance of nickel titanium (NiTi) versus stainless steel (SS) springs during orthodontic space closure. Two-centre parallel group randomized clinical trial. Orthodontic Department University of Manchester Dental Hospital and Orthodontic Department Countess of Chester Hospital, United Kingdom. Forty orthodontic patients requiring fixed appliance treatment were enrolled, each being randomly allocated into either NiTi (n = 19) or SS groups (n = 21). Study models were constructed at the start of the space closure phase (T0) and following the completion of space closure (T1). The rate of space closure achieved for each patient was calculated by taking an average measurement from the tip of the canine to the mesiobuccal groove on the first permanent molar of each quadrant. The study was terminated early due to time constraints. Only 30 patients completed, 15 in each study group. There was no statistically significant difference between the amounts of space closed (mean difference 0.17 mm (95%CI -0.99 to 1.34; P = 0.76)). The mean rate of space closure for NiTi coil springs was 0.58 mm/4 weeks (SD 0.24) and 0.85 mm/4 weeks (SD 0.36) for the stainless steel springs. There was a statistically significant difference between the two groups (P = 0.024), in favour of the stainless steel springs, when the mean values per patient were compared. Our study shows that stainless steel springs are clinically effective; these springs produce as much space closure as their more expensive rivals, the NiTi springs.

  3. Meta-analysis a structural equation modeling approach

    CERN Document Server

    Cheung, Mike W-L

    2015-01-01

    Presents a novel approach to conducting meta-analysis using structural equation modeling. Structural equation modeling (SEM) and meta-analysis are two powerful statistical methods in the educational, social, behavioral, and medical sciences. They are often treated as two unrelated topics in the literature. This book presents a unified framework on analyzing meta-analytic data within the SEM framework, and illustrates how to conduct meta-analysis using the metaSEM package in the R statistical environment. Meta-Analysis: A Structural Equation Modeling Approach begins by introducing the impo

  4. Troughs on Martian Ice Sheets: Analysis of Their Closure and Mass Balance

    Science.gov (United States)

    Fountain, A.; Kargel, J.; Lewis, K.; MacAyeal, D.; Pfeffer, T.; Zwally, J.

    2000-01-01

    At the Copenhagen workshop on Martian polar processes, Ralf Greve commented that the flow regime surrounding scarps and troughs of the Martian polar ice sheets cannot be modeled using traditional "plan view" ice-sheet models. Such models are inadequate because they typically use reduced equations that embody certain simplifications applicable only to terrestrial ice sheets where the upper ice sheet surface is smooth. In response to this suggestion, we have constructed a 2-dimensional, time dependent "side view" (two spatial dimensions: one horizontal, one vertical) model of scarp closure that is designed to overcome the difficulties described by Greve. The purpose of the model is to evaluate the scales of stress variation and styles of flow closure so as to estimate errors that may be encountered by "plan view" models. We show that there may be avenues whereby the complications associated with scarp closure can be overcome in "plan view" models through appropriate parameterizations of 3-dimensional effects. Following this, we apply the flow model to simulate the evolution of a typical scarp on the North Polar Cap of Mars. Our simulations investigate: (a) the role of "radiation trapping" (see our companion abstract) in creating and maintaining "spiral-like" scarps on the ice sheet, (b) the consequences of different flowlaws and ice compositions on scarp evolution and, in particular, scarp age, and (c) the role of dust and debris in scarp evolution.

  5. Hamiltonian formalism of two-dimensional Vlasov kinetic equation.

    Science.gov (United States)

    Pavlov, Maxim V

    2014-12-08

    In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.

  6. Modelling conjugation with stochastic differential equations

    DEFF Research Database (Denmark)

    Philipsen, Kirsten Riber; Christiansen, Lasse Engbo; Hasman, Henrik

    2010-01-01

    Enterococcus faecium strains in a rich exhaustible media. The model contains a new expression for a substrate dependent conjugation rate. A maximum likelihood based method is used to estimate the model parameters. Different models including different noise structure for the system and observations are compared......Conjugation is an important mechanism involved in the transfer of resistance between bacteria. In this article a stochastic differential equation based model consisting of a continuous time state equation and a discrete time measurement equation is introduced to model growth and conjugation of two...... using a likelihood-ratio test and Akaike's information criterion. Experiments indicating conjugation on the agar plates selecting for transconjugants motivates the introduction of an extended model, for which conjugation on the agar plate is described in the measurement equation. This model is compared...

  7. Uncertainty Quantification of Turbulence Model Closure Coefficients for Transonic Wall-Bounded Flows

    Science.gov (United States)

    Schaefer, John; West, Thomas; Hosder, Serhat; Rumsey, Christopher; Carlson, Jan-Renee; Kleb, William

    2015-01-01

    The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-w Model, and the Menter Shear-Stress Trans- port Model. The FUN3D code developed by NASA Langley Research Center was used as the flow solver. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. This study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows.

  8. Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

    Science.gov (United States)

    Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

    2017-11-01

    Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

  9. Meson spectra from two-body dirac equations with minimal interactions

    International Nuclear Information System (INIS)

    Crater, H.W.; Becker, R.L.; Wong, C.Y.

    1991-01-01

    Many authors have used two-body relativistic wave equations with spin in nonperturbative numerical quark model calculations of the meson spectrum. Usually, they adopt a truncation of the Bethe-Salpeter equation of QED and/or scalar. QED and replace the static Coulomb interactions of those field theories with a semiphenomenological Q bar Q potential whose insertion in the Breit terms give the corresponding spin corrections. However, the successes of these wave equations in QED have invariably depended on perturbative treatment of the terms in each beyond the Coulomb terms. There have been no successful nonperturbative numerical test of two-body quantum wave equations in QED, because in most equations the effective potentials beyond the Coulomb are singular and can only be treated perturbatively. This is a glaring omission that we rectify here for the case of the two-body Dirac equations of constraint dynamics. We show in this paper that a nonperturbative numerical treatment of these equations for QED yields the same spectral results as a perturbative treatment of them which in turn agrees with the standard spectral results for positronium and muonium. This establishes that the vector and scalar interaction structures of our equations accurately incorporate field theoretic interactions in a bone fide relativistic wave equation. The last portion of this work will report recent quark model calculations using these equations with the Adler-Piran static Q bar Q potential

  10. Mathematical well-posedness of a two-fluid equations for bubbly two-phase flows

    International Nuclear Information System (INIS)

    Okawa, Tomio; Kataoka, Isao

    2000-01-01

    It is widely known that two-fluid equations used in most engineering applications do not satisfy the necessary condition for being mathematical well-posed as initial-value problems. In the case of stratified two-phase flows, several researchers have revealed that differential models satisfying the necessary condition are to be derived if the pressure difference between the phases is related to the spatial gradient of the void fraction through the effects of gravity or surface tension. While, in the case of dispersed two-phase flows, no physically reasonable method to derive mathematically well-posed two-fluid model has been proposed. In the present study, particularly focusing on the effect of interfacial pressure terms, we derived the mathematically closed form of the volume-averaged two-fluid model for bubbly two-phase flows. As a result of characteristic analyses, it was shown that the proposed two-fluid equations satisfy the necessary condition of mathematical well-posedness if the void fraction is sufficiently small. (author)

  11. Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State

    KAUST Repository

    Qiao, Zhonghua; Sun, Shuyu

    2014-01-01

    In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory

  12. Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

    International Nuclear Information System (INIS)

    Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

    2009-01-01

    The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

  13. I. A model for the magnetic equation of state of liquid 3He. II. An induced interaction model for a two-component Fermi liquid

    International Nuclear Information System (INIS)

    Sanchez-Castro, C.R.

    1988-01-01

    This dissertation is divided in six chapters. Chapter 1 is an introduction to the rest of the dissertation. In it, the author presents the different models for the magnetic equation state of liquid 3 He, a derivation of the induced interaction equations for a one component Fermi liquid, and discuss the basic hamiltonian describing the heavy fermion compounds. In Chapter 2 and Chapter 3, he presents a complete discussion of the thermodynamics and Landau theory of a spin polarized Fermi liquid. A phenomenological model is then developed to predict the polarization dependence of the longitudinal Landau parameters in liquid 3 He. This model predicts a new magnetic equation of state and the possibility of liquid 3 He being 'nearly metamagnetic' at high pressures. Chapter 4 contains a microscopic calculation of the magnetic field dependence of the Landau parameters in a strongly correlated Fermi system using the induced interaction model. The system he studied consists of a single component Fermi liquid with parabolic energy bands, and a large on-site repulsive interaction. In Chapter 5, he presents a complete discussion of the Landau theory of a two component Fermi liquid. Then, he generalizes the induced interaction equations to calculate Landau parameters and scattering amplitudes for an arbitrary, spin polarized, two component Fermi liquid. The resulting equations are used to study a model for the heavy fermion Fermi liquid state: a two band electronic system with an antiferromagnetic interaction between the two bands. Chapter 6 contains the concluding remarks of the dissertation

  14. Critical review of conservation equations for two-phase flow in the U.S. NRC TRACE code

    International Nuclear Information System (INIS)

    Wulff, Wolfgang

    2011-01-01

    Research highlights: → Field equations as implemented in TRACE are incorrect. → Boundary conditions needed for cooling of nuclear fuel elements are wrong. → The two-fluid model in TRACE is not closed. → Three-dimensional flow modeling in TRACE has no basis. - Abstract: The field equations for two-phase flow in the computer code TRAC/RELAP Advanced Computational Engine or TRACE are examined to determine their validity, their capabilities and limitations in resolving nuclear reactor safety issues. TRACE was developed for the NRC to predict thermohydraulic phenomena in nuclear power plants during operational transients and postulated accidents. TRACE is based on the rigorously derived and well-established two-fluid field equations for 1-D and 3-D two-phase flow. It is shown that: (1)The two-fluid field equations for mass conservation as implemented in TRACE are wrong because local mass balances in TRACE are in conflict with mass conservation for the whole reactor system, as shown in Section . (2)Wrong equations of motion are used in TRACE in place of momentum balances, compromising at branch points the prediction of momentum transfer between, and the coupling of, loops in hydraulic networks by impedance (form loss and wall shear) and by inertia and thereby the simulation of reactor component interactions. (3)Most seriously, TRACE calculation of heat transfer from fuel elements is incorrect for single and two-phase flows, because Eq. of the TRACE Manual is wrong (see Section ). (4)Boundary conditions for momentum and energy balances in TRACE are restricted to flow regimes with single-phase wall contact because TRACE lacks constitutive relations for solid-fluid exchange of momentum and heat in prevailing flow regimes. Without a quantified assessment of consequences from (3) to (4), predictions of phasic fluid velocities, fuel temperatures and important safety parameters, e.g., peak clad temperature, are questionable. Moreover, TRACE cannot predict 3-D single- or

  15. Autonomic Closure for Turbulent Flows Using Approximate Bayesian Computation

    Science.gov (United States)

    Doronina, Olga; Christopher, Jason; Hamlington, Peter; Dahm, Werner

    2017-11-01

    Autonomic closure is a new technique for achieving fully adaptive and physically accurate closure of coarse-grained turbulent flow governing equations, such as those solved in large eddy simulations (LES). Although autonomic closure has been shown in recent a priori tests to more accurately represent unclosed terms than do dynamic versions of traditional LES models, the computational cost of the approach makes it challenging to implement for simulations of practical turbulent flows at realistically high Reynolds numbers. The optimization step used in the approach introduces large matrices that must be inverted and is highly memory intensive. In order to reduce memory requirements, here we propose to use approximate Bayesian computation (ABC) in place of the optimization step, thereby yielding a computationally-efficient implementation of autonomic closure that trades memory-intensive for processor-intensive computations. The latter challenge can be overcome as co-processors such as general purpose graphical processing units become increasingly available on current generation petascale and exascale supercomputers. In this work, we outline the formulation of ABC-enabled autonomic closure and present initial results demonstrating the accuracy and computational cost of the approach.

  16. Governing equations for a seriated continuum: an unequal velocity model for two-phase flow

    International Nuclear Information System (INIS)

    Solbrig, C.W.; Hughes, E.D.

    1975-05-01

    The description of the flow of two-phase fluids is important in many engineering devices. Unexpected transient conditions which occur in these devices cannot, in general, be treated with single-component momentum equations. Instead, the use of momentum equations for each phase is necessary in order to describe the varied transient situations which can occur. These transient conditions can include phases moving in the opposite directions, such as steam moving upward and liquid moving downward, as well as phases moving in the same direction. The derivation of continuity and momentum equations for each phase and an overall energy equation for the mixture are presented. Terms describing interphase forces are described. A seriated (series of) continuum is distinguished from an interpenetrating medium by the representation of interphase friction with velocity differences in the former and velocity gradients in the latter. The seriated continuum also considers imbedded stationary solid surfaces such as occur in nuclear reactor cores. These stationary surfaces are taken into account with source terms. Sufficient constitutive equations are presented to form a complete set of equations. Methods are presented to show that all these coefficients are determinable from microscopic models and well known experimental results. Comparison of the present deviation with previous work is also given. The equations derived here may also be employed in certain multiphase, multicomponent flow applications. (U.S.)

  17. Ultrasound evaluation of the cesarean scar: comparison between one- and two layer uterotomy closure

    DEFF Research Database (Denmark)

    Glavind, Julie; Madsen, Lene Duch; Uldbjerg, Niels

    Objectives: To compare the residual myometrial thickness and the size of the cesarean scar defect after one- and two layer uterotomy closure. Methods: From July 2010 a continuous two-layer uterotomy closure technique replaced a continuous one-layer technique after cesarean delivery...... at the Department of Obstetrics and Gynecology at Aarhus University Hospital. A total of 149 consecutively invited women (68 women with one-layer and 81 women with two-layer closure) had their cesarean scar examined with 2D transvaginal sonography (TVS) 6-16 months post partum. Inclusion criteria were non......-pregnant women with one previous elective cesarean, no post-partum uterine infection or uterine re-operation, and no type 1 diabetes. Scar defect width, depth, and residual myometrial thickness were measured on the sagittal plane, and scar defect length was measured on the transverse plane. Results: The median...

  18. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    Energy Technology Data Exchange (ETDEWEB)

    Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)

    2006-12-15

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  19. Two-loop renormalization in the standard model, part III. Renormalization equations and their solutions

    International Nuclear Information System (INIS)

    Actis, S.; Passarino, G.

    2006-12-01

    In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)

  20. Two-fluid equations for a nuclear system with arbitrary motions

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Byoung Jae [Chungnam National University, Daejeon (Korea, Republic of); Kim, Kyung Doo [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2016-10-15

    Ocean nuclear systems include a seabed-type plant, a floating-type plant, and a nuclear-propulsion ship. We asked ourselves, 'What governing equations should be used for ocean nuclear systems?' Since ocean nuclear systems are apt to move arbitrarily, the two-fluid model must be formulated in the non-inertial frame of reference that is undergoing acceleration with respect to an inertial frame. Two-phase flow systems with arbitrary motions are barely reported. Kim et al. (1996) added the centripetal and Euler acceleration forces to the homogeneous equilibrium momentum equation embedded in the RETRAN code. However, they did not look into the mass and energy equations. The purpose of this study is to derive general two-fluid equations in the non-inertial frame of reference, which can be used for safety analysis of ocean nuclear systems. The two-fluid equation forms for scalar properties such as mass, internal energy, and enthalpy equation in the moving frame are the same as those in the absolute frame. On the other hand, the fictitious effect must be included in the momentum equation.

  1. A mapping closure for turbulent scalar mixing using a time-evolving reference field

    Science.gov (United States)

    Girimaji, Sharath S.

    1992-01-01

    A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.

  2. Flow simulation in piping system dead legs using second moment, closure and k-epsilon model

    International Nuclear Information System (INIS)

    Deutsch, E.; Mechitoua, N.; Mattei, J.D.

    1996-01-01

    This paper deals with an industrial application of second moment closure turbulence model in in numerical simulation of 3D turbulent flows in piping system dead legs. Calculations performed with the 3D ESTET code are presented which contrast the performance of k-epsilon eddy viscosity model and second moment closure turbulence models. Coarse (100 000), medium (400 000) and fine (1 500 000) meshes were used. The second moment closure performs significantly better than eddy viscosity model and predicts with a good agreement the vortex penetration in dead legs provided to use sufficiently refined meshes. The results point out the necessity to be able to perform calculations using fine mesh before introducing refined physical models such as second moment closure turbulence model in a numerical code. This study illustrates the ability of second moment closure turbulence model to simulate 3D turbulent industrial flows. Reynolds stress model computation does not require special care, the calculation is carried on as simply as the k-ξ one. The CPU time needed is less that twice the CPU time needed using k-ξ model. (authors)

  3. Results of Washington's phase two study on closure requirements for the Hanford commercial low-level waste facility

    International Nuclear Information System (INIS)

    Anderson, D.C.; Hana, S.L.

    1989-01-01

    This paper reports on the closure design objectives and cover alternatives resulting from the state of Washington's phase two study on closure and long-term care for the Hanford commercial low-level radioactive waste disposal facility. Four approaches to dealing with subsidence and two cover design alternatives are discussed in this paper, along with information on each layer of each cover. Objectives for closure of the Hanford low-level waste facility are also discussed

  4. Contribution to the modelling of two-phase flows in duct: influence of carryover and deposition processes in the case of a dispersed annular configuration

    International Nuclear Information System (INIS)

    Ho-Kee-King, Simone

    1996-01-01

    As the study of two-phase flows is required to assess or optimize the performance of many industrial systems in chemical, thermal or nuclear engineering, this research thesis in fluid mechanics aims at describing the evolution of a two-phase flow in a dispersed annular configuration when passing a convergent nozzle. The study focused on the elaboration of simple, one-dimensional and permanent flows, and is based on experiments performed in the case of a liquid annular injection. The author discusses the mapping of two-phase flows, proposes an overview of their modelling, and proposes a model with its instantaneous local equations and time- and space-averaged equations. He addresses the issues of closure laws for two-field models (friction laws on the walls and at the interfaces, discussion of published experimental results), and of mass transfer laws for three-field models. He reports the development of a droplet carryover rate law and the analysis of published experiments by using the three-field model [fr

  5. Dynamic Modeling Strategy for Flow Regime Transition in Gas-Liquid Two-Phase Flows

    Directory of Open Access Journals (Sweden)

    Xia Wang

    2012-12-01

    Full Text Available In modeling gas-liquid two-phase flows, the concept of flow regimes has been widely used to characterize the global interfacial structure of the flows. Nearly all constitutive relations that provide closures to the interfacial transfers in two-phase flow models, such as the two-fluid model, are flow regime dependent. Current nuclear reactor safety analysis codes, such as RELAP5, classify flow regimes using flow regime maps or transition criteria that were developed for steady-state, fully-developed flows. As two-phase flows are dynamic in nature, it is important to model the flow regime transitions dynamically to more accurately predict the two-phase flows. The present work aims to develop a dynamic modeling strategy to determine flow regimes in gas-liquid two-phase flows through introduction of interfacial area transport equations (IATEs within the framework of a two-fluid model. The IATE is a transport equation that models the interfacial area concentration by considering the creation of the interfacial area, fluid particle (bubble or liquid droplet disintegration, boiling and evaporation, and the destruction of the interfacial area, fluid particle coalescence and condensation. For flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and shapes, namely group-1 and group-2 bubbles. A preliminary approach to dynamically identify the flow regimes is discussed, in which discriminators are based on the predicted information, such as the void fraction and interfacial area concentration. The flow regime predicted with this method shows good agreement with the experimental observations.

  6. Two-Phase Fluid Simulation Using a Diffuse Interface Model with Peng--Robinson Equation of State

    KAUST Repository

    Qiao, Zhonghua

    2014-01-01

    In this paper, two-phase fluid systems are simulated using a diffusive interface model with the Peng-Robinson equation of state (EOS), a widely used realistic EOS for hydrocarbon fluid in the petroleum industry. We first utilize the gradient theory of thermodynamics and variational calculus to derive a generalized chemical equilibrium equation, which is mathematically a second-order elliptic partial differential equation (PDE) in molar density with a strongly nonlinear source term. To solve this PDE, we convert it to a time-dependent parabolic PDE with the main interest in its final steady state solution. A Lagrange multiplier is used to enforce mass conservation. The parabolic PDE is then solved by mixed finite element methods with a semi-implicit time marching scheme. Convex splitting of the energy functional is proposed to construct this time marching scheme, where the volume exclusion effect of an EOS is treated implicitly while the pairwise attraction effect of EOS is calculated explicitly. This scheme is proved to be unconditionally energy stable. Our proposed algorithm is able to solve successfully the spatially heterogeneous two-phase systems with the Peng-Robinson EOS in multiple spatial dimensions, the first time in the literature. Numerical examples are provided with realistic hydrocarbon components to illustrate the theory. Furthermore, our computational results are compared with laboratory experimental data and verified with the Young-Laplace equation with good agreement. This work sets the stage for a broad extension of efficient convex-splitting semi-implicit schemes for numerical simulation of phase field models with a realistic EOS in complex geometries of multiple spatial dimensions.

  7. Two derivations of the master equation of quantum Brownian motion

    International Nuclear Information System (INIS)

    Halliwell, J J

    2007-01-01

    Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model

  8. Two derivations of the master equation of quantum Brownian motion

    Energy Technology Data Exchange (ETDEWEB)

    Halliwell, J J [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)

    2007-03-23

    Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model.

  9. Differential Equations Models to Study Quorum Sensing.

    Science.gov (United States)

    Pérez-Velázquez, Judith; Hense, Burkhard A

    2018-01-01

    Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

  10. Analysis of turbulent separated flows for the NREL airfoil using anisotropic two-equation models at higher angles of attack

    Energy Technology Data Exchange (ETDEWEB)

    Zhang Shijie [Tsinghua University, Beijing (China). School of Architecture; Yuan Xin; Ye Dajun [Tsinghua University, Beijing (China). Dept. of Thermal Engineering

    2001-07-01

    Numerical simulations of the turbulent flow fields at stall conditions are presented for the NREL (National Renewable Energy Laboratory) S809 airfoil. The flow is modelled as compressible, viscous, steady/unsteady and turbulent. Four two-equation turbulence models (isotropic {kappa}-{epsilon} and q-{omega} models, anisotropic {kappa}-{epsilon} and -{omega} models), are applied to close the Reynolds-averaged Navier-Stokes equations, respectively. The governing equations are integrated in time by a new LU-type implicit scheme. To accurately model the convection terms in the mean-flow and turbulence model equations, a modified fourth-order high resolution MUSCL TVD scheme is incorporated. The large-scale separated flow fields and their losses at the stall and post-stall conditions are analyzed for the NREL S809 airfoil at various angles of attack ({alpha}) from 0 to 70 degrees. The numerical results show excellent to fairly good agreement with the experimental data. The feasibility of the present numerical method and the influence of the four turbulence models are also investigated. (author)

  11. Hypersonic expansion of the Fokker--Planck equation

    International Nuclear Information System (INIS)

    Fernandez-Feria, R.

    1989-01-01

    A systematic study of the hypersonic limit of a heavy species diluted in a much lighter gas is made via the Fokker--Planck equation governing its velocity distribution function. In particular, two different hypersonic expansions of the Fokker--Planck equation are considered, differing from each other in the momentum equation of the heavy gas used as the basis of the expansion: in the first of them, the pressure tensor is neglected in that equation while, in the second expansion, the pressure tensor term is retained. The expansions are valid when the light gas Mach number is O(1) or larger and the difference between the mean velocities of light and heavy components is small compared to the light gas thermal speed. They can be applied away from regions where the spatial gradient of the distribution function is very large, but it is not restricted with respect to the temporal derivative of the distribution function. The hydrodynamic equations corresponding to the lowest order of both expansions constitute two different hypersonic closures of the moment equations. For the subsequent orders in the expansions, closed sets of moment equations (hydrodynamic equations) are given. Special emphasis is made on the order of magnitude of the errors of the lowest-order hydrodynamic quantities. It is shown that if the heat flux vanishes initially, these errors are smaller than one might have expected from the ordinary scaling of the hypersonic closure. Also it is found that the normal solution of both expansions is a Gaussian distribution at the lowest order

  12. An integral equation arising in two group neutron transport theory

    International Nuclear Information System (INIS)

    Cassell, J S; Williams, M M R

    2003-01-01

    An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically

  13. Bogomolny equations in certain generalized baby BPS Skyrme models

    Science.gov (United States)

    Stępień, Ł. T.

    2018-01-01

    By using the concept of strong necessary conditions (CSNCs), we derive Bogomolny equations and Bogomol’nyi-Prasad-Sommerfield (BPS) bounds for two certain modifications of the baby BPS Skyrme model: the nonminimal coupling to the gauge field and the k-deformed ungauged model. In particular, we study how the Bogomolny equations and the equation for the potential reflect these two modifications. In both examples, the CSNC method appears to be a very useful tool. We also find certain localized solutions of these Bogomolny equations.

  14. A dynamic IS-LM business cycle model with two time delays in capital accumulation equation

    Science.gov (United States)

    Zhou, Lujun; Li, Yaqiong

    2009-06-01

    In this paper, we analyze a augmented IS-LM business cycle model with the capital accumulation equation that two time delays are considered in investment processes according to Kalecki's idea. Applying stability switch criteria and Hopf bifurcation theory, we prove that time delays cause the equilibrium to lose or gain stability and Hopf bifurcation occurs.

  15. Modeling elephant-mediated cascading effects of water point closure.

    Science.gov (United States)

    Hilbers, Jelle P; Van Langevelde, Frank; Prins, Herbert H T; Grant, C C; Peel, Mike J S; Coughenour, Michael B; De Knegt, Henrik J; Slotow, Rob; Smit, Izak P J; Kiker, Greg A; De Boer, Willem F

    2015-03-01

    Wildlife management to reduce the impact of wildlife on their habitat can be done in several ways, among which removing animals (by either culling or translocation) is most often used. There are, however, alternative ways to control wildlife densities, such as opening or closing water points. The effects of these alternatives are poorly studied. In this paper, we focus on manipulating large herbivores through the closure of water points (WPs). Removal of artificial WPs has been suggested in order to change the distribution of African elephants, which occur in high densities in national parks in Southern Africa and are thought to have a destructive effect on the vegetation. Here, we modeled the long-term effects of different scenarios of WP closure on the spatial distribution of elephants, and consequential effects on the vegetation and other herbivores in Kruger National Park, South Africa. Using a dynamic ecosystem model, SAVANNA, scenarios were evaluated that varied in availability of artificial WPs; levels of natural water; and elephant densities. Our modeling results showed that elephants can indirectly negatively affect the distributions of meso-mixed feeders, meso-browsers, and some meso-grazers under wet conditions. The closure of artificial WPs hardly had any effect during these natural wet conditions. Under dry conditions, the spatial distribution of both elephant bulls and cows changed when the availability of artificial water was severely reduced in the model. These changes in spatial distribution triggered changes in the spatial availability of woody biomass over the simulation period of 80 years, and this led to changes in the rest of the herbivore community, resulting in increased densities of all herbivores, except for giraffe and steenbok, in areas close to rivers. The spatial distributions of elephant bulls and cows showed to be less affected by the closure of WPs than most of the other herbivore species. Our study contributes to ecologically

  16. Method for estimating steam hammer effects on swing-check valves during closure

    International Nuclear Information System (INIS)

    Uram, E.M.

    1976-01-01

    Relationships are developed for estimating the disk impact velocity resulting from a free swing closure of swing-check valves in normal flow and for pipe rupture. They derive from a phase-plane solution of the differential equation for the disk motion that accounts for the nature of the valve pressure drop variation due to steam-hammer effects during closure. For closure in normal flow, the method presented has a more correct foundation than that given in reference where a constant, average valve pressure differential based upon the steady-state pressure drop for the total piping system (which has no real relationship to the steam-hammer-induced valve pressure changes during the closure transient) is used in the valve disk motion equation

  17. Comparison of Perturbed Pathways in Two Different Cell Models for Parkinson's Disease with Structural Equation Model.

    Science.gov (United States)

    Pepe, Daniele; Do, Jin Hwan

    2015-12-16

    Increasing evidence indicates that different morphological types of cell death coexist in the brain of patients with Parkinson's disease (PD), but the molecular explanation for this is still under investigation. In this study, we identified perturbed pathways in two different cell models for PD through the following procedures: (1) enrichment pathway analysis with differentially expressed genes and the Reactome pathway database, and (2) construction of the shortest path model for the enriched pathway and detection of significant shortest path model with fitting time-course microarray data of each PD cell model to structural equation model. Two PD cell models constructed by the same neurotoxin showed different perturbed pathways. That is, one showed perturbation of three Reactome pathways, including cellular senescence, chromatin modifying enzymes, and chromatin organization, while six modules within metabolism pathway represented perturbation in the other. This suggests that the activation of common upstream cell death pathways in PD may result in various down-stream processes, which might be associated with different morphological types of cell death. In addition, our results might provide molecular clues for coexistence of different morphological types of cell death in PD patients.

  18. Ring closure in actin polymers

    Energy Technology Data Exchange (ETDEWEB)

    Sinha, Supurna, E-mail: supurna@rri.res.in [Raman Research Institute, Bangalore 560080 (India); Chattopadhyay, Sebanti [Doon University, Dehradun 248001 (India)

    2017-03-18

    We present an analysis for the ring closure probability of semiflexible polymers within the pure bend Worm Like Chain (WLC) model. The ring closure probability predicted from our analysis can be tested against fluorescent actin cyclization experiments. We also discuss the effect of ring closure on bend angle fluctuations in actin polymers. - Highlights: • Ring closure of biopolymers. • Worm like chain model. • Predictions for experiments.

  19. Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

    Science.gov (United States)

    Guo, Yangyu; Wang, Moran

    2017-10-01

    The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

  20. Development of an arid site closure plan

    International Nuclear Information System (INIS)

    Nyhan, J.W.; Barnes, F.J.

    1987-01-01

    This document describes the development of a prototype plan for the effective closure and stabilization of an arid low-level waste disposal site. This plan will provide demonstrated closure techniques for a trench in a disposal site at Los Alamos. The accuracy of modeling soil water storage by two hydrologic models, CREAMS and HELP, was tested by comparing simulation results with field measurements of soil moisture in eight experimental landfill cover systems having a range of well-defined soil profiles and vegetative covers. Regression analysis showed that CREAMS generally represented soil moisture more accurately than HELP simulations. Precautions for determining parameter values for model input and for interpreting simulation results are discussed. A specific example is presented showing how the field-validated hydrologic models can be used to develop a final prototype closure plan. 15 refs., 13 figs., 3 tabs

  1. Modelling of an homogeneous equilibrium mixture model

    International Nuclear Information System (INIS)

    Bernard-Champmartin, A.; Poujade, O.; Mathiaud, J.; Mathiaud, J.; Ghidaglia, J.M.

    2014-01-01

    We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented. (authors)

  2. Linearised CFD models for wakes

    Energy Technology Data Exchange (ETDEWEB)

    Ott, S.; Berg, J.; Nielsen, Morten

    2011-12-15

    This report describes the development of a fast and reasonably accurate model for the prediction of energy production in offshore wind farms taking wake effects into account. The model has been implemented as a windows application called Fuga which can run in batch mode or as a graphical user interface. Fuga is briefly described. The model is based on a linearization technique which is described in some detail, and linearized, governing equations are derived and written in a standard form based on a mixed-spectral formulation. A new solution method is used to solve the equations which involves intensive use of look-up tables for storage of intermediate results. Due to the linearity of the model, multiple wakes from many turbines can be constructed from the wake of a single, solitary turbine. These are in turn constructed from Fourier components by a fast Fourier integral transform of results derived from generic look-up tables. Three different models, based on three different closures, are examined: 1) the 'simple closure' using an unperturbed eddy viscosity kucentre dotz. 2) the mixing length closure. 3) the E-epsilon closure. Model results are evaluated against offshore wind farm production data from Horns Rev I and the Nysted wind farm, and a comparison with direct wake measurements in an onshore turbine (Nibe B) is also made. A very satisfactory agreement with data is found for the simple closure. The exception is the near wake, just behind the rotor, where all three linearized models fail. The mixing length closure underestimates wake effects in all cases. The E-epsilon closure overestimates wake losses in the offshore farms while it predicts a too shallow and too wide the wake in the onshore case. The simple closure performs distinctly better than the other two. Wind speed data from the the Horns rev met masts are used to further validate Fuga results with the 'simple' closure. Finally, Roedsand 1 and 2 are used as an example to illustrate

  3. Theoretical and pragmatic modelling of governing equations for a two-phase flow in bubbly and annular flow regimes

    International Nuclear Information System (INIS)

    Bottoni, M.; Sengpiel, W.

    1992-01-01

    Starting from the rigorous formulation of the conservation equations for mass, momentum and enthalpy, derived for a two-phase flow by volume averaging microscopic balance equations over Eulerian control cells, the article discusses the formulation of the terms describing exchanges between the phases. Two flow regimes are taken into consideration, bubbly flow, applicable for small or medium void fractions, and annular flow, for large void fractions. When lack of knowledge of volume-averaged physical quantities make the rigorously formulated terms useless for computational purposes, modelling of these terms is discussed. 3 figs., 15 refs

  4. Development of a prototype plan for the effective closure of a waste disposal site in Los Alamos, New Mexico

    International Nuclear Information System (INIS)

    Nyhan, J.; Barnes, F.

    1989-02-01

    The purpose of this study was to develop a prototype plan for the effective closure and stabilization of a semiarid low-level waste disposal site. This prototype plan will provide demonstrated closure techniques for a trench in a disposal site at Los Alamos based on previous shallow land burial (SLB) field research both at the Los Alamos Experimental Engineered Test Facility (EETF), and at a waste disposal area at Los Alamos. The accuracy of modeling soil water storage by two hydrologic models was tested by comparing simulation results with field measurements of soil moisture in eight experimental landfill cover systems at Waste Disposal Area B having a range of well-defined soil profiles and vegetative covers. Regression analysis showed that one of the two models tested represented soil moisture more accurately than the second model. The accuracy of modeling all of the parameters of the water balance equation was then evaluated using field data from the Integrated Systems Demonstration plots at the EETF. Optimized parameters were developed for one model to describe observed values of deep percolation, evapotranspiration, and runoff from the field plots containing an SLB trench cap configuration

  5. Material balance and diet in bioregenerative life support systems: Connection with coefficient of closure

    Science.gov (United States)

    Manukovsky, N. S.; Kovalev, V. S.; Somova, L. A.; Gurevich, Yu. L.; Sadovsky, M. G.

    Bioregenerative life support systems (BLSS) with different coefficients of closure are considered. The 66.2% coefficient of closure achieved in "BIOS-3" facility experiments has been taken as a base value. The increase in coefficient of closure up to 72.6-93.0% is planned due to use of soil-like substrate (SLS) and concentrating of urine. Food values were estimated both in a base variant ("BIOS-3"), and with increases in the coefficient of closure. It is shown that food requirements will be more fully satisfied by internal crop production with an increase in the coefficient of closure of the BLSS. Changes of massflow rates on an 'input-output' and inside BLSS are considered. Equations of synthesis and degradation of organic substances in BLSS were examined using a stoichiometric model. The paper shows that at incomplete closure of BLSS containing SLS there is a problem of nitrogen balancing. To compensate for the removal of nitrogen from the system in urine and feces, it is necessary to introduce food and a nitrogen-containing additive.

  6. Evaluating of air flow movements and thermal comfort in a model room with Euler equation: Two dimensional study

    Energy Technology Data Exchange (ETDEWEB)

    Chafi, Fatima Zohra; Halle, Stephane [Mechanical engineering department, Ecole de technologie superieure, Quebec university, 1100 rue Notre-Dame Ouest, Montreal, Quebec H3C 1K3 (Canada)

    2011-02-15

    This paper presents the results of a study that consists of estimating the temperature distribution and air flow movement in a model room with a numerical model based on the Euler equations. Numerical results obtained for two scenarios of ventilation and heating are compared with the predictions of a Navier-Stokes model, as well as with experimental results. A comparison of the local thermal comfort indices PMV and PPD obtained experimentally and numerically is also presented. Results show that the Euler model is capable of properly estimating the temperature distribution, the air movement and the comfort indices in the room. Furthermore, the use of Euler equations allows a reduction of computational time in the order of 30% compared to the Navier-Stokes modeling. (author)

  7. Quantitative modelling of the closure of meso-scale parallel currents in the nightside ionosphere

    Directory of Open Access Journals (Sweden)

    A. Marchaudon

    2004-01-01

    Full Text Available On 12 January 2000, during a northward IMF period, two successive conjunctions occur between the CUTLASS SuperDARN radar pair and the two satellites Ørsted and FAST. This situation is used to describe and model the electrodynamic of a nightside meso-scale arc associated with a convection shear. Three field-aligned current sheets, one upward and two downward on both sides, are observed. Based on the measurements of the parallel currents and either the conductance or the electric field profile, a model of the ionospheric current closure is developed along each satellite orbit. This model is one-dimensional, in a first attempt and a two-dimensional model is tested for the Ørsted case. These models allow one to quantify the balance between electric field gradients and ionospheric conductance gradients in the closure of the field-aligned currents. These radar and satellite data are also combined with images from Polar-UVI, allowing for a description of the time evolution of the arc between the two satellite passes. The arc is very dynamic, in spite of quiet solar wind conditions. Periodic enhancements of the convection and of electron precipitation associated with the arc are observed, probably associated with quasi-periodic injections of particles due to reconnection in the magnetotail. Also, a northward shift and a reorganisation of the precipitation pattern are observed, together with a southward shift of the convection shear. Key words. Ionosphere (auroral ionosphere; electric fields and currents; particle precipitation – Magnetospheric physics (magnetosphere-ionosphere interactions

  8. Extending the bounds of ‘steady’ RANS closures: Toward an instability-sensitive Reynolds stress model

    International Nuclear Information System (INIS)

    Jakirlić, S.; Maduta, R.

