Zhu, Guangpu
2018-04-17
In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.
Zhu, Guangpu; Kou, Jisheng; Sun, Shuyu; Yao, Jun; Li, Aifen
2018-01-01
In this paper, we consider the numerical approximation of a binary fluid-surfactant phase field model of two-phase incompressible flow. The nonlinearly coupled model consists of two Cahn-Hilliard type equations and incompressible Navier-Stokes equations. Using the Invariant Energy Quadratization (IEQ) approach, the governing system is transformed into an equivalent form, which allows the nonlinear potentials to be treated efficiently and semi-explicitly. we construct a first and a second-order time marching schemes, which are extremely efficient and easy-to-implement, for the transformed governing system. At each time step, the schemes involve solving a sequence of linear elliptic equations, and computations of phase variables, velocity and pressure are totally decoupled. We further establish a rigorous proof of unconditional energy stability for the semi-implicit schemes. Numerical results in both two and three dimensions are obtained, which demonstrate that the proposed schemes are accurate, efficient and unconditionally energy stable. Using our schemes, we investigate the effect of surfactants on droplet deformation and collision under a shear flow. The increase of surfactant concentration can enhance droplet deformation and inhibit droplet coalescence.
Analytic approximations for the elastic moduli of two-phase materials
DEFF Research Database (Denmark)
Zhang, Z. J.; Zhu, Y. K.; Zhang, P.
2017-01-01
Based on the models of series and parallel connections of the two phases in a composite, analytic approximations are derived for the elastic constants (Young's modulus, shear modulus, and Poisson's ratio) of elastically isotropic two-phase composites containing second phases of various volume...
Approximate characteristics for one-dimensional two-phase flows
International Nuclear Information System (INIS)
Sarayloo, A.; Peddleson, J.
1985-01-01
An approximate method for determining the characteristics associated with one-dimensional particulate two-phase flow models is presented. The method is based on iteration and is valid for small particulate volume fractions. The method is applied to several special cases involving incompressible particles suspended in a gas. The influences of certain changes in the physical model are investigated
Implicit approximate Riemann solver for two fluid two phase flow models
International Nuclear Information System (INIS)
Raymond, P.; Toumi, I.; Kumbaro, A.
1993-01-01
This paper is devoted to the description of new numerical methods developed for the numerical treatment of two phase flow models with two velocity fields which are now widely used in nuclear engineering for design or safety calculations. These methods are finite volumes numerical methods and are based on the use of Approximate Riemann Solver's concepts in order to define convective flux versus mean cell quantities. The first part of the communication will describe the numerical method for a three dimensional drift flux model and the extensions which were performed to make the numerical scheme implicit and to have fast running calculations of steady states. Such a scheme is now implemented in the FLICA-4 computer code devoted to 3-D steady state and transient core computations. We will present results obtained for a steady state flow with rod bow effect evaluation and for a Steam Line Break calculation were the 3-D core thermal computation was coupled with a 3-D kinetic calculation and a thermal-hydraulic transient calculation for the four loops of a Pressurized Water Reactor. The second part of the paper will detail the development of an equivalent numerical method based on an approximate Riemann Solver for a two fluid model with two momentum balance equations for the liquid and the gas phases. The main difficulty for these models is due to the existence of differential modelling terms such as added mass effects or interfacial pressure terms which make hyperbolic the model. These terms does not permit to write the balance equations system in a conservative form, and the classical theory for discontinuity propagation for non-linear systems cannot be applied. Meanwhile, the use of non-conservative products theory allows the study of discontinuity propagation for a non conservative model and this will permit the construction of a numerical scheme for two fluid two phase flow model. These different points will be detailed in that section which will be illustrated by
Graf, Daniel; Beuerle, Matthias; Schurkus, Henry F; Luenser, Arne; Savasci, Gökcen; Ochsenfeld, Christian
2018-05-08
An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...
Approximate Riemann solvers and flux vector splitting schemes for two-phase flow
International Nuclear Information System (INIS)
Toumi, I.; Kumbaro, A.; Paillere, H.
1999-01-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
Relaxation and Numerical Approximation of a Two-Fluid Two-Pressure Diphasic Model
International Nuclear Information System (INIS)
Ambroso, A.; Chalons, Ch.; Galie, Th.; Chalons, Ch.; Coquel, F.; Coquel, F.
2009-01-01
This paper is concerned with the numerical approximation of the solutions of a two-fluid two-pressure model used in the modelling of two-phase flows. We present a relaxation strategy for easily dealing with both the nonlinearities associated with the pressure laws and the nonconservative terms that are inherently present in the set of convective equations and that couple the two phases. In particular, the proposed approximate Riemann solver is given by explicit formulas, preserves the natural phase space, and exactly captures the coupling waves between the two phases. Numerical evidences are given to corroborate the validity of our approach. (authors)
Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle
Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.
2018-05-01
Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.
Cold pasta phase in the extended Thomas-Fermi approximation
Avancini, S. S.; Bertolino, B. P.
2015-10-01
In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas-Fermi (ETF) approximation.
Cold pasta phase in the extended Thomas–Fermi approximation
International Nuclear Information System (INIS)
Avancini, S.S.; Bertolino, B.P.
2015-01-01
In this paper, we aim to obtain more accurate values for the transition density to the homogenous phase in the nuclear pasta that occurs in the inner crust of neutron stars. To that end, we use the nonlinear Walecka model at zero temperature and an approach based on the extended Thomas–Fermi (ETF) approximation. (author)
International Nuclear Information System (INIS)
Jiang, R.
2009-01-01
It is difficult to find the optimal solution of the sequential age replacement policy for a finite-time horizon. This paper presents an accurate approximation to find an approximate optimal solution of the sequential replacement policy. The proposed approximation is computationally simple and suitable for any failure distribution. Their accuracy is illustrated by two examples. Based on the approximate solution, an approximate estimate for the total cost is derived.
Directory of Open Access Journals (Sweden)
Xiao-Ying Qin
2014-01-01
Full Text Available An Adomian decomposition method (ADM is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.
Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube
International Nuclear Information System (INIS)
Nigmatulin, R.I.
1995-01-01
The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered
Drift flux model as approximation of two fluid model for two phase dispersed and slug flow in tube
Energy Technology Data Exchange (ETDEWEB)
Nigmatulin, R.I.
1995-09-01
The analysis of one-dimensional schematizing for non-steady two-phase dispersed and slug flow in tube is presented. Quasi-static approximation, when inertia forces because of the accelerations of the phases may be neglected, is considered. Gas-liquid bubbly and slug vertical upward flows are analyzed. Non-trivial theoretical equations for slip velocity for these flows are derived. Juxtaposition of the derived equations for slip velocity with the famous Zuber-Findlay correlation as cross correlation coefficients is criticized. The generalization of non-steady drift flux Wallis theory taking into account influence of wall friction on the bubbly or slug flows for kinematical waves is considered.
Adaptive moving grid methods for two-phase flow in porous media
Dong, Hao
2014-08-01
In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can handle the nonlinearities of the governing equations in an efficient way. The adaptive moving grid method is then used to distribute more grid points near the sharp interfaces, which enables us to obtain accurate numerical solutions with fewer computational resources. The numerical experiments indicate that the proposed moving mesh strategy could be an effective way to approximate two-phase flows in porous media. © 2013 Elsevier B.V. All rights reserved.
Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter.
Kulkarni, Rishikesh; Rastogi, Pramod
2018-02-01
A noise-robust phase unwrapping algorithm is proposed based on state space analysis and polynomial phase approximation using wrapped phase measurement. The true phase is approximated as a two-dimensional first order polynomial function within a small sized window around each pixel. The estimates of polynomial coefficients provide the measurement of phase and local fringe frequencies. A state space representation of spatial phase evolution and the wrapped phase measurement is considered with the state vector consisting of polynomial coefficients as its elements. Instead of using the traditional nonlinear Kalman filter for the purpose of state estimation, we propose to use the linear Kalman filter operating directly with the wrapped phase measurement. The adaptive window width is selected at each pixel based on the local fringe density to strike a balance between the computation time and the noise robustness. In order to retrieve the unwrapped phase, either a line-scanning approach or a quality guided strategy of pixel selection is used depending on the underlying continuous or discontinuous phase distribution, respectively. Simulation and experimental results are provided to demonstrate the applicability of the proposed method.
