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...

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…

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

CFD model of diabatic annular two-phase flow using the Eulerian–Lagrangian approach

International Nuclear Information System (INIS)

Li, Haipeng; Anglart, Henryk

2015-01-01

Highlights: • A CFD model of annular two-phase flow with evaporating liquid film has been developed. • A two-dimensional liquid film model is developed assuming that the liquid film is sufficiently thin. • The liquid film model is coupled to the gas core flow, which is represented using the Eulerian–Lagrangian approach. - Abstract: A computational fluid dynamics (CFD) model of annular two-phase flow with evaporating liquid film has been developed based on the Eulerian–Lagrangian approach, with the objective to predict the dryout occurrence. Due to the fact that the liquid film is sufficiently thin in the diabatic annular flow and at the pre-dryout conditions, it is assumed that the flow in the wall normal direction can be neglected, and the spatial gradients of the dependent variables tangential to the wall are negligible compared to those in the wall normal direction. Subsequently the transport equations of mass, momentum and energy for liquid film are integrated in the wall normal direction to obtain two-dimensional equations, with all the liquid film properties depth-averaged. The liquid film model is coupled to the gas core flow, which currently is represented using the Eulerian–Lagrangian technique. The mass, momentum and energy transfers between the liquid film, gas, and entrained droplets have been taken into account. The resultant unified model for annular flow has been applied to the steam–water flow with conditions typical for a Boiling Water Reactor (BWR). The simulation results for the liquid film flow rate show favorable agreement with the experimental data, with the potential to predict the dryout occurrence based on criteria of critical film thickness or critical film flow rate

Modelling of film condensation in presence of non condensable gases

International Nuclear Information System (INIS)

Genevieve Geffraye; Dominique Bestion; Vladimir Kalitvianski

2005-01-01

Full text of publication follows: This paper presents recent developments in the modelling of the condensation due to heat removal from a wall with a possible presence of hydrogen, nitrogen, or air. This work is mainly concerned with nuclear reactor safety with particular reference to situations related to new reactor design, cold shutdown state and severe accident analysis. Film condensation of steam in presence of nitrogen and helium in a tube has been investigated in the COTURNE experiment in a rather large range of parameters, pressure (from 0.1 to 7 Mpa), heat flux (0.1 to 6 W/cm 2 ), mass fraction of noncondensable gas (0 to 1) and also in presence of superheated steam. The experiment represents a Steam Generator tube of a Pressurised Water Reactor and can simulate both co-current or countercurrent flow of steam and water.The models are implemented in the CATHARE code used for nuclear reactor thermal-hydraulics. The code uses two mass balance equations for liquid and gas, two momentum balance equations for liquid and gas and two energy balance equations for liquid and gas. Additional mass transport equations can be added for each non condensable gas. Heat transfers from wall to liquid film, from liquid to interface and gas to interface are modelled. The liquid film heat transfer coefficient is first investigated in pure saturated steam conditions in the pressure range from 0.1 to 7 Mpa. The CATHARE film condensation model in pure steam conditions is derived from Chen's correlation. Chen proposes a general correlation for the film condensation, covering the wavy-laminar and the turbulent film regimes and taking into account the interfacial friction effect. A large data base of laminar film regime was used including COTURNE data other available data found in the literature. The analysis of these data base suggests an influence of the liquid Reynolds number, according to the Nusselt theory, and also of the Eoetvoes number, with surface tension effects. A

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.

Mathematical Modelling of the Evaporating Liquid Films on the Basis of the Generalized Interface Conditions

Directory of Open Access Journals (Sweden)

Goncharova Olga

2016-01-01

Full Text Available The two-dimensional films, flowing down an inclined, non-uniformly heated substrate are studied. The results contain the new mathematical models developed with the help of the long-wave approximation of the Navier-Stokes and heat transfer equations or Oberbeck-Boussinesq equations in the case, when the generalized conditions are formulated at thermocapillary interface. The evolution equations for the film thickness include the effects of gravity, viscosity, capillarity, thermocapillarity, additional stress effects and evaporation.

Difficulties in modeling dispersed-flow film boiling

International Nuclear Information System (INIS)

Andreani, M.; Yadigaroglu, G.

1991-01-01

Dispersed Flow Film Boiling (DFFB) is characterized by important departures from thermal and velocity equilibrium that make it suitable for modeling with two-fluid models. The fundamental limitations and difficulties imposed by the one-dimensional nature of these models are extensively discussed. The validity of the assumptions and empirical laws used to close the system of conservation equations is critically reviewed, in light of the multidimensional aspects of the problem. Modifications that could improve the physics of the models are identified. (orig.) [de

New exact solutions of sixth-order thin-film equation

Directory of Open Access Journals (Sweden)

Wafaa M. Taha

2014-01-01

Full Text Available TheG′G-expansion method is used for the first time to find traveling-wave solutions for the sixth-order thin-film equation, where related balance numbers are not the usual positive integers. New types of exact traveling-wave solutions, such as – solitary wave solutions, are obtained the sixth-order thin-film equation, when parameters are taken at special values.

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)

A variational model of disjoining pressure: Liquid film on a nonplanar surface

Energy Technology Data Exchange (ETDEWEB)

Silin, D.; Virnovsky, G.

2009-06-01

Variational methods have been successfully used in modelling thin liquid films in numerous theoretical studies of wettability. In this paper, the variational model of the disjoining pressure is extended to the general case of a two-dimensional solid surface. The Helmgoltz free energy functional depends both on the disjoining pressure isotherm and the shape of the solid surface. The augmented Young-Laplace equation (AYLE) is a nonlinear second-order partial differential equation. A number of solutions describing wetting films on spherical grains have been obtained. In the case of cylindrical films, the phase portrait technique describes the entire variety of mathematically feasible solutions. It turns out that a periodic solution, which would describe wave-like wetting films, does not satisfy the Jacobi's condition of the classical calculus of variations. Therefore, such a solution is nonphysical. The roughness of the solid surface significantly affects liquid film stability. AYLE solutions suggest that film rupture is more likely at a location where the pore-wall surface is most exposed into the pore space and the curvature is positive.

A variational approach to a differential equation modeling thin-film flows and pertinent to Tanner's Law

International Nuclear Information System (INIS)

Khuri, S A; Sayfy, Ali

2013-01-01

This study is intended to provide a modified variational algorithm for the numerical solution of the third-order ordinary differential equation y″′ = y -2 which arises in the modeling of thin viscous films with surface tension. The resulting solution is used to solve a problem relevant to Tanner's Law for the speed of a moving three-phase contact line. Numerical results, computational comparisons, suitable error measures and illustrations are provided to testify and demonstrate the convergence and efficiency of the method.

Two-dimensional models for the optical response of thin films

Science.gov (United States)

Li, Yilei; Heinz, Tony F.

2018-04-01

In this work, we present a systematic study of 2D optical models for the response of thin layers of material under excitation by normally incident light. The treatment, within the framework of classical optics, analyzes a thin film supported by a semi-infinite substrate, with both the thin layer and the substrate assumed to exhibit local, isotropic linear response. Starting from the conventional three-dimensional (3D) slab model of the system, we derive a two-dimensional (2D) sheet model for the thin film in which the optical response is described by a sheet optical conductivity. We develop criteria for the applicability of this 2D sheet model for a layer with an optical thickness far smaller than the wavelength of the light. We examine in detail atomically thin semi-metallic and semiconductor van-der-Waals layers and ultrathin metal films as representative examples. Excellent agreement of the 2D sheet model with the 3D slab model is demonstrated over a broad spectral range from the radio frequency limit to the near ultraviolet. A linearized version of system response for the 2D model is also presented for the case where the influence of the optically thin layer is sufficiently weak. Analytical expressions for the applicability and accuracy of the different optical models are derived, and the appropriateness of the linearized treatment for the materials is considered. We discuss the advantages, as well as limitations, of these models for the purpose of deducing the optical response function of the thin layer from experiment. We generalize the theory to take into account in-plane anisotropy, layered thin film structures, and more general substrates. Implications of the 2D model for the transmission of light by the thin film and for the implementation of half- and totally absorbing layers are discussed.

Analogy between soap film and gas dynamics. I. Equations and shock jump conditions

Energy Technology Data Exchange (ETDEWEB)

Wen, C.Y.; Lai, J.Y. [Department of Mechanical Engineering, Da-Yeh University, Chang-Hwa (Taiwan)

2003-01-01

The governing equations of compressible flows in soap films are formulated based on the very specific property equations of soap films. The basic normal shock relations and the Rankine-Hugoniot equation are derived for steady one-dimensional flows in soap films. The results are similar to those of compressible gases. The analogy between compressible flows in soap films and that in gases is discussed. On short time scales, the dynamic response of the film is characterized by the Marangoni elasticity, and soap films are shown to be analogous to compressible gases with a specific heat ratio of {gamma}=1.0. Results for Gibbs elasticity are also presented for reference, and no clear analogy to compressible gases is obtained. (orig.)

Implementation of wall film condensation model to two-fluid model in component thermal hydraulic analysis code CUPID - 15237

International Nuclear Information System (INIS)

Lee, J.H.; Park, G.C.; Cho, H.K.

2015-01-01

In the containment of a nuclear reactor, the wall condensation occurs when containment cooling system and structures remove the mass and energy release and this phenomenon is of great importance to ensure containment integrity. If the phenomenon occurs in the presence of non-condensable gases, their accumulation near the condensate film leads to significant reduction in heat transfer during the condensation. This study aims at simulating the wall film condensation in the presence of non-condensable gas using CUPID, a computational multi-fluid dynamics code, which is developed by the Korea Atomic Energy Research Institute (KAERI) for the analysis of transient two-phase flows in nuclear reactor components. In order to simulate the wall film condensation in containment, the code requires a proper wall condensation model and liquid film model applicable to the analysis of the large scale system. In the present study, the liquid film model and wall film condensation model were implemented in the two-fluid model of CUPID. For the condensation simulation, a wall function approach with heat and mass transfer analogy was applied in order to save computational time without considerable refinement for the boundary layer. This paper presents the implemented wall film condensation model and then, introduces the simulation result using CUPID with the model for a conceptual condensation problem in a large system. (authors)

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.

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

Two-dimensional discrete dislocation models of deformation in polycrystalline thin metal films on substrates

International Nuclear Information System (INIS)

Hartmaier, Alexander; Buehler, Markus J.; Gao, Huajian

2005-01-01

The time-dependent irreversible deformation of polycrystalline thin metal films on substrates is investigated using two-dimensional discrete dislocation dynamics models incorporating essential parameters determined from atomistic studies. The work is focused on the mechanical properties of uncapped films, where diffusive processes play an important role. The simulations incorporate dislocation climb along the grain boundary as well as conservative glide. Despite of severe limitations of the two-dimensional dislocation models, the simulation results are found to largely corroborate experimental findings on different dominant deformation mechanisms at different film thicknesses

Propagation of perturbations for a sixth-order thin film equation

Directory of Open Access Journals (Sweden)

Zhenbang Li

2012-07-01

Full Text Available We consider an initial-boundary problem for a sixth-order thin film equation, which arises in the industrial application of the isolation oxidation of silicon. Relying on some necessary uniform estimates of the approximate solutions, we prove the existence of radial symmetric solutions to this problem in the two-dimensional space. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.

Analytical Solutions of Heat Transfer and Film Thickness with Slip Condition Effect in Thin-Film Evaporation for Two-Phase Flow in Microchannel

Directory of Open Access Journals (Sweden)

Ahmed Jassim Shkarah

2015-01-01

Full Text Available Physical and mathematical model has been developed to predict the two-phase flow and heat transfer in a microchannel with evaporative heat transfer. Sample solutions to the model were obtained for both analytical analysis and numerical analysis. It is assumed that the capillary pressure is neglected (Morris, 2003. Results are provided for liquid film thickness, total heat flux, and evaporating heat flux distribution. In addition to the sample calculations that were used to illustrate the transport characteristics, computations based on the current model were performed to generate results for comparisons with the analytical results of Wang et al. (2008 and Wayner Jr. et al. (1976. The calculated results from the current model match closely with those of analytical results of Wang et al. (2008 and Wayner Jr. et al. (1976. This work will lead to a better understanding of heat transfer and fluid flow occurring in the evaporating film region and develop an analytical equation for evaporating liquid film thickness.

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)

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)

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.

Analytical modeling of inverted annular film boiling

International Nuclear Information System (INIS)

Analytis, G.T.; Yadigaroglu, G.

1985-01-01

By employing a two-fluid formulation similar to the one used in the most recent LWR accident analysis codes, a model for the Inverted Annular Film Boiling region is developed. The conservation equations, together with appropriate constitutive relations are solved numerically and successful comparisons are made between model predictions and heat transfer coefficient distributions measured in a series of single-tube reflooding experiments. The model predicts generally correctly the dependence of the heat transfer coefficient on liquid subcooling and flow rate, through, for some cases, heat transfer is still under-predicted, and an enhancement of the heat exchange from the liquid-vapour interface to the bulk of the liquid is required

Quantum Electrostatic Model for Optical Properties of Nanoscale Gold Films

Directory of Open Access Journals (Sweden)

Qian Haoliang

2015-11-01

Full Text Available The optical properties of thin gold films with thickness varying from 2.5 nm to 30 nm are investigated. Due to the quantum size effect, the optical constants of the thin gold film deviate from the Drude model for bulk material as film thickness decreases, especially around 2.5 nm, where the electron energy level becomes discrete. A theory based on the self-consistent solution of the Schrödinger equation and the Poisson equation is proposed and its predictions agree well with experimental results.

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.

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.

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

3-D modeling of parietal liquid films in internal combustion engines; Modelisation tridimensionnelle des films liquides parietaux dans les moteurs a combustion interne

Energy Technology Data Exchange (ETDEWEB)

Foucart, H

1998-12-11

To simulate the air-fuel mixing in the intake ports and cylinder of an internal combustion engines, a wall fuel liquid film model has been developed for integration in 3D CFD codes. Phenomena taken into account include wall film formation by an impinging spray without splashing effect, film transport such as governed by mass and momentum equations with hot wall effects, and evaporation considering energy equation with an analytical mass transfer formulation developed here. A continuous-fluid method is used to describe the wall film over a three dimensional complex surface. The basic approximation is that of a laminar incompressible boundary layer; the liquid film equations are written in an integral form and solved by a first-order ALE finite volume scheme; the equation system is closed without coefficient fitting requirements. The model has been implemented in a Multi-Block version of KIVA-II (KMB) and tested against problems having theoretical solutions. Then in a first step, it has been compared to the measurements obtained in a cylindrical pipe reproducing the main characteristics of SI engine intake pipe flow and in a second step, it has been compared to the Xiong experiment concerning the film evaporation on a hot wall. The film behaviour is satisfactory reproduced by the computations for a set of operating conditions. Finally, engine calculations were conducted showing the importance of including a liquid film model for the simulations. (author) 54 refs.

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

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)

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)

Note on the hydrodynamic description of thin nematic films: Strong anchoring model

KAUST Repository

Lin, Te-Sheng; Cummings, Linda J.; Archer, Andrew J.; Kondic, Lou; Thiele, Uwe

2013-01-01

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion. © 2013 AIP Publishing LLC.

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.

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)

Modelling the evaporation of a tear film over a contact lens.

Science.gov (United States)

Talbott, Kevin; Xu, Amber; Anderson, Daniel M; Seshaiyer, Padmanabhan

2015-06-01

A contact lens (CL) separates the tear film into a pre-lens tear film (PrLTF), the fluid layer between the CL and the outside environment, and a post-lens tear film (PoLTF), the fluid layer between the CL and the cornea. We examine a model for evaporation of a PrLTF on a modern permeable CL allowing fluid transfer between the PrLTF and the PoLTF. Evaporation depletes the PrLTF, and continued evaporation causes depletion of the PoLTF via fluid loss through the CL. Governing equations include Navier-Stokes, heat and Darcy's equations for the fluid flow and heat transfer in the PrLTF and porous layer. The PoLTF is modelled by a fixed pressure condition on the posterior surface of the CL. The original model is simplified using lubrication theory for the PrLTF and CL applied to a sagittal plane through the eye. We obtain a partial differential equation (PDE) for the PrLTF thickness that is first-order in time and fourth-order in space. This model incorporates evaporation, conjoining pressure effects in the PrLTF, capillarity and heat transfer. For a planar film, we find that this PDE can be reduced to an ordinary differential equation (ODE) that can be solved analytically or numerically. This reduced model allows for interpretation of the various system parameters and captures most of the basic physics contained in the model. Comparisons of ODE and PDE models, including estimates for the loss of fluid through the lens due to evaporation, are given. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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)

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.

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.

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)

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

Analytical modeling of inverted annular film boiling

International Nuclear Information System (INIS)

Analytis, G.T.; Yadigaroglu, G.