    2015-01-01

    Highlights: • A grid-spacing free, instability-sensitive Reynolds stress model is formulated. • The model is capable of capturing turbulence fluctuations. • Substantial improvement concerning proper turbulence activity enhancement is achieved. • The model is intensively validated in a series of 2D and 3D separating flows. • The model feasibility is also checked in some attached flows. - Abstract: The incapability of the conventional Unsteady RANS (Reynolds–Averaged Navier Stokes) models to adequately capture turbulence unsteadiness presents the prime motivation of the present work, which focuses on formulating an instability-sensitive, eddy-resolving turbulence model on the Second-Moment Closure level. The model scheme adopted, functioning as a ‘sub-scale’ model in the Unsteady RANS framework, represents a differential near-wall Reynolds stress model formulated in conjunction with the scale-supplying equation governing the homogeneous part of the inverse turbulent time scale ω h (ω h = ε h /k). The latter equation was straightforwardly obtained from the model equation describing the dynamics of the homogeneous part of the total viscous dissipation rate ε, defined as ε h = ε − 0.5ν∂ 2 k/(∂x j ∂x j ) (Jakirlic and Hanjalic, 2002), by applying the derivation rules to the expression for ω h . The model capability to account for vortex length and time scales variability was enabled through an additional term in the corresponding length-scale determining equation, providing a selective enhancement of its production, pertinent particularly to the highly unsteady separated shear layer region, modeled in terms of the von Karman length scale (comprising the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, 2010). The present model formulation, termed as SRANS model (Sensitized RANS), does not comprise any parameter depending explicitly on grid spacing. The predictive

  9. Analysis of water hammer in two-component two-phase flows

    International Nuclear Information System (INIS)

    Warde, H.; Marzouk, E.; Ibrahim, S.

    1989-01-01

    The water hammer phenomena caused by a sudden valve closure in air-water two-phase flows must be clarified for the safety analysis of LOCA in reactors and further for the safety of boilers, chemical plants, pipe transport of fluids such as petroleum and natural gas. In the present work water hammer phenomena caused by sudden valve closure in two-component two-phase flows are investigated theoretically and experimentally. The phenomena are more complicated than in single phase-flows due to the fact of the presence of compressible component. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved by the method of characteristic. The analysis is extended to include friction in a two-phase mixture depending on the local flow pattern. The profiles of the pressure transients, the propagation velocity of pressure waves and the effect of valve closure on the transient pressure are found. Different two-phase flow pattern and frictional pressure drop correlations were used including Baker, Chesholm and Beggs and Bril correlations. The effect of the flow pattern on the characteristic of wave propagation is discussed primarily to indicate the effect of void fraction on the velocity of wave propagation and on the attenuation of pressure waves. Transient pressure in the mixture were recorded at different air void fractions, rates of uniform valve closure and liquid flow velocities with the aid of pressure transducers, transient wave form recorders interfaced with an on-line pc computer. The results are compared with computation, and good agreement was obtained within experimental accuracy

  10. Comparison between two thoracotomy closure techniques: postoperative pain and pulmonary function.

    Science.gov (United States)

    Leandro, Juliana Duarte; Rodrigues, Olavo Ribeiro; Slaets, Annie France Frere; Schmidt, Aurelino F; Yaekashi, Milton L

    2014-01-01

    To compare two thoracotomy closure techniques (pericostal and transcostal suture) in terms of postoperative pain and pulmonary function. This was a prospective, randomized, double-blind study carried out in the Department of Thoracic Surgery of the Luzia de Pinho Melo Hospital das Clínicas and at the University of Mogi das Cruzes, both located in the city of Mogi das Cruzes, Brazil. We included 30 patients (18-75 years of age) undergoing posterolateral or anterolateral thoracotomy. The patients were randomized into two groups by the type of thoracotomy closure: pericostal suture (PS; n = 16) and transcostal suture (TS; n = 14). Pain intensity during the immediate and late postoperative periods was assessed by a visual analogic scale and the McGill Pain Questionnaire. Spirometry variables (FEV1, FVC, FEV1/FVC ratio, and PEF) were determined in the preoperative period and on postoperative days 21 and 60. Pain intensity was significantly greater in the PS group than in the TS group. Between the preoperative and postoperative periods, there were decreases in the spirometry variables studied. Those decreases were significant in the PS group but not in the TS group. The patients in the TS group experienced less immediate and late post-thoracotomy pain than did those in the PS group, as well as showing smaller reductions in the spirometry parameters. Therefore, transcostal suture is recommended over pericostal suture as the thoracotomy closure technique of choice.

  11. Comparison between two thoracotomy closure techniques: postoperative pain and pulmonary function*

    Science.gov (United States)

    Leandro, Juliana Duarte; Rodrigues, Olavo Ribeiro; Slaets, Annie France Frere; Schmidt, Aurelino F.; Yaekashi, Milton L.

    2014-01-01

    OBJECTIVE: To compare two thoracotomy closure techniques (pericostal and transcostal suture) in terms of postoperative pain and pulmonary function. METHODS: This was a prospective, randomized, double-blind study carried out in the Department of Thoracic Surgery of the Luzia de Pinho Melo Hospital das Clínicas and at the University of Mogi das Cruzes, both located in the city of Mogi das Cruzes, Brazil. We included 30 patients (18-75 years of age) undergoing posterolateral or anterolateral thoracotomy. The patients were randomized into two groups by the type of thoracotomy closure: pericostal suture (PS; n = 16) and transcostal suture (TS; n = 14). Pain intensity during the immediate and late postoperative periods was assessed by a visual analogic scale and the McGill Pain Questionnaire. Spirometry variables (FEV1, FVC, FEV1/FVC ratio, and PEF) were determined in the preoperative period and on postoperative days 21 and 60. RESULTS: Pain intensity was significantly greater in the PS group than in the TS group. Between the preoperative and postoperative periods, there were decreases in the spirometry variables studied. Those decreases were significant in the PS group but not in the TS group. CONCLUSIONS: The patients in the TS group experienced less immediate and late post-thoracotomy pain than did those in the PS group, as well as showing smaller reductions in the spirometry parameters. Therefore, transcostal suture is recommended over pericostal suture as the thoracotomy closure technique of choice. PMID:25210961

  12. An interfacial shear term evaluation study for adiabatic dispersed air–water two-phase flow with the two-fluid model using CFD

    Energy Technology Data Exchange (ETDEWEB)

    Sharma, S.L., E-mail: sharma55@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Hibiki, T.; Ishii, M. [School of Nuclear Engineering, Purdue University, West Lafayette, IN (United States); Schlegel, J.P. [Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO (United States); Buchanan, J.R.; Hogan, K.J. [Bettis Laboratory, Naval Nuclear Laboratory, West Mifflin, PA (United States); Guilbert, P.W. [ANSYS UK Ltd, Oxfordshire (United Kingdom)

    2017-02-15

    Highlights: • Closure form of the interfacial shear term in three-dimensional form is investigated. • Assessment against adiabatic upward bubbly air–water flow data using CFD. • Effect of addition of the interfacial shear term on the phase distribution. - Abstract: In commercially available Computational Fluid Dynamics (CFD) codes such as ANSYS CFX and Fluent, the interfacial shear term is missing in the field momentum equations. The derivation of the two-fluid model (Ishii and Hibiki, 2011) indicates the presence of this term as a momentum source in the right hand side of the field momentum equation. The inclusion of this term is considered important for proper modeling of the interfacial momentum coupling between phases. For separated flows, such as annular flow, the importance of the shear term is understood in the one-dimensional (1-D) form as the major mechanism by which the wall shear is transferred to the gas phase (Ishii and Mishima, 1984). For gas dispersed two-phase flow CFD simulations, it is important to assess the significance of this term in the prediction of phase distributions. In the first part of this work, the closure of this term in three-dimensional (3-D) form in a CFD code is investigated. For dispersed gas–liquid flow, such as bubbly or churn-turbulent flow, bubbles are dispersed in the shear layer of the continuous phase. The continuous phase shear stress is mainly due to the presence of the wall and the modeling of turbulence through the Boussinesq hypothesis. In a 3-D simulation, the continuous phase shear stress can be calculated from the continuous fluid velocity gradient, so that the interfacial shear term can be closed using the local values of the volume fraction and the total stress of liquid phase. This form also assures that the term acts as an action-reaction force for multiple phases. In the second part of this work, the effect of this term on the volume fraction distribution is investigated. For testing the model two

  13. A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

    Science.gov (United States)

    Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

    2016-01-01

    Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

  14. Tight closure and vanishing theorems

    International Nuclear Information System (INIS)

    Smith, K.E.

    2001-01-01

    Tight closure has become a thriving branch of commutative algebra since it was first introduced by Mel Hochster and Craig Huneke in 1986. Over the past few years, it has become increasingly clear that tight closure has deep connections with complex algebraic geometry as well, especially with those areas of algebraic geometry where vanishing theorems play a starring role. The purpose of these lectures is to introduce tight closure and to explain some of these connections with algebraic geometry. Tight closure is basically a technique for harnessing the power of the Frobenius map. The use of the Frobenius map to prove theorems about complex algebraic varieties is a familiar technique in algebraic geometry, so it should perhaps come as no surprise that tight closure is applicable to algebraic geometry. On the other hand, it seems that so far we are only seeing the tip of a large and very beautiful iceberg in terms of tight closure's interpretation and applications to algebraic geometry. Interestingly, although tight closure is a 'characteristic p' tool, many of the problems where tight closure has proved useful have also yielded to analytic (L2) techniques. Despite some striking parallels, there had been no specific result directly linking tight closure and L∼ techniques. Recently, however, the equivalence of an ideal central to the theory of tight closure was shown to be equivalent to a certain 'multiplier ideal' first defined using L2 methods. Presumably, deeper connections will continue to emerge. There are two main types of problems for which tight closure has been helpful: in identifying nice structure and in establishing uniform behavior. The original algebraic applications of tight closure include, for example, a quick proof of the Hochster-Roberts theorem on the Cohen-Macaulayness of rings of invariants, and also a refined version of the Brianqon-Skoda theorem on the uniform behaviour of integral closures of powers of ideals. More recent, geometric

  15. Machine Learning-based discovery of closures for reduced models of dynamical systems

    Science.gov (United States)

    Pan, Shaowu; Duraisamy, Karthik

    2017-11-01

    Despite the successful application of machine learning (ML) in fields such as image processing and speech recognition, only a few attempts has been made toward employing ML to represent the dynamics of complex physical systems. Previous attempts mostly focus on parameter calibration or data-driven augmentation of existing models. In this work we present a ML framework to discover closure terms in reduced models of dynamical systems and provide insights into potential problems associated with data-driven modeling. Based on exact closure models for linear system, we propose a general linear closure framework from viewpoint of optimization. The framework is based on trapezoidal approximation of convolution term. Hyperparameters that need to be determined include temporal length of memory effect, number of sampling points, and dimensions of hidden states. To circumvent the explicit specification of memory effect, a general framework inspired from neural networks is also proposed. We conduct both a priori and posteriori evaluations of the resulting model on a number of non-linear dynamical systems. This work was supported in part by AFOSR under the project ``LES Modeling of Non-local effects using Statistical Coarse-graining'' with Dr. Jean-Luc Cambier as the technical monitor.

  16. Enhancing Understanding of Magnetized High Energy Density Plasmas from Solid Liner Implosions Using Fluid Modeling with Kinetic Closures

    Science.gov (United States)

    Masti, Robert; Srinivasan, Bhuvana; King, Jacob; Stoltz, Peter; Hansen, David; Held, Eric

    2017-10-01

    Recent results from experiments and simulations of magnetically driven pulsed power liners have explored the role of early-time electrothermal instability in the evolution of the MRT (magneto-Rayleigh-Taylor) instability. Understanding the development of these instabilities can lead to potential stabilization mechanisms; thereby providing a significant role in the success of fusion concepts such as MagLIF (Magnetized Liner Inertial Fusion). For MagLIF the MRT instability is the most detrimental instability toward achieving fusion energy production. Experiments of high-energy density plasmas from wire-array implosions have shown the requirement for more advanced physics modeling than that of ideal magnetohydrodynamics. The overall focus of this project is on using a multi-fluid extended-MHD model with kinetic closures for thermal conductivity, resistivity, and viscosity. The extended-MHD model has been updated to include the SESAME equation-of-state tables and numerical benchmarks with this implementation will be presented. Simulations of MRT growth and evolution for MagLIF-relevant parameters will be presented using this extended-MHD model with the SESAME equation-of-state tables. This work is supported by the Department of Energy Office of Science under Grant Number DE-SC0016515.

  17. Full-Thickness Thermal Injury Delays Wound Closure in a Murine Model

    Science.gov (United States)

    2015-01-01

    skin replacement is achieved using autologous skin graft or skin substitute graft. While this strategy of early excision and grafting, first proposed in...several investigators have utilized the more appropriate model of burn eschar excision followed by sponta- neous wound closure or by skin graft or...without the application of a skin graft or a skin substitute graft. Furthermore, the effect of interval burn eschar excision on wound closure is also re

  18. Control Operator for the Two-Dimensional Energized Wave Equation

    Directory of Open Access Journals (Sweden)

    Sunday Augustus REJU

    2006-07-01

    Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

  19. A computer model for dispersed fluid-solid turbulent flows

    International Nuclear Information System (INIS)

    Liu, C.H.; Tulig, T.J.

    1985-01-01

    A computer model is being developed to simulate two-phase turbulent flow phenomena in fluids containing finely dispersed solids. The model is based on a dual-continuum picture of the individual phases and an extension of a two-equation turbulence closure theory. The resulting set of nonlinear partial differential equations are solved using a finite difference procedure with special treatment to promote convergence. The model has been checked against a number of idealized flow problems with known solutions. The authors are currently comparing model predictions with measurements to determine a proper set of turbulence parameters needed for simulating two-phase turbulent flows

  20. Toward a General Theory for Multiphase Turbulence Part I: Development and Gauging of the Model Equations

    Energy Technology Data Exchange (ETDEWEB)

    B. A. Kashiwa; W. B. VanderHeyden

    2000-12-01

    A formalism for developing multiphase turbulence models is introduced by analogy to the phenomenological method used for single-phase turbulence. A sample model developed using the formalism is given in detail. The procedure begins with ensemble averaging of the exact conservation equations, with closure accomplished by using a combination of analytical and experimental results from the literature. The resulting model is applicable to a wide range of common multiphase flows including gas-solid, liquid-solid and gas-liquid (bubbly) flows. The model is positioned for ready extension to three-phase turbulence, or for use in two-phase turbulence in which one phase is accounted for in multiple size classes, representing polydispersivity. The formalism is expected to suggest directions toward a more fundamentally based theory, similar to the way that early work in single-phase turbulence has led to the spectral theory. The approach is unique in that a portion of the total energy decay rate is ascribed to each phase, as is dictated by the exact averaged equations, and results in a transport equation for energy decay rate associated with each phase. What follows is a straightforward definition of a turbulent viscosity for each phase, and accounts for the effect of exchange of fluctuational energy among phases on the turbulent shear viscosity. The model also accounts for the effect of slip momentum transfer among the phases on the production of turbulence kinetic energy and on the tensor character of the Reynolds stress. Collisional effects, when appropriate, are included by superposition. The model reduces to a standard form in limit of a single, pure material, and is expected to do a credible job of describing multiphase turbulent flows in a wide variety of regimes using a single set of coefficients.

  1. Differential equation models for sharp threshold dynamics.

    Science.gov (United States)

    Schramm, Harrison C; Dimitrov, Nedialko B

    2014-01-01

    We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. Published by Elsevier Inc.

  2. Dynamic modeling of interfacial structures via interfacial area transport equation

    International Nuclear Information System (INIS)

    Seungjin, Kim; Mamoru, Ishii

    2005-01-01

    The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

  3. Post-operative analgesic requirement in non-closure and closure of peritoneum during open appendectomy

    International Nuclear Information System (INIS)

    Khan, A.W.; Maqsood, R.; Saleem, M.M.

    2017-01-01

    To compare the mean post-operative analgesic requirement in non-closure and closure of peritoneum during open appendectomy. Study Design: Randomized controlled trial. Place and Duration of Study: Department of General Surgery Combined Military Hospital Quetta, from 1st August 2014 to 30th April 2015. Material and Methods: A total of 60 patients were included in this study and were divided into two groups of 30 each. Patients in group A underwent open appendectomy with closure of peritoneum while patients in group B had non-closure of peritoneum during the same procedure. Post-operatively, pain severity was assessed on visual analogue scale (VAS) numeric pain distress scale. On presence of VAS numeric pain distress scale between 5 to 7, intramuscular (IM) diclofenac sodium was given and on score >7, intravascular (IV) tramadol was given. The final outcome was measured at day 0 and day 1. Results: Pain score and analgesic requirements were significantly less in non-closure group than closure group on day 0 and day 1, showing statistically significant difference between the two groups. Conclusion: Mean post-operative analgesic requirement is significantly less in non-closure group as compared to closure group during open appendectomy. (author)

  4. Advanced modeling of solidification

    International Nuclear Information System (INIS)

    Bousquet-Melou, P.; Fichot, F.; Goyeau, B.; Gobin, D.; Quintard, M.

    2001-01-01

    A theoretical and numerical macroscopic modeling of the solidification of binary mixtures is presented. The growth of a solid-liquid region (mushy zone), represented by a non-homogeneous porous medium, is considered. A macroscopic model for momentum, heat and mass transfer during solidification is derived using the volume averaging method, and the effective transport properties (permeability, effective diffusivities, mass exchange coefficients) are defined by associated closure problems (set of microscopic balance equations). Consequently, the effects of the dendritic geometry (tortuosity) and of microscopic transfer phenomena (dispersion, interfacial exchange) are introduced in the averaged balance equations and in the representation of the effective transport coefficients. This closure method provides an original approach of solidification modeling. The resulting macroscopic model is based on the local thermal equilibrium assumption (one-temperature model) while a two-phase description of macroscopic species transfer is introduced using solid and liquid mass exchange coefficients. The phase diagram is used to predict the solid and liquid equilibrium concentrations at the solid-liquid interface. This two-phase approach extends the classical limiting cases that correspond to the lever-rule and Scheil descriptions. (authors)

  5. Evaluation of a novel trocar-site closure and comparison with a standard Carter-Thomason closure device.

    Science.gov (United States)

    del Junco, Michael; Okhunov, Zhamshid; Juncal, Samuel; Yoon, Renai; Landman, Jaime

    2014-07-01

    The aim of this study was to evaluate and compare a novel trocars-site closure device, the WECK EFx™ Endo Fascial Closure System (EFx) with the Carter-Thomason CloseSure System® (CT) for the closure of laparoscopic trocar site defects created by a 12-mm dilating trocar. We created standardized laparoscopic trocars-site abdominal wall defects in cadaver models using a standard 12-mm laparoscopic dilating trocar. Trocar defects were closed in a randomized fashion using one of the two closure systems. We recorded time and number of attempts needed for complete defect closure. In addition, we recorded the ability to maintain pneumoperitoneum, endoscopic visualization, safety, security, and facility based on the surgeon's subjective evaluations. We compared outcomes for the EFx and CT closure systems. We created 72 standardized laparoscopic trocars-site abdominal wall defects. The mean time needed for complete defect closure was 98.53 seconds (±28.9) for the EFx compared with 133.61 seconds (±54.61) for the CT (Psafety were 2.92 for EFx vs 2.19 for CT (Pvs 1.83 for EFx and CT, respectively (Pvs 2.33 for CT (P=0.022). No significant difference was observed between the EFx and the CT systems for endoscopic visualization (2.28 vs 2.50, P=0.080). In this in vitro cadaver trial, the EFx was superior in terms of time needed to complete defect closure, safety, and facility. CT was superior in terms of maintenance of pneumoperitoneum. Both systems were equal in the number of attempts needed to complete the defect closure and endoscopic visualization.

  6. Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

    Directory of Open Access Journals (Sweden)

    Narcisa Apreutesei

    2014-05-01

    Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.

  7. Simulated precipitation diurnal cycles over East Asia using different CAPE-based convective closure schemes in WRF model

    Science.gov (United States)

    Yang, Ben; Zhou, Yang; Zhang, Yaocun; Huang, Anning; Qian, Yun; Zhang, Lujun

    2018-03-01

    Closure assumption in convection parameterization is critical for reasonably modeling the precipitation diurnal variation in climate models. This study evaluates the precipitation diurnal cycles over East Asia during the summer of 2008 simulated with three convective available potential energy (CAPE) based closure assumptions, i.e. CAPE-relaxing (CR), quasi-equilibrium (QE), and free-troposphere QE (FTQE) and investigates the impacts of planetary boundary layer (PBL) mixing, advection, and radiation on the simulation by using the weather research and forecasting model. The sensitivity of precipitation diurnal cycle to PBL vertical resolution is also examined. Results show that the precipitation diurnal cycles simulated with different closures all exhibit large biases over land and the simulation with FTQE closure agrees best with observation. In the simulation with QE closure, the intensified PBL mixing after sunrise is responsible for the late-morning peak of convective precipitation, while in the simulation with FTQE closure, convective precipitation is mainly controlled by advection cooling. The relative contributions of different processes to precipitation formation are functions of rainfall intensity. In the simulation with CR closure, the dynamical equilibrium in the free troposphere still can be reached, implying the complex cause-effect relationship between atmospheric motion and convection. For simulations in which total CAPE is consumed for the closures, daytime precipitation decreases with increased PBL resolution because thinner model layer produces lower convection starting layer, leading to stronger downdraft cooling and CAPE consumption. The sensitivity of the diurnal peak time of precipitation to closure assumption can also be modulated by changes in PBL vertical resolution. The results of this study help us better understand the impacts of various processes on the precipitation diurnal cycle simulation.

  8. Equations of motion for two-phase flow in a pin bundle of a nuclear reactor

    International Nuclear Information System (INIS)

    Chawla, T.C.; Ishii, M.

    1978-01-01

    By performing Eulerian area averaging over a channel area of the local continuity, momentum, and energy equations for single phase turbulent flow and assuming each phase in two-phase flows to be continuum but coupled by the appropriate 'jump' conditions at the interface, the corresponding axial macroscopic balances for two-fluid model in a pin bundle are obtained. To determine the crossflow, a momentum equation in transverse (to the gap between the pins) direction is obtained for each phase by carrying out Eulerian segment averaging of the local momentum equation, where the segment is taken parallel to the gap. By considering the mixture as a whole, a diffusion model based on drift-flux velocity is formulated. In the axial direction it is expressed in terms of three mixture conservation equations of mass, momentum, and energy with one additional continuity equation for the vapor phase. For the determination of crossflow, transverse momentum equation for a mixture is obtained. It is considered that the previous formulation of the two-phase flow based on the 'slip' flow model and the integral subchannel balances using finite control volumes is inadequate in that the model is heuristic and, a priori, assumes the order of magnitude of the terms, also the model is incomplete and incorrect when applied to two-phase mixtures in thermal non-equilibrium such as during accidental depressurization of a water cooled reactor. The governing equations presented are shown to be a very formal and sound physical basis and are indispensable for physically correct methods of analyzing two-phase flows in a pin bundle. (author)

  9. Infiltration experiment for closure cap evaluation at the Savannah River Site

    International Nuclear Information System (INIS)

    Roddy, N.S.; Cook, J.R.

    1990-01-01

    This document discusses several large waste disposal facilities at the Savannah River Site which are being closed. These facilities include two seepage basins and the low-level waste disposal facility. The key element of the closures is the construction of a cap system to limit the infiltration of water which might reach the disposed waste. Cap designs have been modeled using the Hydrologic Evaluation of Landfill Performance (HELP) computer code. This code was developed by the US Army Corps of Engineers for the Environmental Protection Agency to model the effects of various cap and liner designs on the water balance at landfills. A field experiment has been set up which will allow the results of the HELP Code to be verified at the Savannah River Site (SRS) by measuring the actual water balance created by closure cap configurations which will be used in waste site closures at SRS. Two of the caps will be similar to those used for the planned closure activities. Each one has a specific closure arrangement. Once operational, the experiment will be evaluated for a five-year period

  10. Solution of the two- dimensional heat equation for a rectangular plate

    Directory of Open Access Journals (Sweden)

    Nurcan BAYKUŞ SAVAŞANERİL

    2015-11-01

    Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

  11. Model-Based Comprehensive Analysis of School Closure Policies for Mitigating Influenza Epidemics and Pandemics.

    Science.gov (United States)

    Fumanelli, Laura; Ajelli, Marco; Merler, Stefano; Ferguson, Neil M; Cauchemez, Simon

    2016-01-01

    School closure policies are among the non-pharmaceutical measures taken into consideration to mitigate influenza epidemics and pandemics spread. However, a systematic review of the effectiveness of alternative closure policies has yet to emerge. Here we perform a model-based analysis of four types of school closure, ranging from the nationwide closure of all schools at the same time to reactive gradual closure, starting from class-by-class, then grades and finally the whole school. We consider policies based on triggers that are feasible to monitor, such as school absenteeism and national ILI surveillance system. We found that, under specific constraints on the average number of weeks lost per student, reactive school-by-school, gradual, and county-wide closure give comparable outcomes in terms of optimal infection attack rate reduction, peak incidence reduction or peak delay. Optimal implementations generally require short closures of one week each; this duration is long enough to break the transmission chain without leading to unnecessarily long periods of class interruption. Moreover, we found that gradual and county closures may be slightly more easily applicable in practice as they are less sensitive to the value of the excess absenteeism threshold triggering the start of the intervention. These findings suggest that policy makers could consider school closure policies more diffusely as response strategy to influenza epidemics and pandemics, and the fact that some countries already have some experience of gradual or regional closures for seasonal influenza outbreaks demonstrates that logistic and feasibility challenges of school closure strategies can be to some extent overcome.

  12. Assimilation of Sea Surface Temperature in a doubly, two-way nested primitive equation model of the Ligurian Sea

    Science.gov (United States)

    Barth, A.; Alvera-Azcarate, A.; Rixen, M.; Beckers, J.-M.; Testut, C.-E.; Brankart, J.-M.; Brasseur, P.

    2003-04-01

    The GHER 3D primitive equation model is implemented with three different resolutions: a low resolution model (1/4^o) covering the whole Mediterranean Sea, an intermediate resolution model (1/20^o) of the Liguro-Provençal basin and a high resolution model (1/60^o) simulating the fine mesoscale structures in the Ligurian Sea. Boundary conditions and the averaged fields (feedback) are exchanged between two successive nesting levels. The model of the Ligurian Sea is also coupled with the assimilation package SESAM. It allows to assimilate satellite data and in situ observations using the local adaptative SEEK (Singular Evolutive Extended Kalman) filter. Instead of evolving the error space by the numerically expensive Lyapunov equation, a simplified algebraic equation depending on the misfit between observation and model forecast is used. Starting from the 1st January 1998 the low and intermediate resolution models are spun up for 18 months. The initial conditions for the Ligurian Sea are interpolated from the intermediate resolution model. The three models are then integrated until August 1999. During this period AVHRR Sea Surface Temperature of the Ligurian Sea is assimilated. The results are validated by using CTD and XBT profiles of the SIRENA cruise from the SACLANT Center. The overall objective of this study is pre-operational. It should help to identify limitations and weaknesses of forecasting methods and to suggest improvements of existing operational models.

  13. Two ecological models of academic achievement among diverse students with and without disabilities in transition.

    Science.gov (United States)

    Williams, Terrinieka T; McMahon, Susan D; Keys, Christopher B

    2014-01-01

    School experiences can have positive effects on student academic achievement, yet less is known about intermediary processes that contribute to these positive effects. We examined pathways between school experiences and academic achievement among 117 low-income urban students of color, many with disabilities, who transitioned to other schools following a school closure. Using structural equation modeling, we tested two ecological models that examined the relationships among self-reported school experiences, school support, academic self-efficacy, and school-reported academic achievement. The model in which the relationship between school experiences and academic achievement is mediated by both school support and academic self-efficacy, and that takes previous academic achievement into account, was an excellent fit with the data. The roles of contextual and individual factors as they relate to academic achievement, and the implications of these findings, are discussed.

  14. Amnioserosa cell constriction but not epidermal actin cable tension autonomously drives dorsal closure.

    Science.gov (United States)

    Pasakarnis, Laurynas; Frei, Erich; Caussinus, Emmanuel; Affolter, Markus; Brunner, Damian

    2016-11-01

    Tissue morphogenesis requires coordination of multiple force-producing components. During dorsal closure in fly embryogenesis, an epidermis opening closes. A tensioned epidermal actin/MyosinII cable, which surrounds the opening, produces a force that is thought to combine with another MyosinII force mediating apical constriction of the amnioserosa cells that fill the opening. A model proposing that each force could autonomously drive dorsal closure was recently challenged by a model in which the two forces combine in a ratchet mechanism. Acute force elimination via selective MyosinII depletion in one or the other tissue shows that the amnioserosa tissue autonomously drives dorsal closure while the actin/MyosinII cable cannot. These findings exclude both previous models, although a contribution of the ratchet mechanism at dorsal closure onset remains likely. This shifts the current view of dorsal closure being a combinatorial force-component system to a single tissue-driven closure event.

  15. Comparison of different moment-closure approximations for stochastic chemical kinetics

    Energy Technology Data Exchange (ETDEWEB)

    Schnoerr, David [School of Biological Sciences, University of Edinburgh, Edinburgh (United Kingdom); School of Informatics, University of Edinburgh, Edinburgh (United Kingdom); Sanguinetti, Guido [School of Informatics, University of Edinburgh, Edinburgh (United Kingdom); Grima, Ramon [School of Biological Sciences, University of Edinburgh, Edinburgh (United Kingdom)

    2015-11-14

    In recent years, moment-closure approximations (MAs) of the chemical master equation have become a popular method for the study of stochastic effects in chemical reaction systems. Several different MA methods have been proposed and applied in the literature, but it remains unclear how they perform with respect to each other. In this paper, we study the normal, Poisson, log-normal, and central-moment-neglect MAs by applying them to understand the stochastic properties of chemical systems whose deterministic rate equations show the properties of bistability, ultrasensitivity, and oscillatory behaviour. Our results suggest that the normal MA is favourable over the other studied MAs. In particular, we found that (i) the size of the region of parameter space where a closure gives physically meaningful results, e.g., positive mean and variance, is considerably larger for the normal closure than for the other three closures, (ii) the accuracy of the predictions of the four closures (relative to simulations using the stochastic simulation algorithm) is comparable in those regions of parameter space where all closures give physically meaningful results, and (iii) the Poisson and log-normal MAs are not uniquely defined for systems involving conservation laws in molecule numbers. We also describe the new software package MOCA which enables the automated numerical analysis of various MA methods in a graphical user interface and which was used to perform the comparative analysis presented in this paper. MOCA allows the user to develop novel closure methods and can treat polynomial, non-polynomial, as well as time-dependent propensity functions, thus being applicable to virtually any chemical reaction system.

  16. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  17. A General Nonlinear Fluid Model for Reacting Plasma-Neutral Mixtures

    Energy Technology Data Exchange (ETDEWEB)

    Meier, E T; Shumlak, U

    2012-04-06

    A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed.

  18. Order α'(two-loop) equivalence of the string equations of motion and the σ-model Weyl invariance conditions

    International Nuclear Information System (INIS)

    Metsaev, R.R.; Tseytlin, A.A.

    1987-01-01

    We prove the on-shell equivalence of the order α' terms in the string effective equations (for the graviton, dilaton and the antisymmetric tensor) to the vanishing of the corresponding (two-loop) terms in the Weyl anomaly coefficients for the general bosonic σ-model. We first determine the α' term in the string effective action starting with the known expression for the 3- and 4-point string amplitudes. Then we compute the two-loop β-function in the general σ-model with the antisymmetric tensor coupling. Special emphasis is made on the renormalization scheme dependence of the β-function. Our result disagrees with the previously known one and cannot be manifestly expressed in terms of the generalized curvature for the connection with torsion. We also prove (to the order α' 2 ) that the parallelizable spaces are solutions of the string equations of motion and establish the complete 3-loop expression for the 'central charge' coefficient. (orig.)

  19. Integration of two-phase solid fluid equations in a catchment model for flashfloods, debris flows and shallow slope failures

    KAUST Repository

    Bout, B.; Lombardo, Luigi; van Westen, C.J.; Jetten, V.G.

    2018-01-01

    An integrated, modeling method for shallow landslides, debris flows and catchment hydrology is developed and presented in this paper. Existing two-phase debris flow equations and an adaptation on the infinite slope method are coupled with a full

  20. The conditional moment closure method for modeling lean premixed turbulent combustion

    Science.gov (United States)

    Martin, Scott Montgomery

    Natural gas fired lean premixed gas turbines have become the method of choice for new power generation systems due to their high efficiency and low pollutant emissions. As emission regulations for these combustion systems become more stringent, the use of numerical modeling has become an important a priori tool in designing clean and efficient combustors. Here a new turbulent combustion model is developed in an attempt to improve the state of the art. The Conditional Moment Closure (CMC) method is a new theory that has been applied to non-premixed combustion with good success. The application of the CMC method to premixed systems has been proposed, but has not yet been done. The premixed CMC method replaces the species mass fractions as independent variables with the species mass fractions that are conditioned on a reaction progress variable (RPV). Conservation equations for these new variables are then derived and solved. The general idea behind the CMC method is that the behavior of the chemical species is closely coupled to the reaction progress variable. Thus, species conservation equations that are conditioned on the RPV will have terms involving the fluctuating quantities that are much more likely to be negligible. The CMC method accounts for the interaction between scalar dissipation (micromixing) and chemistry, while de-coupling the kinetics from the bulk flow (macromixing). Here the CMC method is combined with a commercial computational fluid dynamics program, which calculates the large-scale fluid motions. The CMC model is validated by comparison to 2-D reacting backward facing step data. Predicted species, temperature and velocity fields are compared to experimental data with good success. The CMC model is also validated against the University of Washington's 3-D jet stirred reactor (JSR) data, which is an idealized lean premixed combustor. The JSR results are encouraging, but not as good as the backward facing step. The largest source of error is from

  1. Ising models and soliton equations

    International Nuclear Information System (INIS)

    Perk, J.H.H.; Au-Yang, H.

    1985-01-01

    Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained

  2. Elliptic blending model : A new near-wall Reynolds-stress turbulence closure

    NARCIS (Netherlands)

    Manceau, R.; Hanjali?, K.

    2001-01-01

    A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure–strain tensor towards the chosen conventional homogeneous

  3. Modelling and numerical simulation of two-phase flows using the two-fluid two-pressure approach; Modelisation et simulation numerique des ecoulements diphasiques par une approche bifluide a deux pressions

    Energy Technology Data Exchange (ETDEWEB)

    Guillemaud, V

    2007-03-15

    This thesis is devoted to the modelling and numerical simulation of liquid-vapor flows. In order to describe these phase transition flows, a two-fluid two-pressure approach is considered. This description of the liquid-vapor mixing is associated to the seven-equation model introduced by Baer and Nunziato. This work investigates the properties of this model in order to simulate the phase transition flows occurring in nuclear engineering. First, a theoretical thermodynamic framework is constructed to describe the liquid-vapor mixing. Provided with this framework, various modelling choices are suggested for the interaction terms between the phases. These closure laws comply with an entropy inequality. The mathematical properties of this model are thereafter examined. The convective part is associated to a nonconservative hyperbolic system. First, we focus on the definition of its weak solutions. Several flow regimes for the two-phase mixing derive from this analysis. Such regimes for the two-phase flows are analogous to the torrential and fluvial regimes for the shallow-water equations. Furthermore, we establish the linear and nonlinear stabilities of the liquid-vapor equilibrium. Finally, the implementation of a turbulence model and the introduction of a reconstruction process for the interfacial area are investigated in order to refine the description of the interfacial transfers. Using a fractional step approach, a Finite Volume method is at last constructed to simulate this model. First, various nonconservative adaptations of standard Riemann solvers are developed to approach the convective part. Unlike the classic nonconservative framework, these schemes converge towards the same solution. Furthermore, a new relaxation scheme is proposed to approach the interfacial transfers. Provided with these schemes, the whole numerical method preserves the liquid-vapor equilibria. Using this numerical method, a careful comparison between the one- and two-pressure two

  4. A plasma model combined with an improved two-temperature equation for ultrafast laser ablation of dielectrics

    International Nuclear Information System (INIS)

    Jiang Lan; Tsai, H.-L.

    2008-01-01

    It remains a big challenge to theoretically predict the material removal mechanism in femtosecond laser ablation. To bypass this unresolved problem, many calculations of femtosecond laser ablation of nonmetals have been based on the free electron density distribution without the actual consideration of the phase change mechanism. However, this widely used key assumption needs further theoretical and experimental confirmation. By combining the plasma model and improved two-temperature model developed by the authors, this study focuses on investigating ablation threshold fluence, depth, and shape during femtosecond laser ablation of dielectrics through nonthermal processes (the Coulomb explosion and electrostatic ablation). The predicted ablation depths and shapes in fused silica, by using (1) the plasma model only and (2) the plasma model plus the two-temperature equation, are both in agreement with published experimental data. The widely used assumptions for threshold fluence, ablation depth, and shape in the plasma model based on free electron density are validated by the comparison study and experimental data

  5. BHR equations re-derived with immiscible particle effects

    Energy Technology Data Exchange (ETDEWEB)

    Schwarzkopf, John Dennis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Horwitz, Jeremy A. [Stanford Univ., CA (United States)

    2015-05-01

    Compressible and variable density turbulent flows with dispersed phase effects are found in many applications ranging from combustion to cloud formation. These types of flows are among the most challenging to simulate. While the exact equations governing a system of particles and fluid are known, computational resources limit the scale and detail that can be simulated in this type of problem. Therefore, a common method is to simulate averaged versions of the flow equations, which still capture salient physics and is relatively less computationally expensive. Besnard developed such a model for variable density miscible turbulence, where ensemble-averaging was applied to the flow equations to yield a set of filtered equations. Besnard further derived transport equations for the Reynolds stresses, the turbulent mass flux, and the density-specific volume covariance, to help close the filtered momentum and continuity equations. We re-derive the exact BHR closure equations which include integral terms owing to immiscible effects. Physical interpretations of the additional terms are proposed along with simple models. The goal of this work is to extend the BHR model to allow for the simulation of turbulent flows where an immiscible dispersed phase is non-trivially coupled with the carrier phase.