Communication: Random phase approximation renormalized many-body perturbation theory
International Nuclear Information System (INIS)
Bates, Jefferson E.; Furche, Filipp
2013-01-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations
Hybrid flux splitting schemes for numerical resolution of two-phase flows
Energy Technology Data Exchange (ETDEWEB)
Flaatten, Tore
2003-07-01
This thesis deals with the construction of numerical schemes for approximating. solutions to a hyperbolic two-phase flow model. Numerical schemes for hyperbolic models are commonly divided in two main classes: Flux Vector Splitting (FVS) schemes which are based on scalar computations and Flux Difference Splitting (FDS) schemes which are based on matrix computations. FVS schemes are more efficient than FDS schemes, but FDS schemes are more accurate. The canonical FDS schemes are the approximate Riemann solvers which are based on a local decomposition of the system into its full wave structure. In this thesis the mathematical structure of the model is exploited to construct a class of hybrid FVS/FDS schemes, denoted as Mixture Flux (MF) schemes. This approach is based on a splitting of the system in two components associated with the pressure and volume fraction variables respectively, and builds upon hybrid FVS/FDS schemes previously developed for one-phase flow models. Through analysis and numerical experiments it is demonstrated that the MF approach provides several desirable features, including (1) Improved efficiency compared to standard approximate Riemann solvers, (2) Robustness under stiff conditions, (3) Accuracy on linear and nonlinear phenomena. In particular it is demonstrated that the framework allows for an efficient weakly implicit implementation, focusing on an accurate resolution of slow transients relevant for the petroleum industry. (author)
Directory of Open Access Journals (Sweden)
M. Bishehniasar
2017-01-01
Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.
Insight into structural phase transitions from the decoupled anharmonic mode approximation.
Adams, Donat J; Passerone, Daniele
2016-08-03
We develop a formalism (decoupled anharmonic mode approximation, DAMA) that allows calculation of the vibrational free energy using density functional theory even for materials which exhibit negative curvature of the potential energy surface with respect to atomic displacements. We investigate vibrational modes beyond the harmonic approximation and approximate the potential energy surface with the superposition of the accurate potential along each normal mode. We show that the free energy can stabilize crystal structures at finite temperatures which appear dynamically unstable at T = 0. The DAMA formalism is computationally fast because it avoids statistical sampling through molecular dynamics calculations, and is in principle completely ab initio. It is free of statistical uncertainties and independent of model parameters, but can give insight into the mechanism of a structural phase transition. We apply the formalism to the perovskite cryolite, and investigate the temperature-driven phase transition from the P21/n to the Immm space group. We calculate a phase transition temperature between 710 and 950 K, in fair agreement with the experimental value of 885 K. This can be related to the underestimation of the interaction of the vibrational states. We also calculate the main axes of the thermal ellipsoid and can explain the experimentally observed increase of its volume for the fluorine by 200-300% throughout the phase transition. Our calculations suggest the appearance of tunneling states in the high temperature phase. The convergence of the vibrational DOS and of the critical temperature with respect of reciprocal space sampling is investigated using the polarizable-ion model.
Zhang, Du; Su, Neil Qiang; Yang, Weitao
2017-07-20
The GW self-energy, especially G 0 W 0 based on the particle-hole random phase approximation (phRPA), is widely used to study quasiparticle (QP) energies. Motivated by the desirable features of the particle-particle (pp) RPA compared to the conventional phRPA, we explore the pp counterpart of GW, that is, the T-matrix self-energy, formulated with the eigenvectors and eigenvalues of the ppRPA matrix. We demonstrate the accuracy of the T-matrix method for molecular QP energies, highlighting the importance of the pp channel for calculating QP spectra.
Precise and accurate train run data: Approximation of actual arrival and departure times
DEFF Research Database (Denmark)
Richter, Troels; Landex, Alex; Andersen, Jonas Lohmann Elkjær
with the approximated actual arrival and departure times. As a result, all future statistics can now either be based on track circuit data with high precision or approximated actual arrival times with a high accuracy. Consequently, performance analysis will be more accurate, punctuality statistics more correct, KPI...
International Nuclear Information System (INIS)
Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W.; Hughes, E.D.
1975-01-01
Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)
Highly Accurate Calculations of the Phase Diagram of Cold Lithium
Shulenburger, Luke; Baczewski, Andrew
The phase diagram of lithium is particularly complicated, exhibiting many different solid phases under the modest application of pressure. Experimental efforts to identify these phases using diamond anvil cells have been complemented by ab initio theory, primarily using density functional theory (DFT). Due to the multiplicity of crystal structures whose enthalpy is nearly degenerate and the uncertainty introduced by density functional approximations, we apply the highly accurate many-body diffusion Monte Carlo (DMC) method to the study of the solid phases at low temperature. These calculations span many different phases, including several with low symmetry, demonstrating the viability of DMC as a method for calculating phase diagrams for complex solids. Our results can be used as a benchmark to test the accuracy of various density functionals. This can strengthen confidence in DFT based predictions of more complex phenomena such as the anomalous melting behavior predicted for lithium at high pressures. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.
International Nuclear Information System (INIS)
Shin, Y.W.; Wiedermann, A.H.
1984-01-01
Accurate numerical methods for treating the junction and boundary conditions needed in the transient two-phase flows of a piping network were published earlier by us; the same methods are used to formulate the treatment of the material interface as a moving boundary. The method formulated is used in a computer program to calculate sample problems designed to test the numerical methods as to their ability and the accuracy limits for calculation of the transient two-phase flows in the piping network downstream of a PWR pressurizer. Independent exact analytical solutions for the sample problems are used as the basis of a critical evaluation of the proposed numerical methods. The evaluation revealed that the proposed boundary scheme indeed generates very accurate numerical results. However, in some extreme flow conditions, numerical difficulties were experienced that eventually led to numerical instability. This paper discusses further a special technique to overcome the difficulty
International Nuclear Information System (INIS)
Du, Qiang; Yang, Jiang
2017-01-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
DEFF Research Database (Denmark)
Olsen, Thomas; Yan, Jun; Mortensen, Jens Jørgen
2011-01-01
We calculate the potential energy surfaces for graphene adsorbed on Cu(111), Ni(111), and Co(0001) using density functional theory and the random phase approximation (RPA). For these adsorption systems covalent and dispersive interactions are equally important and while commonly used approximations...... for exchange-correlation functionals give inadequate descriptions of either van der Waals or chemical bonds, RPA accounts accurately for both. It is found that the adsorption is a delicate competition between a weak chemisorption minimum close to the surface and a physisorption minimum further from the surface....
Advanced numerical methods for three dimensional two-phase flow calculations
Energy Technology Data Exchange (ETDEWEB)
Toumi, I. [Laboratoire d`Etudes Thermiques des Reacteurs, Gif sur Yvette (France); Caruge, D. [Institut de Protection et de Surete Nucleaire, Fontenay aux Roses (France)
1997-07-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe`s method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations.
Advanced numerical methods for three dimensional two-phase flow calculations
International Nuclear Information System (INIS)
Toumi, I.; Caruge, D.
1997-01-01
This paper is devoted to new numerical methods developed for both one and three dimensional two-phase flow calculations. These methods are finite volume numerical methods and are based on the use of Approximate Riemann Solvers concepts to define convective fluxes versus mean cell quantities. The first part of the paper presents the numerical method for a one dimensional hyperbolic two-fluid model including differential terms as added mass and interface pressure. This numerical solution scheme makes use of the Riemann problem solution to define backward and forward differencing to approximate spatial derivatives. The construction of this approximate Riemann solver uses an extension of Roe's method that has been successfully used to solve gas dynamic equations. As far as the two-fluid model is hyperbolic, this numerical method seems very efficient for the numerical solution of two-phase flow problems. The scheme was applied both to shock tube problems and to standard tests for two-fluid computer codes. The second part describes the numerical method in the three dimensional case. The authors discuss also some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. Such a scheme is not implemented in a thermal-hydraulic computer code devoted to 3-D steady-state and transient computations. Some results obtained for Pressurised Water Reactors concerning upper plenum calculations and a steady state flow in the core with rod bow effect evaluation are presented. In practice these new numerical methods have proved to be stable on non staggered grids and capable of generating accurate non oscillating solutions for two-phase flow calculations
State of the art: two-phase flow calibration techniques
International Nuclear Information System (INIS)
Stanley, M.L.
1977-01-01
The nuclear community faces a particularly difficult problem relating to the calibration of instrumentation in a two-phase flow steam/water environment. The rationale of the approach to water reactor safety questions in the United States demands that accurate measurements of mass flows in a decompressing two-phase flow be made. An accurate measurement dictates an accurate calibration. This paper addresses three questions relating to the state of the art in two-phase calibration: (1) What do we mean by calibration. (2) What is done now. (3) What should be done
Numerical modelling of two phase flow with hysteresis in heterogeneous porous media
Energy Technology Data Exchange (ETDEWEB)
Abreu, E. [Instituto Nacional de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, RJ (Brazil); Furtado, F.; Pereira, F. [University of Wyoming, Laramie, WY (United States). Dept. of Mathematicsatics; Souza, G. [Universidade do Estado do Rio de Janeiro (UERJ), RJ (Brazil)
2008-07-01
Numerical simulators are necessary for the understanding of multiphase flow in porous media in order to optimize hydrocarbon recovery. In this work, the immiscible flow of two incompressible phases, a problem very common in waterflooding of petroleum reservoirs, is considered and numerical simulation techniques are presented. The system of equations which describe this type of flow form a coupled, highly nonlinear system of time-dependent partial differential equations (PDEs). The equation for the saturation of the invading fluid is a convection-dominated, degenerate parabolic PDE whose solutions typically exhibit sharp fronts (i.e., internal layers with strong gradients) and is very difficult to approximate numerically. It is well known that accurate modeling of convective and diffusive processes is one of the most daunting tasks in the numerical approximation of PDEs. Particularly difficult is the case where convection dominates diffusion. Specifically, we consider the injection problem for a model of two-phase (water/oil) flow in a core sample of porous rock, taking into account hysteresis effects in the relative permeability of the oil phase. (author)
Directory of Open Access Journals (Sweden)
Calvo Bernad Esteban
2014-03-01
Full Text Available This paper provides an experimental study of an acoustically forced two-phase air jet generated by a convergent nozzle. The used particles are transparent glass spheres with diameters between 2 and 50 μm (which gives Stokes number of order 1 and the selected forcing frequency (f=400 Hz induces a powerful nearly periodic flow pattern. Measurements were done by a two-colour Phase-Doppler Anemometer. The experimental setup is computer-controlled to provide an accurate control with a high long-term stability. Measurements cover the whole forcing signal cycle. Raw measurements were carefully post-processed to avoid bias induced by the forcing and the instrument setup, as well as obtain right mean values of the dispersed flow. The effect of the forcing and the particle load allows authors to establish the effect of the acoustic forcing and the particle load on the jet.