1987-01-01

By employing a two-fluid formulation similar to the one used in the most recent LWR accident analysis codes, a model for the Inverted Annular Film Boiling region is developed. The conservation equations, together with appropriate closure relations are solved numerically. Successful comparisons are made between model predictions and heat transfer coefficient distributions measured in a series of single-tube reflooding experiments. Generally, the model predicts correctly the dependence of the heat transfer coefficient on liquid subcooling and flow rate; for some cases, however, heat transfer is still under-predicted, and an enhancement of the heat exchange from the liquid-vapour interface to the bulk of the liquid is required. The importance of the initial conditions at the quench front is also discussed. (orig.)

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

Mechanistic model of the inverted annular film boiling

International Nuclear Information System (INIS)

Seok, Ho; Chang, Soon Heung

1989-01-01

An analytical model is developed to predict the heat transfer coefficient and the friction factor in the inverted annular film boiling. The developed model is based on two-fluid mass, momentum and energy balance equations and a theoretical velocity profile. The predictions of the proposed model are compared with the experimental data and the well-established correlations. For the heat transfer coefficient, they agree with the experimental data and are more promising than those of Bromely and Berenson correlations. The present model also accounts the effects of the mass flux and subcooling on the heat transfer. The friction factor predictions agree qualitatively with the experimental measurements, while some cases show a similar behavior with those of the post-CHF dispersed flow obtained from Beattie's correlation

Improving the Validity of Squeeze Film Air-Damping Model of MEMS Devices with Border Effect

Directory of Open Access Journals (Sweden)

Cheng Bai

2014-01-01

Full Text Available Evaluation of squeezed film air damping is critical in the design and control of dynamic MEMS devices. The published squeezed film air damping models are generally derived from the analytical solutions of Reynolds equation or its other modified forms under the supposition of trivial pressure boundary conditions on the peripheral borders. These treatments ignoring the border effect can not give faithful result for structure with smaller air venting gap or the double-gimbaled structure in which the inner frame and outer one affect the air venting. In this paper, we use Green’s function to solve the nonlinear Reynolds equation with inhomogeneous boundary conditions. For two typical normal motion cases of parallel plate, the analytical models of squeeze film damping force with border effect are established. The viscous and inertial losses with real values and image values acoustic impedance are all included in the model. These models reduced the time consumption while giving satisfactory result. Without multifield coupling analysis, the estimation of the dynamic behavior of MEMS device is also allowed, and the simulation of the system performance is more convenient.

Predictive modeling of nanoscale domain morphology in solution-processed organic thin films

Science.gov (United States)

Schaaf, Cyrus; Jenkins, Michael; Morehouse, Robell; Stanfield, Dane; McDowall, Stephen; Johnson, Brad L.; Patrick, David L.

2017-09-01

The electronic and optoelectronic properties of molecular semiconductor thin films are directly linked to their extrinsic nanoscale structural characteristics such as domain size and spatial distributions. In films prepared by common solution-phase deposition techniques such as spin casting and solvent-based printing, morphology is governed by a complex interrelated set of thermodynamic and kinetic factors that classical models fail to adequately capture, leaving them unable to provide much insight, let alone predictive design guidance for tailoring films with specific nanostructural characteristics. Here we introduce a comprehensive treatment of solution-based film formation enabling quantitative prediction of domain formation rates, coverage, and spacing statistics based on a small number of experimentally measureable parameters. The model combines a mean-field rate equation treatment of monomer aggregation kinetics with classical nucleation theory and a supersaturation-dependent critical nucleus size to solve for the quasi-two-dimensional temporally and spatially varying monomer concentration, nucleation rate, and other properties. Excellent agreement is observed with measured nucleation densities and interdomain radial distribution functions in polycrystalline tetracene films. Numerical solutions lead to a set of general design rules enabling predictive morphological control in solution-processed molecular crystalline films.

A two-layer model for buoyant inertial displacement flows in inclined pipes

Science.gov (United States)

Etrati, Ali; Frigaard, Ian A.

2018-02-01

We investigate the inertial flows found in buoyant miscible displacements using a two-layer model. From displacement flow experiments in inclined pipes, it has been observed that for significant ranges of Fr and Re cos β/Fr, a two-layer, stratified flow develops with the heavier fluid moving at the bottom of the pipe. Due to significant inertial effects, thin-film/lubrication models developed for laminar, viscous flows are not effective for predicting these flows. Here we develop a displacement model that addresses this shortcoming. The complete model for the displacement flow consists of mass and momentum equations for each fluid, resulting in a set of four non-linear equations. By integrating over each layer and eliminating the pressure gradient, we reduce the system to two equations for the area and mean velocity of the heavy fluid layer. The wall and interfacial stresses appear as source terms in the reduced system. The final system of equations is solved numerically using a robust, shock-capturing scheme. The equations are stabilized to remove non-physical instabilities. A linear stability analysis is able to predict the onset of instabilities at the interface and together with numerical solution, is used to study displacement effectiveness over different parametric regimes. Backflow and instability onset predictions are made for different viscosity ratios.

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.

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...

A simple geometrical model describing shapes of soap films suspended on two rings

Science.gov (United States)

Herrmann, Felix J.; Kilvington, Charles D.; Wildenberg, Rebekah L.; Camacho, Franco E.; Walecki, Wojciech J.; Walecki, Peter S.; Walecki, Eve S.

2016-09-01

We measured and analysed the stability of two types of soap films suspended on two rings using the simple conical frusta-based model, where we use common definition of conical frustum as a portion of a cone that lies between two parallel planes cutting it. Using frusta-based we reproduced very well-known results for catenoid surfaces with and without a central disk. We present for the first time a simple conical frusta based spreadsheet model of the soap surface. This very simple, elementary, geometrical model produces results surprisingly well matching the experimental data and known exact analytical solutions. The experiment and the spreadsheet model can be used as a powerful teaching tool for pre-calculus and geometry students.

Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

Science.gov (United States)

Liang, Hong; Xu, Jiangrong; Chen, Jiangxing; Wang, Huili; Chai, Zhenhua; Shi, Baochang

2018-03-01

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

Rigorous asymptotics of traveling-wave solutions to the thin-film equation and Tanner’s law

Science.gov (United States)

Giacomelli, Lorenzo; Gnann, Manuel V.; Otto, Felix

2016-09-01

We are interested in traveling-wave solutions to the thin-film equation with zero microscopic contact angle (in the sense of complete wetting without precursor) and inhomogeneous mobility {{h}3}+{λ3-n}{{h}n} , where h, λ, and n\\in ≤ft(\\frac{3}{2},\\frac{7}{3}\\right) denote film height, slip parameter, and mobility exponent, respectively. Existence and uniqueness of these solutions have been established by Maria Chiricotto and the first of the authors in previous work under the assumption of sub-quadratic growth as h\\to ∞ . In the present work we investigate the asymptotics of solutions as h\\searrow 0 (the contact-line region) and h\\to ∞ . As h\\searrow 0 we observe, to leading order, the same asymptotics as for traveling waves or source-type self-similar solutions to the thin-film equation with homogeneous mobility h n and we additionally characterize corrections to this law. Moreover, as h\\to ∞ we identify, to leading order, the logarithmic Tanner profile, i.e. the solution to the corresponding unperturbed problem with λ =0 that determines the apparent macroscopic contact angle. Besides higher-order terms, corrections turn out to affect the asymptotic law as h\\to ∞ only by setting the length scale in the logarithmic Tanner profile. Moreover, we prove that both the correction and the length scale depend smoothly on n. Hence, in line with the common philosophy, the precise modeling of liquid-solid interactions (within our model, the mobility exponent) does not affect the qualitative macroscopic properties of the film.

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

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

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

We focus on a theoretical analysis of nonreactive solute transport in porous media through the volume averaging technique. Darcy-scale transport models based on continuum formulations typically include large scale dispersive processes which are embedded in a pore-scale advection diffusion equation through a Fickian analogy. This formulation has been extensively questioned in the literature due to its inability to depict observed solute breakthrough curves in diverse settings, ranging from the laboratory to the field scales. The heterogeneity of the pore-scale velocity field is one of the key sources of uncertainties giving rise to anomalous (non-Fickian) dispersion in macro-scale porous systems. Some of the models which are employed to interpret observed non-Fickian solute behavior make use of a continuum formulation of the porous system which assumes a two-region description and includes a bimodal velocity distribution. A first class of these models comprises the so-called ''mobile-immobile'' conceptualization, where convective and dispersive transport mechanisms are considered to dominate within a high velocity region (mobile zone), while convective effects are neglected in a low velocity region (immobile zone). The mass exchange between these two regions is assumed to be controlled by a diffusive process and is macroscopically described by a first-order kinetic. An extension of these ideas is the two equation ''mobile-mobile'' model, where both transport mechanisms are taken into account in each region and a first-order mass exchange between regions is employed. Here, we provide an analytical derivation of two region "mobile-mobile" meso-scale models through a rigorous upscaling of the pore-scale advection diffusion equation. Among the available upscaling methodologies, we employ the Volume Averaging technique. In this approach, the heterogeneous porous medium is supposed to be pseudo-periodic, and can be represented through a (spatially) periodic unit cell

A Squeeze-film Damping Model for the Circular Torsion Micro-resonators

Science.gov (United States)

Yang, Fan; Li, Pu

2017-07-01

In recent years, MEMS devices are widely used in many industries. The prediction of squeeze-film damping is very important for the research of high quality factor resonators. In the past, there have been many analytical models predicting the squeeze-film damping of the torsion micro-resonators. However, for the circular torsion micro-plate, the works over it is very rare. The only model presented by Xia et al[7] using the method of eigenfunction expansions. In this paper, The Bessel series solution is used to solve the Reynolds equation under the assumption of the incompressible gas of the gap, the pressure distribution of the gas between two micro-plates is obtained. Then the analytical expression for the damping constant of the device is derived. The result of the present model matches very well with the finite element method (FEM) solutions and the result of Xia’s model, so the present models’ accuracy is able to be validated.

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.

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...

Effect of disjoining pressure in a thin film equation with non-uniform forcing

KAUST Repository

MOULTON, D. E.

2013-08-02

We explore the effect of disjoining pressure on a thin film equation in the presence of a non-uniform body force, motivated by a model describing the reverse draining of a magnetic film. To this end, we use a combination of numerical investigations and analytical considerations. The disjoining pressure has a regularizing influence on the evolution of the system and appears to select a single steady-state solution for fixed height boundary conditions; this is in contrast with the existence of a continuum of locally attracting solutions that exist in the absence of disjoining pressure for the same boundary conditions. We numerically implement matched asymptotic expansions to construct equilibrium solutions and also investigate how they behave as the disjoining pressure is sent to zero. Finally, we consider the effect of the competition between forcing and disjoining pressure on the coarsening dynamics of the thin film for fixed contact angle boundary conditions. Copyright © Cambridge University Press 2013.

Improvement of a wall thinning rate model for liquid droplet impingement erosion. Implementation of liquid film thickness model with consideration of film behavior

International Nuclear Information System (INIS)

Morita, Ryo

2014-01-01

Liquid droplet impingement erosion (LDI) is defined as an erosion phenomenon caused by high-speed droplet attack in a steam flow. Pipe wall thinning by LDI is sometimes observed in a steam piping system of a power plant. As LDI usually occurs very locally and is difficult to detect, predicting LDI location is required for safe operation of power plant systems. Therefore, we have involved in the research program to develop prediction tools that will be used easily in actual power plants. Our previous researches developed a thinning rate evaluation model due to LDI (LDI model) and the evaluation system of the thinning rate and the thinning shape within a practically acceptable time (LDI evaluation system). Though the LDI model can include a cushioning effect of liquid film which is generated on the material surface by droplet impingement as an empirical equation with fluid parameter, the liquid film thickness is not clarified due to complex flow condition. In this study, to improve the LDI model and the LDI evaluation system, an analytical model of the liquid film thickness was proposed with consideration of the liquid film flow behavior on the material surface. The mass balance of the liquid film was considered, and the results of CFD calculations and existing researches were applied to obtain the liquid film thickness in this model. As a result of the LDI evaluation of the new LDI model with liquid film model, improvement of the LDI model was achieved. (author)

Unsteady Flow in a Horizontal Double-Sided Symmetric Thin Liquid Films

Directory of Open Access Journals (Sweden)

Joseph G. ABDULAHAD

2017-06-01

Full Text Available In this paper a mathematical model is constructed to describe a two dimensional incompressible flow in a symmetric horizontal thin liquid film for unsteadies flow. We apply the Navier-Stokes equations with specified boundary conditions and we obtain the equation of the film thickness by using the similarity method in which we can isolate the explicit time dependence and then the shape of the film will depend on one variable only.

Analytical approximate equations for the resistivity and its temperature coefficient in thin polycrystalline metallic films

International Nuclear Information System (INIS)

Tellier, C.R.; Tosser, A.J.

1977-01-01

In the usual thickness range of sputtered metallic films, analytical linearized approximate expressions of polycrystalline film resistivity and its t.c.r. are deduced from the Mayadas-Shatzkes theoretical equations. A good experimental fit is observed for Al rf sputtered metal films. (orig.) [de

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

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)

Bayesian inference of substrate properties from film behavior

International Nuclear Information System (INIS)

Aggarwal, R; Demkowicz, M J; Marzouk, Y M

2015-01-01

We demonstrate that by observing the behavior of a film deposited on a substrate, certain features of the substrate may be inferred with quantified uncertainty using Bayesian methods. We carry out this demonstration on an illustrative film/substrate model where the substrate is a Gaussian random field and the film is a two-component mixture that obeys the Cahn–Hilliard equation. We construct a stochastic reduced order model to describe the film/substrate interaction and use it to infer substrate properties from film behavior. This quantitative inference strategy may be adapted to other film/substrate systems. (paper)

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

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.

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

Modeling growth kinetics of thin films made by atomic layer deposition in lateral high-aspect-ratio structures

Science.gov (United States)

Ylilammi, Markku; Ylivaara, Oili M. E.; Puurunen, Riikka L.

2018-05-01

The conformality of thin films grown by atomic layer deposition (ALD) is studied using all-silicon test structures with long narrow lateral channels. A diffusion model, developed in this work, is used for studying the propagation of ALD growth in narrow channels. The diffusion model takes into account the gas transportation at low pressures, the dynamic Langmuir adsorption model for the film growth and the effect of channel narrowing due to film growth. The film growth is calculated by solving the diffusion equation with surface reactions. An efficient analytic approximate solution of the diffusion equation is developed for fitting the model to the measured thickness profile. The fitting gives the equilibrium constant of adsorption and the sticking coefficient. This model and Gordon's plug flow model are compared. The simulations predict the experimental measurement results quite well for Al2O3 and TiO2 ALD processes.

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.)

Analytical Model of a PZT Thick-Film Triaxial Accelerometer for Optimum Design

DEFF Research Database (Denmark)

Hindrichsen, Christian Carstensen; Almind, Ninia Sejersen; Brodersen, S. H.

2009-01-01

We present a mechanical model of a triaxial micro accelerometer design using PZT thick-film as the sensing material. The model is based on the full anisotropic material tensors and Eulers' beam equation using simplifying assumptions where the smaller stress contributions are ignored. The model...

Model of vortex dynamics in superconducting films in two-coil measurements of the coherence length

Science.gov (United States)

Lemberger, Thomas; Loh, Yen Lee

In two-coil measurements on superconducting films, a magnetic field from a small coil is applied to the center of the film. When the amplitude of the ac field is increased, the film undergoes a transition from the ``Meissner'' state to a state with vortices and antivortices. Ultimately, the vortex density matches the applied magnetic field and field screening is negligible. Experimentally, the field at the transition is related to the superconducting coherence length, although a full theory of the relationship is lacking. We show that the mutual inductance between drive and pickup coils, on opposite sides of the film, as a function of ac field amplitude is well-described by a phenomenological model in which vortices and antivortices appear together in the film at the radius where the induced supercurrent is strongest, and then they move through a landscape of moderately strong vortex pinning sites. Work at OSU supported by DOE-Basic Energy Sciences through Grant No. FG02-08ER46533.

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.)

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.)

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.

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)

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.

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

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.