  6. An Analytical Model for Fatigue Life Prediction Based on Fracture Mechanics and Crack Closure

    DEFF Research Database (Denmark)

    Ibsø, Jan Behrend; Agerskov, Henning

    1996-01-01

    test specimens are compared with fatigue life predictions using a fracture mechanics approach. In the calculation of the fatigue life, the influence of the welding residual stresses and crack closure on the fatigue crack growth is considered. A description of the crack closure model for analytical...... of the analytical fatigue lives. Both the analytical and experimental results obtained show that the Miner rule may give quite unconservative predictions of the fatigue life for the types of stochastic loading studied....... determination of the fatigue life is included. Furthermore, the results obtained in studies of the various parameters that have an influence on the fatigue life, are given. A very good agreement between experimental and analytical results is obtained, when the crack closure model is used in determination...

  7. An Analytical Model for Fatigue Life Prediction Based on Fracture Mechanics and Crack Closure

    DEFF Research Database (Denmark)

    Ibsø, Jan Behrend; Agerskov, Henning

    1996-01-01

    test specimens are compared with fatigue life predictions using a fracture mechanics approach. In the calculation of the fatigue life, the influence of the welding residual stresses and crack closure on the fatigue crack growth is considered. A description of the crack closure model for analytical...... determination of the fatigue life is included. Furthermore, the results obtained in studies of the various parameters that have an influence on the fatigue life, are given. A very good agreement between experimental and analytical results is obtained, when the crack closure model is used in determination...... of the analytical fatigue lives. Both the analytical and experimental results obtained show that the Miner rule may give quite unconservative predictions of the fatigue life for the types of stochastic loading studied....

  8. Differential equation for genus-two characters in arbitrary rational conformal field theories

    International Nuclear Information System (INIS)

    Mathur, S.D.; Sen, A.

    1989-01-01

    We develop a general method for deriving ordinary differential equations for the genus-two ''characters'' of an arbitrary rational conformal field theory using the hyperelliptic representation of the genus-two moduli space. We illustrate our method by explicitly deriving the character differential equations for k=1 SU(2), G 2 , and F 4 WZW models. Our method provides an intrinsic definition of conformal field theories on higher genus Riemann surfaces. (orig.)

  9. Emergent properties during dorsal closure in Drosophila morphogenesis

    International Nuclear Information System (INIS)

    Peralta, X G; Toyama, Y; Edwards, G S; Kiehart, D P

    2008-01-01

    Dorsal closure is an essential stage of Drosophila development that is a model system for research in morphogenesis and biological physics. Dorsal closure involves an orchestrated interplay between gene expression and cell activities that produce shape changes, exert forces and mediate tissue dynamics. We investigate the dynamics of dorsal closure based on confocal microscopic measurements of cell shortening in living embryos. During the mid-stages of dorsal closure we find that there are fluctuations in the width of the leading edge cells but the time-averaged analysis of measurements indicate that there is essentially no net shortening of cells in the bulk of the leading edge, that contraction predominantly occurs at the canthi as part of the process for zipping together the two leading edges of epidermis and that the rate constant for zipping correlates with the rate of movement of the leading edges. We characterize emergent properties that regulate dorsal closure, i.e., a velocity governor and the coordination and synchronization of tissue dynamics

  10. A lattice Boltzmann model for the Burgers-Fisher equation.

    Science.gov (United States)

    Zhang, Jianying; Yan, Guangwu

    2010-06-01

    A lattice Boltzmann model is developed for the one- and two-dimensional Burgers-Fisher equation based on the method of the higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. In order to obtain the two-dimensional Burgers-Fisher equation, vector sigma(j) has been used. And in order to overcome the drawbacks of "error rebound," a new assumption of additional distribution is presented, where two additional terms, in first order and second order separately, are used. Comparisons with the results obtained by other methods reveal that the numerical solutions obtained by the proposed method converge to exact solutions. The model under new assumption gives better results than that with second order assumption. (c) 2010 American Institute of Physics.

  11. The assessment of two-fluid models using critical flow data

    International Nuclear Information System (INIS)

    Shome, B.; Lahey, R.T. Jr.

    1992-01-01

    The behavior of two-phase flow is governed by the thermal-hydraulic transfers occurring across phasic interfaces. If correctly formulated, two-fluid models should yield all conceivable evolutions. Moreover, some experiments may be uniquely qualified for model assessment if they can isolate important closure models. This paper is primarily concerned with the possible assessment of the virtual mass force using air-water critical flow data, in which phase-change effects do not take place. The following conclusions can be drawn from this study: (1) The closure parameters, other than those for cirtual mass, were found to have an insignificant effect on critical flow. In contrast, the void fraction profile and the slip ratio were observed to be sensitive to the virtual mass model. (2) It appears that air-water critical flow experiments may be effectively used for the assessment of the virtual mass force used in two-fluid models. In fact, such experiments are unique in their ability to isolate the spatial gradients in a vm models. It is hoped that this study will help stimulate the conduct of further critical flow experiments for the assessment of two fluid models

  12. Model Compaction Equation

    African Journals Online (AJOL)

    The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

  13. Borehole closure in salt

    International Nuclear Information System (INIS)

    Fuenkajorn, K.; Daemen, J.J.K.

    1988-12-01

    Constitutive law parameters are determined from salt behavior characterization experiments. The results are applied to predict creep (time-dependent) closure of boreholes in salt specimens subjected to various loading configurations. Rheological models (linear and nonlinear viscoelastic and viscoplastic models), empirical models, and physical theory models have been formulated from the results of uniaxial creep tests, strain and stress rate controlled uniaxial tests, constant strain rate triaxial tests, cyclic loading tests, and seismic velocity measurements. Analytical solutions for a thick-walled cylinder subjected to internal and external pressures and for a circular hole in an infinite plate subjected to a biaxial or uniaxial stressfield have been derived from each of the linear viscoelastic models and from one of the empirical laws. The experimental results indicate that the salt samples behave as an elastic-viscoplastic material. The elastic behavior tends to be linear and time-independent. The plastic deformation is time-dependent. The stress increment to strain rate increment ratio gradually decreases as the stress level increases. The transient potential creep law seems to give the simplest satisfactory governing equation describing the viscoplastic behavior of salt during the transient phase. 204 refs., 27 figs., 29 tabs

  14. Separating variables in two-way diffusion equations

    International Nuclear Information System (INIS)

    Fisch, N.J.; Kruskal, M.D.

    1979-10-01

    It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain

  15. Modified Friedmann equation and inflation in a warped codimension-two braneworld

    International Nuclear Information System (INIS)

    Chen Fang; Cline, James M.; Kanno, Sugumi

    2008-01-01

    We study the Friedmann equation for the warped codimension-two braneworld background which most closely resembles the Randall-Sundrum model. Extra matter on the (Planck) 4-brane, with equation of state p θ =(α-1)ρ for the azimuthal pressure, is required to satisfy the junction conditions. For 1 5 the model is intrinsically stable, without the need for a GW field, and in this case we show that inflationary predictions can be modified by the nonstandard Friedmann equation; in particular, it is possible to get an upper limit on the spectral index, large deviations from the consistency condition between the tensor spectrum and ratio r, and large running of the spectral index even though the slow-roll parameters remain small.

  16. Recognition of Equations Using a Two-Dimensional Stochastic Context-Free Grammar

    Science.gov (United States)

    Chou, Philip A.

    1989-11-01

    We propose using two-dimensional stochastic context-free grammars for image recognition, in a manner analogous to using hidden Markov models for speech recognition. The value of the approach is demonstrated in a system that recognizes printed, noisy equations. The system uses a two-dimensional probabilistic version of the Cocke-Younger-Kasami parsing algorithm to find the most likely parse of the observed image, and then traverses the corresponding parse tree in accordance with translation formats associated with each production rule, to produce eqn I troff commands for the imaged equation. In addition, it uses two-dimensional versions of the Inside/Outside and Baum re-estimation algorithms for learning the parameters of the grammar from a training set of examples. Parsing the image of a simple noisy equation currently takes about one second of cpu time on an Alliant FX/80.

  17. Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations

    Science.gov (United States)

    Abdulwahhab, Muhammad Alim

    2016-10-01

    Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.

  18. Risk-based approach to appraise valve closure in the clam Corbicula fluminea in response to waterborne metals

    International Nuclear Information System (INIS)

    Liao, C.-M.; Jou, L.-J.; Chen, B.-C.

    2005-01-01

    We developed a risk-based approach to assess how the valve closure behavior of Asiatic clam Corbicula fluminea responds to waterborne copper (Cu) and cadmium (Cd). We reanalyzed the valve closure response data from published literature to reconstruct the response time-dependent dose-response profiles based on an empirical three-parameter Hill equation model. We integrated probabilistic exposure profiles of measured environmental Cu and Cd concentrations in the western coastal areas of Taiwan with the reconstructed dose-response relationships at different integration times of response to quantitatively estimate the valve response risk. The risk assessment results implicate exposure to waterborne Cu and Cd may pose no significant risk to clam valve activity in the short-time response periods (e.g., <30 min), yet a relative high risk for valve closure response to waterborne Cu at response times greater than 120 min is alarming. We successfully linked reconstructed dose-response profiles and EC50-time relationships associated with the fitted daily valve opening/closing rhythm characterized by a three-parameter lognormal function to predict the time-varying bivalve closure rhythm response to waterborne metals. We parameterized the proposed predictive model that should encourage a risk-management framework for discussion of future design of biological monitoring systems. - A model was developed to link valve closure in clams to concentrations of metals in water

  19. Generalized heat-transport equations: parabolic and hyperbolic models

    Science.gov (United States)

    Rogolino, Patrizia; Kovács, Robert; Ván, Peter; Cimmelli, Vito Antonio

    2018-03-01

    We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman-Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

  20. On the well-posedness of the stochastic Allen–Cahn equation in two dimensions

    International Nuclear Information System (INIS)

    Ryser, Marc D.; Nigam, Nilima; Tupper, Paul F.

    2012-01-01

    White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical systems in space dimensions d = 1, 2, 3. Whereas existence and uniqueness of weak solutions to these equations are well established in one dimension, the situation is different for d ⩾ 2. Despite their popularity in the applied sciences, higher dimensional versions of these SPDE models are generally assumed to be ill-posed by the mathematics community. We study this discrepancy on the specific example of the two dimensional Allen–Cahn equation driven by additive white noise. Since it is unclear how to define the notion of a weak solution to this equation, we regularize the noise and introduce a family of approximations. Based on heuristic arguments and numerical experiments, we conjecture that these approximations exhibit divergent behavior in the continuum limit. The results strongly suggest that shrinking the mesh size in simulations of the two-dimensional white noise-driven Allen–Cahn equation does not lead to the recovery of a physically meaningful limit.

  1. Mathematical models for two-phase stratified pipe flow

    Energy Technology Data Exchange (ETDEWEB)

    Biberg, Dag

    2005-06-01

    . A 5 point resolution in each parameter would thus require 5{sup 13} =1.220.703.125 measurements. Field predictions generally involve model extrapolations. Flow models should therefore be given the best possible mechanistic basis in order to maximize their extrapolation potential. Multiphase pipe flow is a 3-D phenomenon. Flow models should thus ideally be based on a 3-D flow description. 3-D models do not contain many of the inconsistencies associated with traditional correlation based 1-D models, and do thus represent a higher extrapolation potential. The application of conventional 3-D CFD models for field predictions is limited by computer capacity. Evaluation speed is, however, not the only problem. 3-D CFD models remain to be subject to the closure issues and data tuning associated with turbulent flow models in general. They will thus not automatically yield correct flow predictions. The most pressing obstacle towards obtaining more reliable multiphase pipe flow predictions seems to be given by the closure issues related to the complex interaction of the fluids at the interface. No sufficiently general solution to this problem seems to be available at present. Closure issues could in theory be avoided by use of a direct numerical simulation of the governing equations (DNS). The seemingly insurmountable technical difficulties associated with the application of this approach for multiphase pipe flow field predictions do, however, render it out of reach at present. DNS may, however, serve as a numerical lab investigating model closure in less complicated models.

  2. Loop equations for multi-cut matrix models

    International Nuclear Information System (INIS)

    Akemann, G.

    1995-03-01

    The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)

  3. Immiscible two-phase fluid flows in deformable porous media

    Science.gov (United States)

    Lo, Wei-Cheng; Sposito, Garrison; Majer, Ernest

    Macroscopic differential equations of mass and momentum balance for two immiscible fluids in a deformable porous medium are derived in an Eulerian framework using the continuum theory of mixtures. After inclusion of constitutive relationships, the resulting momentum balance equations feature terms characterizing the coupling among the fluid phases and the solid matrix caused by their relative accelerations. These terms, which imply a number of interesting phenomena, do not appear in current hydrologic models of subsurface multiphase flow. Our equations of momentum balance are shown to reduce to the Berryman-Thigpen-Chen model of bulk elastic wave propagation through unsaturated porous media after simplification (e.g., isothermal conditions, neglect of gravity, etc.) and under the assumption of constant volume fractions and material densities. When specialized to the case of a porous medium containing a single fluid and an elastic solid, our momentum balance equations reduce to the well-known Biot model of poroelasticity. We also show that mass balance alone is sufficient to derive the Biot model stress-strain relations, provided that a closure condition for porosity change suggested by de la Cruz and Spanos is invoked. Finally, a relation between elastic parameters and inertial coupling coefficients is derived that permits the partial differential equations of the Biot model to be decoupled into a telegraph equation and a wave equation whose respective dependent variables are two different linear combinations of the dilatations of the solid and the fluid.

  4. Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

    Science.gov (United States)

    Kane, Michael T.; Mroch, Andrew A.; Suh, Youngsuk; Ripkey, Douglas R.

    2009-01-01

    This paper analyzes five linear equating models for the "nonequivalent groups with anchor test" (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a "parameter…

  5. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  6. Two-phase flow models

    International Nuclear Information System (INIS)

    Delaje, Dzh.

    1984-01-01

    General hypothesis used to simplify the equations, describing two-phase flows, are considered. Two-component and one-component models of two-phase flow, as well as Zuber and Findlay model for actual volumetric steam content, and Wallis model, describing the given phase rates, are presented. The conclusion is made, that the two-component model, in which values averaged in time are included, is applicable for the solving of three-dimensional tasks for unsteady two-phase flow. At the same time, using the two-component model, including values, averaged in space only one-dimensional tasks for unsteady two-phase flow can be solved

  7. New Models for Velocity/Pressure-Gradient Correlations in Turbulent Boundary Layers

    Science.gov (United States)

    Poroseva, Svetlana; Murman, Scott

    2014-11-01

    To improve the performance of Reynolds-Averaged Navier-Stokes (RANS) turbulence models, one has to improve the accuracy of models for three physical processes: turbulent diffusion, interaction of turbulent pressure and velocity fluctuation fields, and dissipative processes. The accuracy of modeling the turbulent diffusion depends on the order of a statistical closure chosen as a basis for a RANS model. When the Gram-Charlier series expansions for the velocity correlations are used to close the set of RANS equations, no assumption on Gaussian turbulence is invoked and no unknown model coefficients are introduced into the modeled equations. In such a way, this closure procedure reduces the modeling uncertainty of fourth-order RANS (FORANS) closures. Experimental and direct numerical simulation data confirmed the validity of using the Gram-Charlier series expansions in various flows including boundary layers. We will address modeling the velocity/pressure-gradient correlations. New linear models will be introduced for the second- and higher-order correlations applicable to two-dimensional incompressible wall-bounded flows. Results of models' validation with DNS data in a channel flow and in a zero-pressure gradient boundary layer over a flat plate will be demonstrated. A part of the material is based upon work supported by NASA under award NNX12AJ61A.

  8. Comparison of two neonatal indomethacin protocols: efficacy and outcome for patent ductus arteriosus closure.

    Science.gov (United States)

    Rosito, G; Sum, K; Chorne, N

    2010-10-01

    Indomethacin, a non-selective inhibitor of prostaglandin synthesis, is the gold standard treatment for patent ductus arteriosus (PDA). Indomethacin has been shown to permanently close the ductus and when given prophylactically, it reduces the incidence of PDA (1, 2). This study compares PDA closure and surgical ligation rates between patients using two different indomethacin administration protocols. This is a retrospective comparison analysis of 72 neonates, who received one of two indomethacin administration protocols. Our previous protocol suggested an initial dose of 0·2 mg/kg followed by two 0·1 mg/kg, with doses infused over 4 h and a 24-h dosing interval. A new potentially more useful protocol using the same mg/kg dose regimen but with doses infused over 30 min and a 12-h dosing interval, was evaluated. Each neonate was allowed three courses of treatment before surgical ligation was performed for persistent PDA. There were no statistically significant differences between the two protocol groups when comparing percentages of neonates with gestational age≤28 weeks, birth weight≤1000 g, male gender or receiving indomethacin for the indication of PDA prophylaxis vs. treatment. There was a trend towards a higher PDA closure rate and subsequently a lower PDA ligation rate in the new protocol when compared with the previous protocol. In this small population of premature neonates, there was a trend, but no significant difference, towards increasing PDA closure and lower surgical ligation rates in neonates given indomethacin with more frequent dosing and shorter infusion time. A well-powered randomized controlled trial is now needed. Copyright © 2010 The Authors. JCPT © 2010 Blackwell Publishing Ltd.

  9. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  10. Development and validation of bubble breakup and coalescence constitutive models for the one-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Pellacani, Filippo

    2012-01-01

    A local mechanistic model for bubble coalescence and breakup for the one-group interfacial area transport equation has been developed, in agreement and within the limits of the current understanding, based on an exhaustive survey of the theory and of the state of the art models for bubble dynamics simulation. The new model has been tested using the commercial 3D CFD code ANSYS CFX. Upward adiabatic turbulent air-water bubbly flow has been simulated and the results have been compared with the data obtained in the experimental facility PUMA. The range of the experimental data available spans between 0.5 to 2 m/s liquid velocity and 5 to 15 % volume fraction. For the implementation of the models, both the monodispersed and the interfacial area transport equation approaches have been used. The first one to perform a detailed analysis of the forces and models to reproduce the dynamic of the dispersed phase adequately and to be used in the next phases of the work. Also two different bubble induced turbulence models have been tested to consider the effect of the presence of the gas phase on the turbulence of the liquid phase. The interfacial area transport equation has been successfully implemented into the CFD code and the state of the art breakup and coalescence models have been used for simulation. The limitations of the actual theory have been shown and a new bubble interactions model has been developed. The simulations showed that a considerable improvement is achieved if compared to the state of the art closure models. Limits in the implementation derive from the actual understanding and formulation of the bubbly dynamics. A strong dependency on the interfacial non-drag force models and coefficients have been shown. More experimental and theory work needs to be done in this field to increase the prediction capability of the simulation tools regarding the distribution of the phases along the pipe radius.

  11. Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

    KAUST Repository

    Kou, Jisheng

    2018-02-25

    In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager\\'s reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

  12. Entropy stable modeling of non-isothermal multi-component diffuse-interface two-phase flows with realistic equations of state

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2018-01-01

    In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is derived rigorously through thermodynamical laws and Onsager's reciprocal principle, and it is capable of characterizing compressibility and partial miscibility between multiple fluids. We prove a novel relation among the pressure, temperature and chemical potentials, which results in a new formulation of the momentum conservation equation indicating that the gradients of chemical potentials and temperature become the primary driving force of the fluid motion except for the external forces. A key challenge in numerical simulation is to develop entropy stable numerical schemes preserving the laws of thermodynamics. Based on the convex-concave splitting of Helmholtz free energy density with respect to molar densities and temperature, we propose an entropy stable numerical method, which solves the total energy balance equation directly, and thus, naturally satisfies the first law of thermodynamics. Unconditional entropy stability (the second law of thermodynamics) of the proposed method is proved by estimating the variations of Helmholtz free energy and kinetic energy with time steps. Numerical results validate the proposed method.

  13. Early decision-analytic modeling - a case study on vascular closure devices.

    Science.gov (United States)

    Brandes, Alina; Sinner, Moritz F; Kääb, Stefan; Rogowski, Wolf H

    2015-10-27

    As economic considerations become more important in healthcare reimbursement, decisions about the further development of medical innovations need to take into account not only medical need and potential clinical effectiveness, but also cost-effectiveness. Already early in the innovation process economic evaluations can support decisions on development in specific indications or patient groups by anticipating future reimbursement and implementation decisions. One potential concept for early assessment is value-based pricing. The objective is to assess the feasibility of value-based pricing and product design for a hypothetical vascular closure device in the pre-clinical stage which aims at decreasing bleeding events. A deterministic decision-analytic model was developed to estimate the cost-effectiveness of established vascular closure devices from the perspective of the Statutory Health Insurance system. To identify early benchmarks for pricing and product design, three strategies of determining the product's value are explored: 1) savings from complications avoided by the new device; 2) valuation of the avoided complications based on an assumed willingness-to-pay-threshold (the efficiency frontier approach); 3) value associated with modifying the care pathways within which the device would be applied. Use of established vascular closure devices is dominated by manual compression. The hypothetical vascular closure device reduces overall complication rates at higher costs than manual compression. Maximum cost savings of only about €4 per catheterization could be realized by applying the hypothetical device. Extrapolation of an efficiency frontier is only possible for one subgroup where vascular closure devices are not a dominated strategy. Modifying care in terms of same-day discharge of patients treated with vascular closure devices could result in cost savings of €400-600 per catheterization. It was partially feasible to calculate value-based prices for the

  14. Generalized reduced MHD equations

    International Nuclear Information System (INIS)

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson

  15. Predictions of bubbly flows in vertical pipes using two-fluid models in CFDS-FLOW3D code

    International Nuclear Information System (INIS)

    Banas, A.O.; Carver, M.B.; Unrau, D.

    1995-01-01

    This paper reports the results of a preliminary study exploring the performance of two sets of two-fluid closure relationships applied to the simulation of turbulent air-water bubbly upflows through vertical pipes. Predictions obtained with the default CFDS-FLOW3D model for dispersed flows were compared with the predictions of a new model (based on the work of Lee), and with the experimental data of Liu. The new model, implemented in the CFDS-FLOW3D code, included additional source terms in the open-quotes standardclose quotes κ-ε transport equations for the liquid phase, as well as modified model coefficients and wall functions. All simulations were carried out in a 2-D axisymmetric format, collapsing the general multifluid framework of CFDS-FLOW3D to the two-fluid (air-water) case. The newly implemented model consistently improved predictions of radial-velocity profiles of both phases, but failed to accurately reproduce the experimental phase-distribution data. This shortcoming was traced to the neglect of anisotropic effects in the modelling of liquid-phase turbulence. In this sense, the present investigation should be considered as the first step toward the ultimate goal of developing a theoretically sound and universal CFD-type two-fluid model for bubbly flows in channels

  16. Predictions of bubbly flows in vertical pipes using two-fluid models in CFDS-FLOW3D code

    Energy Technology Data Exchange (ETDEWEB)

    Banas, A.O.; Carver, M.B. [Chalk River Laboratories (Canada); Unrau, D. [Univ. of Toronto (Canada)

    1995-09-01

    This paper reports the results of a preliminary study exploring the performance of two sets of two-fluid closure relationships applied to the simulation of turbulent air-water bubbly upflows through vertical pipes. Predictions obtained with the default CFDS-FLOW3D model for dispersed flows were compared with the predictions of a new model (based on the work of Lee), and with the experimental data of Liu. The new model, implemented in the CFDS-FLOW3D code, included additional source terms in the {open_quotes}standard{close_quotes} {kappa}-{epsilon} transport equations for the liquid phase, as well as modified model coefficients and wall functions. All simulations were carried out in a 2-D axisymmetric format, collapsing the general multifluid framework of CFDS-FLOW3D to the two-fluid (air-water) case. The newly implemented model consistently improved predictions of radial-velocity profiles of both phases, but failed to accurately reproduce the experimental phase-distribution data. This shortcoming was traced to the neglect of anisotropic effects in the modelling of liquid-phase turbulence. In this sense, the present investigation should be considered as the first step toward the ultimate goal of developing a theoretically sound and universal CFD-type two-fluid model for bubbly flows in channels.

  17. Impact of eight closures in controlled industrial conditions on the shelf life of two (red and rosé) wines

    OpenAIRE

    Caille, Soline; Samson, Alain; Salmon, Jean-Michel

    2017-01-01

    Aims: The management of O2, CO2 and SO2 at bottling and the choice of closure are two key factors of the shelf life of bottled wines before bringing them to market. The impact of eight closures (four screw caps, two synthetic stoppers and two technical stoppers) was evaluated on a red Merlot/Tannat wine. The results of a rosé wine are also discussed. Methods and results: Analytical monitoring (O2, CO2, SO2, aphrometric pressure, L*, a*, b*) was carried out over 538 days of storage at 20°C,...

  18. The impact of rural hospital closures on equity of commuting time for haemodialysis patients: simulation analysis using the capacity-distance model.

    Science.gov (United States)

    Matsumoto, Masatoshi; Ogawa, Takahiko; Kashima, Saori; Takeuchi, Keisuke

    2012-07-23

    Frequent and long-term commuting is a requirement for dialysis patients. Accessibility thus affects their quality of lives. In this paper, a new model for accessibility measurement is proposed in which both geographic distance and facility capacity are taken into account. Simulation of closure of rural facilities and that of capacity transfer between urban and rural facilities are conducted to evaluate the impacts of these phenomena on equity of accessibility among dialysis patients. Post code information as of August 2011 of all the 7,374 patients certified by municipalities of Hiroshima prefecture as having first or third grade renal disability were collected. Information on post code and the maximum number of outpatients (capacity) of all the 98 dialysis facilities were also collected. Using geographic information systems, patient commuting times were calculated in two models: one that takes into account road distance (distance model), and the other that takes into account both the road distance and facility capacity (capacity-distance model). Simulations of closures of rural and urban facilities were then conducted. The median commuting time among rural patients was more than twice as long as that among urban patients (15 versus 7 minutes, psimulation, when five rural public facilitiess were closed, Gini coefficient of commuting times among the patients increased by 16%, indicating a substantial worsening of equity, and the number of patients with commuting times longer than 90 minutes increased by 72 times. In contrast, closure of four urban public facilities with similar capacities did not affect these values. Closures of dialysis facilities in rural areas have a substantially larger impact on equity of commuting times among dialysis patients than closures of urban facilities. The accessibility simulations using the capacity-distance model will provide an analytic framework upon which rational resource distribution policies might be planned.

  19. On genus-two solutions for the ILW equation

    Science.gov (United States)

    Tutiya, Y.

    2018-02-01

    The existence of theta function solutions of genus two for the intermediate long-wave equation is established. A numerical example is also presented. The method basically goes along with Krichever's construction of theta function solutions for soliton equations, such as the Kronecker product equation. This idea leads us to a question whether a Riemann surface exists which allows a peculiar abelian integral of the third kind. The answer is affirmative at least for genus-two curves.

  20. Assessment of a simplified set of momentum closure relations for low volume fraction regimes in STAR-CCM+ and OpenFOAM

    International Nuclear Information System (INIS)

    Sugrue, Rosemary; Magolan, Ben; Lubchenko, Nazar; Baglietto, Emilio

    2017-01-01

    Highlights: •A simplified set of momentum closures – Bubbly And Moderate void Fraction (BAMF) – is proposed. •BAMF model is assessed by simulation of 12 cases from the Liu and Bankoff experimental database. •Portability between STAR-CCM+ and OpenFOAM CFD softwares is demonstrated. •Both CFD softwares yield mean flow predictions in close agreement with experimental results. -- Abstract: Multiphase computational fluid dynamics (M-CFD) modeling approaches provide three-dimensional resolution of complex two-phase flow and boiling heat transfer phenomena, which makes them an invaluable tool for nuclear reactor design applications. By virtue of the Eulerian-Eulerian spatial and temporal averaging framework, additional terms manifest in the phase momentum equations that require closure through prescription of interfacial forces in the stream-wise and lateral flow directions, as well as in the near-wall region. These momentum closures are critical to M-CFD prediction of mean flow profiles, including velocity and volume fraction distributions, and yet while an overwhelming number of them has been developed, no consensus exists on how to assemble them to achieve a simplified set of closures that is numerically robust and extensible to a wide array of flow configurations; further, no consistent demonstration has been shown of the cross-code portability of these closures between CFD softwares. To address these challenges, we propose in this work a simplified set of momentum closures for stream-wise drag and lateral redistribution mechanisms—collectively referred to as the Bubbly And Moderate void Fraction (BAMF) model—and assess its performance by simulation of 12 cases from the Liu and Bankoff experimental database using STAR-CCM+ and OpenFOAM. Both CFD softwares yield mean flow predictions that are in close agreement with the experimental results, and also in close agreement with each other. These results confirm the effectiveness of the BAMF model and its

  1. Closure for spent-fuel transport and storage containers

    International Nuclear Information System (INIS)

    Ahner, S.; Knackstedt, H.G.; Srostlik, P.

    1980-01-01

    The container has a transport closure and a shielding closure. This shielding closure consists of two pieces (double closure system), which can be fartened to one another like a bayonet fixing. A central motion of rotation is enough to open the closure. It can be done remote-controlled as well as manually. (DG) [de

  2. Scope and closures

    CERN Document Server

    Simpson, Kyle

    2014-01-01

    No matter how much experience you have with JavaScript, odds are you don’t fully understand the language. This concise yet in-depth guide takes you inside scope and closures, two core concepts you need to know to become a more efficient and effective JavaScript programmer. You’ll learn how and why they work, and how an understanding of closures can be a powerful part of your development skillset.

  3. Is the Langevin phase equation an efficient model for oscillating neurons?

    Science.gov (United States)

    Ota, Keisuke; Tsunoda, Takamasa; Omori, Toshiaki; Watanabe, Shigeo; Miyakawa, Hiroyoshi; Okada, Masato; Aonishi, Toru

    2009-12-01

    The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

  4. Is the Langevin phase equation an efficient model for oscillating neurons?

    International Nuclear Information System (INIS)

    Ota, Keisuke; Tsunoda, Takamasa; Aonishi, Toru; Omori, Toshiaki; Okada, Masato; Watanabe, Shigeo; Miyakawa, Hiroyoshi

    2009-01-01

    The Langevin phase model is an important canonical model for capturing coherent oscillations of neural populations. However, little attention has been given to verifying its applicability. In this paper, we demonstrate that the Langevin phase equation is an efficient model for neural oscillators by using the machine learning method in two steps: (a) Learning of the Langevin phase model. We estimated the parameters of the Langevin phase equation, i.e., a phase response curve and the intensity of white noise from physiological data measured in the hippocampal CA1 pyramidal neurons. (b) Test of the estimated model. We verified whether a Fokker-Planck equation derived from the Langevin phase equation with the estimated parameters could capture the stochastic oscillatory behavior of the same neurons disturbed by periodic perturbations. The estimated model could predict the neural behavior, so we can say that the Langevin phase equation is an efficient model for oscillating neurons.

  5. A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks

    Science.gov (United States)

    Bronstein, Leo; Koeppl, Heinz

    2018-01-01

    Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a flexible parametric family which solves the commonly observed problem of divergences at low system sizes. We also extend the recently introduced entropic matching approach to arbitrary ansatz distributions and Markov processes, demonstrating that it is a special case of variational moment closure. This provides us with a particularly principled approximation method. Finally, we extend the above approaches to cover the approximation of multi-time joint distributions, resulting in a viable alternative to process-level approximations which are often intractable.

  6. Geometrical aspects of solvable two dimensional models

    International Nuclear Information System (INIS)

    Tanaka, K.

    1989-01-01

    It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs

  7. Closure of multi-fluid and kinetic equations for cyclotron-resonant interactions of solar wind ions with Alfvén waves

    Directory of Open Access Journals (Sweden)

    E. Marsch

    1998-01-01

    Full Text Available Based on quasilinear theory, a closure scheme for anisotropic multi-component fluid equations is developed for the wave-particle interactions of ions with electromagnetic Alfvén and ion-cyclotron waves propagating along the mean magnetic field. Acceleration and heating rates are calculated. They may be used in the multi-fluid momentum and energy equations as anomalous transport terms. The corresponding evolution equation for the average wave spectrum is established, and the effective growth/damping rate for the spectrum is calculated. Given a simple power-law spectrum, an anomalous collision frequency can be derived which depends on the slope and average intensity of the spectrum, and on the gyrofrequency and the differential motion (with respect to the wave frame of the actual ion species considered. The wave-particle interaction terms attain simple forms resembling the ones for collisional friction and temperature anisotropy relaxation (due to pitch angle scattering with collision rates that are proportional to the gyrofrequency but diminished substantially by the relative wave energy or the fluctuation level with respect the background field. In addition, a set of quasilinear diffusion equations is derived for the reduced (with respect to the perpendicular velocity component velocity distribution functions (VDFs, as they occur in the wave dispersion equation and the related dielectric function for parallel propagation. These reduced VDFs allow one to describe adequately the most prominent observed features, such as an ion beam and temperature anisotropy, in association with the resonant interactions of the particles with the waves on a kinetic level, yet have the advantage of being only dependent upon the parallel velocity component.

  8. Two-dimensional nonlinear equations of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1985-01-01

    Supersymmetric generalization of two-dimensional nonlinear dynamical equations of gauge theories is presented. The nontrivial dynamics of a physical system in the supersymmetry and supergravity theories for (2+2)-dimensions is described by the integrable embeddings of Vsub(2/2) superspace into the flat enveloping superspace Rsub(N/M), supplied with the structure of a Lie superalgebra. An equation is derived which describes a supersymmetric generalization of the two-dimensional Toda lattice. It contains both super-Liouville and Sinh-Gordon equations

  9. A systematic comparison of two-equation Reynolds-averaged Navier-Stokes turbulence models applied to shock-cloud interactions

    Science.gov (United States)

    Goodson, Matthew D.; Heitsch, Fabian; Eklund, Karl; Williams, Virginia A.

    2017-07-01

    Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-averaged Navier-Stokes turbulence models, and we implement six models in the athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

  10. Variance estimates for transport in stochastic media by means of the master equation

    International Nuclear Information System (INIS)

    Pautz, S. D.; Franke, B. C.; Prinja, A. K.

    2013-01-01

    The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

  11. Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

    International Nuclear Information System (INIS)

    Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

    2017-01-01

    We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

  12. Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

    Science.gov (United States)

    Schaerer, Roman Pascal; Bansal, Pratyuksh; Torrilhon, Manuel

    2017-07-01

    We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) [13], we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

  13. Efficient algorithms and implementations of entropy-based moment closures for rarefied gases

    Energy Technology Data Exchange (ETDEWEB)

    Schaerer, Roman Pascal, E-mail: schaerer@mathcces.rwth-aachen.de; Bansal, Pratyuksh; Torrilhon, Manuel

    2017-07-01

    We present efficient algorithms and implementations of the 35-moment system equipped with the maximum-entropy closure in the context of rarefied gases. While closures based on the principle of entropy maximization have been shown to yield very promising results for moderately rarefied gas flows, the computational cost of these closures is in general much higher than for closure theories with explicit closed-form expressions of the closing fluxes, such as Grad's classical closure. Following a similar approach as Garrett et al. (2015) , we investigate efficient implementations of the computationally expensive numerical quadrature method used for the moment evaluations of the maximum-entropy distribution by exploiting its inherent fine-grained parallelism with the parallelism offered by multi-core processors and graphics cards. We show that using a single graphics card as an accelerator allows speed-ups of two orders of magnitude when compared to a serial CPU implementation. To accelerate the time-to-solution for steady-state problems, we propose a new semi-implicit time discretization scheme. The resulting nonlinear system of equations is solved with a Newton type method in the Lagrange multipliers of the dual optimization problem in order to reduce the computational cost. Additionally, fully explicit time-stepping schemes of first and second order accuracy are presented. We investigate the accuracy and efficiency of the numerical schemes for several numerical test cases, including a steady-state shock-structure problem.

  14. Master equation and two heat reservoirs.

    Science.gov (United States)

    Trimper, Steffen

    2006-11-01

    A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma-sigma and TT'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.

  15. Integrability of a system of two nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhukhunashvili, V.Z.

    1989-01-01

    In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

  16. A deterministic partial differential equation model for dose calculation in electron radiotherapy.

    Science.gov (United States)

    Duclous, R; Dubroca, B; Frank, M

    2010-07-07

    High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

  17. A deterministic partial differential equation model for dose calculation in electron radiotherapy

    Science.gov (United States)

    Duclous, R.; Dubroca, B.; Frank, M.