Accurate and approximate thermal rate constants for polyatomic chemical reactions
International Nuclear Information System (INIS)
Nyman, Gunnar
2007-01-01
In favourable cases it is possible to calculate thermal rate constants for polyatomic reactions to high accuracy from first principles. Here, we discuss the use of flux correlation functions combined with the multi-configurational time-dependent Hartree (MCTDH) approach to efficiently calculate cumulative reaction probabilities and thermal rate constants for polyatomic chemical reactions. Three isotopic variants of the H 2 + CH 3 → CH 4 + H reaction are used to illustrate the theory. There is good agreement with experimental results although the experimental rates generally are larger than the calculated ones, which are believed to be at least as accurate as the experimental rates. Approximations allowing evaluation of the thermal rate constant above 400 K are treated. It is also noted that for the treated reactions, transition state theory (TST) gives accurate rate constants above 500 K. TST theory also gives accurate results for kinetic isotope effects in cases where the mass of the transfered atom is unchanged. Due to neglect of tunnelling, TST however fails below 400 K if the mass of the transferred atom changes between the isotopic reactions
Two correlated quasiparticles states in the principal series approximation
International Nuclear Information System (INIS)
Dukelsky, J.; Dussel, G.G.; Sofia, H.M.
1983-01-01
The principal series approximation is extended to the description of two correlated quasiparticles states, enabling a treatment of these states that takes into account the coupling among the two particle Green's function and the particle-hole one. This description is related to a random phase approximation treatment of collective states in open shell nuclei that includes simultaneously the particle-particle and particle-hole versions of the nuclear residual Hamiltonian. Using separable interactions it is found that the inclusion of the particle-particle part of the Hamiltonians greatly changes the properties of the 2 + states in the Sn isotopes
Energy Technology Data Exchange (ETDEWEB)
Bertrand, Thierry [Inst. de Physique Nucleaire, Lyon-1 Univ., 69 - Villeurbanne (France)
1998-12-11
The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum 40 refs., 33 figs., 14 tabs.
Numerical method for two-phase flow discontinuity propagation calculation
International Nuclear Information System (INIS)
Toumi, I.; Raymond, P.
1989-01-01
In this paper, we present a class of numerical shock-capturing schemes for hyperbolic systems of conservation laws modelling two-phase flow. First, we solve the Riemann problem for a two-phase flow with unequal velocities. Then, we construct two approximate Riemann solvers: an one intermediate-state Riemann solver and a generalized Roe's approximate Riemann solver. We give some numerical results for one-dimensional shock-tube problems and for a standard two-phase flow heat addition problem involving two-phase flow instabilities
Heßelmann, Andreas
2015-04-14
Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.
Collective nuclear excitations with Skyrme-second random-phase approximation
International Nuclear Information System (INIS)
Gambacurta, D.; Catara, F.; Grasso, M.
2010-01-01
Second random-phase approximation (RPA) calculations with a Skyrme force are performed to describe both high- and low-lying excited states in 16 O. The coupling between one particle-one hole and two particle-two hole as well as that between two particle-two hole configurations among themselves are fully taken into account, and the residual interaction is never neglected; we do not resort therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond the standard RPA will be considered in detail in a forthcoming paper. Two approximations are employed here for these rearrangement terms: they are either neglected or evaluated with the RPA procedure. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by the second RPA owing to the huge number of two particle-two hole configurations. A better description of the excitation energies of the low-lying 0 + and 2 + states is obtained with the second RPA than with the RPA.
Numerical modeling of two-phase binary fluid mixing using mixed finite elements
Sun, Shuyu
2012-07-27
Diffusion coefficients of dense gases in liquids can be measured by considering two-phase binary nonequilibrium fluid mixing in a closed cell with a fixed volume. This process is based on convection and diffusion in each phase. Numerical simulation of the mixing often requires accurate algorithms. In this paper, we design two efficient numerical methods for simulating the mixing of two-phase binary fluids in one-dimensional, highly permeable media. Mathematical model for isothermal compositional two-phase flow in porous media is established based on Darcy\\'s law, material balance, local thermodynamic equilibrium for the phases, and diffusion across the phases. The time-lag and operator-splitting techniques are used to decompose each convection-diffusion equation into two steps: diffusion step and convection step. The Mixed finite element (MFE) method is used for diffusion equation because it can achieve a high-order and stable approximation of both the scalar variable and the diffusive fluxes across grid-cell interfaces. We employ the characteristic finite element method with moving mesh to track the liquid-gas interface. Based on the above schemes, we propose two methods: single-domain and two-domain methods. The main difference between two methods is that the two-domain method utilizes the assumption of sharp interface between two fluid phases, while the single-domain method allows fractional saturation level. Two-domain method treats the gas domain and the liquid domain separately. Because liquid-gas interface moves with time, the two-domain method needs work with a moving mesh. On the other hand, the single-domain method allows the use of a fixed mesh. We derive the formulas to compute the diffusive flux for MFE in both methods. The single-domain method is extended to multiple dimensions. Numerical results indicate that both methods can accurately describe the evolution of the pressure and liquid level. © 2012 Springer Science+Business Media B.V.
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
Pairing in a two-dimensional two-band very anisotropic model in the mean field approximation
International Nuclear Information System (INIS)
Fazakas, A.B.; Pitis, R.
1993-09-01
A two-dimensional model is proposed: there are two kinds of sites, with one electronic state per site; tunneling takes place only in one direction; the interaction involves only electrons on different sites. The existence of a phase transition involving interband pairing of electrons is discussed in the mean field approximation. (author)
Matrix model approximations of fuzzy scalar field theories and their phase diagrams
Energy Technology Data Exchange (ETDEWEB)
Tekel, Juraj [Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska Dolina, Bratislava, 842 48 (Slovakia)
2015-12-29
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram with correct features in a qualitative agreement with the previous numerical studies and that the latter gives a phase diagram with features not expected in the phase diagram of the field theory.
Wits, Wessel Willems; Ten Hoeve, Harm Jan; Te Riele Gert, Jan; Van Es, Johannes
2013-01-01
The current invention relates to a system for fast and accurate filling of a two-phase cooling device, comprising a binding device (30) intended to be hermetically mounted onto the cooling device, the binding device (30) comprising a through-hole (32) able to be in fluid contact with the cooling
Wits, Wessel Willems; Ten Hoeve, Harm Jan; Te Riele Gert, Jan; Van Es, Johannes
2013-01-01
The current invention relates to a system for fast and accurate filling of a two- phase cooling device, comprising a binding device (30) intended to be hermetically mounted onto the cooling device, the binding device (30) comprising a through-hole (32) able to be in fluid contact with the cooling
Wits, Wessel Willems; Ten Hoeve, Harm Jan; Te Riele Gert, Jan; Van Es, Johannes; Wits, Wessel Willems; Ten Hoeve, Harm Jan; Te Riele, Gerhardus Wilhelmus; Van Es, Johannes
2014-01-01
The current invention relates to a system for fast and accurate filling of a two-phase cooling device, comprising a binding device (30) intended to be hermetically mounted onto the cooling device, the binding device (30) comprising a through-hole (32) able to be in fluid contact with the cooling
Self-consistent Random Phase Approximation applied to a schematic model of the field theory
International Nuclear Information System (INIS)
Bertrand, Thierry
1998-01-01
The self-consistent Random Phase Approximation (SCRPA) is a method allowing in the mean-field theory inclusion of the correlations in the ground and excited states. It has the advantage of not violating the Pauli principle in contrast to RPA, that is based on the quasi-bosonic approximation; in addition, numerous applications in different domains of physics, show a possible variational character. However, the latter should be formally demonstrated. The first model studied with SCRPA is the anharmonic oscillator in the region where one of its symmetries is spontaneously broken. The ground state energy is reproduced by SCRPA more accurately than RPA, with no violation of the Ritz variational principle, what is not the case for the latter approximation. The success of SCRPA is the the same in case of ground state energy for a model mixing bosons and fermions. At the transition point the SCRPA is correcting RPA drastically, but far from this region the correction becomes negligible, both methods being of similar precision. In the deformed region in the case of RPA a spurious mode occurred due to the microscopical character of the model.. The SCRPA may also reproduce this mode very accurately and actually it coincides with an excitation in the exact spectrum
International Nuclear Information System (INIS)
Yonemitsu, K.; Bishop, A.R.