Multiphysics modeling of two-phase film boiling within porous corrosion deposits

Energy Technology Data Exchange (ETDEWEB)

Jin, Miaomiao, E-mail: mmjin@mit.edu; Short, Michael, E-mail: hereiam@mit.edu

2016-07-01

Porous corrosion deposits on nuclear fuel cladding, known as CRUD, can cause multiple operational problems in light water reactors (LWRs). CRUD can cause accelerated corrosion of the fuel cladding, increase radiation fields and hence greater exposure risk to plant workers once activated, and induce a downward axial power shift causing an imbalance in core power distribution. In order to facilitate a better understanding of CRUD's effects, such as localized high cladding surface temperatures related to accelerated corrosion rates, we describe an improved, fully-coupled, multiphysics model to simulate heat transfer, chemical reactions and transport, and two-phase fluid flow within these deposits. Our new model features a reformed assumption of 2D, two-phase film boiling within the CRUD, correcting earlier models' assumptions of single-phase coolant flow with wick boiling under high heat fluxes. This model helps to better explain observed experimental values of the effective CRUD thermal conductivity. Finally, we propose a more complete set of boiling regimes, or a more detailed mechanism, to explain recent CRUD deposition experiments by suggesting the new concept of double dryout specifically in thick porous media with boiling chimneys. - Highlights: • A two-phase model of CRUD's effects on fuel cladding is developed and improved. • This model eliminates the formerly erroneous assumption of wick boiling. • Higher fuel cladding temperatures are predicted when accounting for two-phase flow. • Double-peaks in thermal conductivity vs. heat flux in experiments are explained. • A “double dryout” mechanism in CRUD is proposed based on the model and experiments.

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.

Selective enhancement of Selényi rings induced by the cross-correlation between the interfaces of a two-dimensional randomly rough dielectric film

Science.gov (United States)

Banon, J.-P.; Hetland, Ø. S.; Simonsen, I.

2018-02-01

By the use of both perturbative and non-perturbative solutions of the reduced Rayleigh equation, we present a detailed study of the scattering of light from two-dimensional weakly rough dielectric films. It is shown that for several rough film configurations, Selényi interference rings exist in the diffusely scattered light. For film systems supported by dielectric substrates where only one of the two interfaces of the film is weakly rough and the other planar, Selényi interference rings are observed at angular positions that can be determined from simple phase arguments. For such single-rough-interface films, we find and explain by a single scattering model that the contrast in the interference patterns is better when the top interface of the film (the interface facing the incident light) is rough than when the bottom interface is rough. When both film interfaces are rough, Selényi interference rings exist but a potential cross-correlation of the two rough interfaces of the film can be used to selectively enhance some of the interference rings while others are attenuated and might even disappear. This feature may in principle be used in determining the correlation properties of interfaces of films that otherwise would be difficult to access.

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)

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

Finite size effects in phase transformation kinetics in thin films and surface layers

International Nuclear Information System (INIS)

Trofimov, Vladimir I.; Trofimov, Ilya V.; Kim, Jong-Il

2004-01-01

In studies of phase transformation kinetics in thin films, e.g. crystallization of amorphous films, until recent time is widely used familiar Kolmogorov-Johnson-Mehl-Avrami (KJMA) statistical model of crystallization despite it is applicable only to an infinite medium. In this paper a model of transformation kinetics in thin films based on a concept of the survival probability for randomly chosen point during transformation process is presented. Two model versions: volume induced transformation (VIT) when the second-phase grains nucleate over a whole film volume and surface induced transformation (SIT) when they form on an interface with two nucleation mode: instantaneous nucleation at transformation onset and continuous one during all the process are studied. At VIT-process due to the finite film thickness effects the transformation profile has a maximum in a film middle, whereas that of the grains population reaches a minimum inhere, the grains density is always higher than in a volume material, and the thinner film the slower it transforms. The transformation kinetics in a thin film obeys a generalized KJMA equation with parameters depending on a film thickness and in limiting cases of extremely thin and thick film it reduces to classical KJMA equation for 2D- and 3D-system, respectively

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.

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.

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.

Effects of Velocity-Slip and Viscosity Variation in Squeeze Film Lubrication of Two Circular Plates

Directory of Open Access Journals (Sweden)

R.R. Rao

2013-03-01

Full Text Available A generalized form of Reynolds equation for two symmetrical surfaces is taken by considering velocity-slip at the bearing surfaces. This equation is applied to study the effects of velocity-slip and viscosity variation for the lubrication of squeeze films between two circular plates. Expressions for the load capacity and squeezing time obtained are also studied theoretically for various parameters. The load capacity and squeezing time decreases due to slip. They increase due to the presence of high viscous layer near the surface and decrease due to low viscous layer.

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.

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

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)

Application of a film flow model to predicting burnout under transient conditions

International Nuclear Information System (INIS)

Leslie, D.C.; Kirby, G.J.

1967-08-01

The film flow model developed previously has been generalised to transient situations by assuming that only convection is changed by the transient; evaporation, deposition and entrainment are assumed to be unaffected. A computer code TRABUT computes the time behaviour of the mass velocity and the quality by the method of characteristics, and then integrates the film flow equations along the same characteristics until the point of burn-out or zero film flow is reached. The time delay between the onset of a transient and burn-out has been computed both for flux and flow transients. These computations have been compared with those made using the standard local conditions hypothesis. The film flow model gives shorter delays in almost all cases, but the difference would not be detectable with present experimental techniques. (author)

Conductance Thin Film Model of Flexible Organic Thin Film Device using COMSOL Multiphysics

Science.gov (United States)

Carradero-Santiago, Carolyn; Vedrine-Pauléus, Josee

We developed a virtual model to analyze the electrical conductivity of multilayered thin films placed above a graphene conducting and flexible polyethylene terephthalate (PET) substrate. The organic layers of poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) as a hole conducting layer, poly(3-hexylthiophene-2,5-diyl) (P3HT), as a p-type, phenyl-C61-butyric acid methyl ester (PCBM) and as n-type, with aluminum as a top conductor. COMSOL Multiphysics was the software we used to develop the virtual model to analyze potential variations and conductivity through the thin-film layers. COMSOL Multiphysics software allows simulation and modeling of physical phenomena represented by differential equations such as heat transfer, fluid flow, electromagnetism, and structural mechanics. In this work, using the AC/DC, electric currents module we defined the geometry of the model and properties for each of the six layers: PET/graphene/PEDOT:PSS/P3HT/PCBM/aluminum. We analyzed the model with varying thicknesses of graphene and active layers (P3HT/PCBM). This simulation allowed us to analyze the electrical conductivity, and visualize the model with varying voltage potential, or bias across the plates, useful for applications in solar cell devices.

Global existence of solutions to a tear film model with locally elevated evaporation rates

Science.gov (United States)

Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P.

2017-07-01

Motivated by a model proposed by Peng et al. (2014) for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDEs for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and present numerical simulations that are in agreement with the analytic results. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.

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.

Modeling Replenishment of Ultrathin Liquid Perfluoro polyether Z Films on Solid Surfaces Using Monte Carlo Simulation

International Nuclear Information System (INIS)

Mayeed, M.S.; Kato, T.

2014-01-01

Applying the reptation algorithm to a simplified perfluoro polyether Z off-lattice polymer model an NVT Monte Carlo simulation has been performed. Bulk condition has been simulated first to compare the average radius of gyration with the bulk experimental results. Then the model is tested for its ability to describe dynamics. After this, it is applied to observe the replenishment of nano scale ultrathin liquid films on solid flat carbon surfaces. The replenishment rate for trenches of different widths (8, 12, and 16 nms for several molecular weights) between two films of perfluoro polyether Z from the Monte Carlo simulation is compared to that obtained solving the diffusion equation using the experimental diffusion coefficients of Ma et al. (1999), with room condition in both cases. Replenishment per Monte Carlo cycle seems to be a constant multiple of replenishment per second at least up to 2 nm replenished film thickness of the trenches over the carbon surface. Considerable good agreement has been achieved here between the experimental results and the dynamics of molecules using reptation moves in the ultrathin liquid films on solid surfaces.

Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions

International Nuclear Information System (INIS)

Thiele, U; Vancea, I; Archer, A J; Robbins, M J; Frastia, L; Stannard, A; Pauliac-Vaujour, E; Martin, C P; Blunt, M O; Moriarty, P J

2009-01-01

We review recent experiments on dewetting thin films of evaporating colloidal nanoparticle suspensions (nanofluids) and discuss several theoretical approaches to describe the ongoing processes including coupled transport and phase changes. These approaches range from microscopic discrete stochastic theories to mesoscopic continuous deterministic descriptions. In particular, we describe (i) a microscopic kinetic Monte Carlo model, (ii) a dynamical density functional theory and (iii) a hydrodynamic thin film model. Models (i) and (ii) are employed to discuss the formation of polygonal networks, spinodal and branched structures resulting from the dewetting of an ultrathin 'postcursor film' that remains behind a mesoscopic dewetting front. We highlight, in particular, the presence of a transverse instability in the evaporative dewetting front, which results in highly branched fingering structures. The subtle interplay of decomposition in the film and contact line motion is discussed. Finally, we discuss a simple thin film model (iii) of the hydrodynamics on the mesoscale. We employ coupled evolution equations for the film thickness profile and mean particle concentration. The model is used to discuss the self-pinning and depinning of a contact line related to the 'coffee-stain' effect. In the course of the review we discuss the advantages and limitations of the different theories, as well as possible future developments and extensions.

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)

Control Operator for the Two-Dimensional Energized Wave Equation

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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.

Numerical solution of conservation equations in the transient model for the system thermal - hydraulics in the Korsar computer code

International Nuclear Information System (INIS)

Yudov, Y.V.

2001-01-01

The functional part of the KORSAR computer code is based on the computational unit for the reactor system thermal-hydraulics and other thermal power systems with water cooling. The two-phase flow dynamics of the thermal-hydraulic network is modelled by KORSAR in one-dimensional two-fluid (non-equilibrium and nonhomogeneous) approximation with the same pressure of both phases. Each phase is characterized by parameters averaged over the channel sections, and described by the conservation equations for mass, energy and momentum. The KORSAR computer code relies upon a novel approach to mathematical modelling of two-phase dispersed-annular flows. This approach allows a two-fluid model to differentiate the effects of the liquid film and droplets in the gas core on the flow characteristics. A semi-implicit numerical scheme has been chosen for deriving discrete analogs the conservation equations in KORSAR. In the semi-implicit numerical scheme, solution of finite-difference equations is reduced to the problem of determining the pressure field at a new time level. For the one-channel case, the pressure field is found from the solution of a system of linear algebraic equations by using the tri-diagonal matrix method. In the branched network calculation, the matrix of coefficients in the equations describing the pressure field is no longer tri-diagonal but has a sparseness structure. In this case, the system of linear equations for the pressure field can be solved with any of the known classical methods. Such an approach is implemented in the existing best-estimate thermal-hydraulic computer codes (TRAC, RELAP5, etc.) For the KORSAR computer code, we have developed a new non-iterative method for calculating the pressure field in the network of any topology. This method is based on the tri-diagonal matrix method and performs well when solving the thermal-hydraulic network problems. (author)

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.

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)

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

Water uptake in free films and coatings using the Brasher and Kingsbury equation: a possible explanation of the different values obtained by electrochemical Impedance spectroscopy and gravimetry

International Nuclear Information System (INIS)

Vosgien Lacombre, C.; Bouvet, G.; Trinh, D.; Mallarino, S.; Touzain, S.

2017-01-01

For many years, the water uptake in organic coatings was measured by EIS and/or gravimetry but differences in water content values were found in almost all studies. The Brasher-Kingsbury equation used in the electrochemical analysis (EIS) is often criticized because elementary assumptions may be unvalid. The origin of the discrepancy between both methods is still of interest because many questions remain open and this study aims to provide new insights to these questions. In this work, free films and coatings of a model epoxy-amine system were immersed in a 3 wt.% NaCl solution. The water uptake in free films was evaluated using gravimetric measurements and EIS, using the Basher-Kingsbury equation. The mass of free-films used in the EIS tests was measured and compare to gravimetric measurements while the water uptake (EIS) in free films was compared to that obtained with coatings. It was found that the mass increase of free films tested with EIS was in agreement with gravimetric measurements but was always lower than the water uptake obtained by EIS. Moreover, the water uptake in free films (EIS) was different from that obtained with coatings. In all cases, it was found that the Basher-Kingsbury equation overestimated the water uptake. It appears that the differences between EIS and gravimetric measurements can be analyzed in terms of geometrical effects. Indeed, the swelling in free films and coatings can be monitored by DMA and SECM during ageing. Finally, by mixing the experimental swelling data and the Brasher-Kingsbury equation, the same value of water uptake was obtained by EIS and gravimetry for coatings.

Surface self-organization in multilayer film coatings

Science.gov (United States)

Shuvalov, Gleb M.; Kostyrko, Sergey A.

2017-12-01

It is a recognized fact that during film deposition and subsequent thermal processing the film surface evolves into an undulating profile. Surface roughness affects many important aspects in the engineering application of thin film materials such as wetting, heat transfer, mechanical, electromagnetic and optical properties. To accurately control the morphological surface modifications at the micro- and nanoscale and improve manufacturing techniques, we design a mathematical model of the surface self-organization process in multilayer film materials. In this paper, we consider a solid film coating with an arbitrary number of layers under plane strain conditions. The film surface has a small initial perturbation described by a periodic function. It is assumed that the evolution of the surface relief is governed by surface and volume diffusion. Based on Gibbs thermodynamics and linear theory of elasticity, we present a procedure for constructing a governing equation that gives the amplitude change of the surface perturbation with time. A parametric study of the evolution equation leads to the definition of a critical undulation wavelength that stabilizes the surface. As a numerical result, the influence of geometrical and physical parameters on the morphological stability of an isotropic two-layered film coating is analyzed.

Macroscopic Modeling of a One-Dimensional Electrochemical Cell using the Poisson-Nernst-Planck Equations

Science.gov (United States)

Yan, David

This thesis presents the one-dimensional equations, numerical method and simulations of a model to characterize the dynamical operation of an electrochemical cell. This model extends the current state-of-the art in that it accounts, in a primitive way, for the physics of the electrolyte/electrode interface and incorporates diffuse-charge dynamics, temperature coupling, surface coverage, and polarization phenomena. The one-dimensional equations account for a system with one or two mobile ions of opposite charge, and the electrode reaction we consider (when one is needed) is a one-electron electrodeposition reaction. Though the modeled system is far from representing a realistic electrochemical device, our results show a range of dynamics and behaviors which have not been observed previously, and explore the numerical challenges required when adding more complexity to a model. Furthermore, the basic transport equations (which are developed in three spatial dimensions) can in future accomodate the inclusion of additional physics, and coupling to more complex boundary conditions that incorporate two-dimensional surface phenomena and multi-rate reactions. In the model, the Poisson-Nernst-Planck equations are used to model diffusion and electromigration in an electrolyte, and the generalized Frumkin-Butler-Volmer equation is used to model reaction kinetics at electrodes. An energy balance equation is derived and coupled to the diffusion-migration equation. The model also includes dielectric polarization effects by introducing different values of the dielectric permittivity in different regions of the bulk, as well as accounting for surface coverage effects due to adsorption, and finite size "crowding", or steric effects. Advection effects are not modeled but could in future be incorporated. In order to solve the coupled PDE's, we use a variable step size second order scheme in time and finite differencing in space. Numerical tests are performed on a simplified system and

Ferromagnetic resonance linewidth and two-magnon scattering in Fe1-xGdx thin films

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Sheng Jiang

2017-05-01

Full Text Available Magnetization dynamics of Fe1-xGdx thin films (0 ≤ x ≤ 22% has been investigated by ferromagnetic resonance (FMR. Out-of-plane magnetic field orientation dependence of resonance field and linewidth has been measured. Resonance field and FMR linewidth have been fitted by the free energy of our system and Landau-Lifshitz-Gilbert (LLG equation. It is found that FMR linewidth contains huge extrinsic components including two-magnon scattering contribution and inhomogeneous broadening for FeGd alloy thin films. In addition, the intrinsic linewidth and real damping constants have been obtained by extracting the extrinsic linewidth. The damping constant enhanced from 0.011 to 0.038 as Gd dopants increase from 0 to 22% which originates from the enhancement of L-S coupling in FeGd thin films. Besides, gyromagnetic ratio, Landé factor g and magnetic anisotropy of our films have also been determined.

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

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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.

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

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

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)

Nanoscale modeling for ultrathin liquid films: Spreading and coupled layering

Science.gov (United States)

Phillips, David Michael

liquid PFPE. The experimental analogue of replenishment is the one-dimensional spreading analysis. PFPEs with functional endgroups demonstrated coupled molecular layering and dewetting phenomena during the spreading analysis, while PFPEs with nonfunctional endgroups did not. All of the PFPE thin films spread via a diffusive process and had diffusion coefficients that depended on the local film thickness. A theoretical analysis is presented here for both the governing equation and the disjoining pressure driving force for the PFPE thin film spreading. For PFPEs with non-functional endgroups, a reasonable analysis is performed on the diffusion coefficient for two classes of film: submonolayer and multilayer. The diffusion coefficient of PFPEs with functional endgroups are qualitatively linked to the gradient of the film disjoining pressure. To augment this theory, both lattice-based and off-lattice Monte Carlo simulations are conducted for PFPE film models. The lattice-based model shows the existence of a critical functional endgroup interaction strength. It is also used to study the break-up of molecular layers for a spreading film via a fractal analysis. The off-lattice model is used to calculate the anisotropic pressure tensor for the model PFPE thin film and subsequently the film disjoining pressure. The model also qualitatively analyzes of the self diffusion in the film.