    2010-07-01

    High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

  18. Numerical schemes for one-point closure turbulence models

    International Nuclear Information System (INIS)

    Larcher, Aurelien

    2010-01-01

    First-order Reynolds Averaged Navier-Stokes (RANS) turbulence models are studied in this thesis. These latter consist of the Navier-Stokes equations, supplemented with a system of balance equations describing the evolution of characteristic scalar quantities called 'turbulent scales'. In so doing, the contribution of the turbulent agitation to the momentum can be determined by adding a diffusive coefficient (called 'turbulent viscosity') in the Navier-Stokes equations, such that it is defined as a function of the turbulent scales. The numerical analysis problems, which are studied in this dissertation, are treated in the frame of a fractional step algorithm, consisting of an approximation on regular meshes of the Navier-Stokes equations by the nonconforming Crouzeix-Raviart finite elements, and a set of scalar convection-diffusion balance equations discretized by the standard finite volume method. A monotone numerical scheme based on the standard finite volume method is proposed so as to ensure that the turbulent scales, like the turbulent kinetic energy (k) and its dissipation rate (ε), remain positive in the case of the standard k - ε model, as well as the k - ε RNG and the extended k - ε - ν 2 models. The convergence of the proposed numerical scheme is then studied on a system composed of the incompressible Stokes equations and a steady convection-diffusion equation, which are both coupled by the viscosities and the turbulent production term. This reduced model allows to deal with the main difficulty encountered in the analysis of such problems: the definition of the turbulent production term leads to consider a class of convection-diffusion problems with an irregular right-hand side belonging to L 1 . Finally, to step towards the unsteady problem, the convergence of the finite volume scheme for a model convection-diffusion equation with L 1 data is proved. The a priori estimates on the solution and on its time derivative are obtained in discrete norms, for

  19. Informed Conjecturing of Solutions for Differential Equations in a Modeling Context

    Science.gov (United States)

    Winkel, Brian

    2015-01-01

    We examine two differential equations. (i) first-order exponential growth or decay; and (ii) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution. We follow with a discussion of the complete analysis afforded by…

  20. Modeling biological gradient formation: combining partial differential equations and Petri nets.

    Science.gov (United States)

    Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

    2016-01-01

    Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

  1. The impact of rural hospital closures on equity of commuting time for haemodialysis patients: simulation analysis using the capacity-distance model

    Directory of Open Access Journals (Sweden)

    Matsumoto Masatoshi

    2012-07-01

    Full Text Available Abstract Background Frequent and long-term commuting is a requirement for dialysis patients. Accessibility thus affects their quality of lives. In this paper, a new model for accessibility measurement is proposed in which both geographic distance and facility capacity are taken into account. Simulation of closure of rural facilities and that of capacity transfer between urban and rural facilities are conducted to evaluate the impacts of these phenomena on equity of accessibility among dialysis patients. Methods Post code information as of August 2011 of all the 7,374 patients certified by municipalities of Hiroshima prefecture as having first or third grade renal disability were collected. Information on post code and the maximum number of outpatients (capacity of all the 98 dialysis facilities were also collected. Using geographic information systems, patient commuting times were calculated in two models: one that takes into account road distance (distance model, and the other that takes into account both the road distance and facility capacity (capacity-distance model. Simulations of closures of rural and urban facilities were then conducted. Results The median commuting time among rural patients was more than twice as long as that among urban patients (15 versus 7 minutes, p  Conclusions Closures of dialysis facilities in rural areas have a substantially larger impact on equity of commuting times among dialysis patients than closures of urban facilities. The accessibility simulations using thecapacity-distance model will provide an analytic framework upon which rational resource distribution policies might be planned.

  2. Development of bubble-induced turbulence model for advanced two-fluid model

    International Nuclear Information System (INIS)

    Hosoi, Hideaki; Yoshida, Hiroyuki

    2011-01-01

    A two-fluid model can simulate two-phase flow by computational cost less than detailed two-phase flow simulation method such as interface tracking method. The two-fluid model is therefore useful for thermal hydraulic analysis in the large-scale domain such as rod bundles. However, since the two-fluid model includes a lot of constitutive equations verified by use of experimental results, it has problems that the result of analyses depends on accuracy of the constitutive equations. To solve these problems, an advanced two-fluid model has been developed by Japan Atomic Energy Agency. In this model, interface tracking method is combined with two-fluid model to accurately predict large interface structure behavior. Liquid clusters and bubbles larger than a computational cell are calculated using the interface tracking method, and those smaller than the cell are simulated by the two-fluid model. The constitutive equations to evaluate the effects of small bubbles or droplets on two-phase flow are also required in the advanced two-fluid model, just as with the conventional two-fluid model. However, the dependency of small bubbles and droplets on two-phase flow characteristics is relatively small, and fewer experimental results are required to verify the characteristics of large interface structures. Turbulent dispersion force model is one of the most important constitutive equations for the advanced two-fluid model. The turbulent dispersion force model has been developed by many researchers for the conventional two-fluid model. However, existing models implicitly include the effects of large bubbles and the deformation of bubbles, and are unfortunately not applicable to the advanced two-fluid model. In the previous study, the authors suggested the turbulent dispersion force model based on the analogy of Brownian motion. And the authors improved the turbulent dispersion force model in consideration of bubble-induced turbulence to improve the analysis results for small

  3. A Two-Stage Approach to Synthesizing Covariance Matrices in Meta-Analytic Structural Equation Modeling

    Science.gov (United States)

    Cheung, Mike W. L.; Chan, Wai

    2009-01-01

    Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…

  4. Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

    International Nuclear Information System (INIS)

    Christen, Thomas; Kassubek, Frank

    2009-01-01

    In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.

  5. Progress Report on SAM Reduced-Order Model Development for Thermal Stratification and Mixing during Reactor Transients

    Energy Technology Data Exchange (ETDEWEB)

    Hu, R. [Argonne National Lab. (ANL), Argonne, IL (United States)

    2017-09-01

    This report documents the initial progress on the reduced-order flow model developments in SAM for thermal stratification and mixing modeling. Two different modeling approaches are pursued. The first one is based on one-dimensional fluid equations with additional terms accounting for the thermal mixing from both flow circulations and turbulent mixing. The second approach is based on three-dimensional coarse-grid CFD approach, in which the full three-dimensional fluid conservation equations are modeled with closure models to account for the effects of turbulence.

  6. 488-1D Ash Basin closure cap help modeling- Microdrain® liner option

    Energy Technology Data Exchange (ETDEWEB)

    Dyer, J. A. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2017-08-03

    At the request of Area Completion Engineering and in support of the 488-1D Ash Basin closure, the Savannah River National Laboratory (SRNL) performed hydrologic simulations of the revised 488-1D Ash Basin closure cap design using the Hydrologic Evaluation of Landfill Performance (HELP) model. The revised design substitutes a MicroDrain Liner®—60-mil low-density polyethylene geomembrane structurally integrated with 130-mil drainage layer—for the previously planned drainage/barrier system—300-mil geosynthetic drainage layer (GDL), 300-mil geosynthetic clay liner (GCL), and 6-inch common fill soil layer. For a 25-year, 24-hour storm event, HELP model v3.07 was employed to (1) predict the peak maximum daily hydraulic head for the geomembrane layer, and (2) ensure that South Carolina Department of Health and Environmental Control (SCDHEC) requirements for the barrier layer (i.e., ≤ 12 inches hydraulic head on top of a barrier having a saturated hydraulic conductivity ≤ 1.0E-05 cm/s) will not be exceeded. A 25-year, 24-hour storm event at the Savannah River Site (SRS) is 6.1 inches rainfall (Weber 1998). HELP model v3.07 results based upon the new planned cap design suggest that the peak maximum daily hydraulic head on the geomembrane barrier layer will be 0.15 inches for a minimum slope equal to 3%, which is two orders of magnitude below the SCDHEC upper limit of 12 inches.

  7. 488-1D Ash basin closure cap help modeling-Microdrain® liner option

    Energy Technology Data Exchange (ETDEWEB)

    Dyer, J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2017-09-06

    At the request of Area Completion Engineering and in support of the 488-1D Ash Basin closure, the Savannah River National Laboratory (SRNL) performed hydrologic simulations of the revised 488-1D Ash Basin closure cap design using the Hydrologic Evaluation of Landfill Performance (HELP) model. The revised design substitutes a MicroDrain Liner®—50-mil linear low-density polyethylene geomembrane structurally integrated with 130-mil drainage layer—for the previously planned drainage/barrier system—300-mil geosynthetic drainage layer (GDL), 300-mil geosynthetic clay liner (GCL), and 6-inch common fill soil layer. For a 25-year, 24-hour storm event, HELP model v3.07 was employed to (1) predict the peak maximum daily hydraulic head for the geomembrane layer, and (2) ensure that South Carolina Department of Health and Environmental Control (SCDHEC) requirements for the barrier layer (i.e., ≤ 12 inches hydraulic head on top of a barrier having a saturated hydraulic conductivity ≤ 1.0E-05 cm/s) will not be exceeded. A 25-year, 24-hour storm event at the Savannah River Site (SRS) is 6.1 inches rainfall (Weber 1998). HELP model v3.07 results based upon the new planned cap design suggest that the peak maximum daily hydraulic head on the geomembrane barrier layer will be 0.179 inches for a minimum slope equal to 3%, which is approximately two orders of magnitude below the SCDHEC upper limit of 12 inches.

  8. Full spectrum of the two-photon and the two-mode quantum Rabi models

    International Nuclear Information System (INIS)

    Dossa, Anselme F.; Avossevou, Gabriel Y. H.

    2014-01-01

    This paper is concerned with the rigorous analytical determination of the spectrum of the two-photon and the two-mode quantum Rabi models. To reach this goal, we exploit the hidden symmetries in these models by means of the unitary and similarity transformations in addition to the Bargmann-Fock space description. In each case, the purely quantum mechanical problem of the Rabi model studied is reduced to solutions for differential equations. This eventually gives a third-order differential equation for each of these models, which is reduced to a second-order differential equation by additional transformations. The analytical expressions of the wave functions describing the energy levels are obtained in terms of the confluent hypergeometric functions

  9. Supporting second grade lower secondary school students’ understanding of linear equation system in two variables using ethnomathematics

    Science.gov (United States)

    Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.

    2018-03-01

    The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.

  10. Zero-dimensional limit of the two-dimensional Lugiato-Lefever equation

    Science.gov (United States)

    Cardoso, Wesley B.; Salasnich, Luca; Malomed, Boris A.

    2017-05-01

    We study effects of tight harmonic-oscillator confinement on the electromagnetic field in a laser cavity by solving the two-dimensional Lugiato-Lefever (2D LL) equation, taking into account self-focusing or defocusing nonlinearity, losses, pump, and the trapping potential. Tightly confined (quasi-zero-dimensional) optical modes (pixels), produced by this model, are analyzed by means of the variational approximation, which provides a qualitative picture of the ensuing phenomena. This is followed by systematic simulations of the time-dependent 2D LL equation, which reveal the shape, stability, and dynamical behavior of the resulting localized patterns. In this way, we produce stability diagrams for the expected pixels. Then, we consider the LL model with the vortical pump, showing that it can produce stable pixels with embedded vorticity (vortex solitons) in remarkably broad stability areas. Alongside confined vortices with the simple single-ring structure, in the latter case the LL model gives rise to stable multi-ring states, with a spiral phase field. In addition to the numerical results, a qualitatively correct description of the vortex solitons is provided by the Thomas-Fermi approximation. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

  11. Biomechanics Strategies for Space Closure in Deep Overbite

    Directory of Open Access Journals (Sweden)

    Harryanto Wijaya

    2013-07-01

    Full Text Available Space closure is an interesting aspect of orthodontic treatment related to principles of biomechanics. It should be tailored individually based on patient’s diagnosis and treatment plan. Understanding the space closure biomechanics basis leads to achieve the desired treatment objective. Overbite deepening and losing posterior anchorage are the two most common unwanted side effects in space closure. Conventionally, correction of overbite must be done before space closure resulted in longer treatment. Application of proper space closure biomechanics strategies is necessary to achieve the desired treatment outcome. This cases report aimed to show the space closure biomechanics strategies that effectively control the overbite as well as posterior anchorage in deep overbite patients without increasing treatment time. Two patients who presented with class II division 1 malocclusion were treated with fixed orthodontic appliance. The primary strategies included extraction space closure on segmented arch that employed two-step space closure, namely single canine retraction simultaneously with incisors intrusion followed by enmasse retraction of four incisors by using differential moment concept. These strategies successfully closed the space, corrected deep overbite and controlled posterior anchorage simultaneously so that the treatment time was shortened. Biomechanics strategies that utilized were effective to achieve the desired treatment outcome.

  12. Slave equations for spin models

    International Nuclear Information System (INIS)

    Catterall, S.M.; Drummond, I.T.; Horgan, R.R.

    1992-01-01

    We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)

  13. How the 2SLS/IV estimator can handle equality constraints in structural equation models: a system-of-equations approach.

    Science.gov (United States)

    Nestler, Steffen

    2014-05-01

    Parameters in structural equation models are typically estimated using the maximum likelihood (ML) approach. Bollen (1996) proposed an alternative non-iterative, equation-by-equation estimator that uses instrumental variables. Although this two-stage least squares/instrumental variables (2SLS/IV) estimator has good statistical properties, one problem with its application is that parameter equality constraints cannot be imposed. This paper presents a mathematical solution to this problem that is based on an extension of the 2SLS/IV approach to a system of equations. We present an example in which our approach was used to examine strong longitudinal measurement invariance. We also investigated the new approach in a simulation study that compared it with ML in the examination of the equality of two latent regression coefficients and strong measurement invariance. Overall, the results show that the suggested approach is a useful extension of the original 2SLS/IV estimator and allows for the effective handling of equality constraints in structural equation models. © 2013 The British Psychological Society.

  14. Maximum Entropy Closure of Balance Equations for Miniband Semiconductor Superlattices

    Directory of Open Access Journals (Sweden)

    Luis L. Bonilla

    2016-07-01

    Full Text Available Charge transport in nanosized electronic systems is described by semiclassical or quantum kinetic equations that are often costly to solve numerically and difficult to reduce systematically to macroscopic balance equations for densities, currents, temperatures and other moments of macroscopic variables. The maximum entropy principle can be used to close the system of equations for the moments but its accuracy or range of validity are not always clear. In this paper, we compare numerical solutions of balance equations for nonlinear electron transport in semiconductor superlattices. The equations have been obtained from Boltzmann–Poisson kinetic equations very far from equilibrium for strong fields, either by the maximum entropy principle or by a systematic Chapman–Enskog perturbation procedure. Both approaches produce the same current-voltage characteristic curve for uniform fields. When the superlattices are DC voltage biased in a region where there are stable time periodic solutions corresponding to recycling and motion of electric field pulses, the differences between the numerical solutions produced by numerically solving both types of balance equations are smaller than the expansion parameter used in the perturbation procedure. These results and possible new research venues are discussed.

  15. Reduction of static field equation of Faddeev model to first order PDE

    International Nuclear Information System (INIS)

    Hirayama, Minoru; Shi Changguang

    2007-01-01

    A method to solve the static field equation of the Faddeev model is presented. For a special combination of the concerned field, we adopt a form which is compatible with the field equation and involves two arbitrary complex functions. As a result, the static field equation is reduced to a set of first order partial differential equations

  16. Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

    Science.gov (United States)

    Su, Bo; Tuo, Xianguo; Xu, Ling

    2017-08-01

    Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

  17. Urethral pressure reflectometry during intra-abdominal pressure increase-an improved technique to characterize the urethral closure function in continent and stress urinary incontinent women.

    Science.gov (United States)

    Saaby, Marie-Louise; Klarskov, Niels; Lose, Gunnar

    2013-11-01

    to assess the urethral closure function by urethral pressure reflectometry (UPR) during intra-abdominal pressure-increase in SUI and continent women. Twenty-five urodynamically proven SUI women and eight continent volunteer women were assessed by ICIQ-SF, pad-weighing test, incontinence diary, and UPR. UPR was conducted during resting and increased intra-abdominal pressure (P(Abd)) by straining. Related values of P(Abd) and urethral opening pressure (P(o)) were plotted into an abdomino-urethral pressuregram. Linear regression of the values was conducted, and the slope of the line ("APIR") and the intercept with the y-axis found. By the equation of the line, Po was calculated for various values of P(Abd), for example, 50 cm H2O (P(o-Abd 50)). The resting P(o) (P(o-rest)) and APIR, respectively, significantly differed in SUI and continent women but could not separate the two groups. The urethral closure equation (UCE) based on P(o-rest) and APIR provided a more detailed characterization of a woman's closure function based on the permanent closure forces (primarily generated by the urethral sphincteric unit) and the adjunctive closure forces (primarily generated by the support system). P(o-Abd 50) and UCE, respectively, which express the combined permanent and adjunctive closure forces and estimate the efficiency of the closure function, separated SUI and continent women and were highly significantly negatively correlated with ICIQ-SF, pad test, and the number of incontinence episodes. New parameters for characterization of the urethral closure function and possible dysfunctions and its efficiency were provided. P(o-Abd 50) and UCE may be used as diagnostic tests and severity measures. © 2013 Wiley Periodicals, Inc.

  18. Numerical predictions of bubbly two-phase flows with OpenFOAM

    International Nuclear Information System (INIS)

    Michta, E.; Fu, K.; Anglart, H.; Angele, K.

    2011-01-01

    A new model for simulation of bubbly two-phase flows has been developed and implemented into an open-source Computational Fluid Dynamics (CFD) code OpenFOAM. The model employs the two-fluid framework with closure relationships for the interfacial momentum transfer. The bubble size is calculated based on the solution of the interfacial area concentration equations. The predictions are validated against a wide range of experimental data containing measured void fraction, the phasic velocity and the interfacial area concentration. The new model demonstrates the ability to capture the wall peaking of void fraction for small bubbles. The predicted levels of void fraction and phasic velocities are in good agreement with measured data. (author)

  19. Parameter Estimates in Differential Equation Models for Population Growth

    Science.gov (United States)

    Winkel, Brian J.

    2011-01-01

    We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and two-species competition models. We discuss student-evolved strategies and offer "Mathematica" code for a gradient search approach. We use historical (1930s) data from microbial studies of the Russian biologist,…

  20. Comparison of two different modelling tools

    DEFF Research Database (Denmark)

    Brix, Wiebke; Elmegaard, Brian

    2009-01-01

    In this paper a test case is solved using two different modelling tools, Engineering Equation Solver (EES) and WinDali, in order to compare the tools. The system of equations solved, is a static model of an evaporator used for refrigeration. The evaporator consists of two parallel channels......, and it is investigated how a non-uniform airflow influences the refrigerant mass flow rate distribution and the total cooling capacity of the heat exchanger. It is shown that the cooling capacity decreases significantly with increasing maldistribution of the airflow. Comparing the two simulation tools it is found...

  1. Mathematical modeling of impact of two metal plates using two-fluid approach

    Science.gov (United States)

    Utkin, P. S.; Fortova, S. V.

    2018-01-01

    The paper is devoted to the development of the two-fluid mathematical model and the computational algorithm for the modeling of two metal plates impact. In one-dimensional case the governing system of equations comprises seven equations: three conservation laws for each fluid and transfer equation for the volume fraction of one of the fluids. Both fluids are considered to be compressible and equilibrium on velocities. Pressures equilibrium is used as fluids interface condition. The system has hyperbolic type but could not be written in the conservative form because of nozzling terms in the right-hand side of the equations. The algorithm is based on the Harten-Lax-van Leer numerical flux function. The robust computation in the presence of the interface boundary is carried out due to the special pressure relaxation procedure. The problem is solved using stiffened gas equations of state for each fluid. The parameters in the equations of state are calibrated using the results of computations using wide-range equations of state for the metals. In simulations of metal plates impact we get two shocks after the initial impact that propagate to the free surfaces of the samples. The characteristics of shock waves are close (maximum relative error in characteristics of shocks is not greater than 7%) to the data from the wide-range equations of states computations.

  2. Central upwind scheme for a compressible two-phase flow model.

    Science.gov (United States)

    Ahmed, Munshoor; Saleem, M Rehan; Zia, Saqib; Qamar, Shamsul

    2015-01-01

    In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

  3. Central upwind scheme for a compressible two-phase flow model.

    Directory of Open Access Journals (Sweden)

    Munshoor Ahmed

    Full Text Available In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.

  4. Preliminary creep and pillar closure data for shales

    International Nuclear Information System (INIS)

    Lomenick, T.F.; Russell, J.E.

    1987-10-01

    The results of fourteen laboratory creep tests on model pillars of four different shales are reported. Initial pillar stresses range from 6.9 MPa (1000 psi) to 69 MPa (10,000 psi) and temperatures range from ambient to 100 0 C. Laboratory response data are used to evaluate the parameters in the transient power-law pillar closure equation similar to that previously used for model pillars of rock salt. The response of the model pillars of shale shows many of the same characteristics as for rock salt. Deformation is enhanced by higher stresses and temperatures, although the shale pillars are not as sensitive to either stress or temperature as are pillars of rock salt. These test results must be considered very preliminary since they represent the initial, or scoping, phase of a comprehensive model pillar test program that will lead to the development and validation of creep laws for clay-rich rocks. 11 refs., 9 figs., 7 tabs

  5. Parallel solutions of the two-group neutron diffusion equations

    International Nuclear Information System (INIS)

    Zee, K.S.; Turinsky, P.J.

    1987-01-01

    Recent efforts to adapt various numerical solution algorithms to parallel computer architectures have addressed the possibility of substantially reducing the running time of few-group neutron diffusion calculations. The authors have developed an efficient iterative parallel algorithm and an associated computer code for the rapid solution of the finite difference method representation of the two-group neutron diffusion equations on the CRAY X/MP-48 supercomputer having multi-CPUs and vector pipelines. For realistic simulation of light water reactor cores, the code employees a macroscopic depletion model with trace capability for selected fission product transients and critical boron. In addition to this, moderator and fuel temperature feedback models are also incorporated into the code. The validity of the physics models used in the code were benchmarked against qualified codes and proved accurate. This work is an extension of previous work in that various feedback effects are accounted for in the system; the entire code is structured to accommodate extensive vectorization; and an additional parallelism by multitasking is achieved not only for the solution of the matrix equations associated with the inner iterations but also for the other segments of the code, e.g., outer iterations

  6. A kinematic view of loop closure.

    Science.gov (United States)

    Coutsias, Evangelos A; Seok, Chaok; Jacobson, Matthew P; Dill, Ken A

    2004-03-01

    We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/. Copyright 2004 Wiley Periodicals, Inc. J Comput Chem 25: 510-528, 2004

  7. New exact solutions for two nonlinear equations

    International Nuclear Information System (INIS)

    Wang Quandi; Tang Minying

    2008-01-01

    In this Letter, we investigate two nonlinear equations given by u t -u xxt +3u 2 u x =2u x u xx +uu xxx and u t -u xxt +4u 2 u x =3u x u xx +uu xxx . Through some special phase orbits we obtain four new exact solutions for each equation above. Some previous results are extended

  8. Meta-analytic structural equation modelling

    CERN Document Server

    Jak, Suzanne

    2015-01-01

    This book explains how to employ MASEM, the combination of meta-analysis (MA) and structural equation modelling (SEM). It shows how by using MASEM, a single model can be tested to explain the relationships between a set of variables in several studies. This book gives an introduction to MASEM, with a focus on the state of the art approach: the two stage approach of Cheung and Cheung & Chan. Both, the fixed and the random approach to MASEM are illustrated with two applications to real data. All steps that have to be taken to perform the analyses are discussed extensively. All data and syntax files are available online, so that readers can imitate all analyses. By using SEM for meta-analysis, this book shows how to benefit from all available information from all available studies, even if few or none of the studies report about all relationships that feature in the full model of interest.

  9. Primary closure after carotid endarterectomy is not inferior to other closure techniques.

    Science.gov (United States)

    Avgerinos, Efthymios D; Chaer, Rabih A; Naddaf, Abdallah; El-Shazly, Omar M; Marone, Luke; Makaroun, Michel S

    2016-09-01

    Primary closure after carotid endarterectomy (CEA) has been much maligned as an inferior technique with worse outcomes than in patch closure. Our purpose was to compare perioperative and long-term results of different CEA closure techniques in a large institutional experience. A consecutive cohort of CEAs between January 1, 2000, and December 31, 2010, was retrospectively analyzed. Closure technique was used to divide patients into three groups: primary longitudinal arteriotomy closure (PRC), patch closure (PAC), and eversion closure (EVC). End points were perioperative events, long-term strokes, and restenosis ≥70%. Multivariate regression models were used to assess the effect of baseline predictors. There were 1737 CEA cases (bilateral, 143; mean age, 71.4 ± 9.3 years; 56.2% men; 35.3% symptomatic) performed during the study period with a mean clinical follow-up of 49.8 ± 36.4 months (range, 0-155 months). More men had primary closure, but other demographic and baseline symptoms were similar between groups. Half the patients had PAC, with the rest evenly distributed between PRC and EVC. The rate of nerve injury was 2.7%, the rate of reintervention for hematoma was 1.5%, and the length of hospital stay was 2.4 ± 3.0 days, with no significant differences among groups. The combined stroke and death rate was 2.5% overall and 3.9% and 1.7% in the symptomatic and asymptomatic cohort, respectively. Stroke and death rates were similar between groups: PRC, 11 (2.7%); PAC, 19 (2.2%); EVC, 13 (2.9%). Multivariate analysis showed baseline symptomatic disease (odds ratio, 2.4; P = .007) and heart failure (odds ratio, 3.1; P = .003) as predictors of perioperative stroke and death, but not the type of closure. Cox regression analysis demonstrated, among other risk factors, no statin use (hazard ratio, 2.1; P = .008) as a predictor of ipsilateral stroke and severe (glomerular filtration rate <30 mL/min/1.73 m(2)) renal insufficiency (hazard ratio, 2.6; P

  10. Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

    Science.gov (United States)

    Schuss, Z; Nadler, B; Eisenberg, R S

    2001-09-01

    Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately

  11. Considerations Regarding Age at Surgery and Fistula Incidence Using One- and Two-stage Closure for Cleft Palate

    Directory of Open Access Journals (Sweden)

    Simona Stoicescu

    2013-12-01

    Full Text Available Introduction: Although cleft lip and palate (CLP is one of the most common congenital malformations, occurring in 1 in 700 live births, there is still no generally accepted treatment protocol. Numerous surgical techniques have been described for cleft palate repair; these techniques can be divided into one-stage (one operation cleft palate repair and two-stage cleft palate closure. The aim of this study is to present our cleft palate team experience in using the two-stage cleft palate closure and the clinical outcomes in terms of oronasal fistula rate. Material and methods: A retrospective analysis was performed on medical records of 80 patients who underwent palate repair over a five-year period, from 2008 to 2012. All cleft palate patients were incorporated. Information on patient’s gender, cleft type, age at repair, one- or two-stage cleft palate repair were collected and analyzed. Results: Fifty-three (66% and twenty-seven (34% patients underwent two-stage and one-stage repair, respectively. According to Veau classification, more than 60% of them were Veau III and IV, associating cleft lip to cleft palate. Fistula occurred in 34% of the two-stage repairs versus 7% of one-stage repairs, with an overall incidence of 24%. Conclusions: Our study has shown that a two-stage cleft palate closure has a higher rate of fistula formation when compared with the one-stage repair. Two-stage repair is the protocol of choice in wide complete cleft lip and palate cases, while one-stage procedure is a good option for cleft palate alone, or some specific cleft lip and palate cases (narrow cleft palate, older age at surgery

  12. An Infectious Pseudoaneurysm Caused by Ventricular Septal Defect Occluder in Patent Ductus Arteriosus Closure in a Two-Year-Old Child.

    Science.gov (United States)

    Li, Dingyang; Qiu, Qiu; Jin, Jing; Zhang, Changdong; Wang, Lijun; Zhang, Gangcheng

    2017-12-12

    We present a case of an infectious pseudoaneurysm after patent ductus arteriosus (PDA) closure with a ventricular septal defect (VSD) occluder in a two-year-old child. The aneurysm grew rapidly but was successfully removed in time and the patient survived. To our knowledge, this is the first report of an infectious pseudoaneurysm caused by VSD occluder in PDA closure.

  13. General method for reducing the two-body Dirac equation

    International Nuclear Information System (INIS)

    Galeao, A.P.; Ferreira, P.L.

    1992-01-01

    A semi relativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schroedinger-type equations is also discussed. (author)

  14. Numerical analysis of turbulent flow and heat transfer in a square sectioned U-bend duct by elliptic-blending second moment closure

    International Nuclear Information System (INIS)

    Shin, Jong Keun; Choi, Young Don; An, Jeong Soo

    2007-01-01

    A second moment turbulence closure using the elliptic-blending equation is introduced to analyze the turbulence and heat transfer in a square sectioned U-bend duct flow. The turbulent heat flux model based on the elliptic concept satisfies the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also has the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. Also, the traditional GGDH heat flux model is compared with the present elliptic concept-based heat flux model. The turbulent heat flux models are closely linked to the elliptic blending second moment closure which is used for the prediction of Reynolds stresses. The predicted results show their reasonable agreement with experimental data for a square sectioned U-bend duct flow field adopted in the present study

  15. 76 FR 72643 - Western Pacific Pelagic Fisheries; Closure of the Hawaii Shallow-Set Pelagic Longline Fishery Due...

    Science.gov (United States)

    2011-11-25

    .... 080225267-91393-03] RIN 0648-XA370 Western Pacific Pelagic Fisheries; Closure of the Hawaii Shallow- Set...: Temporary rule; fishery closure. SUMMARY: NMFS closes the shallow-set pelagic longline fishery north of the Equator for all vessels registered under the Hawaii longline limited access program. The shallow-set...

  16. Comparison of two dose regimens of ibuprofen for the closure of patent ductus arteriosus in preterm newborns,

    Directory of Open Access Journals (Sweden)

    Laura Vargas Dornelles

    2016-06-01

    Full Text Available Abstract Objective: To compare the efficacy of intravenous ibuprofen at high (20-10-10 mg/kg/dose and low doses (10-5-5 mg/kg/dose the closure of patent ductus arteriosus in preterm newborns. Methods: A cohort study with historical control of newborns that received high- and low-dose intravenous ibuprofen, from 2010 to 2013 in a neonatal intensive care unit, for closure of the patent ductus arteriosus, documented by echocardiography. Secondary outcomes included the number of ibuprofen cycles, incidence of bronchopulmonary dysplasia, necrotizing enterocolitis, changes in renal function, and death. Results: Seventy-seven patients received three doses of ibuprofen for the treatment of patent ductus arteriosus, with 33 receiving high-dose and 44 low-dose therapy. The ductus closed after the first cycle in 25 (56.8% low-dose patients and in 17 (51.5% high-dose patients (p > 0.99. Sixteen patients received a second cycle of ibuprofen, and the ductus closed in 50% after low-dose and in 60% after high-dose therapy (p > 0.99. Seven patients required surgery for ductus closure, 13.6% in the low-dose group and 3% in the high-dose group (p = 0.22. Thirty-nine patients developed bronchopulmonary dysplasia, 50% in the low-dose group and 51.5% in the high-dose group (p > 0.99. Twenty-two (50% low-dose patients died vs. 15 (45.5% high-dose patients (p = 0.86. Conclusions: There was no difference in closure of the ductus arteriosus or occurrence of adverse effects between the two dose regimens.

  17. Two-scale approach to oscillatory singularly perturbed transport equations

    CERN Document Server

    Frénod, Emmanuel

    2017-01-01

    This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

  18. Asymptotics for Estimating Equations in Hidden Markov Models

    DEFF Research Database (Denmark)

    Hansen, Jørgen Vinsløv; Jensen, Jens Ledet

    Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...

  19. Two dimensional generalizations of the Newcomb equation

    International Nuclear Information System (INIS)

    Dewar, R.L.; Pletzer, A.

    1989-11-01

    The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs

  20. A closure test for time-specific capture-recapture data

    Science.gov (United States)

    Stanley, T.R.; Burnham, K.P.

    1999-01-01

    The assumption of demographic closure in the analysis of capture-recapture data under closed-population models is of fundamental importance. Yet, little progress has been made in the development of omnibus tests of the closure assumption. We present a closure test for time-specific data that, in principle, tests the null hypothesis of closed-population model M(t) against the open-population Jolly-Seber model as a specific alternative. This test is chi-square, and can be decomposed into informative components that can be interpreted to determine the nature of closure violations. The test is most sensitive to permanent emigration and least sensitive to temporary emigration, and is of intermediate sensitivity to permanent or temporary immigration. This test is a versatile tool for testing the assumption of demographic closure in the analysis of capture-recapture data.

  1. Engineering sustainable ecosystems: using GIS-based habitat modeling for oil sands mine reclamation and closure planning

    International Nuclear Information System (INIS)

    Seel, K.

    1997-01-01

    A GIS model was built to predict the climax vegetation habitat types on reclaimed mine surfaces in the Fort McMurray region of the Mid-Boreal Mixedwood Ecoregion of northwestern Alberta. Regional vegetation habitat types were classified by digital remote sensing using Landsat Thematic Mapper satellite data. Terrain data was derived from a high-resolution digital elevation model. The validated model was applied to the GIS database of Syncrude Canada's Mildred Lake Mine to predict future vegetation patterns based on the final closure mine surface. The results were compared to revegetation and closure plans created by experts to analyze performance and sustainability of reclamation efforts

  2. Exact solutions to two higher order nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Xu Liping; Zhang Jinliang

    2007-01-01

    Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

  3. Experimental and analytical study of interfacial area transport phenomena in a vertical two-phase flow

    International Nuclear Information System (INIS)

    Huh, Byung-Gil; Euh, Dong-Jin; Yun, Byong-Jo; Youn, Young-Jung; Yoon, Han-Yeong; Song, Chul-Hwa

    2005-03-01

    The number density transport equations for various bubble groups are used to predict the void fraction and the interfacial area concentration. As the closure relations for number density transport equation, the coalescence due to random collisions and the breakup due to the impact of turbulent eddies is modified based on the previous studies and the bubble expansion term due to the pressure reduction is considered. Also, the coalescence due to a wake entrainment is modeled newly to apply to the number density transport equation. In order to predict the local experimental data, the code is developed that the two-fluid model is coupled systematically with the number density transport equation for each bubble group. As for the results of the numerical analysis, the void fraction and interfacial area concentration are predicted well by the developed code and models although some deviations exist in the values between the prediction and experiment, especially, for the high void fraction conditions

  4. Experimental and analytical study of interfacial area transport phenomena in a vertical two-phase flow

    Energy Technology Data Exchange (ETDEWEB)

    Huh, Byung-Gil; Euh, Dong-Jin; Yun, Byong-Jo; Youn, Young-Jung; Yoon, Han-Yeong; Song, Chul-Hwa

    2005-03-01

    The number density transport equations for various bubble groups are used to predict the void fraction and the interfacial area concentration. As the closure relations for number density transport equation, the coalescence due to random collisions and the breakup due to the impact of turbulent eddies is modified based on the previous studies and the bubble expansion term due to the pressure reduction is considered. Also, the coalescence due to a wake entrainment is modeled newly to apply to the number density transport equation. In order to predict the local experimental data, the code is developed that the two-fluid model is coupled systematically with the number density transport equation for each bubble group. As for the results of the numerical analysis, the void fraction and interfacial area concentration are predicted well by the developed code and models although some deviations exist in the values between the prediction and experiment, especially, for the high void fraction conditions.

  5. Numerical simulation of two phase flows in heat exchangers

    International Nuclear Information System (INIS)

    Grandotto Biettoli, M.

    2006-04-01

    The author gives an overview of his research activity since 1981. He first gives a detailed presentation of properties and equations of two-phase flows in heat exchangers, and of their mathematical and numerical investigation: semi-local equations (mass conservation, momentum conservation and energy conservation), homogenized conservation equations (mass, momentum and enthalpy conservation, boundary conditions), equation closures, discretization, resolution algorithm, computational aspects and applications. Then, he reports the works performed in the field of turbulent flows, hyperbolic methods, low Mach methods, the Neptune project, and parallel computing

  6. Model identification using stochastic differential equation grey-box models in diabetes.

    Science.gov (United States)

    Duun-Henriksen, Anne Katrine; Schmidt, Signe; Røge, Rikke Meldgaard; Møller, Jonas Bech; Nørgaard, Kirsten; Jørgensen, John Bagterp; Madsen, Henrik

    2013-03-01

    The acceptance of virtual preclinical testing of control algorithms is growing and thus also the need for robust and reliable models. Models based on ordinary differential equations (ODEs) can rarely be validated with standard statistical tools. Stochastic differential equations (SDEs) offer the possibility of building models that can be validated statistically and that are capable of predicting not only a realistic trajectory, but also the uncertainty of the prediction. In an SDE, the prediction error is split into two noise terms. This separation ensures that the errors are uncorrelated and provides the possibility to pinpoint model deficiencies. An identifiable model of the glucoregulatory system in a type 1 diabetes mellitus (T1DM) patient is used as the basis for development of a stochastic-differential-equation-based grey-box model (SDE-GB). The parameters are estimated on clinical data from four T1DM patients. The optimal SDE-GB is determined from likelihood-ratio tests. Finally, parameter tracking is used to track the variation in the "time to peak of meal response" parameter. We found that the transformation of the ODE model into an SDE-GB resulted in a significant improvement in the prediction and uncorrelated errors. Tracking of the "peak time of meal absorption" parameter showed that the absorption rate varied according to meal type. This study shows the potential of using SDE-GBs in diabetes modeling. Improved model predictions were obtained due to the separation of the prediction error. SDE-GBs offer a solid framework for using statistical tools for model validation and model development. © 2013 Diabetes Technology Society.

  7. Analysis of Mining-induced Valley Closure Movements

    Science.gov (United States)

    Zhang, C.; Mitra, R.; Oh, J.; Hebblewhite, B.

    2016-05-01

    Valley closure movements have been observed for decades in Australia and overseas when underground mining occurred beneath or in close proximity to valleys and other forms of irregular topographies. Valley closure is defined as the inward movements of the valley sides towards the valley centreline. Due to the complexity of the local geology and the interplay between several geological, topographical and mining factors, the underlying mechanisms that actually cause this behaviour are not completely understood. A comprehensive programme of numerical modelling investigations has been carried out to further evaluate and quantify the influence of a number of these mining and geological factors and their inter-relationships. The factors investigated in this paper include longwall positional factors, horizontal stress, panel width, depth of cover and geological structures around the valley. It is found that mining in a series passing beneath the valley dramatically increases valley closure, and mining parallel to valley induces much more closure than other mining orientations. The redistribution of horizontal stress and influence of mining activity have also been recognised as important factors promoting valley closure, and the effect of geological structure around the valley is found to be relatively small. This paper provides further insight into both the valley closure mechanisms and how these mechanisms should be considered in valley closure prediction models.