1992-01-01
As a convenient qualitative approach to strongly correlated electronic systems, an inhomogeneous Hartree-Fock plus random-phase approximation is applied to response functions for the two-dimensional multiband Hubbard model for cuprate superconductors. A comparison of the results with those obtained by exact diagonalization by Wagner, Hanke, and Scalapino [Phys. Rev. B 43, 10 517 (1991)] shows that overall structures in optical and magnetic particle-hole excitation spectra are well reproduced by this method. This approach is computationally simple, retains conceptual clarity, and can be calibrated by comparison with exact results on small systems. Most importantly, it is easily extended to larger systems and straightforward to incorporate additional terms in the Hamiltonian, such as electron-phonon interactions, which may play a crucial role in high-temperature superconductivity
Xu, Xuemiao; Zhang, Huaidong; Han, Guoqiang; Kwan, Kin Chung; Pang, Wai-Man; Fang, Jiaming; Zhao, Gansen
2016-04-11
Exterior orientation parameters' (EOP) estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs) for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang'E-1, compared to the existing space resection model.
Directory of Open Access Journals (Sweden)
Xuemiao Xu
2016-04-01
Full Text Available Exterior orientation parameters’ (EOP estimation using space resection plays an important role in topographic reconstruction for push broom scanners. However, existing models of space resection are highly sensitive to errors in data. Unfortunately, for lunar imagery, the altitude data at the ground control points (GCPs for space resection are error-prone. Thus, existing models fail to produce reliable EOPs. Motivated by a finding that for push broom scanners, angular rotations of EOPs can be estimated independent of the altitude data and only involving the geographic data at the GCPs, which are already provided, hence, we divide the modeling of space resection into two phases. Firstly, we estimate the angular rotations based on the reliable geographic data using our proposed mathematical model. Then, with the accurate angular rotations, the collinear equations for space resection are simplified into a linear problem, and the global optimal solution for the spatial position of EOPs can always be achieved. Moreover, a certainty term is integrated to penalize the unreliable altitude data for increasing the error tolerance. Experimental results evidence that our model can obtain more accurate EOPs and topographic maps not only for the simulated data, but also for the real data from Chang’E-1, compared to the existing space resection model.
Number-conserving random phase approximation with analytically integrated matrix elements
International Nuclear Information System (INIS)
Kyotoku, M.; Schmid, K.W.; Gruemmer, F.; Faessler, A.
1990-01-01
In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem
Analysis of expansion phase experiments with improved approximation schemes
International Nuclear Information System (INIS)
Foit, J.J.
1987-05-01
A steady-state flow of a single-phase and incompressible fluid across a singularity is studied. Based on these theoretical considerations new approximation methods for the pressure gradient term in the SIMMER-II momentum equations are proposed which give a satisfactory pressure change in flows across singularities. The expansion phase experiments with a dipplate performed by SRI-International are evaluated to examine the quality of the proposed approximation schemes. (orig.) [de
Electroweak phase transition in two Higgs doublet models
International Nuclear Information System (INIS)
Cline, J.M.; Lemieux, P.
1997-01-01
We reexamine the strength of the first-order phase transition in the electroweak theory supplemented by an extra Higgs doublet. The finite-temperature effective potential V eff is computed to one-loop order, including the summation of ring diagrams, to study the ratio φ c /T c of the Higgs field VEV to the critical temperature. We make a number of improvements over previous treatments, including a consistent treatment of Goldstone bosons in V eff , an accurate analytic approximation to V eff valid for any mass-to-temperature ratios, and use of the experimentally measured top quark mass. For two-Higgs-doublet models, we identify a significant region of parameter space where φ c /T c is large enough for electroweak baryogenesis, and we argue that this identification should persist even at higher orders in perturbation theory. In the case of the minimal supersymmetric standard model, our results indicate that the extra Higgs bosons have little effect on the strength of the phase transition. copyright 1997 The American Physical Society
Extended random-phase approximation with three-body ground-state correlations
International Nuclear Information System (INIS)
Tohyama, M.; Schuck, P.
2008-01-01
An extended random-phase approximation (ERPA) which contains the effects of ground-state correlations up to a three-body level is applied to an extended Lipkin model which contains an additional particle-scattering term. Three-body correlations in the ground state are necessary to preserve the hermiticity of the Hamiltonian matrix of ERPA. Two approximate forms of ERPA which neglect the three-body correlations are also applied to investigate the importance of three-body correlations. It is found that the ground-state energy is little affected by the inclusion of the three-body correlations. On the contrary, three-body correlations for the excited states can become quite important. (orig.)
Phase rainbow refractometry for accurate droplet variation characterization.
Wu, Yingchun; Promvongsa, Jantarat; Saengkaew, Sawitree; Wu, Xuecheng; Chen, Jia; Gréhan, Gérard
2016-10-15
We developed a one-dimensional phase rainbow refractometer for the accurate trans-dimensional measurements of droplet size on the micrometer scale as well as the tiny droplet diameter variations at the nanoscale. The dependence of the phase shift of the rainbow ripple structures on the droplet variations is revealed. The phase-shifting rainbow image is recorded by a telecentric one-dimensional rainbow imaging system. Experiments on the evaporating monodispersed droplet stream show that the phase rainbow refractometer can measure the tiny droplet diameter changes down to tens of nanometers. This one-dimensional phase rainbow refractometer is capable of measuring the droplet refractive index and diameter, as well as variations.
Two-phase-flow models and their limitations
International Nuclear Information System (INIS)
Ishii, M.; Kocamustafaogullari, G.
1982-01-01
An accurate prediction of transient two-phase flow is essential to safety analyses of nuclear reactors under accident conditions. The fluid flow and heat transfer encountered are often extremely complex due to the reactor geometry and occurrence of transient two-phase flow. Recently considerable progresses in understanding and predicting these phenomena have been made by a combination of rigorous model development, advanced computational techniques, and a number of small and large scale supporting experiments. In view of their essential importance, the foundation of various two-phase-flow models and their limitations are discussed in this paper
Random phase approximation applied to solids, molecules, and graphene-metal interfaces
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
The random phase approximation (RPA) is attracting renewed interest as a universal and accurate method for first-principles total energy calculations. The RPA naturally accounts for long-range dispersive forces without compromising accuracy for short-range interactions making the RPA superior...... to semilocal and hybrid functionals in systems dominated by weak van der Waals or mixed covalent-dispersive interactions. In this work, we present plane-wave-based RPA calculations for a broad collection of systems with bond types ranging from strong covalent to van der Waals. Our main result is the RPA...... the RPA captures both the weak covalent and dispersive forces, which are equally important for these systems. We benchmark our implementation in the GPAW electronic structure code by calculating cohesive energies of graphite and a range of covalently bonded solids and molecules as well as the dissociation...
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling
Yudovsky, Dmitry; Durkin, Anthony J.
2011-07-01
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
Dexter, Alex; Race, Alan M; Steven, Rory T; Barnes, Jennifer R; Hulme, Heather; Goodwin, Richard J A; Styles, Iain B; Bunch, Josephine
2017-11-07
Clustering is widely used in MSI to segment anatomical features and differentiate tissue types, but existing approaches are both CPU and memory-intensive, limiting their application to small, single data sets. We propose a new approach that uses a graph-based algorithm with a two-phase sampling method that overcomes this limitation. We demonstrate the algorithm on a range of sample types and show that it can segment anatomical features that are not identified using commonly employed algorithms in MSI, and we validate our results on synthetic MSI data. We show that the algorithm is robust to fluctuations in data quality by successfully clustering data with a designed-in variance using data acquired with varying laser fluence. Finally, we show that this method is capable of generating accurate segmentations of large MSI data sets acquired on the newest generation of MSI instruments and evaluate these results by comparison with histopathology.
Random-phase approximation and broken symmetry
International Nuclear Information System (INIS)
Davis, E.D.; Heiss, W.D.
1986-01-01
The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; it is seen that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements. (author)
Thermodynamics and structure of liquid metals from a consistent optimized random phase approximation
International Nuclear Information System (INIS)
Akinlade, O.; Badirkhan, Z.; Pastore, G.