Falling films on flexible inclines

Science.gov (United States)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

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.

Simple, fast and accurate two-diode model for photovoltaic modules

Energy Technology Data Exchange (ETDEWEB)

Ishaque, Kashif; Salam, Zainal; Taheri, Hamed [Faculty of Electrical Engineering, Universiti Teknologi Malaysia, UTM 81310, Skudai, Johor Bahru (Malaysia)

2011-02-15

This paper proposes an improved modeling approach for the two-diode model of photovoltaic (PV) module. The main contribution of this work is the simplification of the current equation, in which only four parameters are required, compared to six or more in the previously developed two-diode models. Furthermore the values of the series and parallel resistances are computed using a simple and fast iterative method. To validate the accuracy of the proposed model, six PV modules of different types (multi-crystalline, mono-crystalline and thin-film) from various manufacturers are tested. The performance of the model is evaluated against the popular single diode models. It is found that the proposed model is superior when subjected to irradiance and temperature variations. In particular the model matches very accurately for all important points of the I-V curves, i.e. the peak power, short-circuit current and open circuit voltage. The modeling method is useful for PV power converter designers and circuit simulator developers who require simple, fast yet accurate model for the PV module. (author)

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.

Effect of film size on drainage of foam and emulsion films

International Nuclear Information System (INIS)

Malhotra, A.K.; Wasan, D.T.

1987-01-01

All available theoretical analyses for the drainage of thin plane-parallel liquid films, such as those existing between two approaching liquid droplets or bubbles in the coalescence process, predict essentially the same dependence of rate of thinning of the intervening film on its size as is described by the Reynolds equation - that is, drainage time increases with the square of the film radius. Recently, the authors reported experimental data for both foam and emulsion films which showed that the measured drainage times increase with about a 0.8 power of the film radius, a value much smaller than the theoretically predicted value of 2.0. Here they present a hydrodynamic analysis to predict the experimentally observed effect of film size on the kinetics of thinning of emulsion and foam films. They extend the applicability of the Reynolds model by accounting for the flow in the Plateau borders as well as the London-van der Waals forces in the thin film phase. Their theoretical predictions are in good agreement with the experimental data on the dependence of drainage time of both foam and emulsion films on their radii

Horizontal liquid film-mist two phase flow, (1)

International Nuclear Information System (INIS)

Akagawa, Koji; Sakaguchi, Tadashi; Fujii, Terushige; Nakatani, Yoji; Nakaseko, Kosaburo.

1979-01-01

The characteristics of liquid film in annular spray flow, the generation of droplets from liquid film and the transport of droplets to a wall are the important matters in the planning and design of nuclear reactor cooling system and the channels of steam generators. The study on the liquid film spray flow is scarce, and its characteristics are not yet elucidated. The purpose of this series of studies is to clarify the characteristics of liquid film, the generation, diffusion and distribution of droplets and pressure loss in the liquid film spray flow composed of the liquid film on the lower wall and spraying gas flow in a rectangular, horizontal channel. In this paper, the concentration distribution and the diffusion coefficient of droplets on a cross section in the region of flow completion are reported. The experimental apparatuses and the experimental method, the flow rate of droplets and the velocity distribution of gas phase, the concentration distribution and the diffusion coefficient of droplets, and the diameter of generated droplets are explained. The equation for the concentration distribution of droplets using dimensionless characteristic value was derived. The mean diffusion coefficient of droplets was constant on a cross section, and the effects of gravity and turbulent diffusion can be evaluated. (Kako, I.)

Laser short-pulse heating of an aluminum thin film: Energy transfer in electron and lattice sub-systems

Energy Technology Data Exchange (ETDEWEB)

Bin Mansoor, Saad; Sami Yilbas, Bekir, E-mail: bsyilbas@kfupm.edu.sa

2015-08-15

Laser short-pulse heating of an aluminum thin film is considered and energy transfer in the film is formulated using the Boltzmann equation. Since the heating duration is short and the film thickness is considerably small, thermal separation of electron and lattice sub-systems is incorporated in the analysis. The electron–phonon coupling is used to formulate thermal communication of both sub-systems during the heating period. Equivalent equilibrium temperature is introduced to account for the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Temperature predictions of the Boltzmann equation are compared with those obtained from the two-equation model. It is found that temperature predictions from the Boltzmann equation differ slightly from the two-equation model results. Temporal variation of equivalent equilibrium temperature does not follow the laser pulse intensity in the electron sub-system. The time occurrence of the peak equivalent equilibrium temperature differs for electron and lattice sub-systems, which is attributed to phonon scattering in the irradiated field in the lattice sub-system. In this case, time shift is observed for occurrence of the peak temperature in the lattice sub-system.

Laser short-pulse heating of an aluminum thin film: Energy transfer in electron and lattice sub-systems

International Nuclear Information System (INIS)

Bin Mansoor, Saad; Sami Yilbas, Bekir

2015-01-01

Laser short-pulse heating of an aluminum thin film is considered and energy transfer in the film is formulated using the Boltzmann equation. Since the heating duration is short and the film thickness is considerably small, thermal separation of electron and lattice sub-systems is incorporated in the analysis. The electron–phonon coupling is used to formulate thermal communication of both sub-systems during the heating period. Equivalent equilibrium temperature is introduced to account for the average energy of all phonons around a local point when they redistribute adiabatically to an equilibrium state. Temperature predictions of the Boltzmann equation are compared with those obtained from the two-equation model. It is found that temperature predictions from the Boltzmann equation differ slightly from the two-equation model results. Temporal variation of equivalent equilibrium temperature does not follow the laser pulse intensity in the electron sub-system. The time occurrence of the peak equivalent equilibrium temperature differs for electron and lattice sub-systems, which is attributed to phonon scattering in the irradiated field in the lattice sub-system. In this case, time shift is observed for occurrence of the peak temperature in the lattice sub-system

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.

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.)

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

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

Modeling of Melting and Resolidification in Domain of Metal Film Subjected to a Laser Pulse

Directory of Open Access Journals (Sweden)

Majchrzak E.

2016-03-01

Full Text Available Thermal processes in domain of thin metal film subjected to a strong laser pulse are discussed. The heating of domain considered causes the melting and next (after the end of beam impact the resolidification of metal superficial layer. The laser action (a time dependent bell-type function is taken into account by the introduction of internal heat source in the energy equation describing the heat transfer in domain of metal film. Taking into account the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered, the mathematical model of the process is based on the dual phase lag equation supplemented by the suitable boundary-initial conditions. To model the phase transitions the artificial mushy zone is introduced. At the stage of numerical modeling the Control Volume Method is used. The examples of computations are also presented.

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

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.)

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.

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 ...

Two-phase heat and mass transfer in turbulent parallel and countercurrent flows of liquid film and gas

International Nuclear Information System (INIS)

Kholpanov, L.P.; Babak, T.B.; Babak, V.N.; Malyusov, V.A.; Zhavoronkov, N.M.; AN SSSR, Moscow. Inst. Obshchej i Neorganicheskoj Khimii)

1980-01-01

To determine the ways of intensification of heat and mass transfer processes, the direct flow and counterflow heat and mass transfer is analytically investigated during the turbulent flow of a liquid and gas film on the basis of solving the energy equation for liquid and gas film, i.e. the two-phase film heat transfer is investigated from the position of a conjugate task. The analysis of the two-phase heat transfer has shown that it is necessary to know the position of each point in a plane before using this or that formula. Depending on its position on this plane, the heat transfer process will be determined by one or two phases only. It is found, that in the case of a single-phase heat transfer the temperature on the surface remains stable over the channel length. In the case of a two-phase heat transfer it can significantly change over the channel length [ru

Instability of two-layer film flows due to the interacting effects of surfactants, inertia, and gravity

Science.gov (United States)

Kalogirou, Anna

2018-03-01

We consider a two-fluid shear flow where the interface between the two fluids is coated with an insoluble surfactant. An asymptotic model is derived in the thin-layer approximation, consisting of a set of nonlinear partial differential equations describing the evolution of the film and surfactant disturbances at the interface. The model includes important physical effects such as Marangoni forces (caused by the presence of surfactant), inertial forces arising in the thick fluid layer, as well as gravitational forces. The aim of this study is to investigate the effect of density stratification or gravity—represented through the Bond number Bo—on the flow stability and the interplay between the different (de)stabilisation mechanisms. It is found that gravity can either stabilise or destabilise the interface (depending on fluid properties) but not always as intuitively anticipated. Different traveling-wave branches are presented for varying Bo, and the destabilising mechanism associated with the Marangoni forces is discussed.

Modelling Hermetic Compressors Using Different Constraint Equations to Accommodate Multibody Dynamics and Hydrodynamic Lubrication

DEFF Research Database (Denmark)

Estupinan, Edgar Alberto; Santos, Ilmar

2009-01-01

elements are supported by fluid film bearings, where the hydrodynamic interaction forces are described by the Reynolds equation. The system of nonlinear equations is numerically solved for three different restrictive conditions of the motion of the crank, where the third case takes into account lateral...... and tilting oscillations of the extremity of the crankshaft. The numerical results of the behaviour of the journal bearings for each case are presented giving some insights into design parameters such as, maximum oil film pressure, minimum oil film thickness, maximum vibration levels and dynamic reaction...

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

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.

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.

Prediction of liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube development of analytical method under BWR conditions

International Nuclear Information System (INIS)

Utsuno, Hideaki; Kaminaga, Fumito

1998-01-01

A method was developed based on the conservation lows to predict critical heat flux (CHF) causing liquid film dryout in two-phase annular-mist flow in a uniformly heated narrow tube under BWR conditions. The applicable range of the method is within the pressure of 3-9 MPa, mass flux of 500-2,000 kg/m 2 ·s, heat flux of 0.33-2.0 MW/m 2 and boiling length-to-tube diameter ratio of 200-800. The two-phase annular-mist flow was modeled with the three-fluid streams with liquid film, entrained droplets and gas flow. Governing equations of the method are mass continuity and energy conservation on the three-fluid streams. Constitutive equations on the mass transfer which consist of the entrainment fraction at equilibrium and the mass transfer coefficient were newly proposed in this study. Confirmation of the present method were performed in comparison with the available film flow measurements and various CHF data from experiments in uniformly heated narrow tubes under high pressure steam-water conditions. In the heat flux range (q'' 2 ) practical for a BWR, agreement of the present method with CHF data was obtained as, (Averaged ratio) ± (Standard deviation) = 0.984 ± 0.077, which was shown to be the same or better agreement than the widely-used CHF correlations. (author)

Two-phase flow modeling in the rod bundle subchannel analysis

International Nuclear Information System (INIS)

Hisashi, Ninokata

2006-01-01

In order to practice a design-by-analysis of thermohydraulics design of BWR fuel rod bundles, the subchannel analysis would play a major role. There, the immediate concern is improvement in its predictive capability of CHF due in particular to the film dryout (boiling transition phenomena: BT) on the fuel rod surface. Constitutive equations in the subchannel analysis formulation are responsible for the quality of calculated results. The constitutive equations are a result of integration of the local and instantaneous description of two-phase flows over the subchannel control volume. In general, they are expressed in terms of subchannel-control-volume- as well as area-averaged two-phase flow state variables. In principle the information on local and instantaneous physical phenomena taking place inside subchannels must be counted for in the algebraic form of the equations on the basis of a more mechanistic modeling approach. They should include also influences of the multi-dimensional subchannel geometry and fluid material properties. Thermohydraulics phenomena of interests in this deed are: 1) vapor-liquid re-distribution by inter-subchannel exchanges due to the diversion cross flow, turbulent mixing and void drift, 2) liquid film behaviors, 3) transition of two-phase flow regimes, 4) droplet entrainment and deposition and 5) spacer-droplet interactions. These are considered to be five key factors in understanding the BT in BWR fuel rod bundles. In Japan, a university-industry consortium has been formed under the sponsorship of the Ministry of Economics, Trade and Industry. This paper describes an outline of the on-going project and, first, an outline of the current efforts is presented in developing a new two-fluid three field subchannel code NASCA being aimed at predicting onset of BT, and post BT phenomena in advanced BWR fuel rod bundles including those of the tight lattice configuration for a higher conversion. Then the current methodology adopted to improve

Two-phase flow modeling in the rod bundle subchannel analysis

International Nuclear Information System (INIS)

Hisashi, Ninokata

2004-01-01

Full text of publication follows:In order to practice a design-by-analysis of thermohydraulics design of BWR fuel rod bundles, the subchannel analysis would play a major role. There, the immediate concern is improvement in its predictive capability of CHF due in particular to the film dryout (boiling transition phenomena: BT) on the fuel rod surface. Constitutive equations in the subchannel analysis formulation are responsible for the quality of calculated results. The constitutive equations are a result of integration of the local and instantaneous description of two-phase flows over the subchannel control volume. In general, they are expressed in terms of subchannel-control-volume- as well as area-averaged two-phase flow state variables. In principle the information on local and instantaneous physical phenomena taking place inside subchannels must be counted for in the algebraic form of the equations on the basis of a more mechanistic modeling approach. They should include also influences of the multi-dimensional subchannel geometry and fluid material properties. Thermohydraulics phenomena of interests in this deed are: 1) vapor-liquid re-distribution by inter-subchannel exchanges due to the diversion cross flow, turbulent mixing and void drift, 2) liquid film behaviors, 3) transition of two-phase flow regimes, 4) droplet entrainment and deposition and 5) spacer-droplet interactions. These are considered to be five key factors in understanding the BT in BWR fuel rod bundles. In Japan, a university-industry consortium has been formed under the sponsorship of the Ministry of Economics, Trade and Industry. This paper describes an outline of the on-going project and, first, an outline of the current efforts is presented in developing a new two-fluid three field subchannel code NASCA being aimed at predicting onset of BT, and post BT phenomena in advanced BWR fuel rod bundles including those of the tight lattice configuration for a higher conversion. Then the current

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.

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

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.

On the membrane approximation in isothermal film casting

Science.gov (United States)

Hagen, Thomas

2014-08-01

In this work, a one-dimensional model for isothermal film casting is studied. Film casting is an important engineering process to manufacture thin films and sheets from a highly viscous polymer melt. The model equations account for variations in film width and film thickness, and arise from thinness and kinematic assumptions for the free liquid film. The first aspect of our study is a rigorous discussion of the existence and uniqueness of stationary solutions. This objective is approached via the argument principle, exploiting the homotopy invariance of a family of analytic functions. As our second objective, we analyze the linearization of the governing equations about stationary solutions. It is shown that solutions for the associated boundary-initial value problem are given by a strongly continuous semigroup of bounded linear operators. To reach this result, we cast the relevant Cauchy problem in a more accessible form. These transformed equations allow us insight into the regularity of the semigroup, thus yielding the validity of the spectral mapping theorem for the semigroup and the spectrally determined growth property.

Border-crossing model for the diffusive coarsening of two-dimensional and quasi-two-dimensional wet foams

Science.gov (United States)

Schimming, C. D.; Durian, D. J.

2017-09-01

For dry foams, the transport of gas from small high-pressure bubbles to large low-pressure bubbles is dominated by diffusion across the thin soap films separating neighboring bubbles. For wetter foams, the film areas become smaller as the Plateau borders and vertices inflate with liquid. So-called "border-blocking" models can explain some features of wet-foam coarsening based on the presumption that the inflated borders totally block the gas flux; however, this approximation dramatically fails in the wet or unjamming limit where the bubbles become close-packed spheres and coarsening proceeds even though there are no films. Here, we account for the ever-present border-crossing flux by a new length scale defined by the average gradient of gas concentration inside the borders. We compute that it is proportional to the geometric average of film and border thicknesses, and we verify this scaling by numerical solution of the diffusion equation. We similarly consider transport across inflated vertices and surface Plateau borders in quasi-two-dimensional foams. And we show how the d A /d t =K0(n -6 ) von Neumann law is modified by the appearance of terms that depend on bubble size and shape as well as the concentration gradient length scales. Finally, we use the modified von Neumann law to compute the growth rate of the average bubble area, which is not constant.

Examining the validity of Stoney-equation for in-situ stress measurements in thin film electrodes using a large-deformation finite-element procedure

Science.gov (United States)

Wen, Jici; Wei, Yujie; Cheng, Yang-Tse

2018-05-01

During the lithiation and delithiation of a thin film electrode, stress in the electrode is deduced from the curvature change of the film using the Stoney equation. The accuracy of such a measurement is conditioned on the assumptions that (a) the mechanical properties of the electrode remain unchanged during lithiation and (b) small deformation holds. Here, we demonstrate that the change in elastic properties can influence the measurement of the stress in thin film electrodes. We consider the coupling between diffusion and deformation during lithiation and delithiation of thin film electrodes and implement the constitutive behavior in a finite-deformation finite element procedure. We demonstrate that both the variation in elastic properties in thin film electrodes and finite-deformation during lithiation and delithiation would challenge the applicability of the Stoney-equation for in-situ stress measurements of thin film electrodes.