  8. Calculus for cognitive scientists partial differential equation models

    CERN Document Server

    Peterson, James K

    2016-01-01

    This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics.  A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

  9. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

    International Nuclear Information System (INIS)

    Delhaye, J.M.

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  10. The merits of non-tradable quotas as a domestic policy instrument to prevent firm closure

    International Nuclear Information System (INIS)

    Hagem, Cathrine

    2001-05-01

    There is a concern in many countries that a domestic tradable quota system for greenhouse gases, where all emitters must pay for their quotas, may lead to closures of emissions-intensive industrial companies. Allocating quotas free of charge to companies operating in competitive markets has been suggested as a means to reduce the likelihood of closures. Two different designs of quota systems are studied within a two-period model: one where the quotas given free of charge are tradable, and one where the quotas are non-tradable. The two quota systems are compared with respect to their ability both to induce the firms to implement investment in abatement technology and to prevent or postpone closures. (author)

  11. A Class of Two-Component Adler—Bobenko—Suris Lattice Equations

    International Nuclear Information System (INIS)

    Fu Wei; Zhang Da-Jun; Zhou Ru-Guang

    2014-01-01

    We study a class of two-component forms of the famous list of the Adler—Bobenko—Suris lattice equations. The obtained two-component lattice equations are still consistent around the cube and they admit solutions with ‘jumping properties’ between two levels. (general)

  12. Observations on early and delayed colostomy closure.

    Science.gov (United States)

    Tade, A O; Salami, B A; Ayoade, B A

    2011-06-01

    Traditional treatment of a variety of colorectal pathologies had included a diverting colostomy that was closed eight or more weeks later during a readmission. The aim of this retrospective study was to determine the outcomes of early colostomy closure and delayed colostomy closure in patients with temporary colostomies following traumatic and non-traumatic colorectal pathologies. In this study early colostomy closure was the closure of a colostomy within three weeks of its construction, while delayed colostomy closure referred to closure after 3 weeks. Complete records of the 37 adult patients who had temporary colostomy constructed and closed between Jan. 1997 December 2003 for various colorectal pathologies were studied. Fourteen patients had early colostomy closure while 23 had delayed closure. In the early colostomy closure group there were 10 men and 4 women. The mean age of the patients was 28yr with a range of 18-65yr. Colostomies were closed 9-18 days after initial colostomy construction. There was no mortality. Morbidity rate 28.6% (4 out of 14). There were two faecal fistulas (14.3%). Twenty-three patients had delayed colostomy closure 8 weeks to 18 months after initial colostomy construction. These were patients unfit for early surgery after initial colostomy construction because of carcinoma, significant weight loss, or sepsis. There was no mortality. Morbidity rate was 26.1%. There were 3 faecal fistulas (13.2%). Outcomes following early colostomy closure and delayed closure were comparable. Patients fit for surgery should have early closure whilst patients who may have compromised health should have delayed closure.

  13. A small community model for the transmission of infectious diseases: comparison of school closure as an intervention in individual-based models of an influenza pandemic.

    Directory of Open Access Journals (Sweden)

    George J Milne

    Full Text Available BACKGROUND: In the absence of other evidence, modelling has been used extensively to help policy makers plan for a potential future influenza pandemic. METHOD: We have constructed an individual based model of a small community in the developed world with detail down to exact household structure obtained from census collection datasets and precise simulation of household demographics, movement within the community and individual contact patterns. We modelled the spread of pandemic influenza in this community and the effect on daily and final attack rates of four social distancing measures: school closure, increased case isolation, workplace non-attendance and community contact reduction. We compared the modelled results of final attack rates in the absence of any interventions and the effect of school closure as a single intervention with other published individual based models of pandemic influenza in the developed world. RESULTS: We showed that published individual based models estimate similar final attack rates over a range of values for R(0 in a pandemic where no interventions have been implemented; that multiple social distancing measures applied early and continuously can be very effective in interrupting transmission of the pandemic virus for R(0 values up to 2.5; and that different conclusions reached on the simulated benefit of school closure in published models appear to result from differences in assumptions about the timing and duration of school closure and flow-on effects on other social contacts resulting from school closure. CONCLUSION: Models of the spread and control of pandemic influenza have the potential to assist policy makers with decisions about which control strategies to adopt. However, attention needs to be given by policy makers to the assumptions underpinning both the models and the control strategies examined.

  14. Workshop on Engineering Turbulence Modeling

    Science.gov (United States)

    Povinelli, Louis A. (Editor); Liou, W. W. (Editor); Shabbir, A. (Editor); Shih, T.-H. (Editor)

    1992-01-01

    Discussed here is the future direction of various levels of engineering turbulence modeling related to computational fluid dynamics (CFD) computations for propulsion. For each level of computation, there are a few turbulence models which represent the state-of-the-art for that level. However, it is important to know their capabilities as well as their deficiencies in order to help engineers select and implement the appropriate models in their real world engineering calculations. This will also help turbulence modelers perceive the future directions for improving turbulence models. The focus is on one-point closure models (i.e., from algebraic models to higher order moment closure schemes and partial differential equation methods) which can be applied to CFD computations. However, other schemes helpful in developing one-point closure models, are also discussed.

  15. Models and numerical methods for time- and energy-dependent particle transport

    Energy Technology Data Exchange (ETDEWEB)

    Olbrant, Edgar

    2012-04-13

    Particles passing through a medium can be described by the Boltzmann transport equation. Therein, all physical interactions of particles with matter are given by cross sections. We compare different analytical models of cross sections for photons, electrons and protons to state-of-the-art databases. The large dimensionality of the transport equation and its integro-differential form make it analytically difficult and computationally costly to solve. In this work, we focus on the following approximative models to the linear Boltzmann equation: (i) the time-dependent simplified P{sub N} (SP{sub N}) equations, (ii) the M{sub 1} model derived from entropy-based closures and (iii) a new perturbed M{sub 1} model derived from a perturbative entropy closure. In particular, an asymptotic analysis for SP{sub N} equations is presented and confirmed by numerical computations in 2D. Moreover, we design an explicit Runge-Kutta discontinuous Galerkin (RKDG) method to the M{sub 1} model of radiative transfer in slab geometry and construct a scheme ensuring the realizability of the moment variables. Among other things, M{sub 1} numerical results are compared with an analytical solution in a Riemann problem and the Marshak wave problem is considered. Additionally, we rigorously derive a new hierarchy of kinetic moment models in the context of grey photon transport in one spatial dimension. For the perturbed M{sub 1} model, we present numerical results known as the two beam instability or the analytical benchmark due to Su and Olson and compare them to the standard M{sub 1} as well as transport solutions.

  16. Application of statistical dynamical turbulence closures to data assimilation

    International Nuclear Information System (INIS)

    O'Kane, Terence J; Frederiksen, Jorgen S

    2010-01-01

    We describe the development of an accurate yet computationally tractable statistical dynamical closure theory for general inhomogeneous turbulent flows, coined the quasi-diagonal direct interaction approximation closure (QDIA), and its application to problems in data assimilation. The QDIA provides prognostic equations for evolving mean fields, covariances and higher-order non-Gaussian terms, all of which are also required in the formulation of data assimilation schemes for nonlinear geophysical flows. The QDIA is a generalization of the class of direct interaction approximation theories, initially developed by Kraichnan (1959 J. Fluid Mech. 5 497) for isotropic turbulence, to fully inhomogeneous flows and has been further generalized to allow for both inhomogeneous and non-Gaussian initial conditions and long integrations. A regularization procedure or empirical vertex renormalization that ensures correct inertial range spectra is also described. The aim of this paper is to provide a coherent mathematical description of the QDIA turbulence closure and closure-based data assimilation scheme we have labeled the statistical dynamical Kalman filter. The mathematical formalism presented has been synthesized from recent works of the authors with some additional material and is presented in sufficient detail that the paper is of a pedagogical nature.

  17. Comparison of two fibrin glues in anastomoses and skin closure.

    Science.gov (United States)

    Park, W; Kim, W H; Lee, C H; Kim, D Y; Choi, J H; Huh, J W; Sung, H M; Kim, I S; Kweon, O K

    2002-09-01

    To control intra-operative haemorrhage, fibrin glues are preferred by many surgeons because of their biological advantages and convenience of application. Manufacturers have developed a few kinds of fibrin glues with a little difference in their composition. This study was to compare the effectiveness of two commercially available fibrin glues; Greenplast (Green Cross P. D. Company, Yongin, Korea) and Tisseel (Baxter-Immuno AG, Vienna, Austria). They were applied experimentally to several kinds of surgery in dogs - renal vessel anastomosis, partial splenectomy, intestinal anastomosis and incision skin wound - and evaluated for their haemostatic and adhesive effects. When the two glues were applied in renal vessel anastomosis, the amount of haemorrhage in artery and vein decreased significantly. They also decreased the haemorrhage in partial splenectomy. At 10 min after application of the glues to an incision skin wound, the tensile strengths developed were significantly higher than that of control. The present study indicates that two-component fibrin glues have a haemostatic effect as a mechanical barrier in renal vessel anastomosis and an adhesive effect in the early stage of incision skin wound closure, and the two glues have similar effects with no complications.

  18. Numerical simulation of transient, adiabatic, two-dimensional two-phase flow using the two-fluid model

    International Nuclear Information System (INIS)

    Neves Conti, T. das.

    1983-01-01

    A numerical method is developed to simulate adiabatic, transient, two-dimensional two-phase flow. The two-fluid model is used to obtain the mass and momentum conservation equations. These are solved by an iterative algorithm emphoying a time-marching scheme. Based on the corrective procedure of Hirt and Harlow a poisson equation is derived for the pressure field. This equation is finite-differenced and solved by a suitable matrix inversion technique. In the absence of experiment results several numerical tests were made in order to chec accuracy, convergence and stability of the proposed method. Several tests were also performed to check whether the behavior of void fraction and phasic velocities conforms with previous observations. (Author) [pt

  19. Comparison of two dose regimens of ibuprofen for the closure of patent ductus arteriosus in preterm newborns.

    Science.gov (United States)

    Dornelles, Laura Vargas; Corso, Andréa Lúcia; Silveira, Rita de Cássia; Procianoy, Renato Soibelmann

    2016-01-01

    To compare the efficacy of intravenous ibuprofen at high (20-10-10mg/kg/dose) and low doses (10-5-5mg/kg/dose) the closure of patent ductus arteriosus in preterm newborns. A cohort study with historical control of newborns that received high- and low-dose intravenous ibuprofen, from 2010 to 2013 in a neonatal intensive care unit, for closure of the patent ductus arteriosus, documented by echocardiography. Secondary outcomes included the number of ibuprofen cycles, incidence of bronchopulmonary dysplasia, necrotizing enterocolitis, changes in renal function, and death. Seventy-seven patients received three doses of ibuprofen for the treatment of patent ductus arteriosus, with 33 receiving high-dose and 44 low-dose therapy. The ductus closed after the first cycle in 25 (56.8%) low-dose patients and in 17 (51.5%) high-dose patients (p>0.99). Sixteen patients received a second cycle of ibuprofen, and the ductus closed in 50% after low-dose and in 60% after high-dose therapy (p>0.99). Seven patients required surgery for ductus closure, 13.6% in the low-dose group and 3% in the high-dose group (p=0.22). Thirty-nine patients developed bronchopulmonary dysplasia, 50% in the low-dose group and 51.5% in the high-dose group (p>0.99). Twenty-two (50%) low-dose patients died vs. 15 (45.5%) high-dose patients (p=0.86). There was no difference in closure of the ductus arteriosus or occurrence of adverse effects between the two dose regimens. Copyright © 2016 Sociedade Brasileira de Pediatria. Published by Elsevier Editora Ltda. All rights reserved.

  20. The use of a diffuse interface model to estimate effective transport properties for two-phase flows in porous media

    International Nuclear Information System (INIS)

    Fichot, Floriana; Duval, Fabiena; Garcia, Aureliena; Belloni, Julien; Quintard, Michel

    2005-01-01

    Full text of publication follows: In the framework of its research programme on severe nuclear reactor accidents, IRSN investigates the water flooding of an overheated porous bed, where complex two-phase flows are likely to exist. The goal is to describe the flow with a general model, covering rods and debris beds regions in the vessel. A better understanding of the flow at the pore level appears to be necessary in order to justify and improve closure laws of macroscopic models. Although the Direct Numerical Simulation (DNS) of two-phase flows is possible with several methods, applications are now limited to small computational domains, typically of the order of a few centimeters. Therefore, numerical solutions at the reactor scale can only be obtained by using averaged models. Volume averaging is the most traditional way of deriving such models. For nuclear safety codes, a control volume must include a few rods or a few debris particles, with a characteristic dimension of a few centimeters. The difficulty usually met with averaged models is the closure of several transport or source terms which appear in the averaged conservation equations (for example the interfacial drag or the heat transfers between phases) [2]. In the past, the closure of these terms was obtained, when possible, from one-dimensional experiments that allowed measurements of heat flux or pressure drops. For more complex flows, the experimental measurement of local parameters is often impossible and the effective properties cannot be determined easily. An alternative way is to perform 'numerical experiments' with numerical simulations of the local flow. As mentioned above, the domain of application of DNS corresponds to the size of control volumes necessary to derive averaged models. Therefore DNS appears as a powerful tool to investigate the local features of a two-phase flow in complex geometries. Diffuse interface methods provide a way to model flows with interfacial phenomena through an

  1. Uncertainty Quantification of Multi-Phase Closures

    Energy Technology Data Exchange (ETDEWEB)

    Nadiga, Balasubramanya T. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baglietto, Emilio [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

    2017-10-27

    In the ensemble-averaged dispersed phase formulation used for CFD of multiphase ows in nuclear reactor thermohydraulics, closures of interphase transfer of mass, momentum, and energy constitute, by far, the biggest source of error and uncertainty. Reliable estimators of this source of error and uncertainty are currently non-existent. Here, we report on how modern Validation and Uncertainty Quanti cation (VUQ) techniques can be leveraged to not only quantify such errors and uncertainties, but also to uncover (unintended) interactions between closures of di erent phenomena. As such this approach serves as a valuable aide in the research and development of multiphase closures. The joint modeling of lift, drag, wall lubrication, and turbulent dispersion|forces that lead to tranfer of momentum between the liquid and gas phases|is examined in the frame- work of validation of the adiabatic but turbulent experiments of Liu and Banko , 1993. An extensive calibration study is undertaken with a popular combination of closure relations and the popular k-ϵ turbulence model in a Bayesian framework. When a wide range of super cial liquid and gas velocities and void fractions is considered, it is found that this set of closures can be validated against the experimental data only by allowing large variations in the coe cients associated with the closures. We argue that such an extent of variation is a measure of uncertainty induced by the chosen set of closures. We also nd that while mean uid velocity and void fraction pro les are properly t, uctuating uid velocity may or may not be properly t. This aspect needs to be investigated further. The popular set of closures considered contains ad-hoc components and are undesirable from a predictive modeling point of view. Consequently, we next consider improvements that are being developed by the MIT group under CASL and which remove the ad-hoc elements. We use non-intrusive methodologies for sensitivity analysis and calibration (using

  2. An effect comparison between Furlow double opposing Z-plasty and two-flap palatoplasty on velopharyngeal closure.

    Science.gov (United States)

    Dong, Y; Dong, F; Zhang, X; Hao, F; Shi, P; Ren, G; Yong, P; Guo, Y

    2012-05-01

    The aim of this study was to compare velopharyngeal closure between patients who underwent Furlow palatoplasty and two-flap palatoplasty. A retrospective review of 88 patients with incomplete palate cleft was performed. 48 patients (17 males; 31 females) aged 2-28 years received Furlow palatoplasty. 40 patients (17 males; 23 females) aged 2-21 years received two-flap palatoplasty. Velopharyngeal function was categorized as adequate, marginal or inadequate. Complications associated with the operation were documented. Statistically significant differences were not found amongst sex distribution, age at operation, follow-up time, and preoperative speech intelligibility. After primary repairs using Furlow and two-flap palatoplasty, the surgeon's incidence of postoperative palatal fistula was 0%. The complications were not significantly different between the two groups. The authors achieved the lowest reported incidence of postoperative palatal fistulas in primary Furlow palatoplasty. The outcomes of the velopharyngeal closure were better in patients who received Furlow palatoplasty (Pexplanation may be that Furlow palatoplasty can reposition and overlap the divergent palatal muscle and lengthen the soft palate. Copyright © 2012 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

  3. Fractal diffusion equations: Microscopic models with anomalous diffusion and its generalizations

    International Nuclear Information System (INIS)

    Arkhincheev, V.E.

    2001-04-01

    To describe the ''anomalous'' diffusion the generalized diffusion equations of fractal order are deduced from microscopic models with anomalous diffusion as Comb model and Levy flights. It is shown that two types of equations are possible: with fractional temporal and fractional spatial derivatives. The solutions of these equations are obtained and the physical sense of these fractional equations is discussed. The relation between diffusion and conductivity is studied and the well-known Einstein relation is generalized for the anomalous diffusion case. It is shown that for Levy flight diffusion the Ohm's law is not applied and the current depends on electric field in a nonlinear way due to the anomalous character of Levy flights. The results of numerical simulations, which confirmed this conclusion, are also presented. (author)

  4. A Two-Species Cooperative Lotka-Volterra System of Degenerate Parabolic Equations

    OpenAIRE

    Sun, Jiebao; Zhang, Dazhi; Wu, Boying

    2011-01-01

    We consider a cooperating two-species Lotka-Volterra model of degenerate parabolic equations. We are interested in the coexistence of the species in a bounded domain. We establish the existence of global generalized solutions of the initial boundary value problem by means of parabolic regularization and also consider the existence of the nontrivial time-periodic solution for this system.

  5. Exact Solutions for Two Equation Hierarchies

    International Nuclear Information System (INIS)

    Song-Lin, Zhao; Da-Jun, Zhang; Jie, Ji

    2010-01-01

    Bilinear forms and double-Wronskian solutions are given for two hierarchies, the (2+1)-dimensional breaking Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, Jordan block solutions, rational solutions, complexitons and mixed solutions. (general)

  6. Comparison of two equation-of-state models for partially ionized aluminum: Zel'dovich and Raizer's model versus the activity expansion code

    Science.gov (United States)

    Harrach, Robert J.; Rogers, Forest J.

    1981-09-01

    Two equation-of-state (EOS) models for multipy ionized matter are evaluated for the case of an aluminum plasma in the temperature range from about one eV to several hundred eV, spanning conditions of weak to strong ionization. Specifically, the simple analytical mode of Zel'dovich and Raizer and the more comprehensive model comprised by Rogers' plasma physics avtivity expansion code (ACTEX) are used to calculate the specific internal energy ɛ and average degree of ionization Z¯*, as functons of temperature T and density ρ. In the absence of experimental data, these results are compared against each other, covering almost five orders-of-magnitude variation in ɛ and the full range of Z¯* We find generally good agreement between the two sets of results, especially for low densities and for temperatures near the upper end of the rage. Calculated values of ɛ(T) agree to within ±30% over nearly the full range in T for densities below about 1 g/cm3. Similarly, the two models predict values of Z¯*(T) which track each other fairly well; above 20 eV the discrepancy is less than ±20% fpr ρ≲1 g/cm3. Where the calculations disagree, we expect the ACTEX code to be more accurate than Zel'dovich and Raizer's model, by virtue of its more detailed physics content.

  7. Model calculations of doubly closed shell nuclei in the integral-differential equation approach describing the two body correlations

    International Nuclear Information System (INIS)

    Brizzi, R.; Fabre de la Ripelle, M.; Lassaut, M.

    1999-01-01

    The binding energies and root mean square radii obtained from the Integro-Differential Equation Approach (IDEA) and from the Weight Function Approximation (WFA) of the IDEA for an even number of bosons and for 12 C, 16 O and 40 Ca are compared to those recently obtained by the Variational Monte Carlo, Fermi Hypernetted Chain and Coupled Cluster expansion method with model potentials. The IDEA provides numbers very similar to those obtained by other methods although it takes only two-body correlations into account. The analytical expression of the wave function for the WFA is given for bosons in ground state when the interaction pair is outside the potential range. Due to its simple structure, the equations of the IDEA can easily be extended to realistic interaction for nuclei like it has already been done for the tri-nucleon and the 4 He. (authors)

  8. Annotated bibliography of structural equation modelling: technical work.

    Science.gov (United States)

    Austin, J T; Wolfle, L M

    1991-05-01

    Researchers must be familiar with a variety of source literature to facilitate the informed use of structural equation modelling. Knowledge can be acquired through the study of an expanding literature found in a diverse set of publishing forums. We propose that structural equation modelling publications can be roughly classified into two groups: (a) technical and (b) substantive applications. Technical materials focus on the procedures rather than substantive conclusions derived from applications. The focus of this article is the former category; included are foundational/major contributions, minor contributions, critical and evaluative reviews, integrations, simulations and computer applications, precursor and historical material, and pedagogical textbooks. After a brief introduction, we annotate 294 articles in the technical category dating back to Sewall Wright (1921).

  9. Stable estimation of two coefficients in a nonlinear Fisher–KPP equation

    International Nuclear Information System (INIS)

    Cristofol, Michel; Roques, Lionel

    2013-01-01

    We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation of the Fisher–Kolmogorov–Petrovsky–Piskunov type. For the equation u t = DΔu + μ(x) u − γ(x)u 2 in (0, T) × Ω, which corresponds to a classical model of population dynamics in a bounded heterogeneous environment, our results give a stability inequality between the couple of coefficients (μ, γ) and some observations of the solution u. These observations consist in measurements of u: in the whole domain Ω at two fixed times, in a subset ω⊂⊂Ω during a finite time interval and on the boundary of Ω at all times t ∈ (0, T). The proof relies on parabolic estimates together with the parabolic maximum principle and Hopf’s lemma which enable us to use a Carleman inequality. This work extends previous studies on the stable determination of non-constant coefficients in parabolic equations, as it deals with two coefficients and with a nonlinear term. A consequence of our results is the uniqueness of the couple of coefficients (μ, γ), given the observation of u. This uniqueness result was obtained in a previous paper but in the one-dimensional case only. (paper)

  10. Analytic solution of integral equations for molecular fluids

    International Nuclear Information System (INIS)

    Cummings, P.T.

    1984-01-01

    We review some recent progress in the analytic solution of integral equations for molecular fluids. The site-site Ornstein-Zernike (SSOZ) equation with approximate closures appropriate to homonuclear diatomic fluids both with and without attractive dispersion-like interactions has recently been solved in closed form analytically. In this paper, the close relationship between the SSOZ equation for homonuclear dumbells and the usual Ornstein-Zernike (OZ) equation for atomic fluids is carefully elucidated. This relationship is a key motivation for the analytic solutions of the SSOZ equation that have been obtained to date. (author)

  11. Structural equation modeling methods and applications

    CERN Document Server

    Wang, Jichuan

    2012-01-01

    A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a

  12. Relativistic two-body equation for one Dirac and one Duffin-Kemmer particle

    International Nuclear Information System (INIS)

    Krolikowski, W.

    1983-01-01

    A new relativistic two-body wave equation is proposed for one spin-1/2 and one spin-0 or spin-1 particle which, if isolated from each other, are described by the Dirac and the Duffin-Kemmer equation, respectively. For a static mutual interaction this equation splits into two equations: a two-body wave equation for one Dirac and one Klein-Gordon particle (which was introduced by the author previously) and a new two-body wave equation for one Dirac and one Proca particle. The proposed equation may be applied in particular to the quark-diquark system. In Appendix, however, an alternative approach is sketched, where the diquark is described as the point limit of a very close Breit system rather than a Duffin-Kemmer particle. (Author)

  13. Modeling imperfectly repaired system data via grey differential equations with unequal-gapped times

    International Nuclear Information System (INIS)

    Guo Renkuan

    2007-01-01

    In this paper, we argue that grey differential equation models are useful in repairable system modeling. The arguments starts with the review on GM(1,1) model with equal- and unequal-spaced stopping time sequence. In terms of two-stage GM(1,1) filtering, system stopping time can be partitioned into system intrinsic function and repair effect. Furthermore, we propose an approach to use grey differential equation to specify a semi-statistical membership function for system intrinsic function times. Also, we engage an effort to use GM(1,N) model to model system stopping times and the associated operating covariates and propose an unequal-gapped GM(1,N) model for such analysis. Finally, we investigate the GM(1,1)-embed systematic grey equation system modeling of imperfectly repaired system operating data. Practical examples are given in step-by-step manner to illustrate the grey differential equation modeling of repairable system data

  14. Model reduction of multiscale chemical langevin equations: a numerical case study.

    Science.gov (United States)

    Sotiropoulos, Vassilios; Contou-Carrere, Marie-Nathalie; Daoutidis, Prodromos; Kaznessis, Yiannis N

    2009-01-01

    Two very important characteristics of biological reaction networks need to be considered carefully when modeling these systems. First, models must account for the inherent probabilistic nature of systems far from the thermodynamic limit. Often, biological systems cannot be modeled with traditional continuous-deterministic models. Second, models must take into consideration the disparate spectrum of time scales observed in biological phenomena, such as slow transcription events and fast dimerization reactions. In the last decade, significant efforts have been expended on the development of stochastic chemical kinetics models to capture the dynamics of biomolecular systems, and on the development of robust multiscale algorithms, able to handle stiffness. In this paper, the focus is on the dynamics of reaction sets governed by stiff chemical Langevin equations, i.e., stiff stochastic differential equations. These are particularly challenging systems to model, requiring prohibitively small integration step sizes. We describe and illustrate the application of a semianalytical reduction framework for chemical Langevin equations that results in significant gains in computational cost.

  15. Investigation of two and three parameter equations of state for cryogenic fluids

    International Nuclear Information System (INIS)

    Jenkins, S.L.; Majumdar, A.K.; Hendricks, R.C.

    1990-01-01

    Two-phase flows are a common occurrence in cryogenic engines and an accurate evaluation of the heat-transfer coefficient in two-phase flow is of significant importance in their analysis and design. The thermodynamic equation of state plays a key role in calculating the heat transfer coefficient which is a function of thermodynamic and thermophysical properties. An investigation has been performed to study the performance of two- and three-parameter equations of state to calculate the compressibility factor of cryogenic fluids along the saturation loci. The two-parameter equations considered here are van der Waals and Redlich-Kwong equations of state. The three-parameter equation represented here is the generalized Benedict-Webb-Rubin (BWR) equation of Lee and Kesler. Results have been compared with the modified BWR equation of Bender and the extended BWR equations of Stewart. Seven cryogenic fluids have been tested; oxygen, hydrogen, helium, nitrogen, argon, neon, and air. The performance of the generalized BWR equation is poor for hydrogen and helium. The van der Waals equation is found to be inaccurate for air near the critical point. For helium, all three equations of state become inaccurate near the critical point. 13 refs

  16. Comparison of pharyngocutaneous fistula closure with and without bacterial cellulose in a rat model.

    Science.gov (United States)

    Demir, Berat; Sarı, Murat; Binnetoglu, Adem; Yumusakhuylu, Ali Cemal; Filinte, Deniz; Tekin, İshak Özel; Bağlam, Tekin; Batman, Abdullah Çağlar

    2018-04-01

    The present study aimed to compare the effects of bacterial cellulose used for closure of pharyngocutaneous fistulae, a complication of total laryngectomy, with those of primary sutures in a rat model. Thirty female Sprague-Dawley underwent experimental pharyngoesophagotomy and were grouped depending on the material used for pharyngocutaneous fistula closure: group I, which received primary sutures alone, group II, which received bacterial cellulose alone; and group III, which received both. After 7 days, the rats were sacrificed. Pharyngocutaneous fistula development was assessed, the gross wound was inspected, and histological examination was conducted. Pharyngocutaneous fistulae developed in 12 rats (41%) in all: 6 from group I (21%), 4 from group II (14%) and 2 from group III (7%). Fibroblast density and inflammatory cell infiltration were significantly greater in group III than group I. We concluded that bacterial cellulose may be useful for pharyngocutaneous fistula closure. Copyright © 2017 Elsevier B.V. All rights reserved.

  17. Group-theoretical model of developed turbulence and renormalization of the Navier-Stokes equation.

    Science.gov (United States)

    Saveliev, V L; Gorokhovski, M A

    2005-07-01

    On the basis of the Euler equation and its symmetry properties, this paper proposes a model of stationary homogeneous developed turbulence. A regularized averaging formula for the product of two fields is obtained. An equation for the averaged turbulent velocity field is derived from the Navier-Stokes equation by renormalization-group transformation.

  18. Generalized reduced magnetohydrodynamic equations

    International Nuclear Information System (INIS)

    Kruger, S.E.

    1999-01-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics

  19. Generalized modification in the lattice Bhatnagar-Gross-Krook model for incompressible Navier-Stokes equations and convection-diffusion equations.

    Science.gov (United States)

    Yang, Xuguang; Shi, Baochang; Chai, Zhenhua

    2014-07-01

    In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).

  20. Closure requirements

    International Nuclear Information System (INIS)

    Hutchinson, I.P.G.; Ellison, R.D.

    1992-01-01

    Closure of a waste management unit can be either permanent or temporary. Permanent closure may be due to: economic factors which make it uneconomical to mine the remaining minerals; depletion of mineral resources; physical site constraints that preclude further mining and beneficiation; environmental, regulatory or other requirements that make it uneconomical to continue to develop the resources. Temporary closure can occur for a period of several months to several years, and may be caused by factors such as: periods of high rainfall or snowfall which prevent mining and waste disposal; economic circumstances which temporarily make it uneconomical to mine the target mineral; labor problems requiring a cessation of operations for a period of time; construction activities that are required to upgrade project components such as the process facilities and waste management units; and mine or process plant failures that require extensive repairs. Permanent closure of a mine waste management unit involves the provision of durable surface containment features to protect the waters of the State in the long-term. Temporary closure may involve activities that range from ongoing maintenance of the existing facilities to the installation of several permanent closure features in order to reduce ongoing maintenance. This paper deals with the permanent closure features

  1. Strength and water-tightness of the closure head and valves of a model cask under high external pressure

    International Nuclear Information System (INIS)

    Terada, O.; Kumada, M.; Hayakawa, T.; Mochizuki, S.; Ohrui, K.

    1978-01-01

    This paper describes experimental research on the strength and water-tightness of the closure head and attached valves of a model cask under high external pressure, in simulation of its having been accidentally lost in the deep sea. Both the external pressure tests and the corrosion tests were carried out using scale models of the closure head of an 80-ton spent-fuel shipping cask, and the full size pressure relief valves and drain valves which were to be attached to the actual cask. Based on the results of the above tests, evaluations were made, and new information was obtained on the pressure-proof strength and water-tightness of the closure head of the cask and the valves. Lastly, research which is being carried on in Japan on the pressure equalizer is also introduced

  2. Modelling of gas generation in deep geological repositories after closure

    International Nuclear Information System (INIS)

    Poller, A.; Mayer, G.; Darcis M; Smith, P.

    2016-12-01

    In deep geological repositories for radioactive waste, significant quantities of gases will be generated in the long term as a result of various processes, notably the anaerobic corrosion of metals and the degradation of organic materials. Therefore, the impact of gas production on post-closure safety of the repositories needs to be assessed as part of a safety case. The present report provides a comprehensive description of the quantitative modelling of gas generation and associated water consumption during the post-closure phase of deep geological repositories in Opalinus Clay based on current scientific knowledge and on current preliminary repository designs. This includes a presentation of the modelling basis, namely the conceptual and mathematical models, the input data used, the computer tools developed, the relevant uncertainties and principal programme / design options, as well as the derivation, analysis and discussion of specific assessment cases. The modelling is carried out separately for the two main sources of gas, which are the emplaced waste including the disposal containers; and the construction materials. The contribution of construction materials to gas generation rates in emplacement tunnels for spent fuel (SF) and vitrified high-level waste (HLW) is significant during several thousand years after closure. In the long term, however, the corrosion of the disposal canisters, which are in the reference case assumed to be fabricated of carbon steel, accounts for the vast majority of the total gas produced in these tunnels. The contribution of construction materials in emplacement caverns for long lived intermediate-level waste (ILW) and low- and intermediate-level waste (L/ILW) to gas generation is generally small. In ILW emplacement caverns, gas generation is generally dominated by hydrogen generation from the corrosion of cast iron Mosaik-II waste containers for PWR internals and from the corrosion of aluminium in operational waste from the

  3. Modelling of gas generation in deep geological repositories after closure

    Energy Technology Data Exchange (ETDEWEB)

    Poller, A. [National Cooperative for the Disposal of Radioactive Waste (NAGRA), Wettingen (Switzerland); Mayer, G.; Darcis M [AF-Consult Switzerland Ltd, Baden-Dättwil, (Switzerland); Smith, P. [Safety Assessment Management Ltd, Henley-On-Thames, Oxfordshire (United Kingdom)

    2016-12-15

    In deep geological repositories for radioactive waste, significant quantities of gases will be generated in the long term as a result of various processes, notably the anaerobic corrosion of metals and the degradation of organic materials. Therefore, the impact of gas production on post-closure safety of the repositories needs to be assessed as part of a safety case. The present report provides a comprehensive description of the quantitative modelling of gas generation and associated water consumption during the post-closure phase of deep geological repositories in Opalinus Clay based on current scientific knowledge and on current preliminary repository designs. This includes a presentation of the modelling basis, namely the conceptual and mathematical models, the input data used, the computer tools developed, the relevant uncertainties and principal programme / design options, as well as the derivation, analysis and discussion of specific assessment cases. The modelling is carried out separately for the two main sources of gas, which are the emplaced waste including the disposal containers; and the construction materials. The contribution of construction materials to gas generation rates in emplacement tunnels for spent fuel (SF) and vitrified high-level waste (HLW) is significant during several thousand years after closure. In the long term, however, the corrosion of the disposal canisters, which are in the reference case assumed to be fabricated of carbon steel, accounts for the vast majority of the total gas produced in these tunnels. The contribution of construction materials in emplacement caverns for long lived intermediate-level waste (ILW) and low- and intermediate-level waste (L/ILW) to gas generation is generally small. In ILW emplacement caverns, gas generation is generally dominated by hydrogen generation from the corrosion of cast iron Mosaik-II waste containers for PWR internals and from the corrosion of aluminium in operational waste from the

  4. A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

    Science.gov (United States)

    Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

    2017-09-01

    Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

  5. Modeling of superconductors based on the timedependent Ginsburg-Landau equations

    Science.gov (United States)

    Grishakov, K. S.; Degtyarenko, P. N.; Degtyarenko, N. N.; Elesin, V. F.; Kruglov, V. S.

    2009-11-01

    Results of modeling of superconductor magnetization process based on a numerical solution of the timedependent Ginsburg-Landau equations are presented. Methods of grid approximation of the equations and method of finite elements are used. Two-dimensional patterns of changes in the order parameter and supercurrent distribution in superconductors are calculated and visualized. The main results are in agreement with the well-known representations for type I and II superconductors.

  6. Pan-nitinol occluder and special delivery device for closure of patent ductus arteriosus: a canine-model feasibility study.

    Science.gov (United States)

    Jiang, Hai-bin; Bai, Yuan; Zong, Gang-jun; Han, Lin; Li, Wei-ping; Lu, Yang; Qin, Yong-wen; Zhao, Xian-xian

    2013-01-01

    The aim of this study was to evaluate a new type of occluder for patent ductus arteriosus. Patent ductus arteriosus was established in a canine model by anastomosing a length of autologous jugular vein to the descending aorta and the left pulmonary artery in an end-to-side fashion. Transcatheter closure of each patent ductus arteriosus was performed on 10 dogs, which were then monitored for as long as 6 months with aortography, echocardiography, and histologic evaluation. Transcatheter closure with use of the novel pan-nitinol device was successful in all canine models. Postoperative echocardiography showed that the location and shape of the occluders were normal, without any residual shunting. Further histologic evaluation confirmed that the occluder surface was completely endothelialized 3 months after implantation. Transcatheter patent ductus arteriosus closure with the pan-nitinol occluder can be performed safely and successfully in a canine model and shows good biological compatibility and low mortality rates.

  7. Compilation of current literature on seals, closures, and leakage for radioactive material packagings

    International Nuclear Information System (INIS)

    Warrant, M.M.; Ottinger, C.A.

    1989-01-01

    This report presents an overview of the features that affect the sealing capability of radioactive material packagings currently certified by the US Nuclear Regulatory Commission. The report is based on a review of current literature on seals, closures, and leakage for radioactive material packagings. Federal regulations that relate to the sealing capability of radioactive material packagings, as well as basic equations for leakage calculations and some of the available leakage test procedures are presented. The factors which affect the sealing capability of a closure, including the properties of the sealing surfaces, the gasket material, the closure method and the contents are discussed in qualitative terms. Information on the general properties of both elastomer and metal gasket materials and some specific designs are presented. A summary of the seal material, closure method, and leakage tests for currently certified packagings with large diameter seals is provided. 18 figs., 9 tabs

  8. Key financial ratios can foretell hospital closures.

    Science.gov (United States)

    Lynn, M L; Wertheim, P

    1993-11-01

    An analysis of various financial ratios sampled from open and closed hospitals shows that certain leverage, liquidity, capital efficiency, and resource availability ratios can predict hospital closure up to two years in advance of the closure with an accuracy of nearly 75 percent.

  9. A first course in structural equation modeling

    CERN Document Server

    Raykov, Tenko

    2012-01-01

    In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...