2000-05-01
We study thermodynamics and structural properties of several liquid metals to assess the validity of the generalized non-local model potential (GNMP) of Li et. al. [J.Phys. F16,309 (1986)]. By using a new thermodynamically consistent version of the optimized random phase approximation (ORPA), especially adapted to continuous reference potentials, we improve our previous results obtained within the variational approach based on the Gibbs - Bogoliubov inequality. Hinging on the unified and very accurate evaluation of structure factors and thermodynamic quantities provided by the ORPA, we find that the GNMP yields satisfactory results for the alkali metals, however, those for the polyvalent metals point to a substantial inadequacy of the GNMP for high valence systems. (author)
RCS estimation of linear and planar dipole phased arrays approximate model
Singh, Hema; Jha, Rakesh Mohan
2016-01-01
In this book, the RCS of a parallel-fed linear and planar dipole array is derived using an approximate method. The signal propagation within the phased array system determines the radar cross section (RCS) of phased array. The reflection and transmission coefficients for a signal at different levels of the phased-in scattering array system depend on the impedance mismatch and the design parameters. Moreover the mutual coupling effect in between the antenna elements is an important factor. A phased array system comprises of radiating elements followed by phase shifters, couplers, and terminating load impedance. These components lead to respective impedances towards the incoming signal that travels through them before reaching receive port of the array system. In this book, the RCS is approximated in terms of array factor, neglecting the phase terms. The mutual coupling effect is taken into account. The dependence of the RCS pattern on the design parameters is analyzed. The approximate model is established as a...
International Nuclear Information System (INIS)
Lima, F M S
2009-01-01
In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ∼ θ being accurate only for amplitudes below 7 deg., his experimental results are for a pendulum oscillating with an amplitude of about 18 deg., therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments. (letters and comments)
Benchmark tests and spin adaptation for the particle-particle random phase approximation
Energy Technology Data Exchange (ETDEWEB)
Yang, Yang; Steinmann, Stephan N.; Peng, Degao [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Aggelen, Helen van, E-mail: Helen.VanAggelen@UGent.be [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Department of Inorganic and Physical Chemistry, Ghent University, 9000 Ghent (Belgium); Yang, Weitao, E-mail: Weitao.Yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)
2013-11-07
The particle-particle random phase approximation (pp-RPA) provides an approximation to the correlation energy in density functional theory via the adiabatic connection [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)]. It has virtually no delocalization error nor static correlation error for single-bond systems. However, with its formal O(N{sup 6}) scaling, the pp-RPA is computationally expensive. In this paper, we implement a spin-separated and spin-adapted pp-RPA algorithm, which reduces the computational cost by a substantial factor. We then perform benchmark tests on the G2/97 enthalpies of formation database, DBH24 reaction barrier database, and four test sets for non-bonded interactions (HB6/04, CT7/04, DI6/04, and WI9/04). For the G2/97 database, the pp-RPA gives a significantly smaller mean absolute error (8.3 kcal/mol) than the direct particle-hole RPA (ph-RPA) (22.7 kcal/mol). Furthermore, the error in the pp-RPA is nearly constant with the number of atoms in a molecule, while the error in the ph-RPA increases. For chemical reactions involving typical organic closed-shell molecules, pp- and ph-RPA both give accurate reaction energies. Similarly, both RPAs perform well for reaction barriers and nonbonded interactions. These results suggest that the pp-RPA gives reliable energies in chemical applications. The adiabatic connection formalism based on pairing matrix fluctuation is therefore expected to lead to widely applicable and accurate density functionals.
Analytical approximations to seawater optical phase functions of scattering
Haltrin, Vladimir I.
2004-11-01
This paper proposes a number of analytical approximations to the classic and recently measured seawater light scattering phase functions. The three types of analytical phase functions are derived: individual representations for 15 Petzold, 41 Mankovsky, and 91 Gulf of Mexico phase functions; collective fits to Petzold phase functions; and analytical representations that take into account dependencies between inherent optical properties of seawater. The proposed phase functions may be used for problems of radiative transfer, remote sensing, visibility and image propagation in natural waters of various turbidity.
Warm ''pasta'' phase in the Thomas-Fermi approximation
International Nuclear Information System (INIS)
Avancini, Sidney S.; Menezes, Debora P.; Chiacchiera, Silvia; Providencia, Constanca
2010-01-01
In the present article, the 'pasta' phase is studied at finite temperatures within a Thomas-Fermi (TF) approach. Relativistic mean-field models, both with constant and density-dependent couplings, are used to describe this frustrated system. We compare the present results with previous ones obtained within a phase-coexistence description and conclude that the TF approximation gives rise to a richer inner ''pasta'' phase structure and the homogeneous matter appears at higher densities. Finally, the transition density calculated within TF is compared with the results for this quantity obtained with other methods.
Quasilinear theory without the random phase approximation
International Nuclear Information System (INIS)
Weibel, E.S.; Vaclavik, J.
1980-08-01
The system of quasilinear equations is derived without making use of the random phase approximation. The fluctuating quantities are described by the autocorrelation function of the electric field using the techniques of Fourier analysis. The resulting equations posses the necessary conservation properties, but comprise new terms which hitherto have been lost in the conventional derivations
International Nuclear Information System (INIS)
Sharp, Leah Z.; Egorova, Dassia; Domcke, Wolfgang
2010-01-01
Two-dimensional (2D) photon-echo spectra of a single subunit of the Fenna-Matthews-Olson (FMO) bacteriochlorophyll trimer of Chlorobium tepidum are simulated, employing the equation-of-motion phase-matching approach (EOM-PMA). We consider a slightly extended version of the previously proposed Frenkel exciton model, which explicitly accounts for exciton coherences in the secular approximation. The study is motivated by a recent experiment reporting long-lived coherent oscillations in 2D transients [Engel et al., Nature 446, 782 (2007)] and aims primarily at accurate simulations of the spectroscopic signals, with the focus on oscillations of 2D peak intensities with population time. The EOM-PMA accurately accounts for finite pulse durations as well as pulse-overlap effects and does not invoke approximations apart from the weak-field limit for a given material system. The population relaxation parameters of the exciton model are taken from the literature. The effects of various dephasing mechanisms on coherence lifetimes are thoroughly studied. It is found that the experimentally detected multiple frequencies in peak oscillations cannot be reproduced by the employed FMO model, which calls for the development of a more sophisticated exciton model of the FMO complex.
A test of the adhesion approximation for gravitational clustering
Melott, Adrian L.; Shandarin, Sergei; Weinberg, David H.
1993-01-01
We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.
Burgess, Helen J; Wyatt, James K; Park, Margaret; Fogg, Louis F
2015-06-01
There is a need for the accurate assessment of circadian phase outside of the clinic/laboratory, particularly with the gold standard dim light melatonin onset (DLMO). We tested a novel kit designed to assist in saliva sampling at home for later determination of the DLMO. The home kit includes objective measures of compliance to the requirements for dim light and half-hourly saliva sampling. Participants were randomized to one of two 10-day protocols. Each protocol consisted of two back-to-back home and laboratory phase assessments in counterbalanced order, separated by a 5-day break. Laboratory or participants' homes. Thirty-five healthy adults, age 21-62 y. N/A. Most participants received at least one 30-sec epoch of light > 50 lux during the home phase assessments (average light intensity 4.5 lux), but on average for light > 50 lux or sampling errors. There was no significant difference between the home and laboratory DLMOs (P > 0.05); on average the home DLMOs occurred 9.6 min before the laboratory DLMOs. The home DLMOs were highly correlated with the laboratory DLMOs (r = 0.91, P dim light melatonin onsets (DLMOs) demonstrates that including objective measures of light exposure and sample timing during home saliva sampling can lead to accurate home DLMOs. Circadian Phase Assessments at Home, http://clinicaltrials.gov/show/NCT01487252, NCT01487252. © 2015 Associated Professional Sleep Societies, LLC.
Heskes, Tom; Eisinga, Rob; Breitling, Rainer
2014-11-21
The rank product method is a powerful statistical technique for identifying differentially expressed molecules in replicated experiments. A critical issue in molecule selection is accurate calculation of the p-value of the rank product statistic to adequately address multiple testing. Both exact calculation and permutation and gamma approximations have been proposed to determine molecule-level significance. These current approaches have serious drawbacks as they are either computationally burdensome or provide inaccurate estimates in the tail of the p-value distribution. We derive strict lower and upper bounds to the exact p-value along with an accurate approximation that can be used to assess the significance of the rank product statistic in a computationally fast manner. The bounds and the proposed approximation are shown to provide far better accuracy over existing approximate methods in determining tail probabilities, with the slightly conservative upper bound protecting against false positives. We illustrate the proposed method in the context of a recently published analysis on transcriptomic profiling performed in blood. We provide a method to determine upper bounds and accurate approximate p-values of the rank product statistic. The proposed algorithm provides an order of magnitude increase in throughput as compared with current approaches and offers the opportunity to explore new application domains with even larger multiple testing issue. The R code is published in one of the Additional files and is available at http://www.ru.nl/publish/pages/726696/rankprodbounds.zip .
Non-Hermitian wave packet approximation for coupled two-level systems in weak and intense fields
Energy Technology Data Exchange (ETDEWEB)
Puthumpally-Joseph, Raiju; Charron, Eric [Institut des Sciences Moléculaires d’Orsay (ISMO), CNRS, Univ. Paris-Sud, Université Paris-Saclay, F-91405 Orsay (France); Sukharev, Maxim [Science and Mathematics Faculty, College of Letters and Sciences, Arizona State University, Mesa, Arizona 85212 (United States)
2016-04-21
We introduce a non-Hermitian Schrödinger-type approximation of optical Bloch equations for two-level systems. This approximation provides a complete and accurate description of the coherence and decoherence dynamics in both weak and strong laser fields at the cost of losing accuracy in the description of populations. In this approach, it is sufficient to propagate the wave function of the quantum system instead of the density matrix, providing that relaxation and dephasing are taken into account via automatically adjusted time-dependent gain and decay rates. The developed formalism is applied to the problem of scattering and absorption of electromagnetic radiation by a thin layer comprised of interacting two-level emitters.