Experimental study on two-dimensional film flow with local measurement methods

Energy Technology Data Exchange (ETDEWEB)

Yang, Jin-Hwa, E-mail: evo03@snu.ac.kr [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Cho, Hyoung-Kyu [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of); Kim, Seok [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Euh, Dong-Jin, E-mail: djeuh@kaeri.re.kr [Korea Atomic Energy Research Institute, 989-111, Daedeok-daero, Yuseong-gu, Daejeon 305-600 (Korea, Republic of); Park, Goon-Cherl [Nuclear Thermal-Hydraulic Engineering Laboratory, Seoul National University, Gwanak 599, Gwanak-ro, Gwanak-gu, Seoul 151-742 (Korea, Republic of)

2015-12-01

velocity of the liquid film was discussed. Also the local velocity profiles of air and liquid film and the liquid film thickness distribution were presented. These local experimental data of two-dimensional film flow which simulated the two-phase cross flow can be used to validate the multidimensional models in the system analysis codes and CFD codes.

Experimental study on two-dimensional film flow with local measurement methods

International Nuclear Information System (INIS)

Yang, Jin-Hwa; Cho, Hyoung-Kyu; Kim, Seok; Euh, Dong-Jin; Park, Goon-Cherl

2015-01-01

velocity of the liquid film was discussed. Also the local velocity profiles of air and liquid film and the liquid film thickness distribution were presented. These local experimental data of two-dimensional film flow which simulated the two-phase cross flow can be used to validate the multidimensional models in the system analysis codes and CFD codes.

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.

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.)

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…

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

Numerical simulations of electrohydrodynamic evolution of thin polymer films

Science.gov (United States)

Borglum, Joshua Christopher

Recently developed needleless electrospinning and electrolithography are two successful techniques that have been utilized extensively for low-cost, scalable, and continuous nano-fabrication. Rational understanding of the electrohydrodynamic principles underneath these nano-manufacturing methods is crucial to fabrication of continuous nanofibers and patterned thin films. This research project is to formulate robust, high-efficiency finite-difference Fourier spectral methods to simulate the electrohydrodynamic evolution of thin polymer films. Two thin-film models were considered and refined. The first was based on reduced lubrication theory; the second further took into account the effect of solvent drying and dewetting of the substrate. Fast Fourier Transform (FFT) based spectral method was integrated into the finite-difference algorithms for fast, accurately solving the governing nonlinear partial differential equations. The present methods have been used to examine the dependencies of the evolving surface features of the thin films upon the model parameters. The present study can be used for fast, controllable nanofabrication.

Real-time kinetic modeling of YSZ thin film roughness deposited by e-beam evaporation technique

International Nuclear Information System (INIS)

Galdikas, A.; Cerapaite-Trusinskiene, R.; Laukaitis, G.; Dudonis, J.

2008-01-01

In the present study, the process of yttrium-stabilized zirconia (YSZ) thin films deposition on optical quartz (SiO 2 ) substrates using e-beam deposition technique controlling electron gun power is analyzed. It was found that electron gun power influences the non-monotonous kinetics of YSZ film surface roughness. The evolution of YSZ thin film surface roughness was analyzed by a kinetic model. The model is based on the rate equations and includes processes of surface diffusion of the adatoms and the clusters, nucleation, growth and coalescence of islands in the case of thin film growth in Volmer-Weber mode. The analysis of the experimental results done by modeling explains non-monotonous kinetics and dependence of the surface roughness on the electron gun power. A good quantitative agreement with experimental results is obtained taking into account the initial roughness of the substrate surface and the amount of the clusters in the flux of evaporated material.

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....

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.

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.

Homogenization models for thin rigid structured surfaces and films.

Science.gov (United States)

Marigo, Jean-Jacques; Maurel, Agnès

2016-07-01

A homogenization method for thin microstructured surfaces and films is presented. In both cases, sound hard materials are considered, associated with Neumann boundary conditions and the wave equation in the time domain is examined. For a structured surface, a boundary condition is obtained on an equivalent flat wall, which links the acoustic velocity to its normal and tangential derivatives (of the Myers type). For a structured film, jump conditions are obtained for the acoustic pressure and the normal velocity across an equivalent interface (of the Ventcels type). This interface homogenization is based on a matched asymptotic expansion technique, and differs slightly from the classical homogenization, which is known to fail for small structuration thicknesses. In order to get insight into what causes this failure, a two-step homogenization is proposed, mixing classical homogenization and matched asymptotic expansion. Results of the two homogenizations are analyzed in light of the associated elementary problems, which correspond to problems of fluid mechanics, namely, potential flows around rigid obstacles.

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.

Film traffic queueing model for the DUMC radiology department

International Nuclear Information System (INIS)

Humphrey, L.M.; Ravin, C.E.

1988-01-01

This paper discusses the radiology department traffic model for Duke University Medical Center (DUMC) which simulates the flow of film through the department, and then incorporates the effect of introducing a PACS-type system into present operations. Each Radiology Section is considered separately for queuing of two types of film: old film (from previous exams) and new film (from the present exam). The amount of film in each queue at any time is controlled by controlling hours of operation, service times, delay, and arrival rates. The model also takes into account the use of film in each major radiology area. This gives some idea of the load on a device in that area as well as the amount of storage needed to adequately handle its daily load is local storage at the display device is desired

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.

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.

The generation of two-dimensional vortices by transverse oscillation of a soap film

International Nuclear Information System (INIS)

Afenchenko, V.O.; Ezersky, A.B.; Kiyashko, S.V.; Rabinovich, M.I.; Weidman, P.D.

1998-01-01

An experimental investigation of the dynamics of horizontal soap films stretched over circular or square boundaries undergoing periodic transverse oscillations at frequencies in the range 20 - 200 Hz is reported. Concomitant with modes of transverse flexural oscillations, it was observed that two-dimensional vortices in the plane of the film are excited. The vortices may be either (i) large, scaling with the size of the cavity or (ii) small, localized at a wavelength or half-wavelength of the membrane modes. In the experiments a stable generation of one, two, hor-ellipsis, ten pairs of counter-rotating vortices were observed in finite regions of amplitude-frequency parameter space. The circulation strength of vortices in a given vortex pattern increases with increasing external forcing and with decreasing soap film thickness. A theoretical model based on the wave-boundary interaction of excited Marangoni waves reveals a vorticity generation mechanism active in vibrating soap films. This model shows that vorticity is generated throughout the entire liquid volume by viscous diffusion, and qualitatively reproduces many steady vortex patterns observed in the experiment. However, the model cannot explain the existence of the sometimes intense vortices observed far from the film boundary that do not appear to be generated by diffusive processes. copyright 1998 American Institute of Physics

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

Surface morphology modelling for the resistivity analysis of low temperature sputtered indium tin oxide thin films on polymer substrates

International Nuclear Information System (INIS)

Yin Xuesong; Tang Wu; Weng Xiaolong; Deng Longjiang

2009-01-01

Amorphous or weakly crystalline indium tin oxide (ITO) thin film samples have been prepared on polymethylmethacrylate and polyethylene terephthalate substrates by RF-magnetron sputtering at a low substrate temperature. The surface morphological and electrical properties of the ITO layers were measured by atomic force microscopy (AFM) and a standard four-point probe measurement. The effect of surface morphology on the resistivity of ITO thin films was studied, which presented some different variations from crystalline films. Then, a simplified film system model, including the substrate, continuous ITO layer and ITO surface grain, was proposed to deal with these correlations. Based on this thin film model and the AFM images, a quadratic potential was introduced to simulate the characteristics of the ITO surface morphology, and the classical Kronig-Penney model, the semiconductor electrical theory and the modified Neugebauer-Webb model were used to expound the detailed experimental results. The modelling equation was highly in accord with the experimental variations of the resistivity on the characteristics of the surface morphology.

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

A Variational approach to thin film hydrodynamics of binary mixtures

KAUST Repository

Xu, Xinpeng

2015-02-04

In order to model the dynamics of thin films of mixtures, solutions, and suspensions, a thermodynamically consistent formulation is needed such that various coexisting dissipative processes with cross couplings can be correctly described in the presence of capillarity, wettability, and mixing effects. In the present work, we apply Onsager\\'s variational principle to the formulation of thin film hydrodynamics for binary fluid mixtures. We first derive the dynamic equations in two spatial dimensions, one along the substrate and the other normal to the substrate. Then, using long-wave asymptotics, we derive the thin film equations in one spatial dimension along the substrate. This enables us to establish the connection between the present variational approach and the gradient dynamics formulation for thin films. It is shown that for the mobility matrix in the gradient dynamics description, Onsager\\'s reciprocal symmetry is automatically preserved by the variational derivation. Furthermore, using local hydrodynamic variables, our variational approach is capable of introducing diffusive dissipation beyond the limit of dilute solute. Supplemented with a Flory-Huggins-type mixing free energy, our variational approach leads to a thin film model that treats solvent and solute in a symmetric manner. Our approach can be further generalized to include more complicated free energy and additional dissipative processes.

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.

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.

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

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

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…

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.

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

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…

Modeling of metal thin film growth: Linking angstrom-scale molecular dynamics results to micron-scale film topographies

Science.gov (United States)

Hansen, U.; Rodgers, S.; Jensen, K. F.

2000-07-01

A general method for modeling ionized physical vapor deposition is presented. As an example, the method is applied to growth of an aluminum film in the presence of an ionized argon flux. Molecular dynamics techniques are used to examine the surface adsorption, reflection, and sputter reactions taking place during ionized physical vapor deposition. We predict their relative probabilities and discuss their dependence on energy and incident angle. Subsequently, we combine the information obtained from molecular dynamics with a line of sight transport model in a two-dimensional feature, incorporating all effects of reemission and resputtering. This provides a complete growth rate model that allows inclusion of energy- and angular-dependent reaction rates. Finally, a level-set approach is used to describe the morphology of the growing film. We thus arrive at a computationally highly efficient and accurate scheme to model the growth of thin films. We demonstrate the capabilities of the model predicting the major differences on Al film topographies between conventional and ionized sputter deposition techniques studying thin film growth under ionized physical vapor deposition conditions with different Ar fluxes.

A model system to mimic environmentally active surface film roughness and hydrophobicity.

Science.gov (United States)

Grant, Jacob S; Shaw, Scott K

2017-10-01

This work presents the development and initial assessment of a laboratory platform to allow quantitative studies on model urban films. The platform consists of stearic acid and eicosane mixtures that are solution deposited from hexanes onto smooth, solid substrates. We show that this model has distinctive capabilities to better mimic a naturally occurring film's morphology and hydrophobicity, two important parameters that have not previously been incorporated into model film systems. The physical and chemical properties of the model films are assessed using a variety of analytical instruments. The film thickness and roughness are probed via atomic force microscopy while the film composition, wettability, and water uptake are analyzed by Fourier transform infrared spectroscopy, contact angle goniometry, and quartz crystal microbalance, respectively. Simulated environmental maturation is achieved by exposing the film to regulated amounts of UV/ozone. Ultimately, oxidation of the film is monitored by the analytical techniques mentioned above and proceeds as expected to produce a utile model film system. Including variable roughness and tunable surface coverage results in several key advantages over prior model systems, and will more accurately represent native urban film behavior. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Effect of Polar Lipids on Tear Film Dynamics

KAUST Repository

Aydemir, E.

2010-06-17

In this paper, we present a mathematical model describing the effect of polar lipids, excreted by glands in the eyelid and present on the surface of the tear film, on the evolution of a pre-corneal tear film. We aim to explain the interesting experimentally observed phenomenon that the tear film continues to move upward even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled non-linear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that increasing the concentration of the lipid increases the flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system. © 2010 Society for Mathematical Biology.

Model Lung Surfactant Films: Why Composition Matters

Energy Technology Data Exchange (ETDEWEB)

Selladurai, Sahana L.; Miclette Lamarche, Renaud; Schmidt, Rolf; DeWolf, Christine E.

2016-10-18

Lung surfactant replacement therapies, Survanta and Infasurf, and two lipid-only systems both containing saturated and unsaturated phospholipids and one containing additional palmitic acid were used to study the impact of buffered saline on the surface activity, morphology, rheology, and structure of Langmuir monolayer model membranes. Isotherms and Brewster angle microscopy show that buffered saline subphases induce a film expansion, except when the cationic protein, SP-B, is present in sufficient quantities to already screen electrostatic repulsion, thus limiting the effect of changing pH and adding counterions. Grazing incidence X-ray diffraction results indicate an expansion not only of the liquid expanded phase but also an expansion of the lattice of the condensed phase. The film expansion corresponded in all cases with a significant reduction in the viscosity and elasticity of the films. The viscoelastic parameters are dominated by liquid expanded phase properties and do not appear to be dependent on the structure of the condensed phase domains in a phase separated film. The results highlight that the choice of subphase and film composition is important for meaningful interpretations of measurements using model systems.

Theoretical model for thin ferroelectric films and the multilayer structures based on them

Energy Technology Data Exchange (ETDEWEB)

Starkov, A. S., E-mail: starkov@iue.tuwien.ac.at; Pakhomov, O. V. [St. Petersburg National Research Univeristy ITMO, Institute of Refrigeration and Biotechnologies (Russian Federation); Starkov, I. A. [Vienna University of Technology, Institute for Microelectronics (Austria)

2013-06-15

A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data.

Theoretical model for thin ferroelectric films and the multilayer structures based on them

International Nuclear Information System (INIS)

Starkov, A. S.; Pakhomov, O. V.; Starkov, I. A.

2013-01-01

A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data

Theoretical model for thin ferroelectric films and the multilayer structures based on them

Science.gov (United States)

Starkov, A. S.; Pakhomov, O. V.; Starkov, I. A.

2013-06-01

A modified Weiss mean-field theory is used to study the dependence of the properties of a thin ferroelectric film on its thickness. The possibility of introducing gradient terms into the thermodynamic potential is analyzed using the calculus of variations. An integral equation is introduced to generalize the well-known Langevin equation to the case of the boundaries of a ferroelectric. An analysis of this equation leads to the existence of a transition layer at the interface between ferroelectrics or a ferroelectric and a dielectric. The permittivity of this layer is shown to depend on the electric field direction even if the ferroelectrics in contact are homogeneous. The results obtained in terms of the Weiss model are compared with the results of the models based on the correlation effect and the presence of a dielectric layer at the boundary of a ferroelectric and with experimental data.

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

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.

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.

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.)

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.

Soap film flows: Statistics of two-dimensional turbulence

International Nuclear Information System (INIS)

Vorobieff, P.; Rivera, M.; Ecke, R.E.

1999-01-01

Soap film flows provide a very convenient laboratory model for studies of two-dimensional (2-D) hydrodynamics including turbulence. For a gravity-driven soap film channel with a grid of equally spaced cylinders inserted in the flow, we have measured the simultaneous velocity and thickness fields in the irregular flow downstream from the cylinders. The velocity field is determined by a modified digital particle image velocimetry method and the thickness from the light scattered by the particles in the film. From these measurements, we compute the decay of mean energy, enstrophy, and thickness fluctuations with downstream distance, and the structure functions of velocity, vorticity, thickness fluctuation, and vorticity flux. From these quantities we determine the microscale Reynolds number of the flow R λ ∼100 and the integral and dissipation scales of 2D turbulence. We also obtain quantitative measures of the degree to which our flow can be considered incompressible and isotropic as a function of downstream distance. We find coarsening of characteristic spatial scales, qualitative correspondence of the decay of energy and enstrophy with the Batchelor model, scaling of energy in k space consistent with the k -3 spectrum of the Kraichnan endash Batchelor enstrophy-scaling picture, and power-law scalings of the structure functions of velocity, vorticity, vorticity flux, and thickness. These results are compared with models of 2-D turbulence and with numerical simulations. copyright 1999 American Institute of Physics

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

Simulated Thin-Film Growth and Imaging

Science.gov (United States)

Schillaci, Michael

2001-06-01

Thin-films have become the cornerstone of the electronics, telecommunications, and broadband markets. A list of potential products includes: computer boards and chips, satellites, cell phones, fuel cells, superconductors, flat panel displays, optical waveguides, building and automotive windows, food and beverage plastic containers, metal foils, pipe plating, vision ware, manufacturing equipment and turbine engines. For all of these reasons a basic understanding of the physical processes involved in both growing and imaging thin-films can provide a wonderful research project for advanced undergraduate and first-year graduate students. After producing rudimentary two- and three-dimensional thin-film models incorporating ballsitic deposition and nearest neighbor Coulomb-type interactions, the QM tunneling equations are used to produce simulated scanning tunneling microscope (SSTM) images of the films. A discussion of computational platforms, languages, and software packages that may be used to accomplish similar results is also given.