  10. A Study of Enhanced, Higher Order Boussinesq-Type Equations and Their Numerical Modelling

    DEFF Research Database (Denmark)

    Banijamali, Babak

    model is designated for the solution of higher-order Boussinesq-type equations, formulated in terms of the horizontal velocity at an arbitrary depth vector. Various discretisation techniques and grid definitions have been considered in this endeavour, undertaking a detailed analysis of the selected......This project has encompassed efforts in two separate veins: on the one hand, the acquiring of highly accurate model equations of the Boussinesq-type, and on the other hand, the theoretical and practical work in implementing such equations in the form of conventional numerical models, with obvious...... potential for applications to the realm of numerical modelling in coastal engineering. The derivation and analysis of several forms of higher-order in dispersion and non-linearity Boussinesq-type equations have been undertaken, obtaining and investigating the properties of a new and generalised class...

  11. Gas-evolution oscillators. 10. A model based on a delay equation

    Energy Technology Data Exchange (ETDEWEB)

    Bar-Eli, K.; Noyes, R.M. [Univ. of Oregon, Eugene, OR (United States)

    1992-09-17

    This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas.

  12. Gas-evolution oscillators. 10. A model based on a delay equation

    International Nuclear Information System (INIS)

    Bar-Eli, K.; Noyes, R.M.

    1992-01-01

    This paper develops a simplified method to model the behavior of a gas-evolution oscillator with two differential delay equations in two unknowns consisting of the population of dissolved molecules in solution and the pressure of the gas

  13. Parametric reduced models for the nonlinear Schrödinger equation.

    Science.gov (United States)

    Harlim, John; Li, Xiantao

    2015-05-01

    Reduced models for the (defocusing) nonlinear Schrödinger equation are developed. In particular, we develop reduced models that only involve the low-frequency modes given noisy observations of these modes. The ansatz of the reduced parametric models are obtained by employing a rational approximation and a colored-noise approximation, respectively, on the memory terms and the random noise of a generalized Langevin equation that is derived from the standard Mori-Zwanzig formalism. The parameters in the resulting reduced models are inferred from noisy observations with a recently developed ensemble Kalman filter-based parametrization method. The forecasting skill across different temperature regimes are verified by comparing the moments up to order four, a two-time correlation function statistics, and marginal densities of the coarse-grained variables.

  14. Structural Equation Model Trees

    Science.gov (United States)

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  15. A Kinetic Model for the Sedimentation of Rod--Like Particles

    KAUST Repository

    Helzel, Christiane; Tzavaras, Athanasios

    2015-01-01

    We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier-Stokes) equation and describing the motion of a suspension of rigid rods in gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. We provide a quantitative analysis of cluster formation. We derive a nonlinear moment closure model, which consists of evolution equations for the density and second order moments and that uses the structure of spherical harmonics to suggest a closure strategy. For a rectilinear flow we employ the moment closure together with a quasi-dynamic approximation to derive an effective equation. The effective equation is an advectiondiffusion equation with nonisotropic diffusion coupled to a Poisson equation, and belongs to the class of the so-called flux-limited Keller-Segel models. For shear flows, we provide an argument for the validity of the effective equation and perform numerical comparisons that indicate good agreement between the original system and the effective theory. For rectilinear flow we show numerical results which indicate that the quasi-dynamic provides accurate approximations. Finally, a linear stability analysis on the moment system shows that linear theory predicts a wavelength selection mechanism for the cluster width, provided that the Reynolds number is larger than zero.

  16. A Kinetic Model for the Sedimentation of Rod--Like Particles

    KAUST Repository

    Helzel, Christiane

    2015-10-12

    We consider a coupled system consisting of a kinetic equation coupled to a macroscopic Stokes (or Navier-Stokes) equation and describing the motion of a suspension of rigid rods in gravity. A reciprocal coupling leads to the formation of clusters: The buoyancy force creates a macroscopic velocity gradient that causes the microscopic particles to align so that their sedimentation reinforces the formation of clusters of higher particle density. We provide a quantitative analysis of cluster formation. We derive a nonlinear moment closure model, which consists of evolution equations for the density and second order moments and that uses the structure of spherical harmonics to suggest a closure strategy. For a rectilinear flow we employ the moment closure together with a quasi-dynamic approximation to derive an effective equation. The effective equation is an advectiondiffusion equation with nonisotropic diffusion coupled to a Poisson equation, and belongs to the class of the so-called flux-limited Keller-Segel models. For shear flows, we provide an argument for the validity of the effective equation and perform numerical comparisons that indicate good agreement between the original system and the effective theory. For rectilinear flow we show numerical results which indicate that the quasi-dynamic provides accurate approximations. Finally, a linear stability analysis on the moment system shows that linear theory predicts a wavelength selection mechanism for the cluster width, provided that the Reynolds number is larger than zero.

  17. Transport equation and shock waves

    International Nuclear Information System (INIS)

    Besnard, D.

    1981-04-01

    A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma

  18. A comparison of two endoscopic closures: over-the-scope clip (OTSC) versus KING closure (endoloop plus clips) in a randomized long-term experimental study

    Czech Academy of Sciences Publication Activity Database

    Doležel, R.; Ryska, O.; Kollár, M.; Juhásová, Jana; Kalvach, J.; Ryska, M.; Martínek, J.

    2016-01-01

    Roč. 30, č. 11 (2016), s. 4910-4916 ISSN 0930-2794 R&D Projects: GA MZd(CZ) NT13634; GA MŠk ED2.1.00/03.0124 Institutional support: RVO:67985904 Keywords : NOTES * endoscopic closure * KING closure * over-the-scope clip Subject RIV: FJ - Surgery incl. Transplants Impact factor: 3.747, year: 2016

  19. Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

    Science.gov (United States)

    Avissar, Roni; Chen, Fei

    1993-01-01

    Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes

  20. Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations.

    Science.gov (United States)

    Meffin, Hamish; Tahayori, Bahman; Grayden, David B; Burkitt, Anthony N

    2012-12-01

    Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace's equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite's membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

  1. Hanford Patrol Academy Demolition Sites Closure Plan

    International Nuclear Information System (INIS)

    1992-11-01

    From 1975 to 1991 the Hanford Patrol Academy Demolition Sites (HPADS) were used for demolition events. These demolition events were a form of thermal treatment for spent or abandoned chemical waste. Because the HPADS will no longer be used for this thermal activity, the sites will be closed. Closure will be conducted pursuant to the requirements of the Washington State Department of Ecology (Ecology) Dangerous Waste Regulations, Washington Administrative Code (WAC) 173-303-610 and 40 CFR 270.1. Closure also will satisfy closure requirements of WAC 173-303-680 and for the thermal treatment closure requirements of 40 CFR 265.381. This closure plan presents a description of the HPADS, the history of the waste treated, and the approach that will be followed to close the HPADS. Because dangerous waste does not include the source, special nuclear, and by-product material components of mixed waste, radionuclides are not within the scope of WAC 173-303 or of this closure plan. The information on radionuclides is provided only for general knowledge where appropriate. Only dangerous constituents derived from HPADS operations will be addressed in this closure plan in accordance with WAC 173-303-610(2)(b)(i). The HPADS are actually two distinct soil closure areas within the Hanford Patrol Academy training area

  2. Generalized continuity equations from two-field Schrödinger Lagrangians

    Science.gov (United States)

    Spourdalakis, A. G. B.; Pappas, G.; Morfonios, C. Â. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.

    2016-11-01

    A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of P T -symmetric quantum mechanics and paraxial optics.

  3. Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear

    Directory of Open Access Journals (Sweden)

    H. Z. Baumert

    2009-03-01

    Full Text Available This paper extends a turbulence closure-like model for stably stratified flows into a new dynamic domain in which turbulence is generated by internal gravity waves rather than mean shear. The model turbulent kinetic energy (TKE, K balance, its first equation, incorporates a term for the energy transfer from internal waves to turbulence. This energy source is in addition to the traditional shear production. The second variable of the new two-equation model is the turbulent enstrophy (Ω. Compared to the traditional shear-only case, the Ω-equation is modified to account for the effect of the waves on the turbulence time and space scales. This modification is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean shear when turbulence is produced exclusively by internal waves. This paper is part 1 of a continuing theoretical development. It accounts for mean shear- and internal wave-driven mixing only in the two limits of mean shear and no waves and waves but no mean shear, respectively.

    The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000b. At small energy density E of the internal wave field, the turbulent dissipation rate (ε scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. This is observed, for example, in the highly energetic tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.

  4. Evaluation of the Momentum Closure Schemes in MPAS-Ocean

    Science.gov (United States)

    Zhao, Shimei; Liu, Yudi; Liu, Wei

    2018-04-01

    In order to compare and evaluate the performances of the Laplacian viscosity closure, the biharmonic viscosity closure, and the Leith closure momentum schemes in the MPAS-Ocean model, a variety of physical quantities, such as the relative reference potential energy (RPE) change, the RPE time change rate (RPETCR), the grid Reynolds number, the root mean square (RMS) of kinetic energy, and the spectra of kinetic energy and enstrophy, are calculated on the basis of results of a 3D baroclinic periodic channel. Results indicate that: 1) The RPETCR demonstrates a saturation phenomenon in baroclinic eddy tests. The critical grid Reynolds number corresponding to RPETCR saturation differs between the three closures: the largest value is in the biharmonic viscosity closure, followed by that in the Laplacian viscosity closure, and that in the Leith closure is the smallest. 2) All three closures can effectively suppress spurious dianeutral mixing by reducing the grid Reynolds number under sub-saturation conditions of the RPETCR, but they can also damage certain physical processes. Generally, the damage to the rotation process is greater than that to the advection process. 3) The dissipation in the biharmonic viscosity closure is strongly dependent on scales. Most dissipation concentrates on small scales, and the energy of small-scale eddies is often transferred to large-scale kinetic energy. The viscous dissipation in the Laplacian viscosity closure is the strongest on various scales, followed by that in the Leith closure. Note that part of the small-scale kinetic energy is also transferred to large-scale kinetic energy in the Leith closure. 4) The characteristic length scale L and the dimensionless parameter D in the Leith closure are inherently coupled. The RPETCR is inversely proportional to the product of D and L. When the product of D and L is constant, both the simulated RPETCR and the inhibition of spurious dianeutral mixing are the same in all tests using the Leith

  5. Numerical Predictions of Bubbly Two-Phase Flows with OpenFOAM

    Directory of Open Access Journals (Sweden)

    Edouard Michta

    2012-12-01

    Full Text Available A new model for simulation of bubbly two-phase flows has been developed and implemented into an open-source Computational Fluid Dynamics (CFD code OpenFOAM. The model employs the two-fluid framework with closure relationships for the interfacial momentum transfer. The bubble size is calculated based on the solution of the transport equation of the interfacial area concentration. The predictions are validated against selected data obtained in the DEDALE experiment and containing the measured void fraction, the phasic velocities and the interfacial area concentration. In general, good agreement between calculated and measured data is demonstrated; however, the relative phasic velocity is systematically over-predicted. The levels of void fraction and the observed wall void peaking are well captured in the calculations.

  6. Methods for the solution of the two-dimensional radiation-transfer equation

    International Nuclear Information System (INIS)

    Weaver, R.; Mihalas, D.; Olson, G.

    1982-01-01

    We use the variable Eddington factor (VEF) approximation to solve the time-dependent two-dimensional radiation transfer equation. The transfer equation and its moments are derived for an inertial frame of reference in cylindrical geometry. Using the VEF tensor to close the moment equations, we manipulate them into a combined moment equation that results in an energy equation, which is automatically flux limited. There are two separable facets in this method of solution. First, given the variable Eddington tensor, we discuss the efficient solution of the combined moment matrix equation. The second facet of the problem is the calculation of the variable Eddington tensor. Several options for this calculation, as well as physical limitations on the use of locally-calculated Eddington factors, are discussed

  7. Turbulence modeling for mass transfer enhancement by separation and reattachment with two-equation eddy-viscosity models

    International Nuclear Information System (INIS)

    Xiong Jinbiao; Koshizuka, Seiichi; Sakai, Mikio

    2011-01-01

    Highlights: → We selected and evaluated five two-equation eddy-viscosity turbulence models for modeling the separated and reattaching flow. → The behavior of the models in the simple flow is not consistent with that in the separated and reattaching flow. → The Abe-Kondoh-Nagano model is the best one among the selected model. → Application of the stress limiter and the Kato-Launder modification in the Abe-Kondoh-Nagano model helps to improve prediction of the peak mass transfer coefficient in the orifice flow. → The value of turbulent Schmidt number is investigated. - Abstract: The prediction of mass transfer rate is one of the key elements for estimation of the flow accelerated corrosion (FAC) rate. Three low Reynolds number (LRN) k-ε models (Lam-Bremhorst (LB), Abe-Kondoh-Nagano (AKN) and Hwang-Lin (HL)), one LRN k-ω (Wilcox, WX) model and the k-ω SST model are tested for the computation of the high Schmidt number mass transfer, especially in the flow through an orifice. The models are tested in the computation of three types of flow: (1) the fully developed pipe flow, (2) the flow over a backward facing step, (3) the flow through an orifice. The HL model shows a good performance in predicting mass transfer in the fully developed pipe flow but fails to give reliable prediction in the flow through an orifice. The WX model and the k-ω SST model underpredict the mass transfer rate in the flow types 1 and 3. The LB model underestimates the mass transfer in the flow type 1, but shows abnormal behavior at the reattaching point in type 3. Synthetically evaluating all the models in all the computed case, the AKN model is the best one; however, the prediction is still not satisfactory. In the evaluation in the flow over a backward facing step shows k-ω SST model shows superior performance. This is interpreted as an implication that the combination of the k-ε model and the stress limiter can improve the model behavior in the recirculation bubble. Both the

  8. Modeling of combined effects of divertor closure and advanced magnetic configuration on detachment in DIII-D by SOLPS

    Science.gov (United States)

    Si, H.; Guo, H. Y.; Covele, B.; Leonard, A. W.; Watkins, J. G.; Thomas, D.; Ding, R.

    2018-05-01

    One of the major challenges facing the design and operation of next-step high-power steady-state fusion devices is to develop a divertor solution for handling power exhaust, while ensuring acceptable divertor target plate erosion, which necessitates access to divertor detachment at relative low main plasma densities compatible with current drive and high plasma confinement. Detailed modeling with SOLPS is carried out to examine the effect of divertor closure on detachment with the normal single null divertor (SD) configuration, as well as one of the advanced divertor configurations, such as x-divertor (XD) respectively. The SOLPS modeling for a high confinement plasma in DIII-D finds that increasing divertor closure with SD reduces the upstream separatrix density at the onset of detachment from 1.18× {{10}19} {{m}-3} to 0.88× {{10}19} {{m}-3} . Moreover, coupling the divertor closure with XD further promotes the onset of divertor detachment at a still lower upstream separatrix density, down to the value of 0.67× {{10}19} {{m}-3} , thus, showing that divertor closure and advanced magnetic configuration can work synergistically to facilitate divertor detachment.

  9. Influence of Closure & Non-Closure of the Visceral and Parietal Peritoneum on Post Cesarean Morbidity

    Directory of Open Access Journals (Sweden)

    Tabasi Z.

    2010-01-01

    Full Text Available AbstractBackground and Objectives: One of the most important issues in promoting mother and child health is reducing the morbidity rate after cesarean section. The aim of this study was to investigate the influence of closure and non-closure of the visceral and parietal peritoneum on post cesarean morbidity in women attending Shabihkhani Maternity Hospital in Kashan, Iran.Methods: This study was conducted with a single blind randomized clinical trial method on 100 parturient women that underwent emergency or elective cesarean section. Patients with previous cesarean section and or abdominal surgery, diseases such as hypertension, diabetes mellitus and premature rupture of membrane and pre operative bleeding, were excluded from this study. Then, the participants were randomly divided into two groups: in one group both peritoneal layers were closed while in the other group, they were not closed. Post operative morbidity including fever, bleeding, post operative pain, analgesic consumption and time of operation were assessed. Data were analyzed with t-tests, and χ2 and a P<0.05 were considered significant.Results: In this study, there were no significant differences between the two groups with respect to age, gestational age, the reason for caesarean section and gravidity, nor were there any differences with respect to the incidence of fever or bleeding and was similar between the two groups, but there was a significant difference between the two groups regarding to feeling of severe pain (P=0.0003, analgesic consumption (P=0.0003 and time of operation (P=0.004. In the non-closure group, dose of analgesic drugs, pain severity and time of operation were less than those of the other group.Conclusion: The Findings showed that non-closure of peritoneal layers as a shorter and simpler procedure has no influence on increasing post cesarean morbidity. Therefore, due to maternal health promotion and early neonatal breastfeeding, non closure of peritoneal

  10. Structural equations for Killing tensors of order two. II

    International Nuclear Information System (INIS)

    Hauser, I.; Malhiot, R.J.

    1975-01-01

    In a preceding paper, a new form of the structural equations for any Killing tensor of order two have been derived; these equations constitute a system analogous to the Killing vector equations Nabla/sub alpha/ K/sub beta/ = ω/sub alpha beta/ = -ω/sub beta alpha/ and Nabla/sub gamma/ ω/sub alpha beta = R/sub alpha beta gamma delta/ K/sup delta/. The first integrability condition for the Killing tensor structural equations is now derived. The structural equations and the integrability condition have forms which can readily be expressed in terms of a null tetrad to furnish a Killing tensor parallel of the Newman--Penrose equations; this is briefly described. The integrability condition implies the new result, for any given space--time, that the dimension of the set of second-order Killing tensors attains its maximum possible value of 50 only if the space--time is of constant curvature. Potential applications of the structural equations are discussed

  11. Geomorphic dam-break flows. Part I: conceptual model

    OpenAIRE

    Leal, JGAB; Ferreira, RML; Cardoso, AH

    2010-01-01

    Proceedings of the Institution of Civil Engineers - Water Management 163 Issue WM6 This paper presents a one-dimensional conceptual model for simulating geomorphic dam-break flows. The model is based on conservation laws drawn from continuum mixture theory that are integrated over the flow depth,assuming that the f10w is composed of two transport layers. Closure equations were derived from the review and reanalysis of previous studies on granular flow,debris f10w and sheet flow. The sedime...

  12. Continuum methods of physical modeling continuum mechanics, dimensional analysis, turbulence

    CERN Document Server

    Hutter, Kolumban

    2004-01-01

    The book unifies classical continuum mechanics and turbulence modeling, i.e. the same fundamental concepts are used to derive model equations for material behaviour and turbulence closure and complements these with methods of dimensional analysis. The intention is to equip the reader with the ability to understand the complex nonlinear modeling in material behaviour and turbulence closure as well as to derive or invent his own models. Examples are mostly taken from environmental physics and geophysics.

  13. Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration

    KAUST Repository

    Vignal, Philippe

    2015-06-01

    In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.

  14. An Optimization Principle for Deriving Nonequilibrium Statistical Models of Hamiltonian Dynamics

    Science.gov (United States)

    Turkington, Bruce

    2013-08-01

    A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. Given a vector of resolved variables, selected to describe the macroscopic state of the system, a family of quasi-equilibrium probability densities on phase space corresponding to the resolved variables is employed as a statistical model, and the evolution of the mean resolved vector is estimated by optimizing over paths of these densities. Specifically, a cost function is constructed to quantify the lack-of-fit to the microscopic dynamics of any feasible path of densities from the statistical model; it is an ensemble-averaged, weighted, squared-norm of the residual that results from submitting the path of densities to the Liouville equation. The path that minimizes the time integral of the cost function determines the best-fit evolution of the mean resolved vector. The closed reduced equations satisfied by the optimal path are derived by Hamilton-Jacobi theory. When expressed in terms of the macroscopic variables, these equations have the generic structure of governing equations for nonequilibrium thermodynamics. In particular, the value function for the optimization principle coincides with the dissipation potential that defines the relation between thermodynamic forces and fluxes. The adjustable closure parameters in the best-fit reduced equations depend explicitly on the arbitrary weights that enter into the lack-of-fit cost function. Two particular model reductions are outlined to illustrate the general method. In each example the set of weights in the optimization principle contracts into a single effective closure parameter.

  15. Numerical simulations of air–water cap-bubbly flows using two-group interfacial area transport equation

    International Nuclear Information System (INIS)

    Wang, Xia; Sun, Xiaodong

    2014-01-01

    Highlights: • Two-group interfacial area transport equation was implemented into a three-field two-fluid model in Fluent. • Numerical model was developed for cap-bubbly flows in a narrow rectangular flow channel. • Numerical simulations were performed for cap-bubbly flows with uniform void inlets and with central peaked void inlets. • Code simulations showed a significant improve over the conventional two-fluid model. - Abstract: Knowledge of cap-bubbly flows is of great interest due to its role in understanding of the flow regime transition from bubbly to slug or churn-turbulent flows. One of the key characteristics of such flows is the existence of bubbles in different sizes and shapes associated with their distinctive dynamic natures. This important feature is, however, generally not well captured by many available two-phase flow modeling approaches. In this study, a modified two-fluid model, namely a three-field, two-fluid model, is proposed. In this model, bubbles are categorized into two groups, i.e., spherical/distorted bubbles as Group-1 while cap/churn-turbulent bubbles as Group-2. A two-group interfacial area transport equation (IATE) is implemented to describe dynamic changes of interfacial structure in each bubble group, resulting from intra- and inter-group interactions and phase changes due to evaporation and condensation. Attention is also paid to appropriate constitutive relations of the interfacial transfers due to mechanical and thermal non-equilibrium between the different fields. The proposed three-field, two-fluid model is used to predict the phase distributions of adiabatic air–water flows in a confined rectangular duct. Good agreement between the simulation results from the proposed model and relevant experimental data indicates that the proposed model is promising as an improved computational tool for two-phase cap-bubbly flow simulations in rectangular flow ducts

  16. Using Difference Equation to Model Discrete-time Behavior in System Dynamics Modeling

    NARCIS (Netherlands)

    Hesan, R.; Ghorbani, A.; Dignum, M.V.

    2014-01-01

    In system dynamics modeling, differential equations have been used as the basic mathematical operator. Using difference equation to build system dynamics models instead of differential equation, can be insightful for studying small organizations or systems with micro behavior. In this paper we

  17. One-dimensional integral equations for a system of three identical particles in the boundary condition models and the possibility of changing the off-shell behaviour of the two-particle t-matrix

    International Nuclear Information System (INIS)

    Efimov, V.N.; Schulz, H.

    1976-01-01

    It is shown that in the framework of the boundary condition models (BCM) for the two-particle interaction the Schroedinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle t-matrix and therefore to simulate three particle effects. (Auth.)

  18. A Two-Stage Estimation Method for Random Coefficient Differential Equation Models with Application to Longitudinal HIV Dynamic Data.

    Science.gov (United States)

    Fang, Yun; Wu, Hulin; Zhu, Li-Xing

    2011-07-01

    We propose a two-stage estimation method for random coefficient ordinary differential equation (ODE) models. A maximum pseudo-likelihood estimator (MPLE) is derived based on a mixed-effects modeling approach and its asymptotic properties for population parameters are established. The proposed method does not require repeatedly solving ODEs, and is computationally efficient although it does pay a price with the loss of some estimation efficiency. However, the method does offer an alternative approach when the exact likelihood approach fails due to model complexity and high-dimensional parameter space, and it can also serve as a method to obtain the starting estimates for more accurate estimation methods. In addition, the proposed method does not need to specify the initial values of state variables and preserves all the advantages of the mixed-effects modeling approach. The finite sample properties of the proposed estimator are studied via Monte Carlo simulations and the methodology is also illustrated with application to an AIDS clinical data set.

  19. Structural-equation models of migration: an example from the Upper Midwest USA.

    Science.gov (United States)

    Cadwallader, M

    1985-01-01

    "To date, most migration models have been specified in terms of a single equation, whereby a set of regional characteristics are used to predict migration rates for various kinds of spatial units. These models are inadequate in at least two respects. First, they omit any causal links between the explanatory variables, thus ignoring indirect effects between these variables and migration. Second, they ignore the possibility of reciprocal causation, or feedback effects, between migration and the explanatory variables...." The author uses data for State Economic Areas to construct a path model and simultaneous-equation model to identify both indirect and feedback effects on migration in the Upper Midwestern United States. "On the basis of the path model, it is suggested that the direct effects of many variables on migration are at least partially offset by the indirect effects, whereas the simultaneous-equation model emphasizes the reciprocal relationship between income and migration." excerpt

  20. Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

    Science.gov (United States)

    Ablowitz, Mark; Biondini, Gino; Wang, Qiao

    2017-09-01

    Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

  1. Two-phase flow model with nonequilibrium and critical flow

    International Nuclear Information System (INIS)

    Sureau, H.; Houdayer, G.

    1976-01-01

    The model proposed includes the three conservation equations (mass, momentum, energy) applied to the two phase flows and a fourth partial derivative equation which takes into account the nonequilibriums and describes the mass transfer process. With this model, the two phase critical flow tests performed on the Moby-Dick loop (CENG) with several geometries, are interpreted by a unique law. Extrapolations to industrial dimension problems show that geometry and size effects are different from those obtained with earlier models (Zaloudek, Moody, Fauske) [fr

  2. Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

    Science.gov (United States)

    Hwang, Chi-en; Cleary, T. Anne

    The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

  3. Critical behavior in two-dimensional quantum gravity and equations of motion of the string

    International Nuclear Information System (INIS)

    Das, S.R.; Dhar, A.; Wadia, S.R.

    1990-01-01

    The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discuss an example of such a trajectory in the space containing the c ≤ 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models

  4. Material balance and diets in biological life support systems: a relationship with a coefficient of closure

    Science.gov (United States)

    Manukovsky, N. S.; Kovalev, V. S.; Somova, L. A.

    Biological life support systems (BLSS) of various coefficients of closure were considered The basic coefficient of closure was accepted equal to 66%. With increase in coefficient of closure food requirements for the greater degree should be satisfied due to the manufacture of food inside the BLSS. In this connection food values were estimated both in the basic variant, and in those with increased coefficients of closure. Metabolic massflow rates were estimated at the input and output of the BLSS as well as inside it. Human massflow rates were submitted on the basis of characteristics of the 'reference man'. Stoichiometric synthesis - degradation equations of organic substances in the BLSS were obtained. A problem of nitrogen imbalance was shown to occur under an incomplete BLSS closure. To compensate losses of nitrogen with urine and feces, food and nitrogen-containing additives should be introduced into the BLSS.

  5. Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

    Science.gov (United States)

    Cheung, Mike W.-L.; Cheung, Shu Fai

    2016-01-01

    Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

  6. Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

    Science.gov (United States)

    Wang, Chi R.

    2005-01-01

    This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation

  7. Dyson-Schwinger equations for the non-linear σ-model

    International Nuclear Information System (INIS)

    Drouffe, J.M.; Flyvbjerg, H.

    1989-08-01

    Dyson-Schwinger equations for the O(N)-symmetric non-linear σ-model are derived. They are polynomials in N, hence 1/N-expanded ab initio. A finite, closed set of equations is obtained by keeping only the leading term and the first correction term in this 1/N-series. These equations are solved numerically in two dimensions on square lattices measuring 50x50, 100x100, 200x200, and 400x400. They are also solved analytically at strong coupling and at weak coupling in a finite volume. In these two limits the solution is asymptotically identical to the exact strong- and weak-coupling series through the first three terms. Between these two limits, results for the magnetic susceptibility and the mass gap are identical to the Monte Carlo results available for N=3 and N=4 within a uniform systematic error of O(1/N 3 ), i.e. the results seem good to O(1/N 2 ), though obtained from equations that are exact only to O(1/N). This is understood by seeing the results as summed infinite subseries of the 1/N-series for the exact susceptibility and mass gap. We conclude that the kind of 1/N-expansion presented here converges as well as one might ever hope for, even for N as small as 3. (orig.)

  8. Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics

    Directory of Open Access Journals (Sweden)

    Weam Alharbi

    2018-04-01

    Full Text Available A telegraph equation is believed to be an appropriate model of population dynamics as it accounts for the directional persistence of individual animal movement. Being motivated by the problem of habitat fragmentation, which is known to be a major threat to biodiversity that causes species extinction worldwide, we consider the reaction–telegraph equation (i.e., telegraph equation combined with the population growth on a bounded domain with the goal to establish the conditions of species survival. We first show analytically that, in the case of linear growth, the expression for the domain’s critical size coincides with the critical size of the corresponding reaction–diffusion model. We then consider two biologically relevant cases of nonlinear growth, i.e., the logistic growth and the growth with a strong Allee effect. Using extensive numerical simulations, we show that in both cases the critical domain size of the reaction–telegraph equation is larger than the critical domain size of the reaction–diffusion equation. Finally, we discuss possible modifications of the model in order to enhance the positivity of its solutions.

  9. A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops.

    Directory of Open Access Journals (Sweden)

    Réka Albert

    2017-09-01

    Full Text Available Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA. This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs of the protein kinase OPEN STOMATA 1 (OST1 and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich component as well as its in- and out-components. The network's domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed

  10. A new discrete dynamic model of ABA-induced stomatal closure predicts key feedback loops.

    Science.gov (United States)

    Albert, Réka; Acharya, Biswa R; Jeon, Byeong Wook; Zañudo, Jorge G T; Zhu, Mengmeng; Osman, Karim; Assmann, Sarah M

    2017-09-01

    Stomata, microscopic pores in leaf surfaces through which water loss and carbon dioxide uptake occur, are closed in response to drought by the phytohormone abscisic acid (ABA). This process is vital for drought tolerance and has been the topic of extensive experimental investigation in the last decades. Although a core signaling chain has been elucidated consisting of ABA binding to receptors, which alleviates negative regulation by protein phosphatases 2C (PP2Cs) of the protein kinase OPEN STOMATA 1 (OST1) and ultimately results in activation of anion channels, osmotic water loss, and stomatal closure, over 70 additional components have been identified, yet their relationships with each other and the core components are poorly elucidated. We integrated and processed hundreds of disparate observations regarding ABA signal transduction responses underlying stomatal closure into a network of 84 nodes and 156 edges and, as a result, established those relationships, including identification of a 36-node, strongly connected (feedback-rich) component as well as its in- and out-components. The network's domination by a feedback-rich component may reflect a general feature of rapid signaling events. We developed a discrete dynamic model of this network and elucidated the effects of ABA plus knockout or constitutive activity of 79 nodes on both the outcome of the system (closure) and the status of all internal nodes. The model, with more than 1024 system states, is far from fully determined by the available data, yet model results agree with existing experiments in 82 cases and disagree in only 17 cases, a validation rate of 75%. Our results reveal nodes that could be engineered to impact stomatal closure in a controlled fashion and also provide over 140 novel predictions for which experimental data are currently lacking. Noting the paucity of wet-bench data regarding combinatorial effects of ABA and internal node activation, we experimentally confirmed several predictions

  11. Integrable discretizations for the short-wave model of the Camassa-Holm equation

    International Nuclear Information System (INIS)

    Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

    2010-01-01

    The link between the short-wave model of the Camassa-Holm equation (SCHE) and bilinear equations of the two-dimensional Toda lattice equation is clarified. The parametric form of the N-cuspon solution of the SCHE in Casorati determinant is then given. Based on the above finding, integrable semi-discrete and full-discrete analogues of the SCHE are constructed. The determinant solutions of both semi-discrete and fully discrete analogues of the SCHE are also presented.

  12. Comparison of two mathematical models for describing heat-induced cell killing

    International Nuclear Information System (INIS)

    Roti Roti, J.L.; Henle, K.J.

    1980-01-01

    A computer-based minimization algorithm is utilized to obtain the optimum fits of two models to hyperthermic cell killing data. The models chosen are the multitarget, single-hit equation, which is in general use, and the linear-quadratic equation, which has been applied to cell killing by ionizing irradiation but not to heat-induced cell killing. The linear-quadratic equation fits hyperthermic cell killing data as well as the multitarget, single-hit equation. Both parameters of the linear-quadratic equation obey the Arrhenius law, whereas only one of the two parameters of the multitarget, single-hit equation obeys the Arrhenius law. Thus the linear-quadratic function can completely define cell killing as a function of both time and temperature. In addition, the linear-quadratic model will provide a simplified approach to the study of the synergism between heat and X irradiation

  13. Solution of spatially homogeneous model Boltzmann equations by means of Lie groups of transformations

    International Nuclear Information System (INIS)

    Foroutan, A.

    1992-05-01

    The essential mathematical challenge in transport theory is based on the nonlinearity of the integro-differential equations governing classical thermodynamic systems on molecular kinetic level. It is the aim of this thesis to gain exact analytical solutions to the model Boltzmann equation suggested by Tjon and Wu. Such solutions afford a deeper insight into the dynamics of rarefied gases. Tjon and Wu have provided a stochastic model of a Boltzmann equation. Its transition probability depends only on the relative speed of the colliding particles. This assumption leads in the case of two translational degrees of freedom to an integro-differential equation of convolution type. According to this convolution structure the integro-differential equation is Laplace transformed. The result is a nonlinear partial differential equation. The investigation of the symmetries of this differential equation by means of Lie groups of transformation enables us to transform the originally nonlinear partial differential equation into ordinary differential equation into ordinary differential equations of Bernoulli type. (author)

  14. Introduction to computation and modeling for differential equations

    CERN Document Server

    Edsberg, Lennart

    2008-01-01

    An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

  15. Radioactive waste disposal sites: Two successful closures at Tinker Air Force Base

    International Nuclear Information System (INIS)

    McKenzie, G.; Mohatt, J.V.; Kowall, S.J.; Jarvis, M.F.

    1993-06-01

    This article describes remediation and closure of two radioactive waste disposal sites at Tinker Air Force Base, Oklahoma, making them exemption regulatory control. The approach consisted of careful exhumation and assessment of soils in sites expected to be contaminated based on historical documentation, word of mouth, and geophysical surveys; removal of buried objects that had gamma radiation exposure levels above background; and confirmation that the soil containing residual radium-226 was below an activity level equal to no more than a 10 mrem/yr annual dose equivalent. In addition, 4464 kg of chemically contaminated excavated soils were removed for disposal. After remediation, the sites met standards for unrestricted use. These sites were two of the first three Air Force radioactive disposal sites to be closed and were the first to be closed under Draft NUREG/CR-5512

  16. Surgical repair of tricuspid valve leaflet tear following percutaneous closure of perimembranous ventricular septal defect using Amplatzer duct occluder I: Report of two cases

    Directory of Open Access Journals (Sweden)

    Saatchi Mahesh Kuwelker

    2017-01-01

    Full Text Available Tricuspid valve (TV injury following transcatheter closure of perimembranous ventricular septal defect (PMVSD with Amplatzer ductal occluder I (ADO I, requiring surgical repair, is rare. We report two cases of TV tear involving the anterior and septal leaflets following PMVSD closure using ADO I. In both the patients, the subvalvular apparatus remained unaffected. The patients presented with severe tricuspid regurgitation (TR 6 weeks and 3 months following the device closure. They underwent surgical repair with patch augmentation of the TV leaflets. Postoperatively, both are asymptomatic with a mild residual TR.

  17. One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

    Science.gov (United States)

    Sakaguchi, Hidetsugu; Ishibashi, Kazuya

    2018-06-01

    We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

  18. Phenomenological neutron star equations of state. 3-window modeling of QCD matter

    Energy Technology Data Exchange (ETDEWEB)

    Kojo, Toru [University of Illinois at Urbana-Champaign, Department of Physics, Urbana, Illinois (United States)

    2016-03-15

    We discuss the 3-window modeling of cold, dense QCD matter equations of state at density relevant to neutron star properties. At low baryon density, n{sub B} equations of state that are constrained by empirical observations at density n{sub B} ∝ n{sub s} and neutron star radii. At high density, n{sub B} >or similar 5n{sub s}, we use the percolated quark matter equations of state which must be very stiff to pass the two-solar mass constraints. The intermediate domain at 2 equations of state are inferred by interpolating hadronic and percolated quark matter equations of state. Possible forms of the interpolation are severely restricted by the condition on the (square of) speed of sound, 0 ≤ c{sub s}{sup 2} ≤ 1. The characteristics of the 3-window equation of state are compared with those of conventional hybrid and self-bound quark matters. Using a schematic quark model for the percolated domain, it is argued that the two-solar mass constraint requires the model parameters to be as large as their vacuum values, indicating that the gluon dynamics remains strongly non-perturbative to n{sub B} ∝ 10n{sub s}. The hyperon puzzle is also briefly discussed in light of quark descriptions. (orig.)

  19. Percutaneous closure of a large aortic paravalvular leak using two duct occluder devices

    Directory of Open Access Journals (Sweden)

    Navaneetha Sasikumar

    2013-05-01

    Full Text Available A 21-year-old male presented with severe aortic paravalvular leak. He had undergone three cardiac surgeries and also had chronic kidney disease. It was decided for a trans-catheter closure owing to the risks of a fourth surgery and co-morbidity. The device was sized based on angiogram, balloon sizing and two dimensional transesophageal echo. There was significant residual leak after deployment of first device. Hence the defect was re-crossed and two duct occluder devices were positioned across the leak from two arterial access. After confirming position and satisfactory reduction in paravalvular leak, the devices were released in tandem. There was near abolition of leak. The patient is asymptomatic at three months follow up. Larger paravalvular leaks are better addressed with two devices of smaller size rather than a single large device. Technical considerations while deploying multiple devices are discussed.

  20. Applying an economical scale-aware PDF-based turbulence closure model in NOAA NCEP GCMs.

    Science.gov (United States)

    Belochitski, A.; Krueger, S. K.; Moorthi, S.; Bogenschutz, P.; Cheng, A.