Semi-classical approximation to path integrals - phases and catastrophes
International Nuclear Information System (INIS)
Levit, S.
1977-01-01
Problems of phases and catastrophes were encountered when trying to apply the classical S-matrix theory to the scattering phenomena in nuclear physics. The path integral formulation provided a suitable basis for the treatment of these and related problems. Within conventional mathematical language it was possible to give practical prescriptions and discuss their limitations. Since the semi-classical (stationary phase) approximation is commonly used in any application of the path integral method, the results are not restricted to the scattering problems and may be of general interest. The derivation of the uniform approximations in the energy representation should use the exact path integral expression as the starting point, rather than performing Fourier transforms on the expressions derived in the present lecture. (B.G.)
Application of the random phase approximation to complex problems in materials science
International Nuclear Information System (INIS)
Schimka, L.
2012-01-01
This thesis is devoted to the assessment and application of the random phase approximation (RPA) in the adiabatic-connection fluctuation-dissipation (ACFD) framework in solid state physics. The first part presents a review of density functional theory (DFT) and the ACFD theorem in the RPA. This includes an introduction to the many-body problem as well as a description of the implementation of the RPA in the Vienna Ab-initio Simulation Package (VASP). In the results part, the quality of the RPA is assessed and its performance compared to three (beyond) DFT functionals. The experimental values are corrected for the effect of phonon zero-point vibrational energies which were calculated at the DFT level from ab-initio. We find that the RPA describes all bonding situations very accurately, making it a promising candidate for more complex problems in solid state physics. In light of these findings, we investigate the carbon-water interaction in two specific cases: the adsorption of water on benzene and the adsorption of water on a graphene layer. We compare our results to a different correlated method: diffusion Monte Carlo (DMC). We find very good agreement and thus believe that our values can serve as a benchmark for the development of other DFT functionals to treat water-carbon interfaces. The highlight of this thesis is the successful application of the RPA to the long-standing and (at DFT level) unsolved CO adsorption puzzle. We show results for CO adsorption on Cu, late 4d metals and Pt. RPA is at present the only ab-initio method that describes adsorption and surface energies accurately at the same time and predicts the correct adsorption site in every single case. (author) [de
Energy Technology Data Exchange (ETDEWEB)
Shu, Yu-Chen, E-mail: ycshu@mail.ncku.edu.tw [Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (South), Tainan 701, Taiwan (China); Chern, I-Liang, E-mail: chern@math.ntu.edu.tw [Department of Applied Mathematics, National Chiao Tung University, Hsin Chu 300, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China); Mathematics Division, National Center for Theoretical Sciences (Taipei Office), Taipei 106, Taiwan (China); Chang, Chien C., E-mail: mechang@iam.ntu.edu.tw [Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan (China); Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China)
2014-10-15
Most elliptic interface solvers become complicated for complex interface problems at those “exceptional points” where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule ( (1D63)) which is double-helix shape and composed of hundreds of atoms.
Variational random phase approximation for the anharmonic oscillator
International Nuclear Information System (INIS)
Dukelsky, J.; Schuck, P.
1990-04-01
The recently derived Variational Random Phase Approximation is examined using the anharmonic oscillator model. Special attention is paid to the ground state RPA wave function and the convergence of the proposed truncation scheme to obtain the diagonal density matrix. Comparison with the standard Coupled Cluster method is made
Interacting-fermion approximation in the two-dimensional ANNNI model
International Nuclear Information System (INIS)
Grynberg, M.D.; Ceva, H.
1990-12-01
We investigate the effect of including domain-walls interactions in the two-dimensional axial next-nearest-neighbor Ising or ANNNI model. At low temperatures this problem is reduced to a one-dimensional system of interacting fermions which can be treated exactly. It is found that the critical boundaries of the low-temperature phases are in good agreement with those obtained using a free-fermion approximation. In contrast with the monotonic behavior derived from the free-fermion approach, the wall density or wave number displays reentrant phenomena when the ratio of the next-nearest-neighbor and nearest-neighbor interactions is greater than one-half. (author). 17 refs, 2 figs
Toward a consistent random phase approximation based on the relativistic Hartree approximation
International Nuclear Information System (INIS)
Price, C.E.; Rost, E.; Shepard, J.R.; McNeil, J.A.
1992-01-01
We examine the random phase approximation (RPA) based on a relativistic Hartree approximation description for nuclear ground states. This model includes contributions from the negative energy sea at the one-loop level. We emphasize consistency between the treatment of the ground state and the RPA. This consistency is important in the description of low-lying collective levels but less important for the longitudinal (e,e') quasielastic response. We also study the effect of imposing a three-momentum cutoff on negative energy sea contributions. A cutoff of twice the nucleon mass improves agreement with observed spin-orbit splittings in nuclei compared to the standard infinite cutoff results, an effect traceable to the fact that imposing the cutoff reduces m * /m. Consistency is much more important than the cutoff in the description of low-lying collective levels. The cutoff model also provides excellent agreement with quasielastic (e,e') data
International Nuclear Information System (INIS)
Martin, Stephen P.
2003-01-01
I present a method for accurately calculating the pole mass of the lightest Higgs scalar boson in supersymmetric extensions of the standard model, using a mass-independent renormalization scheme. The Higgs scalar self-energies are approximated by supplementing the exact one-loop results with the second derivatives of the complete two-loop effective potential in Landau gauge. I discuss the dependence of this approximation on the choice of renormalization scale, and note the existence of particularly poor choices, which fortunately can be easily identified and avoided. For typical input parameters, the variation in the calculated Higgs boson mass over a wide range of renormalization scales is found to be of the order of a few hundred MeV or less, and is significantly improved over previous approximations
International Nuclear Information System (INIS)
White, R D; Robson, R E; Schmidt, B; Morrison, Michael A
2003-01-01
The 'two-term' approximation (representation of the electron distribution by the first two terms of an expansion in spherical harmonics in velocity space) continues to occupy a central role in the low-temperature plasma physics literature, in spite of the mass of evidence illustrating its inadequacy in the swarm (free diffusion) limit for many molecular gases. Part of the problem lies in the failure of many authors to specify quantitatively what they mean when they say that the two-term approximation is 'acceptable'. Thus for example, an error of 10% in transport coefficients may well be acceptable in many plasma applications, but for analysis of highly accurate swarm experiments to compare with ab initio and beam-derived cross-sections, 0.1% or less is required, making 'multi-term' analysis mandatory. While reconciliation of the swarm and plasma literature along the lines of two different accuracy regimes may thus be possible, we dispute claims that the two-term approximation is generally satisfactory for inversion of swarm experiment data to obtain electron impact cross-sections. The unsatisfactory nature of other assumptions implicit in much of the modern plasma kinetic theory literature is also discussed
Self-similar factor approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.; Sornette, D.
2003-01-01
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
Assessment of correlation energies based on the random-phase approximation
International Nuclear Information System (INIS)
Paier, Joachim; Ren, Xinguo; Rinke, Patrick; Scheffler, Matthias; Scuseria, Gustavo E; Grüneis, Andreas; Kresse, Georg
2012-01-01
The random-phase approximation to the ground state correlation energy (RPA) in combination with exact exchange (EX) has brought the Kohn-Sham (KS) density functional theory one step closer towards a universal, ‘general purpose first-principles method’. In an effort to systematically assess the influence of several correlation energy contributions beyond RPA, this paper presents dissociation energies of small molecules and solids, activation energies for hydrogen transfer and non-hydrogen transfer reactions, as well as reaction energies for a number of common test sets. We benchmark EX + RPA and several flavors of energy functionals going beyond it: second-order screened exchange (SOSEX), single-excitation (SE) corrections, renormalized single-excitation (rSE) corrections and their combinations. Both the SE correction and the SOSEX contribution to the correlation energy significantly improve on the notorious tendency of EX + RPA to underbind. Surprisingly, activation energies obtained using EX + RPA based on a KS reference alone are remarkably accurate. RPA + SOSEX + rSE provides an equal level of accuracy for reaction as well as activation energies and overall gives the most balanced performance, because of which it can be applied to a wide range of systems and chemical reactions. (paper)
Transient two-phase performance of LOFT reactor coolant pumps
International Nuclear Information System (INIS)
Chen, T.H.; Modro, S.M.
1983-01-01
Performance characteristics of Loss-of-Fluid Test (LOFT) reactor coolant pumps under transient two-phase flow conditions were obtained based on the analysis of two large and small break loss-of-coolant experiments conducted at the LOFT facility. Emphasis is placed on the evaluation of the transient two-phase flow effects on the LOFT reactor coolant pump performance during the first quadrant operation. The measured pump characteristics are presented as functions of pump void fraction which was determined based on the measured density. The calculated pump characteristics such as pump head, torque (or hydraulic torque), and efficiency are also determined as functions of pump void fractions. The importance of accurate modeling of the reactor coolant pump performance under two-phase conditions is addressed. The analytical pump model, currently used in most reactor analysis codes to predict transient two-phase pump behavior, is assessed
Pineda, M.; Stamatakis, M.