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.

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,…

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...

Film Cooling Optimization Using Numerical Computation of the Compressible Viscous Flow Equations and Simplex Algorithm

Directory of Open Access Journals (Sweden)

Ahmed M. Elsayed

2013-01-01

Full Text Available Film cooling is vital to gas turbine blades to protect them from high temperatures and hence high thermal stresses. In the current work, optimization of film cooling parameters on a flat plate is investigated numerically. The effect of film cooling parameters such as inlet velocity direction, lateral and forward diffusion angles, blowing ratio, and streamwise angle on the cooling effectiveness is studied, and optimum cooling parameters are selected. The numerical simulation of the coolant flow through flat plate hole system is carried out using the “CFDRC package” coupled with the optimization algorithm “simplex” to maximize overall film cooling effectiveness. Unstructured finite volume technique is used to solve the steady, three-dimensional and compressible Navier-Stokes equations. The results are compared with the published numerical and experimental data of a cylindrically round-simple hole, and the results show good agreement. In addition, the results indicate that the average overall film cooling effectiveness is enhanced by decreasing the streamwise angle for high blowing ratio and by increasing the lateral and forward diffusion angles. Optimum geometry of the cooling hole on a flat plate is determined. In addition, numerical simulations of film cooling on actual turbine blade are performed using the flat plate optimal hole geometry.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

Science.gov (United States)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

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.

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.

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.

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

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

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.

Measurement of thickness of thin water film in two-phase flow by capacitance method

International Nuclear Information System (INIS)

Sun, R.K.; Kolbe, W.F.; Leskovar, B.; Turko, B.

1981-09-01

A technique has been developed for measuring water film thickness in a two-phase annular flow system by the capacitance method. An experimental model of the flow system with two types of electrodes mounted on the inner wall of a cylindrical tube has been constructed and evaluated. The apparatus and its ability to observe fluctuations and wave motions of the water film passing over the electrodes is described in some detail

Description of spin reorientation transition in Au/Co/Au sandwich with Co film thickness within a simple phenomenological model of ferromagnetic film

International Nuclear Information System (INIS)

Popov, A.P.

2012-01-01

Simple phenomenological model of ferromagnetic film characterized by equal energies of surface anisotropies at two sides of a film (symmetric film) is considered. The model is used to describe a two-step spin reorientation transition (SRT) in Au/Co/Au sandwich with Co film thickness: the SRT from perpendicular to canted noncollinear (CNC) state at N ⊥ =6.3 atomic layers and the subsequent SRT from CNC to in-plane state at N ∥ =10.05 atomic layers. Analytic expressions for the stability criterion of collinear perpendicular and in-plane states of a film are derived with account of discrete location of atomic layers. The dependence of borders that separate regions corresponding to various magnetic states of a film in the (k B ,k S )-diagram on film thickness N is established. k S (k B ) is surface (bulk) reduced anisotropy constant. The comparison of theory with experiment related to Au/Co/Au sandwich shows that there is a whole region in the (k B ,k S )-diagram corresponding to experimentally determined values of threshold film thicknesses N ⊥ =6.3 and N ∥ =10.05. The comparison of this region with similar region determined earlier for a bare Co/Au film within the same model of asymmetric film and characterized by N ⊥ =3.5, N ∥ =5.5 shows that the intersection of these regions is not empty. Hence, both the SRT in Au/Co/Au sandwich and in bare Co/Au film with Co film thickness can be described within the same model using the same magnitudes of model parameters k S , k B . Based on this result we conclude that the energy of Neel surface anisotropy at free Co surface is negligible compared to the energy of Co–Au interface anisotropy. It is demonstrated that the destabilization of collinear states in symmetric film leads to occurrence of the ground CNC state and two novel metastable CNC states. These three CNC states exhibit different kinds of symmetry. In case of asymmetric film only ground CNC state occurs on destabilization of collinear states of a film

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)

Calculation of viscoelastic properties of edible films: application of three models

Directory of Open Access Journals (Sweden)

CHANDRA Prabir K.

2000-01-01

Full Text Available The viscoelastic properties of edible films can provide information at the structural level of the biopolymers used. The objective of this work was to test three simple models of linear viscoelastic theory (Maxwell, Generalized Maxwell with two units in parallel, and Burgers using the results of stress relaxation tests in edible films of myofibrillar proteins of Nile Tilapia. The films were elaborated according to a casting technique and pre-conditioned at 58% relative humidity and 22ºC for 4 days. The testing sample (15mm x 118mm was submitted to tests of stress relaxation in an equipment of physical measurements, TA.XT2i. The deformation, imposed to the sample, was 1%, guaranteeing the permanency in the domain of the linear viscoelasticity. The models were fitted to experimental data (stress x time by nonlinear regression. The Generalized Maxwell model with two units in parallel and the Burgers model represented the relaxation curves of stress satisfactorily. The viscoelastic properties varied in a way that they were less dependent on the thickness of the films.

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.

Using COMSOL Multiphysics Software to Analyze the Thin Film Resistance Model of a Conductor on PET

Science.gov (United States)

Carradero-Santiago, Carolyn; Merced-Sanabria, Milzaida; Vedrine-Pauléus, Josee

2015-03-01

In this research work, we will develop a virtual model to analyze the electrical conductivity of a thin film with three layers, one of graphene or conducting metal film, polyethylene terephthalate (PET) and Poly(3,4-ethylenedioxythiophene) Polystyrene sulfonate (PEDOT:PSS). COMSOL Multiphysics will be the software use to develop the virtual model to analyze the thin-film layers. COMSOL software allows simulation and modelling of physical phenomena represented by differential equations such as that of heat transfer, fluid movement, electromagnetism and structural mechanics. In the work, we will define the geometry of the model; in this case we want three layers-PET, the conducting layer and PEDOT:PSS. We will then add the materials and assign PET as the lower layer, the above conductor as the middle layer and the PEDOT:PSS as the upper layer. We will analyze the model with varying thickness of the top conducting layer. This simulation will allow us to analyze the electrical conductivity, and visualize the model with varying voltage potential, or bias across the plates.

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...

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

A Drain Current Model Based on the Temperature Effect of a-Si:H Thin-Film Transistors

International Nuclear Information System (INIS)

Qiang Lei; Yao Ruo-He

2012-01-01

Based on the differential Ohm's law and Poisson's equation, an analytical model of the drain current for a-Si:H thin-film transistors is developed. This model is proposed to elaborate the temperature effect on the drain current, which indicates that the drain current is linear with temperature in the range of 290-360 K, and the results fit well with the experimental data

A model problem for estimation of moving-film time relaxation at sudden change of boundary conditions

Science.gov (United States)

Smirnovsky, Alexander A.; Eliseeva, Viktoria O.

2018-05-01

The study of the film flow occurred under the influence of a gas slug flow is of definite interest in heat and mass transfer during the motion of a coolant in the second circuit of a nuclear water-water reactor. Thermohydraulic codes are usually used for analysis of the such problems in which the motion of the liquid film and the vapor is modeled on the basis of a one-dimensional balance equations. Due to a greater inertia of the liquid film motion, film flow parameters changes with a relaxation compared with gas flow. We consider a model problem of film flow under the influence of friction from gas slug flow neglecting such effects as wave formation, droplet breakage and deposition on the film surface, evaporation and condensation. Such a problem is analogous to the well-known problems of Couette and Stokes flows. An analytical solution has been obtained for laminar flow. Numerical RANS-based simulation of turbulent flow was performed using OpenFOAM. It is established that the relaxation process is almost self-similar. This fact opens a possibility of obtaining valuable correlations for the relaxation time.

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)

Modelling of Outer and Inner Film Oil Pressure for Floating Ring Bearing Clearance in Turbochargers

International Nuclear Information System (INIS)

Zhang Hao; Shi Zhanqun; Gu Fengshou; Ball, Andrew

2011-01-01

Floating ring bearing is widely used in turbochargers to undertake the extreme condition of high rotating speed and high operating temperature. It is also the most concerned by the designers and users alike due to its high failure rate and high maintenance cost. Any little clearance change may result in oil leakage, which in turn cause blue smoke or black smoke according to leakage types. However, there is no condition monitoring of this bearing because it is almost impossible to measure the clearance especially the inner clearance, in which the inner oil film directly bears the high speed rotation. In stead of measuring clearance directly, this paper has proposed a method that uses film pressure as a measure to monitor the bearing clearance and its variation. A non-linear mathematical model is developed by using Reynolds equations with non-linear oil film pressure. A full description of the outer and inner film is provided along both axial and radial directions. A numerical simulation is immediately carried out. Variable clearance changes are investigated using the mathematical model. Results show the relationship between clearance and film pressure.

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.

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.

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

Large Eddy simulation of flat plate film cooling at high blowing ratio using open FOAM

Science.gov (United States)

Baagherzadeh Hushmandi, Narmin

2018-06-01

In this work, numerical analysis was performed to predict the behaviour of high Reynolds number turbulent cross-flows used in film cooling applications. The geometry included one row of three discrete coolant holes inclined at 30 degrees to the main flow. In the computational model, the width of the channel was cut into one sixth and symmetry boundaries were applied in the centreline of the coolant hole and along the line of symmetry between two adjacent holes. One of the main factors that affect the performance of film cooling is the blowing ratio of coolant to the main flow. A blowing ratio equal to two was chosen in this study. Analysis showed that the common practice CFD models that employ RANS equations together with turbulence modelling under predict the film cooling effectiveness up to a factor of four. However, LES method showed better agreement of film cooling effectiveness both in tendency and absolute values compared with experimental results.

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)

Numerical simulation of gas-liquid two-phase flow behavior with condensation heat transfer

International Nuclear Information System (INIS)

Takamori, Kazuhide; Murase, Michio; Baba, Yoshikazu; Aihara, Tsuyoshi.

1995-01-01

In this study, condensation heat transfer experiments were performed in order to verify a condensation heat transfer model coupled with a three-dimensional two-phase flow analysis. In the heat transfer model, the liquid film flow rate on the heat transfer tubes was calculated by a mass balance equation and the liquid film thickness was calculated from the liquid film flow rate using Nusselt's laminar flow model and Fujii's equation for steam velocity effect. In the experiments, 112 horizontal staggered tubes with an outer diameter of 16 mm and length of 0.55 m were used. Steam and spray water were supplied to the test section, and inlet quality was controlled by the spray water flow rate. The temperature was 100degC and the pressure was 0.1 MPa. The overall heat transfer coefficients were measured for inlet quality of 13-100%. From parameter calculations for the falling liquid film ratio from the upper tubes to the lower tubes, the calculated overall heat transfer coefficients agreed with the data to within ±5% at the falling liquid film ratio of 0.7. (author)

Modeling and sensitivity analysis of mass transfer in active multilayer polymeric film for food applications

Science.gov (United States)

Bedane, T.; Di Maio, L.; Scarfato, P.; Incarnato, L.; Marra, F.

2015-12-01

The barrier performance of multilayer polymeric films for food applications has been significantly improved by incorporating oxygen scavenging materials. The scavenging activity depends on parameters such as diffusion coefficient, solubility, concentration of scavenger loaded and the number of available reactive sites. These parameters influence the barrier performance of the film in different ways. Virtualization of the process is useful to characterize, design and optimize the barrier performance based on physical configuration of the films. Also, the knowledge of values of parameters is important to predict the performances. Inverse modeling and sensitivity analysis are sole way to find reasonable values of poorly defined, unmeasured parameters and to analyze the most influencing parameters. Thus, the objective of this work was to develop a model to predict barrier properties of multilayer film incorporated with reactive layers and to analyze and characterize their performances. Polymeric film based on three layers of Polyethylene terephthalate (PET), with a core reactive layer, at different thickness configurations was considered in the model. A one dimensional diffusion equation with reaction was solved numerically to predict the concentration of oxygen diffused into the polymer taking into account the reactive ability of the core layer. The model was solved using commercial software for different film layer configurations and sensitivity analysis based on inverse modeling was carried out to understand the effect of physical parameters. The results have shown that the use of sensitivity analysis can provide physical understanding of the parameters which highly affect the gas permeation into the film. Solubility and the number of available reactive sites were the factors mainly influencing the barrier performance of three layered polymeric film. Multilayer films slightly modified the steady transport properties in comparison to net PET, giving a small reduction

Modified hyperbolic sine model for titanium dioxide-based memristive thin films

Science.gov (United States)

Abu Bakar, Raudah; Syahirah Kamarozaman, Nur; Fazlida Hanim Abdullah, Wan; Herman, Sukreen Hana

2018-03-01

Since the emergence of memristor as the newest fundamental circuit elements, studies on memristor modeling have been evolved. To date, the developed models were based on the linear model, linear ionic drift model using different window functions, tunnelling barrier model and hyperbolic-sine function based model. Although using hyperbolic-sine function model could predict the memristor electrical properties, the model was not well fitted to the experimental data. In order to improve the performance of the hyperbolic-sine function model, the state variable equation was modified. On the one hand, the addition of window function cannot provide an improved fitting. By multiplying the Yakopcic’s state variable model to Chang’s model on the other hand resulted in the closer agreement with the TiO2 thin film experimental data. The percentage error was approximately 2.15%.

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

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)

DOE Final Report: A Unified Understanding of Residual Stress in Thin Films: Kinetic Models, Experiments and Simulations

Energy Technology Data Exchange (ETDEWEB)

Chason, Eric [Brown Univ., Providence, RI (United States)

2018-02-01

Thin films are critical for a wide range of advanced technologies. However, the deposited films often have high levels of residual stress that can limit their performance or lead to failure. The stress is known to depend on many variables, including the processing conditions, type of material, deposition technique and the film’s microstructure. The goal of this DOE program was to develop a fundamental understanding of how the different processes that control thin film growth under different conditions can be related to the development of stress. In the program, systematic experiments were performed or analyzed that related the stress to the processing conditions that were used. Measurements of stress were obtained for films that were grown at different rates, different solutions (for electrodeposition), different particle energies (for sputter deposition) and different microstructures. Based on this data, models were developed to explain the observed dependence on the different parameters. The models were based on considering the balance among different stress-inducing mechanism occurring as the film grows (for both non-energetic and energetic deposition). Comparison of the model predictions with the experiments enabled the kinetic parameters to be determined for different materials. The resulting model equations provide a comprehensive picture of how stress changes with the processing conditions that can be used to optimize the growth of thin films.

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.

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)

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.

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)

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).

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)

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

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)

Analyses of multi-irradiation film for system alignments in stereotactic radiotherapy (SRT) and radiosurgery (SRS)

International Nuclear Information System (INIS)

Jen-San Tsai

1996-01-01

In stereotactic radiosurgery, a seven-irradiation film was used to define any discrepancy between the beam and target centres. A mathematical model based on the linac alignment and target set-up was developed to diagnose the discrepancies of the seven-irradiation film between the beam and simulation target centres. From the measured data of the multi-irradiation film, this mathematical model leads to five parameters in seven equations. Twin computer codes were employed to solve the five parameters from the seven equations. By feeding the discrepancy data into the two computer codes, the sources of the target-to-beam discrepancy were revealed. From these decoded sources, the target coordinates were adjusted and then the seven-irradiation film procedure was repeated. This discrepancy thus obtained was found to be drastically reduced. Some decoded parameters were consistently verified by direct measurements. This demonstrates that the present mathematical model and computer code do reveal the causes of the target-to-beam misalignment and gantry sag. In a further effort to test the feasibility of the mathematical model and the computer codes, the target's lateral coordinate was deliberately offset by 1.5 mm and then another seven-irradiation film was taken. By inserting these discrepancies into the computer codes, it was found that the deviation was consistent with the intentional offset. In addition, the mathematical model and computer codes are applicable to any multi-irradiation technique. (author)

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

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.

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

Film boiling heat transfer in liquid helium

International Nuclear Information System (INIS)

Inai, Nobuhiko

1979-01-01

The experimental data on the film boiling heat transfer in liquid helium are required for investigating the stability of superconducting wires. On the other hand, liquid helium has the extremely different physical properties as compared with the liquids at normal temperature such as water. In this study, the experiments on pool boiling were carried out, using the horizontal top surface of a 20 mm diameter copper cylinder in liquid helium. For observing individual bubbles, the experiments on film boiling from a horizontal platinum wire were performed separately in liquid nitrogen and liquid helium, and photographs of floating-away bubbles were taken. The author pointed out the considerable upward shift of the boiling curve near the least heat flux point in film boiling from the one given by the Berenson's equation which has been said to agree comparatively well with the data on the film boiling of the liquids at normal temperature, and the reason was investigated. Consequently, a model for film boiling heat transfer was presented. Also one equation expressing the film boiling at low heat flux for low temperature liquids was proposed. It represents well the tendency to shift from Berenson's equation of the experimental data on film boiling at the least heat flux point for liquid helium, liquid nitrogen and water having extremely different physical properties. Some discussions are added at the end of the paper. (Wakatsuki, Y.)