    2017-12-01

    A novel unified representation of sub-grid scale (SGS) turbulence, cloudiness, and shallow convection is being implemented into the NOAA NCEP Global Forecasting System (GFS) general circulation model. The approach, known as Simplified High Order Closure (SHOC), is based on predicting a joint PDF of SGS thermodynamic variables and vertical velocity, and using it to diagnose turbulent diffusion coefficients, SGS fluxes, condensation, and cloudiness. Unlike other similar methods, comparatively few new prognostic variables needs to be introduced, making the technique computationally efficient. In the base version of SHOC it is SGS turbulent kinetic energy (TKE), and in the developmental version — SGS TKE, and variances of total water and moist static energy (MSE). SHOC is now incorporated into a version of GFS that will become a part of the NOAA Next Generation Global Prediction System based around NOAA GFDL's FV3 dynamical core, NOAA Environmental Modeling System (NEMS) coupled modeling infrastructure software, and a set novel physical parameterizations. Turbulent diffusion coefficients computed by SHOC are now used in place of those produced by the boundary layer turbulence and shallow convection parameterizations. Large scale microphysics scheme is no longer used to calculate cloud fraction or the large-scale condensation/deposition. Instead, SHOC provides these quantities. Radiative transfer parameterization uses cloudiness computed by SHOC. An outstanding problem with implementation of SHOC in the NCEP global models is excessively large high level tropical cloudiness. Comparison of the moments of the SGS PDF diagnosed by SHOC to the moments calculated in a GigaLES simulation of tropical deep convection case (GATE), shows that SHOC diagnoses too narrow PDF distributions of total cloud water and MSE in the areas of deep convective detrainment. A subsequent sensitivity study of SHOC's diagnosed cloud fraction (CF) to higher order input moments of the SGS PDF

  1. On the modelling and the analysis of two-phase flow instabilities in pipeline-riser systems; Modelisation et analyse des instabilites d'ecoulements diphasiques dans les conduites petrolieres du type pipeline-riser

    Energy Technology Data Exchange (ETDEWEB)

    Zakarian, E.

    2000-03-10

    Recent estimations predict that over half the remaining offshore oil and gas reserves are located in deep water and marginal fields. For such reserves, economic recovery methods are required. Then, multiphase flows are transported within pipelines and separated on treatment platforms built in shallow water or processed in onshore facilities. Unfortunately, hydrodynamic instabilities may occur whenever gas and liquid flow in a pipeline, generating serious operating problems. This dissertation presents a new way to model two-phase flows in pipelines such as pipeline-riser systems. Equations are algebraic and differential. Their smoothness depends on the closure laws of the problem such as slip or friction laws. Smooth forms of these closure laws are presented for the first time in this dissertation. Therefore, a mathematical analysis of our model fits into a classical frame: a linear analysis leads to an analytical expression of the boundary between stable and unstable flows. A nonlinear analysis provides for the first time, the bifurcation curves of gas-liquid flows in pipe-riser systems, locally round their stability boundary. (author)

  2. Modeling of bubble coalescence and disintegration in confined upward two-phase flow

    International Nuclear Information System (INIS)

    Sun Xiaodong; Kim, Seungjin; Ishii, Mamoru; Beus, Stephen G.

    2004-01-01

    This paper presents the modeling of bubble interaction mechanisms in the two-group interfacial area transport equation (IATE) for confined gas-liquid two-phase flow. The transport equation is applicable to bubbly, cap-turbulent, and churn-turbulent flow regimes. In the two-group IATE, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 and cap/slug/churn-turbulent bubbles as Group 2. Thus, two sets of equations are used to describe the generation and destruction rates of bubble number density, void fraction, and interfacial area concentration for the two groups of bubbles due to bubble expansion and compression, coalescence and disintegration, and phase change. Five major bubble interaction mechanisms are identified for the gas-liquid two-phase flow of interest, and are analytically modeled as the source/sink terms for the transport equation in the confined flow. These models include both intra-group and inter-group bubble interactions

  3. Fitting ARMA Time Series by Structural Equation Models.

    Science.gov (United States)

    van Buuren, Stef

    1997-01-01

    This paper outlines how the stationary ARMA (p,q) model (G. Box and G. Jenkins, 1976) can be specified as a structural equation model. Maximum likelihood estimates for the parameters in the ARMA model can be obtained by software for fitting structural equation models. The method is applied to three problem types. (SLD)

  4. The reservoir model: a differential equation model of psychological regulation.

    Science.gov (United States)

    Deboeck, Pascal R; Bergeman, C S

    2013-06-01

    Differential equation models can be used to describe the relationships between the current state of a system of constructs (e.g., stress) and how those constructs are changing (e.g., based on variable-like experiences). The following article describes a differential equation model based on the concept of a reservoir. With a physical reservoir, such as one for water, the level of the liquid in the reservoir at any time depends on the contributions to the reservoir (inputs) and the amount of liquid removed from the reservoir (outputs). This reservoir model might be useful for constructs such as stress, where events might "add up" over time (e.g., life stressors, inputs), but individuals simultaneously take action to "blow off steam" (e.g., engage coping resources, outputs). The reservoir model can provide descriptive statistics of the inputs that contribute to the "height" (level) of a construct and a parameter that describes a person's ability to dissipate the construct. After discussing the model, we describe a method of fitting the model as a structural equation model using latent differential equation modeling and latent distribution modeling. A simulation study is presented to examine recovery of the input distribution and output parameter. The model is then applied to the daily self-reports of negative affect and stress from a sample of older adults from the Notre Dame Longitudinal Study on Aging. (PsycINFO Database Record (c) 2013 APA, all rights reserved).

  5. Infering and Calibrating Triadic Closure in a Dynamic Network

    Science.gov (United States)

    Mantzaris, Alexander V.; Higham, Desmond J.

    In the social sciences, the hypothesis of triadic closure contends that new links in a social contact network arise preferentially between those who currently share neighbours. Here, in a proof-of-principle study, we show how to calibrate a recently proposed evolving network model to time-dependent connectivity data. The probabilistic edge birth rate in the model contains a triadic closure term, so we are also able to assess statistically the evidence for this effect. The approach is shown to work on data generated synthetically from the model. We then apply this methodology to some real, large-scale data that records the build up of connections in a business-related social networking site, and find evidence for triadic closure.

  6. Different physical structures of solutions for two related Zakharov-Kuznetsov equations

    International Nuclear Information System (INIS)

    Lai Shaoyong; Yin Jun; Wu Yonghong

    2008-01-01

    The auxiliary differential equation approach and the symbolic computation system Maple are employed to investigate two types of related Zakharov-Kuznetsov equations with variable coefficients. The exact solutions to the equations are constructed analytically under certain circumstances. It is shown that the variable coefficients of the derivative terms of the equations result in their semi-travelling wave solutions

  7. A Dual Regime Reactive Transport Model for Simulation of High Level Waste Tank Closure Scenarios - 13375

    International Nuclear Information System (INIS)

    Sarkar, Sohini; Kosson, David S.; Brown, Kevin; Garrabrants, Andrew C.; Meeussen, Hans; Van der Sloot, Hans

    2013-01-01

    A numerical simulation framework is presented in this paper for estimating evolution of pH and release of major species from grout within high-level waste tanks after closure. This model was developed as part of the Cementitious Barriers Partnership. The reactive transport model consists of two parts - (1) transport of species, and (2) chemical reactions. The closure grout can be assumed to have varying extents of cracking and composition for performance assessment purposes. The partially or completely degraded grouted tank is idealized as a dual regime system comprising of a mobile region having solid materials with cracks and macro-pores, and an immobile/stagnant region having solid matrix with micropores. The transport profiles of the species are calculated by incorporating advection of species through the mobile region, diffusion of species through the immobile/stagnant region, and exchange of species between the mobile and immobile regions. A geochemical speciation code in conjunction with the pH dependent test data for a grout material is used to obtain a mineral set that best describes the trends in the test data of the major species. The dual regime reactive transport model predictions are compared with the release data from an up-flow column percolation test. The coupled model is then used to assess effects of crack state of the structure, rate and composition of the infiltrating water on the pH evolution at the grout-waste interface. The coupled reactive transport model developed in this work can be used as part of the performance assessment process for evaluating potential risks from leaching of a cracked tank containing elements of human health and environmental concern. (authors)

  8. A Dual Regime Reactive Transport Model for Simulation of High Level Waste Tank Closure Scenarios - 13375

    Energy Technology Data Exchange (ETDEWEB)

    Sarkar, Sohini; Kosson, David S.; Brown, Kevin; Garrabrants, Andrew C. [Consortium for Risk Assessment with Stakeholder Participation - CRESP, Vanderbilt University, Nashville, TN (United States); Meeussen, Hans [Consortium for Risk Assessment with Stakeholder Participation - CRESP, Nuclear Research and Consultancy Group, Petten (Netherlands); Van der Sloot, Hans [Consortium for Risk Assessment with Stakeholder Participation - CRESP, Hans Van der Sloot Consultancy (Netherlands)

    2013-07-01

    A numerical simulation framework is presented in this paper for estimating evolution of pH and release of major species from grout within high-level waste tanks after closure. This model was developed as part of the Cementitious Barriers Partnership. The reactive transport model consists of two parts - (1) transport of species, and (2) chemical reactions. The closure grout can be assumed to have varying extents of cracking and composition for performance assessment purposes. The partially or completely degraded grouted tank is idealized as a dual regime system comprising of a mobile region having solid materials with cracks and macro-pores, and an immobile/stagnant region having solid matrix with micropores. The transport profiles of the species are calculated by incorporating advection of species through the mobile region, diffusion of species through the immobile/stagnant region, and exchange of species between the mobile and immobile regions. A geochemical speciation code in conjunction with the pH dependent test data for a grout material is used to obtain a mineral set that best describes the trends in the test data of the major species. The dual regime reactive transport model predictions are compared with the release data from an up-flow column percolation test. The coupled model is then used to assess effects of crack state of the structure, rate and composition of the infiltrating water on the pH evolution at the grout-waste interface. The coupled reactive transport model developed in this work can be used as part of the performance assessment process for evaluating potential risks from leaching of a cracked tank containing elements of human health and environmental concern. (authors)

  9. The Wertheim integral equation theory with the ideal chain approximation and a dimer equation of state: Generalization to mixtures of hard-sphere chain fluids

    International Nuclear Information System (INIS)

    Chang, J.; Sandler, S.I.

    1995-01-01

    We have extended the Wertheim integral equation theory to mixtures of hard spheres with two attraction sites in order to model homonuclear hard-sphere chain fluids, and then solved these equations with the polymer-Percus--Yevick closure and the ideal chain approximation to obtain the average intermolecular and overall radial distribution functions. We obtain explicit expressions for the contact values of these distribution functions and a set of one-dimensional integral equations from which the distribution functions can be calculated without iteration or numerical Fourier transformation. We compare the resulting predictions for the distribution functions with Monte Carlo simulation results we report here for five selected binary mixtures. It is found that the accuracy of the prediction of the structure is the best for dimer mixtures and declines with increasing chain length and chain-length asymmetry. For the equation of state, we have extended the dimer version of the thermodynamic perturbation theory to the hard-sphere chain mixture by introducing the dimer mixture as an intermediate reference system. The Helmholtz free energy of chain fluids is then expressed in terms of the free energy of the hard-sphere mixture and the contact values of the correlation functions of monomer and dimer mixtures. We compared with the simulation results, the resulting equation of state is found to be the most accurate among existing theories with a relative average error of 1.79% for 4-mer/8-mer mixtures, which is the worst case studied in this work. copyright 1995 American Institute of Physics

  10. Derivation of a volume-averaged neutron diffusion equation; Atomos para el desarrollo de Mexico

    Energy Technology Data Exchange (ETDEWEB)

    Vazquez R, R.; Espinosa P, G. [UAM-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico D.F. 09340 (Mexico); Morales S, Jaime B. [UNAM, Laboratorio de Analisis en Ingenieria de Reactores Nucleares, Paseo Cuauhnahuac 8532, Jiutepec, Morelos 62550 (Mexico)]. e-mail: rvr@xanum.uam.mx

    2008-07-01

    This paper presents a general theoretical analysis of the problem of neutron motion in a nuclear reactor, where large variations on neutron cross sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the volume-averaged neutron diffusion equation (e.g., effective neutron diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the volume averaged diffusion equation include two corrections factor: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. (Author)

  11. On Equilibria of the Two-fluid Model in Magnetohydrodynamics

    International Nuclear Information System (INIS)

    Frantzeskakis, Dimitri J.; Stratis, Ioannis G.; Yannacopoulos, Athanasios N.

    2004-01-01

    We show how the equilibria of the two-fluid model in magnetohydrodynamics can be described by the double curl equation and through the study of this equation we study some properties of these equilibria

  12. Contribution to the verification and the validation of an unsteady two-phase flow model

    International Nuclear Information System (INIS)

    Liu, Yujie

    2013-01-01

    This thesis contributes to the verification and the validation of the Baer-Nunziato (BN) model, to model water hammer phenomena in industrial piping systems. It consists of two parts, the first is to model water hammer flows with the BN model in Eulerian representation and the second is to extend this model to the ALE (Arbitrary Lagrangian Eulerian) formalism so as to take into account fluid-structure interaction (FSI). To model water hammer flows, closure laws of the BN model concerning the interfacial/source terms and the equations of state (EOS) were first studied. Then the whole system was simulated with a fractional step method including two steps, one for the resolution of the convective part, the other for the source terms. For the convective part, the Rusanov scheme was first checked, and some stability problems have been observed. Thus a more stable fractional step scheme has been proposed and verified. Regarding the source terms, four non-instantaneous relaxation schemes which represent the return to equilibrium of pressure, the transfers of momentum, heat and mass were successively applied. These schemes have been extended to 'generalized Stiffened Gas' EOS in order to represent phase-change. After regaining some typical phenomena associated with water hammer flows, the BN model was validated with the Simpson experiment, a classical water hammer test case, and the Canon experience, a rapid decompression of fluid in a high pressure duct. Moreover, the model was compared with two homogeneous models on these two experiments. Finally, an ALE version of the BN model was implemented, and verified on a case of wave propagation in a 'single' phase flow and a two-phase flow in a flexible pipe. The variation of wave propagation speed due to the coupling between the fluid and the structure has been well retrieved. The validation was performed on an experiment which examines the response of a pipe filled with water, subjected to a violent pressure peak (140 bar

  13. Road Closures

    Data.gov (United States)

    Montgomery County of Maryland — This is an up to date map of current road closures in Montgomery County.This dataset is updated every few minutes from the Department of Transportation road closure...

  14. Generalized Roe's numerical scheme for a two-fluid model

    International Nuclear Information System (INIS)

    Toumi, I.; Raymond, P.

    1993-01-01

    This paper is devoted to a mathematical and numerical study of a six equation two-fluid model. We will prove that the model is strictly hyperbolic due to the inclusion of the virtual mass force term in the phasic momentum equations. The two-fluid model is naturally written under a nonconservative form. To solve the nonlinear Riemann problem for this nonconservative hyperbolic system, a generalized Roe's approximate Riemann solver, is used, based on a linearization of the nonconservative terms. A Godunov type numerical scheme is built, using this approximate Riemann solver. 10 refs., 5 figs,

  15. Linear causal modeling with structural equations

    CERN Document Server

    Mulaik, Stanley A

    2009-01-01

    Emphasizing causation as a functional relationship between variables that describe objects, Linear Causal Modeling with Structural Equations integrates a general philosophical theory of causation with structural equation modeling (SEM) that concerns the special case of linear causal relations. In addition to describing how the functional relation concept may be generalized to treat probabilistic causation, the book reviews historical treatments of causation and explores recent developments in experimental psychology on studies of the perception of causation. It looks at how to perceive causal

  16. Modeling and Prediction Using Stochastic Differential Equations

    DEFF Research Database (Denmark)

    Juhl, Rune; Møller, Jan Kloppenborg; Jørgensen, John Bagterp

    2016-01-01

    Pharmacokinetic/pharmakodynamic (PK/PD) modeling for a single subject is most often performed using nonlinear models based on deterministic ordinary differential equations (ODEs), and the variation between subjects in a population of subjects is described using a population (mixed effects) setup...... deterministic and can predict the future perfectly. A more realistic approach would be to allow for randomness in the model due to e.g., the model be too simple or errors in input. We describe a modeling and prediction setup which better reflects reality and suggests stochastic differential equations (SDEs...

  17. Verification and Validation of the k-kL Turbulence Model in FUN3D and CFL3D Codes

    Science.gov (United States)

    Abdol-Hamid, Khaled S.; Carlson, Jan-Renee; Rumsey, Christopher L.

    2015-01-01

    The implementation of the k-kL turbulence model using multiple computational uid dy- namics (CFD) codes is reported herein. The k-kL model is a two-equation turbulence model based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's equation is well suited for term-by-term mod- eling and displays useful features compared to other two-equation models. An important di erence is that this formulation leads to the inclusion of higher-order velocity derivatives in the source terms of the scale equations. This can enhance the ability of the Reynolds- averaged Navier-Stokes (RANS) solvers to simulate unsteady ows. The present report documents the formulation of the model as implemented in the CFD codes Fun3D and CFL3D. Methodology, veri cation and validation examples are shown. Attached and sepa- rated ow cases are documented and compared with experimental data. The results show generally very good comparisons with canonical and experimental data, as well as matching results code-to-code. The results from this formulation are similar or better than results using the SST turbulence model.

  18. Working covariance model selection for generalized estimating equations.

    Science.gov (United States)

    Carey, Vincent J; Wang, You-Gan

    2011-11-20

    We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice. Copyright © 2011 John Wiley & Sons, Ltd.

  19. Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients

    International Nuclear Information System (INIS)

    Khmelnytskaya, K.V.; Rosu, H.C.; Gonzalez, A.

    2010-01-01

    We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically coupled second-order differential equations. We solve analytically these parametric periodic problems along the whole real axis. Next, the analytically solved model is used as a case study for a powerful numerical approach that is employed here for the first time in the investigation of the energy band structure of periodic not necessarily regular potentials. The approach is based on the well-known self-matching procedure of James (1949) and implements the spectral parameter power series solutions introduced by Kravchenko (2008). We obtain additionally an efficient series representation of the Hill discriminant based on Kravchenko's series.

  20. RETRAN nonequilibrium two-phase flow model for operational transient analyses

    International Nuclear Information System (INIS)

    Paulsen, M.P.; Hughes, E.D.

    1982-01-01

    The field balance equations, flow-field models, and equation of state for a nonequilibrium two-phase flow model for RETRAN are given. The differential field balance model equations are: (1) conservation of mixture mass; (2) conservation of vapor mass; (3) balance of mixture momentum; (4) a dynamic-slip model for the velocity difference; and (5) conservation of mixture energy. The equation of state is formulated such that the liquid phase may be subcooled, saturated, or superheated. The vapor phase is constrained to be at the saturation state. The dynamic-slip model includes wall-to-phase and interphase momentum exchanges. A mechanistic vapor generation model is used to describe vapor production under bulk subcooling conditions. The speed of sound for the mixture under nonequilibrium conditions is obtained from the equation of state formulation. The steady-state and transient solution methods are described

  1. Interferometric Imaging Directly with Closure Phases and Closure Amplitudes

    Science.gov (United States)

    Chael, Andrew A.; Johnson, Michael D.; Bouman, Katherine L.; Blackburn, Lindy L.; Akiyama, Kazunori; Narayan, Ramesh

    2018-04-01

    Interferometric imaging now achieves angular resolutions as fine as ∼10 μas, probing scales that are inaccessible to single telescopes. Traditional synthesis imaging methods require calibrated visibilities; however, interferometric calibration is challenging, especially at high frequencies. Nevertheless, most studies present only a single image of their data after a process of “self-calibration,” an iterative procedure where the initial image and calibration assumptions can significantly influence the final image. We present a method for efficient interferometric imaging directly using only closure amplitudes and closure phases, which are immune to station-based calibration errors. Closure-only imaging provides results that are as noncommittal as possible and allows for reconstructing an image independently from separate amplitude and phase self-calibration. While closure-only imaging eliminates some image information (e.g., the total image flux density and the image centroid), this information can be recovered through a small number of additional constraints. We demonstrate that closure-only imaging can produce high-fidelity results, even for sparse arrays such as the Event Horizon Telescope, and that the resulting images are independent of the level of systematic amplitude error. We apply closure imaging to VLBA and ALMA data and show that it is capable of matching or exceeding the performance of traditional self-calibration and CLEAN for these data sets.

  2. Modeling and numerical study of two phase flow

    International Nuclear Information System (INIS)

    Champmartin, A.

    2011-01-01

    This thesis describes the modelization and the simulation of two-phase systems composed of droplets moving in a gas. The two phases interact with each other and the type of model to consider directly depends on the type of simulations targeted. In the first part, the two phases are considered as fluid and are described using a mixture model with a drift relation (to be able to follow the relative velocity between the two phases and take into account two velocities), the two-phase flows are assumed at the equilibrium in temperature and pressure. This part of the manuscript consists of the derivation of the equations, writing a numerical scheme associated with this set of equations, a study of this scheme and simulations. A mathematical study of this model (hyperbolicity in a simplified framework, linear stability analysis of the system around a steady state) was conducted in a frame where the gas is assumed baro-tropic. The second part is devoted to the modelization of the effect of inelastic collisions on the particles when the time of the simulation is shorter and the droplets can no longer be seen as a fluid. We introduce a model of inelastic collisions for droplets in a spray, leading to a specific Boltzmann kernel. Then, we build caricatures of this kernel of BGK type, in which the behavior of the first moments of the solution of the Boltzmann equation (that is mass, momentum, directional temperatures, variance of the internal energy) are mimicked. The quality of these caricatures is tested numerically at the end. (author) [fr

  3. Response of Mediterranean circulation to Miocene shoaling and closure of the Indian Gateway : A model study

    NARCIS (Netherlands)

    De La Vara, Alba; Meijer, Paul

    2016-01-01

    In this regional ocean model study, we explore the effect of the Early to Middle Miocene shoaling and closure of the Indian Gateway on Mediterranean circulation and its exchange with the adjacent oceans. For this we use the regional ocean circulation model "sbPOM" and a collection of bathymetries

  4. Comparison of multi-fluid moment models with particle-in-cell simulations of collisionless magnetic reconnection

    International Nuclear Information System (INIS)

    Wang, Liang; Germaschewski, K.; Hakim, Ammar H.; Bhattacharjee, A.

    2015-01-01

    We introduce an extensible multi-fluid moment model in the context of collisionless magnetic reconnection. This model evolves full Maxwell equations and simultaneously moments of the Vlasov-Maxwell equation for each species in the plasma. Effects like electron inertia and pressure gradient are self-consistently embedded in the resulting multi-fluid moment equations, without the need to explicitly solving a generalized Ohm's law. Two limits of the multi-fluid moment model are discussed, namely, the five-moment limit that evolves a scalar pressures for each species and the ten-moment limit that evolves the full anisotropic, non-gyrotropic pressure tensor for each species. We first demonstrate analytically and numerically that the five-moment model reduces to the widely used Hall magnetohydrodynamics (Hall MHD) model under the assumptions of vanishing electron inertia, infinite speed of light, and quasi-neutrality. Then, we compare ten-moment and fully kinetic particle-in-cell (PIC) simulations of a large scale Harris sheet reconnection problem, where the ten-moment equations are closed with a local linear collisionless approximation for the heat flux. The ten-moment simulation gives reasonable agreement with the PIC results regarding the structures and magnitudes of the electron flows, the polarities and magnitudes of elements of the electron pressure tensor, and the decomposition of the generalized Ohm's law. Possible ways to improve the simple local closure towards a nonlocal fully three-dimensional closure are also discussed

  5. Two models for the dynamics of a cross flow heat exchanger

    Energy Technology Data Exchange (ETDEWEB)

    Hopkinson, A [Control and Instrumentation Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)

    1962-12-15

    Two models of a cross flow heat exchanger, a concentric tube counter flow model and a cross flow model, are studied theoretically. Differential equations describing the behaviour of the models are derived and from them equations for the steady state temperatures and the temperature transfer functions are obtained. (author)

  6. Influence of Closure & Non-Closure of the Visceral and Parietal Peritoneum on Post Cesarean Morbidity

    Directory of Open Access Journals (Sweden)

    Z Tabasi

    2012-05-01

    Full Text Available

    Background and Objectives: One of the most important issues in promoting mother and child health is reducing the morbidity rate after cesarean section. The aim of this study was to investigate the influence of closure and non-closure of the visceral and parietal peritoneum on post cesarean morbidity in women attending Shabihkhani Maternity Hospital in Kashan, Iran.

    Methods: This study was conducted with a single blind randomized clinical trial method on 100 parturient women that underwent emergency or elective cesarean section. Patients with previous cesarean section and or abdominal surgery, diseases such as hypertension, diabetes mellitus and premature rupture of membrane and pre operative bleeding, were excluded from this study. Then, the participants were randomly divided into two groups: in one group both peritoneal layers were closed while in the other group, they were not closed. Post operative morbidity including fever, bleeding, post operative pain, analgesic consumption and time of operation were assessed. Data were analyzed with t-tests, and χ2 and a P<0.05 were considered significant.

    Results: In this study, there were no significant differences between the two groups with respect to age, gestational age, the reason for caesarean section and gravidity, nor were there any differences with respect to the incidence of fever or bleeding and was similar between the two groups, but there was a significant difference between the two groups regarding to feeling of severe pain (P=0.0003, analgesic consumption (P=0.0003 and time of operation (P=0.004. In the non-closure group, dose of analgesic drugs, pain severity and time of operation were less than those of the other group.

    Conclusion: The
  7. Partial Differential Equations Modeling and Numerical Simulation

    CERN Document Server

    Glowinski, Roland

    2008-01-01

    This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...

  8. Seven-year follow-up of percutaneous closure of patent foramen ovale.

    Science.gov (United States)

    Mirzada, Naqibullah; Ladenvall, Per; Hansson, Per-Olof; Johansson, Magnus Carl; Furenäs, Eva; Eriksson, Peter; Dellborg, Mikael

    2013-12-01

    Observational studies favor percutaneous closure of patent foramen ovale (PFO) over medical treatment to reduce recurrent stroke while randomized trials fail to demonstrate significant superiority of percutaneous PFO closure. Few long-term studies are available post PFO closure. This study reports long-term clinical outcomes after percutaneous PFO closure. Between 1997 and 2006, 86 consecutive eligible patients with cerebrovascular events, presumably related to PFO, underwent percutaneous PFO closure. All 86 patients were invited to a long-term follow-up, which was carried out during 2011 and 2012. Percutaneous PFO closure was successfully performed in 85 of 86 patients. The follow-up rate was 100%. No cardiovascular or cerebrovascular deaths occurred. Two patients (both women) died from lung cancer during follow-up. Follow-up visits were conducted for 64 patients and the remaining 20 patients were followed up by phone. The mean follow-up time was 7.3 years (5 to 12.4 years). Mean age at PFO closure was 49 years. One patient had a minor stroke one month after PFO closure and a transient ischemic attack (TIA) two years afterwards. One other patient suffered from a TIA six years after closure. No long-term device-related complications were observed. Percutaneous PFO closure was associated with very low risk of recurrent stroke and is suitable in most patients. We observed no mortality and no long-term device-related complications related to PFO closure, indicating that percutaneous PFO closure is a safe and efficient treatment even in the long term.

  9. Relativistic two-and three-particle scattering equations using instant and light-front dynamics

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1992-01-01

    Starting from the Bethe-Salpeter equation for two particles in the ladder approximation and integrating over the time component of momentum we derive three dimensional scattering integral equations satisfying constraints of unitarity and relativity, both employing the light-front and instant-form variables. The equations we arrive at are those first derived by Weinberg and by Blankenbecler and Sugar, and are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. We extends this procedure to the case of three particles interacting via two-particle separable potentials. Using light-front and instant form variables we suggest a couple of three dimensional three-particle scattering equations satisfying constraints of two and three-particle unitarity and relativity. The three-particle light-front equation is shown to be approximately related by a transformation of variables to one of the instant-form three-particle equations. (author)

  10. Motion of curves and solutions of two multi-component mKdV equations

    International Nuclear Information System (INIS)

    Yao Ruoxia; Qu Changzheng; Li Zhibin

    2005-01-01

    Two classes of multi-component mKdV equations have been shown to be integrable. One class called the multi-component geometric mKdV equation is exactly the system for curvatures of curves when the motion of the curves is governed by the mKdV flow. In this paper, exact solutions including solitary wave solutions of the two- and three-component mKdV equations are obtained, the symmetry reductions of the two-component geometric mKdV equation to ODE systems corresponding to it's Lie point symmetry groups are also given. Curves and their behavior corresponding to solitary wave solutions of the two-component geometric mKdV equation are presented

  11. The two modes extension to the Berk-Breizman equation: Delayed differential equations and asymptotic solutions

    International Nuclear Information System (INIS)

    Marczynski, Slawomir

    2011-01-01

    The integro-differential Berk-Breizman (BB) equation, describing the evolution of particle-driven wave mode is transformed into a simple delayed differential equation form ν∂a(τ)/∂τ=a(τ) -a 2 (τ- 1) a(τ- 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.

  12. Model Selection and Risk Estimation with Applications to Nonlinear Ordinary Differential Equation Systems

    DEFF Research Database (Denmark)

    Mikkelsen, Frederik Vissing

    eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various......Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... package, episode. This package incorporates a collection of sparsity inducing penalties into two types of loss functions: a squared loss function relying on numerically solving the equations and an approximate loss function based on inverse collocation methods. The goal of this framework is to provide...

  13. Turbulent mass flux closure modeling for variable density turbulence in the wake of an air-entraining transom stern

    Science.gov (United States)

    Hendrickson, Kelli; Yue, Dick

    2016-11-01

    This work presents the development and a priori testing of closure models for the incompressible highly-variable density turbulent (IHVDT) flow in the near wake region of a transom stern. This complex, three-dimensional flow includes three regions with distinctly different flow behavior: (i) the convergent corner waves that originate from the body and collide on the ship center plane; (ii) the "rooster tail" that forms from the collision; and (iii) the diverging wave train. The characteristics of these regions involve violent free-surface flows and breaking waves with significant turbulent mass flux (TMF) at Atwood number At = (ρ2 -ρ1) / (ρ2 +ρ1) 1 for which there is little guidance in turbulence closure modeling for the momentum and scalar transport along the wake. Utilizing datasets from high-resolution simulations of the near wake of a canonical three-dimensional transom stern using conservative Volume-of-Fluid (cVOF), implicit Large Eddy Simulation (iLES), and Boundary Data Immersion Method (BDIM), we develop explicit algebraic turbulent mass flux closure models that incorporate the most relevant physical processes. Performance of these models in predicting the turbulent mass flux in all three regions of the wake will be presented. Office of Naval Research.

  14. Chaotic difference equations in two variables and their multidimensional perturbations

    International Nuclear Information System (INIS)

    Juang Jonq; Li, Ming-Chia; Malkin, Mikhail

    2008-01-01

    We consider difference equations Φ λ (y n , y n+1 , ..., y n+m ) = 0, n element of Z, of order m with parameter λ close to that exceptional value λ 0 for which the function Φ depends on two variables: Φ λ 0 (x 0 ,…, x m )=ξ(x N ,x N+L ) with 0 ≤ N, N + L ≤ m. It is also assumed that for the equation ξ(x, y) = 0, there is a branch y = ψ(x) with positive topological entropy h top (ψ). Under these assumptions we prove that in the set of bi-infinite solutions of the difference equation with λ in some neighbourhood of λ 0 , there is a closed (in the product topology) invariant set to which the restriction of the shift map has topological entropy arbitrarily close to h top (ψ)/|L|, and moreover, orbits of this invariant set depend continuously on λ not only in the product topology but also in the uniform topology. We then apply this result to establish chaotic behaviour for Arneodo–Coullet–Tresser maps near degenerate ones, for quadratic volume preserving automorphisms of R 3 and for several lattice models including the generalized cellular neural networks (CNNs), the time discrete version of the CNNs and coupled Chua's circuit

  15. Non-perturbative effects in two-dimensional lattice O(N) models

    International Nuclear Information System (INIS)

    Ogilvie, M.C.; Maryland Univ., College Park

    1981-01-01

    Non-abelian analogues of Kosterlitz-Thouless vortices may have important effects in two-dimensional lattice spin systems with O(N) symmetries. Renormalization group equations which include these effects are developed in two ways. The first set of equations extends the renormalization group equations of Kosterlitz to 0(N) spin systems, in a form suggested by Cardy and Hamber. The second is derived from a Villain-type 0(N) model using Migdal's recursion relations. Using these equations, the part played by topological excitations int he crossover from weak to strong coupling behavior is studied. Another effect which influences crossover behavior is also discussed; irrelevant operators which occur naturally in lattice theories can make important contributions to the renormalization group flow in the crossover region. When combined with conventional perturbative results, these two effects may explain the observed crossover behavior of these models. (orig.)

  16. Relativistic two-fermion equations with form factors and anomalous magnetic moment interactions

    International Nuclear Information System (INIS)

    Ahmed, S.

    1977-04-01

    Relativistic equations for two-fermion systems are derived from quantum field theory taking into account the form factors of the particles. When the q 2 dependence of the form factors is disregarded, in the static approximation, the two-fermion equations with Coulomb and anomalous magnetic moment interactions are obtained. Separating the angular variables, a sixteen-component relativistic radial equation are finally given

  17. Singular Linear Differential Equations in Two Variables

    NARCIS (Netherlands)

    Braaksma, B.L.J.; Put, M. van der

    2008-01-01

    The formal and analytic classification of integrable singular linear differential equations has been studied among others by R. Gerard and Y. Sibuya. We provide a simple proof of their main result, namely: For certain irregular systems in two variables there is no Stokes phenomenon, i.e. there is no

  18. Alternans promotion in cardiac electrophysiology models by delay differential equations.

    Science.gov (United States)

    Gomes, Johnny M; Dos Santos, Rodrigo Weber; Cherry, Elizabeth M

    2017-09-01

    Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

  19. Alternans promotion in cardiac electrophysiology models by delay differential equations

    Science.gov (United States)

    Gomes, Johnny M.; dos Santos, Rodrigo Weber; Cherry, Elizabeth M.

    2017-09-01

    Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

  20. Study of a Model Equation in Detonation Theory

    KAUST Repository

    Faria, Luiz; Kasimov, Aslan R.; Rosales, Rodolfo R.

    2014-01-01

    Here we analyze properties of an equation that we previously proposed to model the dynamics of unstable detonation waves [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Model for shock wave chaos, Phys. Rev. Lett., 110 (2013), 104104]. The equation

  1. Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.

    Science.gov (United States)

    Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J

    2017-03-01

    Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.

  2. A solution of the Schrodinger equation with two-body correlations included

    International Nuclear Information System (INIS)

    Fabre de la Ripelle, M.

    1984-01-01

    A procedure for introducing the two-body correlations in the solution of the Schrodinger equation is described. The N-body Schrodinger equation for nucleons subject to two-(or many)-body N-N interaction has never been solved with accuracy except for few-body systems. Indeed it is difficult to take the two-body correlations generated by the interaction into account in the wave function

  3. Unsteady interfacial coupling of two-phase flow models

    International Nuclear Information System (INIS)

    Hurisse, O.

    2006-01-01

    The primary coolant circuit in a nuclear power plant contains several distinct components (vessel, core, pipes,...). For all components, specific codes based on the discretization of partial differential equations have already been developed. In order to obtain simulations for the whole circuit, the interfacial coupling of these codes is required. The approach examined within this work consists in coupling codes by providing unsteady information through the coupling interface. The numerical technique relies on the use of an interface model, which is combined with the basic strategy that was introduced by Greenberg and Leroux in order to compute approximations of steady solutions of non-homogeneous hyperbolic systems. Three different coupling cases have been examined: (i) the coupling of a one-dimensional Euler system with a two-dimensional Euler system; (ii) the coupling of two distinct homogeneous two-phase flow models; (iii) the coupling of a four-equation homogeneous model with the standard two-fluid model. (author)

  4. Lattice Boltzmann model for simulating immiscible two-phase flows

    International Nuclear Information System (INIS)

    Reis, T; Phillips, T N

    2007-01-01

    The lattice Boltzmann equation is often promoted as a numerical simulation tool that is particularly suitable for predicting the flow of complex fluids. This paper develops a two-dimensional 9-velocity (D2Q9) lattice Boltzmann model for immiscible binary fluids with variable viscosities and density ratio using a single relaxation time for each fluid. In the macroscopic limit, this model is shown to recover the Navier-Stokes equations for two-phase flows. This is achieved by constructing a two-phase component of the collision operator that induces the appropriate surface tension term in the macroscopic equations. A theoretical expression for surface tension is determined. The validity of this analysis is confirmed by comparing numerical and theoretical predictions of surface tension as a function of density. The model is also shown to predict Laplace's law for surface tension and Poiseuille flow of layered immiscible binary fluids. The spinodal decomposition of two fluids of equal density but different viscosity is then studied. At equilibrium, the system comprises one large low viscosity bubble enclosed by the more viscous fluid in agreement with theoretical arguments of Renardy and Joseph (1993 Fundamentals of Two-Fluid Dynamics (New York: Springer)). Two other simulations, namely the non-equilibrium rod rest and the coalescence of two bubbles, are performed to show that this model can be used to simulate two fluids with a large density ratio

  5. Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

    Science.gov (United States)

    Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

    2018-06-01

    In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

  6. Generalized latent variable modeling multilevel, longitudinal, and structural equation models

    CERN Document Server

    Skrondal, Anders; Rabe-Hesketh, Sophia

    2004-01-01

    This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models.

  7. CIRSE Vascular Closure Device Registry

    International Nuclear Information System (INIS)

    Reekers, Jim A.; Müller-Hülsbeck, Stefan; Libicher, Martin; Atar, Eli; Trentmann, Jens; Goffette, Pierre; Borggrefe, Jan; Zeleňák, Kamil; Hooijboer, Pieter; Belli, Anna-Maria

    2011-01-01

    Purpose: Vascular closure devices are routinely used after many vascular interventional radiology procedures. However, there have been no major multicenter studies to assess the safety and effectiveness of the routine use of closure devices in interventional radiology. Methods: The CIRSE registry of closure devices with an anchor and a plug started in January 2009 and ended in August 2009. A total of 1,107 patients were included in the registry. Results: Deployment success was 97.2%. Deployment failure specified to access type was 8.8% [95% confidence interval (95% CI) 5.0–14.5] for antegrade access and 1.8% (95% CI 1.1–2.9) for retrograde access (P = 0.001). There was no difference in deployment failure related to local PVD at the access site. Calcification was a reason for deployment failure in only 5.9 cm, and two vessel occlusions. Conclusion: The conclusion of this registry of closure devices with an anchor and a plug is that the use of this device in interventional radiology procedures is safe, with a low incidence of serious access site complications. There seems to be no difference in complications between antegrade and retrograde access and other parameters.