2017-07-01
Modeling the kinetics of surface catalyzed reactions is essential for the design of reactors and chemical processes. The majority of microkinetic models employ mean-field approximations, which lead to an approximate description of catalytic kinetics by assuming spatially uncorrelated adsorbates. On the other hand, kinetic Monte Carlo (KMC) methods provide a discrete-space continuous-time stochastic formulation that enables an accurate treatment of spatial correlations in the adlayer, but at a significant computation cost. In this work, we use the so-called cluster mean-field approach to develop higher order approximations that systematically increase the accuracy of kinetic models by treating spatial correlations at a progressively higher level of detail. We further demonstrate our approach on a reduced model for NO oxidation incorporating first nearest-neighbor lateral interactions and construct a sequence of approximations of increasingly higher accuracy, which we compare with KMC and mean-field. The latter is found to perform rather poorly, overestimating the turnover frequency by several orders of magnitude for this system. On the other hand, our approximations, while more computationally intense than the traditional mean-field treatment, still achieve tremendous computational savings compared to KMC simulations, thereby opening the way for employing them in multiscale modeling frameworks.
Approximated transport-of-intensity equation for coded-aperture x-ray phase-contrast imaging.
Das, Mini; Liang, Zhihua
2014-09-15
Transport-of-intensity equations (TIEs) allow better understanding of image formation and assist in simplifying the "phase problem" associated with phase-sensitive x-ray measurements. In this Letter, we present for the first time to our knowledge a simplified form of TIE that models x-ray differential phase-contrast (DPC) imaging with coded-aperture (CA) geometry. The validity of our approximation is demonstrated through comparison with an exact TIE in numerical simulations. The relative contributions of absorption, phase, and differential phase to the acquired phase-sensitive intensity images are made readily apparent with the approximate TIE, which may prove useful for solving the inverse phase-retrieval problem associated with these CA geometry based DPC.
Two-phase flow in volatile oil reservoir using two-phase pseudo-pressure well test method
Energy Technology Data Exchange (ETDEWEB)
Sharifi, M.; Ahmadi, M. [Calgary Univ., AB (Canada)
2009-09-15
A study was conducted to better understand the behaviour of volatile oil reservoirs. Retrograde condensation occurs in gas-condensate reservoirs when the flowing bottomhole pressure (BHP) lowers below the dewpoint pressure, thus creating 4 regions in the reservoir with different liquid saturations. Similarly, when the BHP of volatile oil reservoirs falls below the bubblepoint pressure, two phases are created in the region around the wellbore, and a single phase (oil) appears in regions away from the well. In turn, higher gas saturation causes the oil relative permeability to decrease towards the near-wellbore region. Reservoir compositional simulations were used in this study to predict the fluid behaviour below the bubblepoint. The flowing bottomhole pressure was then exported to a well test package to diagnose the occurrence of different mobility regions. The study also investigated the use of a two-phase pseudo-pressure method on volatile and highly volatile oil reservoirs. It was concluded that this method can successfully predict the true permeability and mechanical skin. It can also distinguish between mechanical skin and condensate bank skin. As such, the two-phase pseudo-pressure method is particularly useful for developing after-drilling well treatment and enhanced oil recovery process designs. However, accurate relative permeability and PVT data must be available for reliable interpretation of the well test in volatile oil reservoirs. 18 refs., 3 tabs., 9 figs.
Hou, Jiangyong
2016-02-05
In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.
Hou, Jiangyong; Chen, Jie; Sun, Shuyu; Chen, Zhangxin
2016-01-01
In this paper, we present a hybrid method, which consists of a mixed-hybrid finite element method and a penalty discontinuous Galerkin method, for the approximation of a fractional flow formulation of a two-phase flow problem in heterogeneous media with discontinuous capillary pressure. The fractional flow formulation is comprised of a wetting phase pressure equation and a wetting phase saturation equation which are coupled through a total velocity and the saturation affected coefficients. For the wetting phase pressure equation, the continuous mixed-hybrid finite element method space can be utilized due to a fundamental property that the wetting phase pressure is continuous. While it can reduce the computational cost by using less degrees of freedom and avoiding the post-processing of velocity reconstruction, this method can also keep several good properties of the discontinuous Galerkin method, which are important to the fractional flow formulation, such as the local mass balance, continuous normal flux and capability of handling the discontinuous capillary pressure. For the wetting phase saturation equation, the penalty discontinuous Galerkin method is utilized due to its capability of handling the discontinuous jump of the wetting phase saturation. Furthermore, an adaptive algorithm for the hybrid method together with the centroidal Voronoi Delaunay triangulation technique is proposed. Five numerical examples are presented to illustrate the features of proposed numerical method, such as the optimal convergence order, the accurate and efficient velocity approximation, and the applicability to the simulation of water flooding in oil field and the oil-trapping or barrier effect phenomena.
International Nuclear Information System (INIS)
Olive, J.
1990-01-01
The design, operation and safety of nuclear components requires increasingly accurate knowledge of two-phase flows. This knowledge is also necessary for some studies related to electricity applications. The author presents some concrete examples showing the range of problems and the complexity of the phenomena involved in these types of flows. Then, the basic principles of their numerical modelling are explained, as well as the new tendency to use increasingly local and refined models. The newest computer codes developed at EDF are briefly presented. Experimental studies dealing with twophase flow are also referred to, and their connections to numerical modelling are explained. Emphasis is placed on the major efforts devoted to the development of new test rigs and instrumentation [fr
Inference Under a Wright-Fisher Model Using an Accurate Beta Approximation
DEFF Research Database (Denmark)
Tataru, Paula; Bataillon, Thomas; Hobolth, Asger
2015-01-01
frequencies and the influence of evolutionary pressures, such as mutation and selection. Despite its simple mathematical formulation, exact results for the distribution of allele frequency (DAF) as a function of time are not available in closed analytic form. Existing approximations build......, the probability of being on the boundary can be positive, corresponding to the allele being either lost or fixed. Here, we introduce the beta with spikes, an extension of the beta approximation, which explicitly models the loss and fixation probabilities as two spikes at the boundaries. We show that the addition...
Marrone, Salvatore; Colagrossi, Andrea; Di Mascio, Andrea; Le Touzé, David
2016-05-01
The study of energetic free-surface flows is challenging because of the large range of interface scales involved due to multiple fragmentations and reconnections of the air-water interface with the formation of drops and bubbles. Because of their complexity the investigation of such phenomena through numerical simulation largely increased during recent years. Actually, in the last decades different numerical models have been developed to study these flows, especially in the context of particle methods. In the latter a single-phase approximation is usually adopted to reduce the computational costs and the model complexity. While it is well known that the role of air largely affects the local flow evolution, it is still not clear whether this single-phase approximation is able to predict global flow features like the evolution of the global mechanical energy dissipation. The present work is dedicated to this topic through the study of a selected problem simulated with both single-phase and two-phase models. It is shown that, interestingly, even though flow evolutions are different, energy evolutions can be similar when including or not the presence of air. This is remarkable since, in the problem considered, with the two-phase model about half of the energy is lost in the air phase while in the one-phase model the energy is mainly dissipated by cavity collapses.
The infinite limit as an eliminable approximation for phase transitions
Ardourel, Vincent
2018-05-01
It is generally claimed that infinite idealizations are required for explaining phase transitions within statistical mechanics (e.g. Batterman 2011). Nevertheless, Menon and Callender (2013) have outlined theoretical approaches that describe phase transitions without using the infinite limit. This paper closely investigates one of these approaches, which consists of studying the complex zeros of the partition function (Borrmann et al., 2000). Based on this theory, I argue for the plausibility for eliminating the infinite limit for studying phase transitions. I offer a new account for phase transitions in finite systems, and I argue for the use of the infinite limit as an approximation for studying phase transitions in large systems.
International Nuclear Information System (INIS)
Saleh, K.
2012-01-01
This thesis deals with the Baer-Nunziato two-phase flow model. The main objective of this work is to propose some techniques to cope with phase vanishing regimes which produce important instabilities in the model and its numerical simulations. Through analysis and simulation methods using Suliciu relaxation approximations, we prove that in these regimes, the solutions can be stabilised by introducing some extra dissipation of the total mixture entropy. In a first approach, called the Eulerian approach, the exact resolution of the relaxation Riemann problem provides an accurate entropy-satisfying numerical scheme, which turns out to be much more efficient in terms of CPU-cost than the classical and very simple Rusanov's scheme. Moreover, the scheme is proved to handle the vanishing phase regimes with great stability. The scheme, first developed in 1D, is then extended in 3D and implemented in an industrial code developed by EDF. The second approach, called the acoustic splitting approach, considers a separation of fast acoustic waves from slow material waves. The objective is to avoid the resonance due to the interaction between these two types of waves, and to allow an implicit treatment of the acoustics, while material waves are explicitly discretized. The resulting scheme is very simple and allows to deal simply with phase vanishing. The originality of this work is to use new dissipative closure laws for the interfacial velocity and pressure, in order to control the solutions of the Riemann problem associated with the acoustic step, in the phase vanishing regimes. (author)
Approximating second-order vector differential operators on distorted meshes in two space dimensions
International Nuclear Information System (INIS)
Hermeline, F.