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.

Numerical and experimental modeling of liquid metal thin film flows in a quasi-coplanar magentic field

Energy Technology Data Exchange (ETDEWEB)

Morley, Neil B. [Univ. of California, Los Angeles, CA (United States)

1994-01-01

Liquid metal film protection of plasma-facing surfaces in fusion reactors is proposed in an effort to counter the adverse effects of high heat and particle fluxes from the burning plasma. Concerns still exist about establishing the required flow in presence of strong magnetic fields and plasma momentum flux typical of a reactor environment. In this work, the flow behavior of the film is examined under such conditions. Analysis of MHD equations as they apply to liquid metal flows with a free surface in the fully-developed limit was undertaken. Solution yields data for velocity profiles and uniform film heights vs key design parameters (channel size, magnetic field magnitude/orientation, channel slope, wall conductivity). These results are compared to previous models to determine accuracy of simplifying assumptions, in particular Hartmann averaging of films along {rvec B}. Effect of a plasma momentum flux on the thin films is also analyzed. The plasma momentum is strong enough in the cases examined to seriously upset the film, especially for lighter elements like Li. Ga performed much better and its possible use is bolstered by calculations. In an experiment in the MeGA-loop MHD facility, coplanar, wide film flow was found to be little affected by the magnetic field due to the elongated nature of the film. Both MHD drag and partial laminarization are observed, supporting the fully- developed film model predictions of the onset of MHD drag and duct flow estimations for flow laminarization.

Numerical and experimental modeling of liquid metal thin film flows in a quasi-coplanar magentic field

International Nuclear Information System (INIS)

Morley, N.B.

1994-01-01

Liquid metal film protection of plasma-facing surfaces in fusion reactors is proposed in an effort to counter the adverse effects of high heat and particle fluxes from the burning plasma. Concerns still exist about establishing the required flow in presence of strong magnetic fields and plasma momentum flux typical of a reactor environment. In this work, the flow behavior of the film is examined under such conditions. Analysis of MHD equations as they apply to liquid metal flows with a free surface in the fully-developed limit was undertaken. Solution yields data for velocity profiles and uniform film heights vs key design parameters (channel size, magnetic field magnitude/orientation, channel slope, wall conductivity). These results are compared to previous models to determine accuracy of simplifying assumptions, in particular Hartmann averaging of films along rvec B. Effect of a plasma momentum flux on the thin films is also analyzed. The plasma momentum is strong enough in the cases examined to seriously upset the film, especially for lighter elements like Li. Ga performed much better and its possible use is bolstered by calculations. In an experiment in the MeGA-loop MHD facility, coplanar, wide film flow was found to be little affected by the magnetic field due to the elongated nature of the film. Both MHD drag and partial laminarization are observed, supporting the fully- developed film model predictions of the onset of MHD drag and duct flow estimations for flow laminarization

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)).

Mathematical modeling of wiped-film evaporators

International Nuclear Information System (INIS)

Sommerfeld, J.T.

1976-05-01

A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes

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.

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.

Flow patterns in vertical two-phase flow

International Nuclear Information System (INIS)

McQuillan, K.W.; Whalley, P.B.

1985-01-01

This paper is concerned with the flow patterns which occur in upwards gas-liquid two-phase flow in vertical tubes. The basic flow patterns are described and the use of flow patter maps is discussed. The transition between plug flow and churn flow is modelled under the assumption that flooding of the falling liquid film limits the stability of plug flow. The resulting equation is combined with other flow pattern transition equations to produce theoretical flow pattern maps, which are then tested against experimental flow pattern data. Encouraging agreement is obtained

Controlling wear failure of graphite-like carbon film in aqueous environment: Two feasible approaches

International Nuclear Information System (INIS)

Wang Yongxin; Wang Liping; Xue Qunji

2011-01-01

Friction and wear behaviors of graphite-like carbon (GLC) films in aqueous environment were investigated by a reciprocating sliding tribo-meter with ball-on-disc contact. Film structures and wear scars were studied by scanning electron microscope (SEM), energy dispersive spectroscopy (EDS) and a non-contact 3D surface profiler. A comprehensive wear model of the GLC film in aqueous environment was established, and two feasible approaches to control critical factor to the corresponding wear failure were discussed. Results showed that wear loss of GLC films in aqueous environment was characterized by micro-plough and local delamination. Due to the significant material loss, local delamination of films was critical to wear failure of GLC film in aqueous environment if the film was not prepared properly. The initiation and propagation of micro-cracks within whole films closely related to the occurrence of the films delamination from the interface between interlayer and substrate. The increase of film density by adjusting the deposition condition would significantly reduce the film delamination from substrate, meanwhile, fabricating a proper interlayer between substrate and GLC films to prevent the penetration of water molecules into the interface between interlayer and substrate could effectively eliminate the delamination.

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...

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...

Thermal conductivity model for nanoporous thin films

Science.gov (United States)

Huang, Congliang; Zhao, Xinpeng; Regner, Keith; Yang, Ronggui

2018-03-01

Nanoporous thin films have attracted great interest because of their extremely low thermal conductivity and potential applications in thin thermal insulators and thermoelectrics. Although there are some numerical and experimental studies about the thermal conductivity of nanoporous thin films, a simplified model is still needed to provide a straightforward prediction. In this paper, by including the phonon scattering lifetimes due to film thickness boundary scattering, nanopore scattering and the frequency-dependent intrinsic phonon-phonon scattering, a fitting-parameter-free model based on the kinetic theory of phonon transport is developed to predict both the in-plane and the cross-plane thermal conductivities of nanoporous thin films. With input parameters such as the lattice constants, thermal conductivity, and the group velocity of acoustic phonons of bulk silicon, our model shows a good agreement with available experimental and numerical results of nanoporous silicon thin films. It illustrates that the size effect of film thickness boundary scattering not only depends on the film thickness but also on the size of nanopores, and a larger nanopore leads to a stronger size effect of the film thickness. Our model also reveals that there are different optimal structures for getting the lowest in-plane and cross-plane thermal conductivities.

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.

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

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.

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…

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

Nonlinear Analysis of Actuation Performance of Shape Memory Alloy Composite Film Based on Silicon Substrate

Directory of Open Access Journals (Sweden)

Shuangshuang Sun

2014-01-01

Full Text Available The mechanical model of the shape memory alloy (SMA composite film with silicon (Si substrate was established by the method of mechanics of composite materials. The coupled action between the SMA film and Si substrate under thermal loads was analyzed by combining static equilibrium equations, geometric equations, and physical equations. The material nonlinearity of SMA and the geometric nonlinearity of bending deformation were both considered. By simulating and analyzing the actuation performance of the SMA composite film during one cooling-heating thermal cycle, it is found that the final cooling temperature, boundary condition, and the thickness of SMA film have significant effects on the actuation performance of the SMA composite film. Besides, the maximum deflection of the SMA composite film is affected obviously by the geometric nonlinearity of bending deformation when the thickness of SMA film is very large.

Probing-models for interdigitated electrode systems with ferroelectric thin films

Science.gov (United States)

Nguyen, Cuong H.; Nigon, Robin; Raeder, Trygve M.; Hanke, Ulrik; Halvorsen, Einar; Muralt, Paul

2018-05-01

In this paper, a new method to characterize ferroelectric thin films with interdigitated electrodes is presented. To obtain accurate properties, all parasitic contributions should be subtracted from the measurement results and accurate models for the ferroelectric film are required. Hence, we introduce a phenomenological model for the parasitic capacitance. Moreover, two common analytical models based on conformal transformations are compared and used to calculate the capacitance and the electric field. With a thin film approximation, new simplified electric field and capacitance formulas are derived. By using these formulas, more consistent CV, PV and stress-field loops for samples with different geometries are obtained. In addition, an inhomogeneous distribution of the permittivity due to the non-uniform electric field is modelled by finite element simulation in an iterative way. We observed that this inhomogeneous distribution can be treated as a homogeneous one with an effective value of the permittivity.

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.

Modeling axisymmetric flows dynamics of films, jets, and drops

CERN Document Server

Middleman, Stanley

1995-01-01

This concise book is intended to fulfill two purposes: to provide an important supplement to classic texts by carrying fluid dynamics students on into the realm of free boundary flows; and to demonstrate the art of mathematical modeling based on knowledge, intuition, and observation. In the authors words, the overall goal is make the complex simple, without losing the essence--the virtue--of the complexity.Modeling Axisymmetric Flows: Dynamics of Films, Jets, and Drops is the first book to cover the topics of axisymmetric laminar flows; free-boundary flows; and dynamics of drops, jets, and films. The text also features comparisons of models to experiments, and it includes a large selection of problems at the end of each chapter.Key Features* Contains problems at the end of each chapter* Compares real-world experimental data to theory* Provides one of the first comprehensive examinations of axisymmetric laminar flows, free-boundary flows, and dynamics of drops, jets, and films* Includes development of basic eq...

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.

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

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

A forced convective heat transfer model for two-phase hydrogen systems

International Nuclear Information System (INIS)

Pasch, J.; Anghaie, S.

2007-01-01

A consistent event in the use of hydrogen in nuclear thermal propulsion is film boiling, in which the wall heat is so large that liquid can not exist at the wall. Instead, vapor interfaces with the wall and liquid flows in the core of the duct. To better understand heat transfer under these conditions, a select set of hydrogen test data from these conditions are analyzed. This paper presents the results of an extensive literature search for film boiling heat transfer models. A representative cross-section of these models is then applied to the data. The heat transfer coefficient data were found difficult to predict and highly dependent upon the flow regime. Pre-critical heat flux correlations completely fail to predict the heat transfer of inverted film boiling conditions. Pool boiling models for inverted film boiling also are inappropriate. Current force convection models for inverted film boiling, while far better than the previous two classes of models, still generate large predictive errors. It is recommended that for the inverted annular film boiling flow regime the modified equilibrium bulk Dittus-Boelter model be used. For agitated inverted annular film boiling and dispersed film boiling regimes associated with positive equilibrium qualities, the Hendricks model should be used. (A.C.)

Extracted sericin from silk waste for film formation

Directory of Open Access Journals (Sweden)

Rungsinee Sothornvit

2010-03-01

Full Text Available Sericin is the second main component in cocoons, which are removed in the silk reeling process of the raw silk industry and in the silk waste degumming of the spun silk industry. The main amino acid of sericin, serine, exhibits a skin moisturing and antiwrinkle action, which is interesting to use for film formation in this study. The extraction conditions of sericin from two silk wastes, pieced cocoon and inferior knubbs were studied to find the optimum extraction conditions. Boiling water extraction was considered based on the response surface methodology (RSM in order to identify the important factors for the sericin extraction. The two factors considered were time and temperature. Both factors were needed to be independent parameters in the predicted equation in order to improve the model fit with R2 = 0.84. The components ofextracted sericin were 18.24% serine, 9.83% aspatate, and 5.51% glycine with a molecular weight of 132 kDa. Film formationfrom extracted sericin was carried out to find the optimum conditions. Extracted sericin could not form a stand-alonefilm. Therefore, polysaccharide polymers, such as glucomannan, were incorporated with glycerol to form a flexible film.Sericin-based films were characterized for its properties in terms of solubility and permeability before application. It wasfound that sericin-based films showed a film flexibility and solubility without an increasing film water vapor permeability.

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

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.

Advertising media strategies in the film industry

OpenAIRE

Elliott, Caroline; Simmons, Robert

2011-01-01

The primary aim of this article is to estimate the multiple determinants of film advertising expenditures in four important media, namely television, press, outdoor and radio, in the UK. First, television advertising, the leading film advertising medium, is examined as part of a system of equations, capturing the interdependences between advertising, the number of screens on which films are initially shown and box office revenues. Then a reduced form model is put forward to reveal the determi...

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

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

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.)

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.

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

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.

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

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…

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

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.…

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

Coulomb-gas scaling, superfluid films, and the XY model

International Nuclear Information System (INIS)

Minnhagen, P.; Nylen, M.

1985-01-01

Coulomb-gas-scaling ideas are invoked as a link between the superfluid density of two-dimensional 4 He films and the XY model; the Coulomb-gas-scaling function epsilon(X) is extracted from experiments and is compared with Monte Carlo simulations of the XY model. The agreement is found to be excellent

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.)

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.

Thin films of soft matter

CERN Document Server

Kalliadasis, Serafim

2007-01-01

A detailed overview and comprehensive analysis of the main theoretical and experimental advances on free surface thin film and jet flows of soft matter is given. At the theoretical front the book outlines the basic equations and boundary conditions and the derivation of low-dimensional models for the evolution of the free surface. Such models include long-wave expansions and equations of the boundary layer type and are analyzed via linear stability analysis, weakly nonlinear theories and strongly nonlinear analysis including construction of stationary periodic and solitary wave and similarity solutions. At the experimental front a variety of very recent experimental developments is outlined and the link between theory and experiments is illustrated. Such experiments include spreading drops and bubbles, imbibitions, singularity formation at interfaces and experimental characterization of thin films using atomic force microscopy, ellipsometry and contact angle measurements and analysis of patterns using Minkows...

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.

Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance.

Science.gov (United States)

Martin, S J; Bandey, H L; Cernosek, R W; Hillman, A R; Brown, M J

2000-01-01

We derive a lumped-element, equivalent-circuit model for the thickness-shear mode (TSM) resonator with a viscoelastic film. This modified Butterworth-Van Dyke model includes in the motional branch a series LCR resonator, representing the quartz resonance, and a parallel LCR resonator, representing the film resonance. This model is valid in the vicinity of film resonance, which occurs when the acoustic phase shift across the film is an odd multiple of pi/2 rad. For low-loss films, this model accurately predicts the frequency changes and damping that arise at resonance and is a reasonable approximation away from resonance. Elements of the parallel LCR resonator are explicitly related to film properties and can be interpreted in terms of elastic energy storage and viscous power dissipation. The model leads to a simple graphical interpretation of the coupling between the quartz and film resonances and facilitates understanding of the resulting responses. These responses are compared with predictions from the transmission-line and Sauerbrey models.

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

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)

Dynamical mechanism of the liquid film motor

Science.gov (United States)

Liu, Zhong-Qiang; Li, Ying-Jun; Zhang, Guang-Cai; Jiang, Su-Rong

2011-02-01

The paper presents a simple dynamical model to systemically explain the rotation mechanism of the liquid film motor reported by experiments. The field-induced-plasticity effect of the liquid film is introduced into our model, in which the liquid film in crossed electric fields is considered as a Bingham plastic fluid with equivalent electric dipole moment. Several analytic results involving the torque of rotation, the scaling relation of the threshold fields, and the dynamics equation of a square film and its solution are obtained. We find that the rotation of the liquid film motor originates from the continuous competition between the destruction and the reestablishment of the polarization equilibrium maintained by the external electric field, which is free from the boundary effects. Most experimental phenomena observed in direct current electric fields are interpreted well.

Domain Engineered Magnetoelectric Thin Films for High Sensitivity Resonant Magnetic Field Sensors

Science.gov (United States)

2011-12-01

band gap of highly textured PZT thin films. The deposition process variables were - argon and oxygen flows, chamber pressure, RF power (DC Bias...needed another parameter to equate with the number of unknowns in the resultant model equations. From Figure 24, electronic polarizability affects the... Polarizability and Optical dielectric response of a thin.film , ., ,__~--~---\\- 000 01’ "󈧶 Ots Tncnt.re"’°l Effective Polarizability = Reddy

Linking rigid multibody systems via controllable thin fluid films

DEFF Research Database (Denmark)

Estupinan, Edgar Alberto; Santos, Ilmar

2009-01-01

, this paper gives a theoretical contribution to the combined fields of fluid–structure interaction and vibration control. The methodology is applied to a reciprocating linear compressor, where the dynamics of the mechanical components are described with help of multibody dynamics. The crank is linked......This work deals with the mathematical modelling of multibody systems interconnected via thin fluid films. The dynamics of the fluid films can be actively controlled by means of different types of actuators, allowing significant vibration reduction of the system components. In this framework...... to the rotor via a thin fluid film, where the hydrodynamic pressure is described by the Reynolds equation, which is modified to accommodate the controllable lubrication conditions. The fluid film forces are coupled to the set of nonlinear equations that describes the dynamics of the reciprocating linear...

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

Migration of antioxidants from polylactic acid films, a parameter estimation approach: Part I - A model including convective mass transfer coefficient.