  8. Model Servqual Dengan Pendekatan Structural Equation Modeling (Studi Pada Mahasiswa Sistem Informasi)

    OpenAIRE

    Nurfaizal, Yusmedi

    2015-01-01

    Penelitian ini berjudul “MODEL SERVQUAL DENGAN PENDEKATAN STRUCTURAL EQUATION MODELING (Studi Pada Mahasiswa Sistem Informasi)”. Tujuan penelitian ini adalah untuk mengetahui model Servqual dengan pendekatan Structural Equation Modeling pada mahasiswa sistem informasi. Peneliti memutuskan untuk mengambil sampel sebanyak 100 responden. Untuk menguji model digunakan analisis SEM. Hasil penelitian menunjukkan bahwa tangibility, reliability responsiveness, assurance dan emphaty mempunyai pengaruh...

  9. Basic equations of interfacial area transport in gas-liquid two-phase flow

    International Nuclear Information System (INIS)

    Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.

    2011-01-01

    The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)

  10. The computation of turbulent recirculating flow using curvilinear finite differences. Application of the k - epsilon model to the flow in dredged trenches

    International Nuclear Information System (INIS)

    Alfrink, B.J.

    1981-08-01

    The report treats the computation of turbulent recirculating flow in dredged trenches. The mathematical model consists of the full two-dimensional unsteady Reynolds equations, formulated in primitive variables. Turbulence closure is obtained by means of a two-equation (k - epsilon) model. The numerical technique is based on the use of curvilinear finite differences in space and of fractional steps in time. A procedure is proposed to apply the model for varying roughness circumstances. The value of the Von Karman constant can be determined from geometric information. Afterwards, only the c 1 -constant is adapted by means of a degenerated epsilon-equation. The report describes an extensive sensitivity study for the inlet conditions and the empirical constants. Ultimately, the results of the mathematical model are very satisfactory. Compared with laboratory experiments, the recirculation length is only underpredicted with 10%

  11. Parameter Estimation of Partial Differential Equation Models.

    Science.gov (United States)

    Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

    2013-01-01

    Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

  12. Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

    Science.gov (United States)

    Danwanichakul, Panu; Glandt, Eduardo D

    2004-11-15

    We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

  13. A discrete model of a modified Burgers' partial differential equation

    Science.gov (United States)

    Mickens, R. E.; Shoosmith, J. N.

    1990-01-01

    A new finite-difference scheme is constructed for a modified Burger's equation. Three special cases of the equation are considered, and the 'exact' difference schemes for the space- and time-independent forms of the equation are presented, along with the diffusion-free case of Burger's equation modeled by a difference equation. The desired difference scheme is then obtained by imposing on any difference model of the initial equation the requirement that, in the appropriate limits, its difference scheme must reduce the results of the obtained equations.

  14. Covariant two-particle wave functions for model quasipotential allowing exact solutions

    International Nuclear Information System (INIS)

    Kapshaj, V.N.; Skachkov, N.B.

    1982-01-01

    Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

  15. A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties

    Energy Technology Data Exchange (ETDEWEB)

    Vlaykov, Dimitar G., E-mail: Dimitar.Vlaykov@ds.mpg.de [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen (Germany); Grete, Philipp [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Schmidt, Wolfram [Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg (Germany); Schleicher, Dominik R. G. [Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C (Chile)

    2016-06-15

    Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.

  16. Methods of mathematical modelling continuous systems and differential equations

    CERN Document Server

    Witelski, Thomas

    2015-01-01

    This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

  17. Revisiting the Landau fluid closure.

    Science.gov (United States)

    Hunana, P.; Zank, G. P.; Webb, G. M.; Adhikari, L.

    2017-12-01

    Advanced fluid models that are much closer to the full kinetic description than the usual magnetohydrodynamic description are a very useful tool for studying astrophysical plasmas and for interpreting solar wind observational data. The development of advanced fluid models that contain certain kinetic effects is complicated and has attracted much attention over the past years. Here we focus on fluid models that incorporate the simplest possible forms of Landau damping, derived from linear kinetic theory expanded about a leading-order (gyrotropic) bi-Maxwellian distribution function f_0, under the approximation that the perturbed distribution function f_1 is gyrotropic as well. Specifically, we focus on various Pade approximants to the usual plasma response function (and to the plasma dispersion function) and examine possibilities that lead to a closure of the linear kinetic hierarchy of fluid moments. We present re-examination of the simplest Landau fluid closures.

  18. Quintom models with an equation of state crossing -1

    International Nuclear Information System (INIS)

    Zhao Wen; Zhang Yang

    2006-01-01

    In this paper, we investigate a kind of special quintom model, which is made of a quintessence field φ 1 and a phantom field φ 2 , and the potential function has the form of V(φ 1 2 -φ 2 2 ). This kind of quintom field can be separated into two kinds: the hessence model, which has the state of φ 1 2 >φ 2 2 , and the hantom model with the state φ 1 2 2 2 . We discuss the evolution of these models in the ω-ω ' plane (ω is the state equation of the dark energy, and ω ' is its time derivative in units of Hubble time), and find that according to ω>-1 or ' plane can be divided into four parts. The late time attractor solution, if existing, is always quintessencelike or Λ-like for hessence field, so the big rip does not exist. But for hantom field, its late time attractor solution can be phantomlike or Λ-like, and sometimes, the big rip is unavoidable. Then we consider two special cases: one is the hessence field with an exponential potential, and the other is with a power law potential. We investigate their evolution in the ω-ω ' plane. We also develop a theoretical method of constructing the hessence potential function directly from the effective equation-of-state function ω(z). We apply our method to five kinds of parametrizations of equation-of-state parameter, where ω crossing -1 can exist, and find they all can be realized. At last, we discuss the evolution of the perturbations of the quintom field, and find the perturbations of the quintom δ Q and the metric Φ are all finite even at the state of ω=-1 and ω ' ≠0

  19. Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

    Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

  20. Lattice Boltzmann model for high-order nonlinear partial differential equations.

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  1. Lattice Boltzmann model for high-order nonlinear partial differential equations

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  2. Covariant two-particle wave functions for model quasipotentials admitting exact solutions

    International Nuclear Information System (INIS)

    Kapshaj, V.N.; Skachkov, N.B.

    1983-01-01

    Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

  3. Equation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity.

    Directory of Open Access Journals (Sweden)

    Rebecca B Hoyle

    Full Text Available Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity.

  4. Dynamic data analysis modeling data with differential equations

    CERN Document Server

    Ramsay, James

    2017-01-01

    This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

  5. Spontaneous Closure of Patent Ductus Arteriosus in Infants ≤1500 g.

    Science.gov (United States)

    Semberova, Jana; Sirc, Jan; Miletin, Jan; Kucera, Jachym; Berka, Ivan; Sebkova, Sylva; O'Sullivan, Sinead; Franklin, Orla; Stranak, Zbynek

    2017-08-01

    Patent ductus arteriosus (PDA) remains a challenging issue in very low birth weight (VLBW) infants, and its management varies widely. Our aim in this study was to document the natural course of ductus arteriosus in a cohort of VLBW infants who underwent conservative PDA management with no medical or surgical intervention. A retrospective cohort study conducted in 2 European level-3 neonatal units. A total of 368 VLBW infants were born within the study period. Two hundred and ninety-seven infants were free of congenital malformations or heart defects and survived to hospital discharge. Out of those, 280 infants received truly conservative PDA management. In 237 (85%) of nontreated infants, the PDA closed before hospital discharge. The Kaplan-Meier model was used to document the incidence proportion of PDA closure over time for different gestational age groups. The median time to ductal closure was 71, 13, 8, and 6 days in closure before hospital discharge and neonatal morbidities. The likelihood of PDA spontaneous closure in VLBW infants is extremely high. We provide in our findings a platform for future placebo-controlled trials focused on the smallest and youngest infants. Copyright © 2017 by the American Academy of Pediatrics.

  6. A model for non-equilibrium, non-homogeneous two-phase critical flow

    International Nuclear Information System (INIS)

    Bassel, Wageeh Sidrak; Ting, Daniel Kao Sun

    1999-01-01

    Critical two phase flow is a very important phenomena in nuclear reactor technology for the analysis of loss of coolant accident. Several recent papers, Lee and Shrock (1990), Dagan (1993) and Downar (1996) , among others, treat the phenomena using complex models which require heuristic parameters such as relaxation constants or interfacial transfer models. In this paper a mathematical model for one dimensional non equilibrium and non homogeneous two phase flow in constant area duct is developed. The model is constituted of three conservation equations type mass ,momentum and energy. Two important variables are defined in the model: equilibrium constant in the energy equation and the impulse function in the momentum equation. In the energy equation, the enthalpy of the liquid phase is determined by a linear interpolation function between the liquid phase enthalpy at inlet condition and the saturated liquid enthalpy at local pressure. The interpolation coefficient is the equilibrium constant. The momentum equation is expressed in terms of the impulse function. It is considered that there is slip between the liquid and vapor phases, the liquid phase is in metastable state and the vapor phase is in saturated stable state. The model is not heuristic in nature and does not require complex interface transfer models. It is proved numerically that for the critical condition the partial derivative of two phase pressure drop with respect to the local pressure or to phase velocity must be zero.This criteria is demonstrated by numerical examples. The experimental work of Fauske (1962) and Jeandey (1982) were analyzed resulting in estimated numerical values for important parameters like slip ratio, equilibrium constant and two phase frictional drop. (author)

  7. Two-field and drift-flux models with application to nuclear reactor safety

    International Nuclear Information System (INIS)

    Travis, J.R.

    1986-01-01

    The ideas of the two-field (6 equation model) and drift-flux (4 equation model) description of two-phase flows are presented. Several example calculations relating to reactor safety are discussed and comparisons of the numerical results and experimental data are shown to be in good agreement. 16 refs., 32 figs

  8. Closure The Definitive Guide

    CERN Document Server

    Bolin, Michael

    2010-01-01

    If you're ready to use Closure to build rich web applications with JavaScript, this hands-on guide has precisely what you need to learn this suite of tools in depth. Closure makes it easy for experienced JavaScript developers to write and maintain large and complex codebases -- as Google has demonstrated by using Closure with Gmail, Google Docs, and Google Maps. Author and Closure contributor Michael Bolin has included numerous code examples and best practices, as well as valuable information not available publicly until now. You'll learn all about Closure's Library, Compiler, Templates, tes

  9. Nonlinear damped Schrodinger equation in two space dimensions

    Directory of Open Access Journals (Sweden)

    Tarek Saanouni

    2015-04-01

    Full Text Available In this article, we study the initial value problem for a semi-linear damped Schrodinger equation with exponential growth nonlinearity in two space dimensions. We show global well-posedness and exponential decay.

  10. Percutaneous Patent Ductus Arteriosus (PDA) Closure in Very Preterm Infants: Feasibility and Complications.

    Science.gov (United States)

    Backes, Carl H; Cheatham, Sharon L; Deyo, Grace M; Leopold, Scott; Ball, Molly K; Smith, Charles V; Garg, Vidu; Holzer, Ralf J; Cheatham, John P; Berman, Darren P

    2016-02-12

    Percutaneous closure of patent ductus arteriosus (PDA) in term neonates is established, but data regarding outcomes in infants born very preterm (closure at weights closure. Twenty-five percent (13/52) of infants were closure. Compared to precatheterization trends, percutaneous PDA closure resulted in improved respiratory status, including less exposure to mechanical ventilation (mixed effects logistic model, Pclosure at weights closure versus alternative (surgical ligation) management strategies. © 2016 The Authors. Published on behalf of the American Heart Association, Inc., by Wiley Blackwell.

  11. Central-Upwind Schemes for Two-Layer Shallow Water Equations

    KAUST Repository

    Kurganov, Alexander; Petrova, Guergana

    2009-01-01

    We derive a second-order semidiscrete central-upwind scheme for one- and two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is well-balanced in the sense that stationary steady-state solutions

  12. Evaluation of in vivo biocompatibility of different devices for interventional closure of the patent ductus arteriosus in an animal model

    OpenAIRE

    Sigler, M; Handt, S; Seghaye, M; von Bernuth, G; Grabitz, R

    2000-01-01

    OBJECTIVE—To evaluate the in vivo biocompatibility of three different devices following interventional closure of a patent ductus arteriosus (PDA) in an animal model.
MATERIALS AND METHODS—A medical grade stainless steel coil (n = 8), a nickel/titanium coil (n = 10), and a polyvinylalcohol foam plug knitted on a titanium wire frame (n = 11) were used for interventional closure of PDA in a neonatal lamb model. The PDA had been maintained by repetitive angioplasty. Between one and 278 days afte...

  13. Two-state approximation of the Fadeev-Hahn equations

    International Nuclear Information System (INIS)

    Brener, S.E.

    1993-01-01

    The equations have been chosen which allow both to solve the scattering problems and to calculate the parameters of bound states of three particles with Coulomb interaction when the system energy is below the decay to three separate particles. The method of constructing of equations which are most suitable for concrete problems is considered. Different numerical schemes to calculate the low energy scattering cross sections with two-particle clusterization in 'in' and 'out' collision's channels have been developed. The bounds of applied approaches were determined and the peculiarities connected with differently defined reaction amplitudes under these approaches have been considered. The interpretation of obtained results at different definitions of reaction amplitudes was demonstrated, and the elastic, inelastic cross sections and muon transfer rates in hydrogen isotope mesic atom collisions have been calculated using Fadeev-Hahn equations. (author)

  14. External intermittency prediction using AMR solutions of RANS turbulence and transported PDF models

    Science.gov (United States)

    Olivieri, D. A.; Fairweather, M.; Falle, S. A. E. G.

    2011-12-01

    External intermittency in turbulent round jets is predicted using a Reynolds-averaged Navier-Stokes modelling approach coupled to solutions of the transported probability density function (pdf) equation for scalar variables. Solutions to the descriptive equations are obtained using a finite-volume method, combined with an adaptive mesh refinement algorithm, applied in both physical and compositional space. This method contrasts with conventional approaches to solving the transported pdf equation which generally employ Monte Carlo techniques. Intermittency-modified eddy viscosity and second-moment turbulence closures are used to accommodate the effects of intermittency on the flow field, with the influence of intermittency also included, through modifications to the mixing model, in the transported pdf equation. Predictions of the overall model are compared with experimental data on the velocity and scalar fields in a round jet, as well as against measurements of intermittency profiles and scalar pdfs in a number of flows, with good agreement obtained. For the cases considered, predictions based on the second-moment turbulence closure are clearly superior, although both turbulence models give realistic predictions of the bimodal scalar pdfs observed experimentally.

  15. Development and validation of an Eulerian model towards the simulation of fuel injection in internal combustion engines; Developpement et validation d'un modele eulerien en vue de la simulation des jets de carburants dans les moteurs a combustion interne

    Energy Technology Data Exchange (ETDEWEB)

    Truchot, B.

    2005-12-15

    The objective of this work is to develop an Eulerian two phase model to improve the prediction of fuel injection in internal combustion engines, particularly the dense liquid zone close to the nozzle. Lagrangian models, usually used in engine simulations, are based on the assumption of dispersed two phase flows with low liquid volume fraction, which is not fulfilled in the case of direct injection engine technology. Different Eulerian approaches are available in the literature. Physical phenomena that occur near the nozzle and characteristics of each model lead to the choice of a two fluids two pressures model. Several open terms appear in the equations of the model: exchange between the two phases and turbulent correlations. Closures of exchange terms are based on the spherical droplets hypothesis while a RANS approach is adopted to close turbulent correlations. This model has been integrated in the IFP CFD code, IFP-C3D. Several numerical tests and analytical validations (for single and two phase flows) have been then carried out in order to check the correct implementation of equations and the predictivity of the model and closures. Modifications in the turbulent model of the gas have required validations in both the gas phase (flow behind a sudden enlargement) and the liquid phase (pure liquid injection). A two phase mixing layer has been then used to validate the whole model. Finally, injection tests have been achieved under realistic conditions (similar to those encountered in automotive engines) in order to check the feasibility of engine computations using the developed Eulerian approach. These tests have also allowed to check the compatibility of this approach with the specificities of engine simulations (especially mesh movement). (author)

  16. Local two-phase modeling of the water-steam flows occurring in steam generators

    International Nuclear Information System (INIS)

    Denefle, Romain

    2013-01-01

    The present study is related to the need of modeling the two-phase flows occurring in a steam generator (liquid at inlet and vapour at outlet). The choice is made to investigate a hybrid modeling of the flow, considering the gas phase as two separated fields, each one being modeled with different closure laws. In so doing, the small and spherical bubbles are modeled through a dispersed approach within the two-fluid model, and the distorted bubbles are simulated with an interface locating method. The main outcome is about the implementation, the verification and the validation of the model dedicated to the large and distorted bubbles, as well as the coupling of the two approaches for the gas, allowing the presentation of demonstration calculations using the so-called hybrid approach. (author)

  17. Blowup with vorticity control for a 2D model of the Boussinesq equations

    Science.gov (United States)

    Hoang, V.; Orcan-Ekmekci, B.; Radosz, M.; Yang, H.

    2018-06-01

    We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.

  18. Reflood completion report: Volume 1. A phenomenological thermal-hydraulic model of hot rod bundles experiencing simultaneous bottom and top quenching and an optimization methodology for closure development

    International Nuclear Information System (INIS)

    Nelson, R.A. Jr.; Pimentel, D.A.; Jolly-Woodruff, S.; Spore, J.

    1998-04-01

    In this report, a phenomenological model of simultaneous bottom-up and top-down quenching is developed and discussed. The model was implemented in the TRAC-PF1/MOD2 computer code. Two sets of closure relationships were compared within the study, the Absolute set and the Conditional set. The Absolute set of correlations is frequently viewed as the pure set because the correlations is frequently viewed as the pure set because the correlations utilize their original coefficients as suggested by the developer. The Conditional set is a modified set of correlations with changes to the correlation coefficient only. Results for these two sets indicate quite similar results. This report also summarizes initial results of an effort to investigate nonlinear optimization techniques applied to the closure model development. Results suggest that such techniques can provide advantages for future model development work, but that extensive expertise is required to utilize such techniques (i.e., the model developer must fully understand both the physics of the process being represented and the computational techniques being employed). The computer may then be used to improve the correlation of computational results with experiments

  19. ECONOMETRIC APPROACH TO DIFFERENCE EQUATIONS MODELING OF EXCHANGE RATES CHANGES

    Directory of Open Access Journals (Sweden)

    Josip Arnerić

    2010-12-01

    Full Text Available Time series models that are commonly used in econometric modeling are autoregressive stochastic linear models (AR and models of moving averages (MA. Mentioned models by their structure are actually stochastic difference equations. Therefore, the objective of this paper is to estimate difference equations containing stochastic (random component. Estimated models of time series will be used to forecast observed data in the future. Namely, solutions of difference equations are closely related to conditions of stationary time series models. Based on the fact that volatility is time varying in high frequency data and that periods of high volatility tend to cluster, the most successful and popular models in modeling time varying volatility are GARCH type models and their variants. However, GARCH models will not be analyzed because the purpose of this research is to predict the value of the exchange rate in the levels within conditional mean equation and to determine whether the observed variable has a stable or explosive time path. Based on the estimated difference equation it will be examined whether Croatia is implementing a stable policy of exchange rates.

  20. Evaluation of stiffness and plastic deformation of active ceramic self-ligating bracket clips after repetitive opening and closure movements.

    Science.gov (United States)

    Carneiro, Grace Kelly Martins; Roque, Juliano Alves; Segundo, Aguinaldo Silva Garcez; Suzuki, Hideo

    2015-01-01

    The aim of this study was to assess whether repetitive opening and closure of self-ligating bracket clips can cause plastic deformation of the clip. Three types of active/interactive ceramic self-ligating brackets (n = 20) were tested: In-Ovation C, Quicklear and WOW. A standardized controlled device performed 500 cycles of opening and closure movements of the bracket clip with proper instruments and techniques adapted as recommended by the manufacturer of each bracket type. Two tensile tests, one before and one after the repetitive cycles, were performed to assess the stiffness of the clips. To this end, a custom-made stainless steel 0.40 x 0.40 mm wire was inserted into the bracket slot and adapted to the universal testing machine (EMIC DL2000), after which measurements were recorded. On the loading portion of the loading-unloading curve of clips, the slope fitted a first-degree equation curve to determine the stiffness/deflection rate of the clip. The results of plastic deformation showed no significant difference among bracket types before and after the 500 cycles of opening and closure (p = 0.811). There were significant differences on stiffness among the three types of brackets (p = 0.005). The WOW bracket had higher mean values, whereas Quicklear bracket had lower values, regardless of the opening/closure cycle. Repetitive controlled opening and closure movements of the clip did not alter stiffness or cause plastic deformation.

  1. Evaluation of stiffness and plastic deformation of active ceramic self-ligating bracket clips after repetitive opening and closure movements

    Directory of Open Access Journals (Sweden)

    Grace Kelly Martins Carneiro

    2015-08-01

    Full Text Available OBJECTIVE: The aim of this study was to assess whether repetitive opening and closure of self-ligating bracket clips can cause plastic deformation of the clip.METHODS: Three types of active/interactive ceramic self-ligating brackets (n = 20 were tested: In-Ovation C, Quicklear and WOW. A standardized controlled device performed 500 cycles of opening and closure movements of the bracket clip with proper instruments and techniques adapted as recommended by the manufacturer of each bracket type. Two tensile tests, one before and one after the repetitive cycles, were performed to assess the stiffness of the clips. To this end, a custom-made stainless steel 0.40 x 0.40 mm wire was inserted into the bracket slot and adapted to the universal testing machine (EMIC DL2000, after which measurements were recorded. On the loading portion of the loading-unloading curve of clips, the slope fitted a first-degree equation curve to determine the stiffness/deflection rate of the clip.RESULTS: The results of plastic deformation showed no significant difference among bracket types before and after the 500 cycles of opening and closure (p = 0.811. There were significant differences on stiffness among the three types of brackets (p = 0.005. The WOW bracket had higher mean values, whereas Quicklear bracket had lower values, regardless of the opening/closure cycle.CONCLUSION: Repetitive controlled opening and closure movements of the clip did not alter stiffness or cause plastic deformation.

  2. Discrete ellipsoidal statistical BGK model and Burnett equations

    Science.gov (United States)

    Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

    2018-06-01

    A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

  3. Reduction of structured population models to threshold-type delay equations and functional differential equations: A case study

    Energy Technology Data Exchange (ETDEWEB)

    Smith, H.L. (Arizona State Univ., Tempe (United States))

    1993-01-01

    It is shown by way of a simple example that certain structured population models lead naturally to differential delay equations of the threshold type and that these equations can be transformed in a natural way to functional differential equations. The model examined can be viewed as a model of competition between adults and juveniles of a single population. The results indicate the possibility that this competition leads to instability. 28 refs., 2 figs.

  4. Stochastic differential equation model to Prendiville processes

    International Nuclear Information System (INIS)

    Granita; Bahar, Arifah

    2015-01-01

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

  5. Stochastic differential equation model to Prendiville processes

    Energy Technology Data Exchange (ETDEWEB)

    Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

    2015-10-22

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  6. Reinvestigation into Closure Predictions of Room D at the Waste Isolation Pilot Plant

    Energy Technology Data Exchange (ETDEWEB)

    Reedlunn, Benjamin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-10-01

    Room D was an in-situ, isothermal, underground experiment conducted at theWaste Isolation Pilot Plant between 1984 and 1991. The room was carefully instrumented to measure the horizontal and vertical closure immediately upon excavation and for several years thereafter. Early finite element simulations of salt creep around Room D under predicted the vertical closure by 4.5×, causing investigators to explore a series of changes to the way Room D was modeled. Discrepancies between simulations and measurements were resolved through a series of adjustments to model parameters, which were openly acknowledged in published reports. Interest in Room D has been rekindled recently by the U.S./German Joint Project III and Project WEIMOS, which seek to improve the predictions of rock salt constitutive models. Joint Project participants calibrate their models solely against laboratory tests, and benchmark the models against underground experiments, such as room D. This report describes updating legacy Room D simulations to today’s computational standards by rectifying several numerical issues. Subsequently, the constitutive model used in previous modeling is recalibrated two different ways against a suite of new laboratory creep experiments on salt extracted from the repository horizon of the Waste Isolation Pilot Plant. Simulations with the new, laboratory-based, calibrations under predict Room D vertical closure by 3.1×. A list of potential improvements is discussed.

  7. Reinvestigation into Closure Predictions of Room D at the Waste Isolation Pilot Plant

    Energy Technology Data Exchange (ETDEWEB)

    Reedlunn, Benjamin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-09-27

    Room D was an in-situ, isothermal, underground experiment conducted at the Waste Isolation Pilot Plant between 1984 and 1991. The room was carefully instrumented to measure the horizontal and vertical closure immediately upon excavation and for several years thereafter. Early finite element simulations of salt creep around Room D under-predicted the vertical closure by 4.5×, causing investigators to explore a series of changes to the way Room D was modeled. Discrepancies between simulations and measurements were resolved through a series of adjustments to model parameters, which were openly acknowledged in published reports. Interest in Room D has been rekindled recently by the U.S./German Joint Project III and Project WEIMOS, which seek to improve the predictions of rock salt constitutive models. Joint Project participants calibrate their models solely against laboratory tests, and benchmark the models against underground experiments, such as room D. This report describes updating legacy Room D simulations to today’s computational standards by rectifying several numerical issues. Subsequently, the constitutive model used in previous modeling is recalibrated two different ways against a suite of new laboratory creep experiments on salt extracted from the repository horizon of the Waste Isolation Pilot Plant. Simulations with the new, laboratory-based, calibrations under-predict Room D vertical closure by 3.1×. A list of potential improvements is discussed.

  8. Optimal Portfolio of Corporate Investment and Consumption Problem under Market Closure: Inflation Case

    Directory of Open Access Journals (Sweden)

    Zongyuan Huang

    2013-01-01

    Full Text Available We present the model of corporate optimal investment with consideration of the influence of inflation and the difference between the market opening and market closure. In our model, the investor has three market activities of his or her choice: investment in project A, investment in project B, and consumption. The optimal strategy for the investor is obtained using the Hamilton-Jacobi-Bellman equation which is derived using the dynamic programming principle. Further along, a specific case, the Hyperbolic Absolute Risk Aversion case, is discussed in detail, where the explicit optimal strategy can be obtained using a very simple and direct method. At the very end, we present some simulation results along with a brief analysis of the relationship between the optimal strategy and other factors.

  9. The dispersionless Lax equations and topological minimal models

    International Nuclear Information System (INIS)

    Krichever, I.

    1992-01-01

    It is shown that perturbed rings of the primary chiral fields of the topological minimal models coincide with some particular solutions of the dispersionless Lax equations. The exact formulae for the tree level partition functions, of A n topological minimal models are found. The Virasoro constraints for the analogue of the τ-function of the dispersionless Lax equation corresponding to these models are proved. (orig.)

  10. Application of Peleg\\'s Equation to Model Water Absorption in ...

    African Journals Online (AJOL)

    Sorghum and millet water absorption characteristics at temperature range 20 to 500C were investigated using the Peleg\\'s model or equation. Two sorghum varieties and one pearl millet variety were used in this investigation. Water absorption characteristics of the grain were investigated by soaking samples of the grain in ...

  11. Effective dark energy equation of state in interacting dark energy models

    International Nuclear Information System (INIS)

    Avelino, P.P.; Silva, H.M.R. da

    2012-01-01

    In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

  12. Effective dark energy equation of state in interacting dark energy models

    Energy Technology Data Exchange (ETDEWEB)

    Avelino, P.P., E-mail: ppavelin@fc.up.pt [Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto (Portugal); Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal); Silva, H.M.R. da, E-mail: hilberto.silva@gmail.com [Departamento de Fisica e Astronomia da Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto (Portugal)

    2012-07-24

    In models where dark matter and dark energy interact non-minimally, the total amount of matter in a fixed comoving volume may vary from the time of recombination to the present time due to energy transfer between the two components. This implies that, in interacting dark energy models, the fractional matter density estimated using the cosmic microwave background assuming no interaction between dark matter and dark energy will in general be shifted with respect to its true value. This may result in an incorrect determination of the equation of state of dark energy if the interaction between dark matter and dark energy is not properly accounted for, even if the evolution of the Hubble parameter as a function of redshift is known with arbitrary precision. In this Letter we find an exact expression, as well as a simple analytical approximation, for the evolution of the effective equation of state of dark energy, assuming that the energy transfer rate between dark matter and dark energy is described by a simple two-parameter model. We also provide analytical examples where non-phantom interacting dark energy models mimic the background evolution and primary cosmic microwave background anisotropies of phantom dark energy models.

  13. Solution of two energy-group neutron diffusion equation by triangular elements

    International Nuclear Information System (INIS)

    Correia Filho, A.

    1981-01-01

    The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt

  14. Simulated Leaching (Migration) Study for a Model Container-Closure System Applicable to Parenteral and Ophthalmic Drug Products.

    Science.gov (United States)

    Jenke, Dennis; Egert, Thomas; Hendricker, Alan; Castner, James; Feinberg, Tom; Houston, Christopher; Hunt, Desmond G; Lynch, Michael; Nicholas, Kumudini; Norwood, Daniel L; Paskiet, Diane; Ruberto, Michael; Smith, Edward J; Holcomb, Frank; Markovic, Ingrid

    2017-01-01

    A simulating leaching (migration) study was performed on a model container-closure system relevant to parenteral and ophthalmic drug products. This container-closure system consisted of a linear low-density polyethylene bottle (primary container), a polypropylene cap and an elastomeric cap liner (closure), an adhesive label (labeling), and a foil overpouch (secondary container). The bottles were filled with simulating solvents (aqueous salt/acid mixture at pH 2.5, aqueous buffer at pH 9.5, and 1/1 v/v isopropanol/water), a label was affixed to the filled and capped bottles, the filled bottles were placed into the foil overpouch, and the filled and pouched units were stored either upright or inverted for up to 6 months at 40 °C. After storage, the leaching solutions were tested for leached substances using multiple complementary analytical techniques to address volatile, semi-volatile, and non-volatile organic and inorganic extractables as potential leachables.The leaching data generated supported several conclusions, including that (1) the extractables (leachables) profile revealed by a simulating leaching study can qualitatively be correlated with compositional information for materials of construction, (2) the chemical nature of both the extracting medium and the individual extractables (leachables) can markedly affect the resulting profile, and (3) while direct contact between a drug product and a system's material of construction may exacerbate the leaching of substances from that material by the drug product, direct contact is not a prerequisite for migration and leaching to occur. LAY ABSTRACT: The migration of container-related extractables from a model pharmaceutical container-closure system and into simulated drug product solutions was studied, focusing on circumstances relevant to parenteral and ophthalmic drug products. The model system was constructed specifically to address the migration of extractables from labels applied to the outside of the

  15. Two-point model for divertor transport

    International Nuclear Information System (INIS)

    Galambos, J.D.; Peng, Y.K.M.

    1984-04-01

    Plasma transport along divertor field lines was investigated using a two-point model. This treatment requires considerably less effort to find solutions to the transport equations than previously used one-dimensional (1-D) models and is useful for studying general trends. It also can be a valuable tool for benchmarking more sophisticated models. The model was used to investigate the possibility of operating in the so-called high density, low temperature regime

  16. On integrability of a noncommutative q-difference two-dimensional Toda lattice equation

    Energy Technology Data Exchange (ETDEWEB)

    Li, C.X., E-mail: trisha_li2001@163.com [School of Mathematical Sciences, Capital Normal University, Beijing 100048 (China); Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Nimmo, J.J.C., E-mail: jonathan.nimmo@glasgow.ac.uk [School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QW (United Kingdom); Shen, Shoufeng, E-mail: mathssf@zjut.edu.cn [Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023 (China)

    2015-12-18

    In our previous work (C.X. Li and J.J.C. Nimmo, 2009 [18]), we presented a generalized type of Darboux transformations in terms of a twisted derivation in a unified form. The twisted derivation includes ordinary derivatives, forward difference operators, super derivatives and q-difference operators as its special cases. This result not only enables one to recover the known Darboux transformations and quasideterminant solutions to the noncommutative KP equation, the non-Abelian two-dimensional Toda lattice equation, the non-Abelian Hirota–Miwa equation and the super KdV equation, but also inspires us to investigate quasideterminant solutions to q-difference soliton equations. In this paper, we first construct the bilinear Bäcklund transformations for the known bilinear q-difference two-dimensional Toda lattice equation (q-2DTL) and then derive a Lax pair whose compatibility gives a formally different nonlinear q-2DTL equation and finally obtain its quasideterminant solutions by iterating its Darboux transformations. - Highlights: • Examples are given to illustrate the extensive applications of twisted derivations. • Bilinear Bäcklund transformation is constructed for the known q-2DTL equation. • Lax pair is obtained for an equivalent q-2DTL equation. • Quasideterminant solutions are found for the nc q-2DTL equation.

  17. Teaching Modeling with Partial Differential Equations: Several Successful Approaches

    Science.gov (United States)

    Myers, Joseph; Trubatch, David; Winkel, Brian

    2008-01-01

    We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

  18. Anterior Segment Imaging Predicts Incident Gonioscopic Angle Closure.

    Science.gov (United States)

    Baskaran, Mani; Iyer, Jayant V; Narayanaswamy, Arun K; He, Yingke; Sakata, Lisandro M; Wu, Renyi; Liu, Dianna; Nongpiur, Monisha E; Friedman, David S; Aung, Tin

    2015-12-01

    To investigate the incidence of gonioscopic angle closure after 4 years in subjects with gonioscopically open angles but varying degrees of angle closure detected on anterior segment optical coherence tomography (AS OCT; Visante; Carl Zeiss Meditec, Dublin, CA) at baseline. Prospective, observational study. Three hundred forty-two subjects, mostly Chinese, 50 years of age or older, were recruited, of whom 65 were controls with open angles on gonioscopy and AS OCT at baseline, and 277 were cases with baseline open angles on gonioscopy but closed angles (1-4 quadrants) on AS OCT scans. All subjects underwent gonioscopy and AS OCT at baseline (horizontal and vertical single scans) and after 4 years. The examiner performing gonioscopy was masked to the baseline and AS OCT data. Angle closure in a quadrant was defined as nonvisibility of the posterior trabecular meshwork by gonioscopy and visible iridotrabecular contact beyond the scleral spur in AS OCT scans. Gonioscopic angle closure in 2 or 3 quadrants after 4 years. There were no statistically significant differences in age, ethnicity, or gender between cases and controls. None of the control subjects demonstrated gonioscopic angle closure after 4 years. Forty-eight of the 277 subjects (17.3%; 95% confidence interval [CI], 12.8-23; P < 0.0001) with at least 1 quadrant of angle closure on AS OCT at baseline demonstrated gonioscopic angle closure in 2 or more quadrants, whereas 28 subjects (10.1%; 95% CI, 6.7-14.6; P < 0.004) demonstrated gonioscopic angle closure in 3 or more quadrants after 4 years. Individuals with more quadrants of angle closure on baseline AS OCT scans had a greater likelihood of gonioscopic angle closure developing after 4 years (P < 0.0001, chi-square test for trend for both definitions of angle closure). Anterior segment OCT imaging at baseline predicts incident gonioscopic angle closure after 4 years among subjects who have gonioscopically open angles and iridotrabecular contact on AS OCT at

  19. Impact of Different Standard Type A7A Drum Closure-Ring Practices on Gasket Contraction and Bolt Closure Distance– 15621

    Energy Technology Data Exchange (ETDEWEB)

    Ketusky, Edward [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Blanton, Paul [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL); Bobbitt, John H. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)

    2015-03-11

    The Department of Energy, the Savannah River National Laboratory, several manufacturers of specification drums, and the United States Department of Transportation (DOT) are collaborating in the development of a guidance document for DOE contractors and vendors who wish to qualify containers to DOT 7A Type A requirements. Currently, the effort is focused on DOT 7A Type A 208-liter (55-gallons) drums with a standard 12-gauge bolted closure ring. The U.S. requirements, contained in Title 49, Part 178.350 “Specification 7A; general packaging, Type A specifies a competent authority review of the packaging is not required for the transport of (Class 7) radioactive material containing less than Type A quantities of radioactive material. For Type AF drums, a 4 ft. regulatory free drop must be performed, such that the drum “suffers maximum damage.” Although the actual orientation is not defined by the specification, recent studies suggest that maximum damage would result from a shallow angle top impact, where kinetic energy is transferred to the lid, ultimately causing heavy damage to the lid, or even worse, causing the lid to come off. Since each vendor develops closure recommendations/procedures for the drums they manufacture, key parameters applied to drums during closing vary based on vendor. As part of the initial phase of the collaboration, the impact of the closure variants on the ability of the drum to suffer maximum damage is investigated. Specifically, closure testing is performed varying: 1) the amount of torque applied to the closure ring bolt; and, 2) stress relief protocol, including: a) weight of hammer; and, b) orientation that the hammer hits the closure ring. After closure, the amount of drum lid gasket contraction and the distance that the closure bolt moves through the closure ring is measured.

  20. Optimization and large scale computation of an entropy-based moment closure

    Science.gov (United States)

    Kristopher Garrett, C.; Hauck, Cory; Hill, Judith

    2015-12-01

    We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.