Science.gov (United States)

Samsudin, Hayati; Auras, Rafael; Burgess, Gary; Dolan, Kirk; Soto-Valdez, Herlinda

2018-03-01

A two-step solution based on the boundary conditions of Crank's equations for mass transfer in a film was developed. Three driving factors, the diffusion (D), partition (K p,f ) and convective mass transfer coefficients (h), govern the sorption and/or desorption kinetics of migrants from polymer films. These three parameters were simultaneously estimated. They provide in-depth insight into the physics of a migration process. The first step was used to find the combination of D, K p,f and h that minimized the sums of squared errors (SSE) between the predicted and actual results. In step 2, an ordinary least square (OLS) estimation was performed by using the proposed analytical solution containing D, K p,f and h. Three selected migration studies of PLA/antioxidant-based films were used to demonstrate the use of this two-step solution. Additional parameter estimation approaches such as sequential and bootstrap were also performed to acquire a better knowledge about the kinetics of migration. The proposed model successfully provided the initial guesses for D, K p,f and h. The h value was determined without performing a specific experiment for it. By determining h together with D, under or overestimation issues pertaining to a migration process can be avoided since these two parameters are correlated. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

A dynamic film model of the pulsating heat pipe

International Nuclear Information System (INIS)

Nikolayev, Vadim S.

2011-01-01

This article deals with the numerical modeling of the pulsating heat pipe (PHP) and is based on the film evaporation/condensation model recently applied to the single-bubble PHP (Das et al., 2010, 'Thermally Induced Two-Phase Oscillating Flow Inside a Capillary Tube', Int. J. Heat Mass Transfer, 53(19-20), pp. 3905-3913). The described numerical code can treat the PHP of an arbitrary number of bubbles and branches. Several phenomena that occur inside the PHP are taken into account: coalescence of liquid plugs, film junction or rupture, etc. The model reproduces some of the experimentally observed regimes of functioning of the PHP such as chaotic or intermittent oscillations of large amplitudes. Some results on the PHP heat transfer are discussed. (author)

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.)

Quasi-two-dimensional superconductivity in wurtzite-structured InN films

International Nuclear Information System (INIS)

Ling, D.C.; Cheng, J.H.; Lo, Y.Y.; Du, C.H.; Chiu, A.P.; Chang, P.H.; Chang, C.A.

2007-01-01

C-axis oriented InN films with wurtzite structure were grown on sapphire(0001) substrate by MOCVD method. Superconductivity with transition onset temperature T c,onset around 3.5 K has been characterized by magnetotransport measurements in fields up to 9 Tesla for films with carrier concentration in the range of 1 x 10 19 cm -3 to 7 x 10 20 cm -3 . Among them, the film with a nitridation buffer layer has the highest zero-resistance temperature T c0 of 2 K. The normal-state magnetoresistance follows Kohler's rule ΔR/R∝(H/R) 2 , indicating that there is a single species of charge carrier with single scattering time at all points on the Fermi surface. The extrapolated value of zero-temperature upper critical field H c2 ab (0) and H c2 c (0) is estimated to be 5900 G and 2800 G, respectively, giving rise to the anisotropy parameter γ about 2.1. The angular dependence of the upper critical field is in good agreement with the behavior predicted by Lawrence-Doniach model in the two-dimensional (2D) limit strongly suggesting that the InN film is a quasi-2D superconductor. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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

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)

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).

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

Distortion of liquid film discharging from twin-fluid atomizer

Science.gov (United States)

Mehring, C.; Sirignano, W. A.

2001-11-01

The nonlinear distortion and disintegration of a thin liquid film exiting from a two-dimensional twin-fluid atomizer is analyzed numerically. Pulsed gas jets impacting on both sides of the discharging liquid film at the atomizer exit generate dilational and/or sinuous deformations of the film. Both liquid phase and gas phase are inviscid and incompressible. For the liquid phase the so-called long-wavelength approximation is employed yielding a system of unsteady one-dimensional equations for the planar film. Solution of Laplace's equation for the velocity potential yields the gas-phase velocity field on both sides of the liquid stream. Coupling between both phases is described through kinematic and dynamic boundary conditions at the phase interfaces, and includes the solution of the unsteady Bernoulli equation to determine the gas-phase pressure along the interfaces. Both gas- and liquid-phase equations are solved simultaneously. Solution of Laplace's equation for the gas streams is obtained by means of a boundary-element method. Numerical solutions for the liquid phase use the Lax-Wendroff method with Richtmyer splitting. Sheet distortion resulting from the stagnation pressure of the impacting gas jets and subsequent disturbance amplification due to Kelvin-Helmholtz effects are studied for various combinations of gas-pulse timing, gas-jet impact angles, gas-to-liquid-density ratio, liquid-phase Weber number and gas-jet-to-liquid-jet-momentum ratio. Dilational and sinuous oscillations of the liquid are examined and film pinch-off is predicted.

Determination of dryout localization using a five-equation model of annular flow for boiling in minichannels

OpenAIRE

Wajs Jan; Mikielewicz Dariusz

2017-01-01

Detailed studies have suggested that the critical heat flux in the form of dryout in minichannels occurs when the combined effects of entrainment, deposition, and evaporation of the film make the film flow rate go gradually and smoothly to zero. Most approaches so far used the mass balance equation for the liquid film with appropriate formulations for the rate of deposition and entrainment respectively. It must be acknowledged that any discrepancy in determination of deposition and entrainmen...

Generalized bipolariton model. propagation of a ultrashort laser pulse through a thin semiconductor film in the conditions of two-photon generation of biexcitons

International Nuclear Information System (INIS)

Igor Beloussov

2013-01-01

A generalized bipolariton model is proposed. Bipolaritons is formed from virtual excitons of four kinds. There exists both attractive and repulsive interaction between these excitons, though only excitons of a specific type can interact with light. A substantial difference between conventional and our models is shown for the case of nonlinear transmission/reflection of ultrashort laser pulses by a thin semiconductor film under two-photon generation of biexcitons. (author)

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

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

Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation

Energy Technology Data Exchange (ETDEWEB)

Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel

2009-06-15

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)

Ginzburg-Landau vortices driven by the Landau-Lifshitz-Gilbert equation

International Nuclear Information System (INIS)

Kurzke, Matthias; Melcher, Christof; Moser, Roger; Spirn, Daniel

2009-01-01

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg-Landau vortices for sphere-valued maps. In particular we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization is ruled by the Landau-Lifshitz-Gilbert equation, which combines characteristic properties of a nonlinear Schroedinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation. (orig.)

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,

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

Evaluation method for two-phase flow and heat transfer in a feed-water heater

International Nuclear Information System (INIS)

Takamori, Kazuhide; Minato, Akihiko

1993-01-01

A multidimensional analysis code for two-phase flow using a two-fluid model was improved by taking into consideration the condensation heat transfer, film thickness, and film velocity, in order to develop an evaluation method for two-phase flow and heat transfer in a feed-water heater. The following results were obtained by a two-dimensional analysis of a feed-water heater for a power plant. (1) In the model, the film flowed downward in laminar flow due to gravity, with droplet entrainment and deposition. For evaluation of the film thickness, Fujii's equation was used in order to account for forced convection of steam flow. (2) Based on the former experimental data, the droplet deposition coefficient and droplet entrainment rate of liquid film were determined. When the ratio at which the liquid film directly flowed from an upper heat transfer tube to a lower heat transfer tube was 0.7, the calculated total heat transfer rate agreed with the measured value of 130 MW. (3) At the upper region of a heat transfer tube bundle where film thickness was thin, and at the outer region of a heat transfer tube bundle where steam velocity was high, the heat transfer rate was large. (author)

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...

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.

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.

Comparison of Surface-enhanced Raman Scattering Spectra of Two Kinds of Silver Nanoplate Films

Institute of Scientific and Technical Information of China (English)

TAO Jin-long; TANG Bin; XU Shu-ping; PAN Ling-yun; XU Wei-qing

2012-01-01

Surface-enhanced Raman scattering(SERS) spectra of different silver nanoplate self-assembled films at different excitation wavelengths were fairly compared.Shape conversion from silver nanoprisms to nanodisks on slides was in situ carried out.The SERS spectra of 4-mercaptopyridine(4-MPY) on these anisotropic silver nanoparticle self-assembled films present that strong enhancement appeared when the excitation line and the surface plasmon resonance(SPR) band of silver substrate overlapped.In this model,the influence of the crystal planes of silver nanoplates on SERS enhancement could be ignored because the basal planes were nearly unchanged in two kinds of silver nanoplate self-assembled films.

Optical modelling of photoluminescence emitted by thin doped films

International Nuclear Information System (INIS)

Pigeat, P.; Easwarakhanthan, T.; Briancon, J.L.; Rinnert, H.

2011-01-01

Photoluminescence (PL) spectra emitted by doped films are deformed owing to film thickness-dependent wave interference. This hampers knowing well their PL generating mechanisms as well as designing photonic devices with suitable geometries that improve their PL efficiency. We develop in this paper an energy model for PL emitted by doped films considering the interaction between the wavelength-differing incident standing and emitted waves, their energy transfer in-between, and the interferences undergone by both. The film optical constants are estimated fitting the model to the measured PL. This simple model has thus allowed us to interpret the evolution of PL emitted by Er-doped AlN films prepared on Si substrates by reactive magnetron sputtering. The shapes, the amplitudes, and the illusive sub-spectral features of the PL spectra depend essentially on the film thickness. The model further predicts high sensitivity for PL emitted by non-homogenously doped stacked-films to incident light wavelengths and film-thickness variations. This property has potential applications in tracking wavelength variations and in measuring physical quantities producing thickness variations. This model may be used to optimise PL efficiency of photonic devices through different film geometries and optical properties.

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

Morphology of the cumulative logistic distribution when used as a model of radiologic film characteristic curves

International Nuclear Information System (INIS)

Prince, J.R.

1988-01-01

The cumulative logistic distribution (CLD) is an empiric model for film characteristic curves. Characterizing the shape parameters of the CLD in terms of contrast, latitude and speed is required. The CLD is written as Υ-F=D/[1+EXP-(Κ+κ 1 X)] where Υ is the optical density (OD) at log exposure X, F is fog level, D is a constant equal to Dm-F, Κ and κ 1 are shape parameters, and Dm is the maximum attainable OD. Further analysis demonstrates that when Κ is held constant, Κ 1 characterizes contrast (the larger κ 1 , the greater the contrast) and hence latitude; when κ 1 is held constant, Κ characterizes film speed (the larger Κ is, the faster the film). These equations and concepts are further illustrated with examples from radioscintigraphy, diagnostic radiology, and light sensitometry

The shape of soap films and Plateau borders

International Nuclear Information System (INIS)

Fortes, M A; Teixeira, P I C; Deus, A M

2007-01-01

We have calculated the shapes of flat liquid films, and of the transition region to the associated Plateau borders (PBs), by integrating the Laplace equation with a position-dependent surface tension γ(x), where 2x is the local film thickness. We discuss films in either zero or non-zero gravity, using standard γ(x) potentials for the interaction between the two bounding surfaces. We have investigated the effects of the film flatness, liquid underpressure, and gravity on the shape of films and their PBs. Films may exhibit 'humps' and/or 'dips' associated with inflection points and minima of the film thickness. Finally, we propose an asymptotic analytical solution for the film width profile

The shape of soap films and Plateau borders

Energy Technology Data Exchange (ETDEWEB)

Fortes, M A [Departamento de Engenharia de Materiais and Instituto de Ciencia e Engenharia de Materiais e SuperfIcies, Instituto Superior Tecnico, Avenida Rovisco Pais, P-1049-001 Lisbon (Portugal); Teixeira, P I C [Instituto Superior de Engenharia de Lisboa Rua Conselheiro EmIdio Navarro 1, P-1950-062 Lisbon (Portugal); Deus, A M [Departamento de Engenharia de Materiais and Instituto de Ciencia e Engenharia de Materiais e SuperfIcies, Instituto Superior Tecnico, Avenida Rovisco Pais, P-1049-001 Lisbon (Portugal)

2007-06-20

We have calculated the shapes of flat liquid films, and of the transition region to the associated Plateau borders (PBs), by integrating the Laplace equation with a position-dependent surface tension {gamma}(x), where 2x is the local film thickness. We discuss films in either zero or non-zero gravity, using standard {gamma}(x) potentials for the interaction between the two bounding surfaces. We have investigated the effects of the film flatness, liquid underpressure, and gravity on the shape of films and their PBs. Films may exhibit 'humps' and/or 'dips' associated with inflection points and minima of the film thickness. Finally, we propose an asymptotic analytical solution for the film width profile.

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

Film thickness in gas-liquid two-phase flow, (2)

International Nuclear Information System (INIS)

Sekoguchi, Kotohiko; Fukano, Toru; Kawakami, Yasushi; Shimizu, Hideo.

1977-01-01

The effect of four rectangular obstacles inserted into a circular tube has been studied in gas-liquid two-phase flow. The obstacles are set on the inner wall of the tube, and the ratio of the opening is 0.6. The water film flows partially through the obstacles. The minimum thickness of water film was measured in relation to flow speed. The serious effect of the obstacles was seen against the formation of water film, and drainage under the obstacles and backward flow play important roles. Since water film can flow partially through the obstacles, the film in case of the rectangular obstacles in thicker than that in case of an orifice when the gas flow speed was slower than 5 m/s. However, when the gas flow speed is over 5 m/s, the film thickness was thinner. The minimum film thickness of downstream of the obstacles was almost same as that in case of no obstacle. The minimum film thickness of up stream depends on the location of measurement due to the effect of drainage. (Kato, T.)

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.

Droplet size effects on film drainage between droplet and substrate.

Science.gov (United States)

Steinhaus, Benjamin; Spicer, Patrick T; Shen, Amy Q

2006-06-06

When a droplet approaches a solid surface, the thin liquid film between the droplet and the surface drains until an instability forms and then ruptures. In this study, we utilize microfluidics to investigate the effects of film thickness on the time to film rupture for water droplets in a flowing continuous phase of silicone oil deposited on solid poly(dimethylsiloxane) (PDMS) surfaces. The water droplets ranged in size from millimeters to micrometers, resulting in estimated values of the film thickness at rupture ranging from 600 nm down to 6 nm. The Stefan-Reynolds equation is used to model film drainage beneath both millimeter- and micrometer-scale droplets. For millimeter-scale droplets, the experimental and analytical film rupture times agree well, whereas large differences are observed for micrometer-scale droplets. We speculate that the differences in the micrometer-scale data result from the increases in the local thin film viscosity due to confinement-induced molecular structure changes in the silicone oil. A modified Stefan-Reynolds equation is used to account for the increased thin film viscosity of the micrometer-scale droplet drainage case.

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)

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...

A model of film boiling in the presence of electric fields

Energy Technology Data Exchange (ETDEWEB)

Carrica, P.M.; Masson, V.; Clausse, A. [Centro Atomico Bariloche and Instituto Balseiro, Barilochi (Argentina)

1995-09-01

Recently it was found that, when a strong electric field is applied around a heated wire, two distinct film boiling heat transfer regimes are observed. In this paper, a semi-empirical model is derived to analyze the pool boiling process in the presence of non uniform electric field. The model takes into account the dielectrophoretic force acting on the bubbles as they grow and the effect of the electric field on the most dangerous wavelength. It is shown how the transition between the two film boiling regimes is possible for high strength electric fields. The threshold voltage for transition, transition heat fluxes and hysteresis values are compared with experimental outcomes showing a satisfactory agreement.

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...

Numerical study of heat and mass transfer during evaporation of a thin liquid film

Directory of Open Access Journals (Sweden)

Oubella M’hand

2015-01-01

Full Text Available A numerical study of mixed convection heat and mass transfer with film evaporation in a vertical channel is developed. The emphasis is focused on the effects of vaporization of three different liquid films having widely different properties, along the isothermal and wetted walls on the heat and mass transfer rates in the channel. The induced laminar downward flow is a mixture of blowing dry air and vapour of water, methanol or acetone, assumed as ideal gases. A two-dimensional steady state and elliptical flow model, connected with variable thermo-physical properties, is used and the phase change problem is based on thin liquid film assumptions. The governing equations of the model are solved by a finite volume method and the velocity-pressure fields are linked by SIMPLE algorithm. The numerical results, including the velocity, temperature and concentration profiles, as well as axial variations of Nusselt numbers, Sherwood number and dimensionless film evaporation rate are presented for two values of inlet temperature and Reynolds number. It was found that lower the inlet temperature and Re, the higher the induced flows cooling with respect of most volatile film. The better mass transfer rates related with film evaporation are found for a system with low mass diffusion coefficient.

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)

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

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.

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...

Discovery in Film, Book Two.

Science.gov (United States)

Gordon, Malcolm W.

Approximately 80 16 millimeter (16mm) short films are reviewed in this introduction and guide which attempts to be comprehensive in touching the major areas and styles of 16mm films now being produced. An attempt is made to describe as carefully as possible the style and content of each film and suggest ways in which the films might be used. Films…

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

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.)

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

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

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.