2008-01-01
A new finite volume method is presented for approximating second-order vector differential operators in two space dimensions. This method allows distorted triangle or quadrilateral meshes to be used without the numerical results being too much altered. The matrices that need to be inverted are symmetric positive definite therefore, the most powerful linear solvers can be applied. The method has been tested on a few second-order vector partial differential equations coming from elasticity and fluids mechanics areas. These numerical experiments show that it is second-order accurate and locking-free. (authors)
Energy Technology Data Exchange (ETDEWEB)
Toumi, I.; Kumbaro, A.; Paillere, H
1999-07-01
These course notes, presented at the 30. Von Karman Institute Lecture Series in Computational Fluid Dynamics, give a detailed and through review of upwind differencing methods for two-phase flow models. After recalling some fundamental aspects of two-phase flow modelling, from mixture model to two-fluid models, the mathematical properties of the general 6-equation model are analysed by examining the Eigen-structure of the system, and deriving conditions under which the model can be made hyperbolic. The following chapters are devoted to extensions of state-of-the-art upwind differencing schemes such as Roe's Approximate Riemann Solver or the Characteristic Flux Splitting method to two-phase flow. Non-trivial steps in the construction of such solvers include the linearization, the treatment of non-conservative terms and the construction of a Roe-type matrix on which the numerical dissipation of the schemes is based. Extension of the 1-D models to multi-dimensions in an unstructured finite volume formulation is also described; Finally, numerical results for a variety of test-cases are shown to illustrate the accuracy and robustness of the methods. (authors)
Barrett, John W.; Garcke, Harald; Nürnberg, Robert
2017-01-01
A finite element method for the evolution of a two-phase membrane in a sharp interface formulation is introduced. The evolution equations are given as an $L^2$--gradient flow of an energy involving an elastic bending energy and a line energy. In the two phases Helfrich-type evolution equations are prescribed, and on the interface, an evolving curve on an evolving surface, highly nonlinear boundary conditions have to hold. Here we consider both $C^0$-- and $C^1$--matching conditions for the su...
Synthesis Of Ultrasound Field Sources Based on Phase Screen Approximation
Directory of Open Access Journals (Sweden)
Sukhanov Dmitry
2018-01-01
Full Text Available Here is proposed the method for synthesizing the sources of an acoustic field on the basis of an approximation of the phase screen. The technology of manufacturing ultrasonic phased arrays providing the formation of a field of a given distribution is proposed. An experimental setup has been developed for the formation of a vortex field at a distance of 10 cm.
Directory of Open Access Journals (Sweden)
Souichi Telada
2014-07-01
Full Text Available A highly accurate two-color interferometer with automatic correction of the refractive index of air was developed for crustal strain observation. The two-color interferometer, which can measure a geometrical distance of approximately 70 m, with a relative resolution of 2 × 10−9, clearly detected a change in strain due to earth tides in spite of optical measurement in air. Moreover, a large strain quake due to an earthquake could be observed without disturbing the measurement. We demonstrated the advantages of the two-color interferometer in air for geodetic observation.
Energy Technology Data Exchange (ETDEWEB)
Jemai, M
2004-07-01
In the present thesis we have applied the self consistent random phase approximation (SCRPA) to the Hubbard model with a small number of sites (a chain of 2, 4, 6,... sites). Earlier SCRPA had produced very good results in other models like the pairing model of Richardson. It was therefore interesting to see what kind of results the method is able to produce in the case of a more complex model like the Hubbard model. To our great satisfaction the case of two sites with two electrons (half-filling) is solved exactly by the SCRPA. This may seem a little trivial but the fact is that other respectable approximations like 'GW' or the approach with the Gutzwiller wave function yield results still far from exact. With this promising starting point, the case of 6 sites at half filling was considered next. For that case, evidently, SCRPA does not any longer give exact results. However, they are still excellent for a wide range of values of the coupling constant U, covering for instance the phase transition region towards a state with non zero magnetisation. We consider this as a good success of the theory. Non the less the case of 4 sites (a plaquette), as indeed all cases with 4n sites at half filling, turned out to have a problem because of degeneracies at the Hartree Fock level. A generalisation of the present method, including in addition to the pairs, quadruples of Fermions operators (called second RPA) is proposed to also include exactly the plaquette case in our approach. This is therefore a very interesting perspective of the present work. (author)
Atomic structure calculations using the relativistic random phase approximation
International Nuclear Information System (INIS)
Cheng, K.T.; Johnson, W.R.
1981-01-01
A brief review is given for the relativistic random phase approximation (RRPA) applied to atomic transition problems. Selected examples of RRPA calculations on discrete excitations and photoionization are given to illustrate the need of relativistic many-body theories in dealing with atomic processes where both relativity and correlation are important
Coded diffraction system in X-ray crystallography using a boolean phase coded aperture approximation
Pinilla, Samuel; Poveda, Juan; Arguello, Henry
2018-03-01
Phase retrieval is a problem present in many applications such as optics, astronomical imaging, computational biology and X-ray crystallography. Recent work has shown that the phase can be better recovered when the acquisition architecture includes a coded aperture, which modulates the signal before diffraction, such that the underlying signal is recovered from coded diffraction patterns. Moreover, this type of modulation effect, before the diffraction operation, can be obtained using a phase coded aperture, just after the sample under study. However, a practical implementation of a phase coded aperture in an X-ray application is not feasible, because it is computationally modeled as a matrix with complex entries which requires changing the phase of the diffracted beams. In fact, changing the phase implies finding a material that allows to deviate the direction of an X-ray beam, which can considerably increase the implementation costs. Hence, this paper describes a low cost coded X-ray diffraction system based on block-unblock coded apertures that enables phase reconstruction. The proposed system approximates the phase coded aperture with a block-unblock coded aperture by using the detour-phase method. Moreover, the SAXS/WAXS X-ray crystallography software was used to simulate the diffraction patterns of a real crystal structure called Rhombic Dodecahedron. Additionally, several simulations were carried out to analyze the performance of block-unblock approximations in recovering the phase, using the simulated diffraction patterns. Furthermore, the quality of the reconstructions was measured in terms of the Peak Signal to Noise Ratio (PSNR). Results show that the performance of the block-unblock phase coded apertures approximation decreases at most 12.5% compared with the phase coded apertures. Moreover, the quality of the reconstructions using the boolean approximations is up to 2.5 dB of PSNR less with respect to the phase coded aperture reconstructions.
Static correlation beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian Sommer
2014-01-01
derived from Hedin's equations (Random Phase Approximation (RPA), Time-dependent Hartree-Fock (TDHF), Bethe-Salpeter equation (BSE), and Time-Dependent GW) all reproduce the correct dissociation limit. We also show that the BSE improves the correlation energies obtained within RPA and TDHF significantly...... and confirms that BSE greatly improves the RPA and TDHF results despite the fact that the BSE excitation spectrum breaks down in the dissociation limit. In contrast, second order screened exchange gives a poor description of the dissociation limit, which can be attributed to the fact that it cannot be derived...
Accurate switching intensities and length scales in quasi-phase-matched materials
DEFF Research Database (Denmark)
Bang, Ole; Graversen, Torben Winther; Corney, Joel Frederick
2001-01-01
We consider unseeded typeI second-harmonic generation in quasi-phase-matched quadratic nonlinear materials and derive an accurate analytical expression for the evolution of the average intensity. The intensity- dependent nonlinear phase mismatch that is due to the cubic nonlinearity induced...... by quasi phase matching is found. The equivalent formula for the intensity of maximum conversion, the crossing of which changes the one-period nonlinear phase shift of the fundamental abruptly by p , corrects earlier estimates [Opt.Lett. 23, 506 (1998)] by a factor of 5.3. We find the crystal lengths...... that are necessary to obtain an optimal flat phase versus intensity response on either side of this separatrix intensity....
International Nuclear Information System (INIS)
Amusia, M.Y.; Cherepkov, N.A.; Zivanovic, D.; Radojevic, V.
1976-01-01
The photoionization cross sections and the oscillator strengths for helium, lithium, and beryllium atoms are calculated in the framework of the random-phase approximation with exchange. The energy-level shift for discrete transitions is taken into account consistently in this approximation. The results are compared with other many-body calculations and with experimental data. The comparison shows that the random-phase approximation with exchange can even be used for systems with a small number of particles
An implicit second order numerical method for two-fluid models
International Nuclear Information System (INIS)
Toumi, I.
1995-01-01
We present an implicit upwind numerical method for a six equation two-fluid model based on a linearized Riemann solver. The construction of this approximate Riemann solver uses an extension of Roe's scheme. Extension to second order accurate method is achieved using a piecewise linear approximation of the solution and a slope limiter method. For advancing in time, a linearized implicit integrating step is used. In practice this new numerical method has proved to be stable and capable of generating accurate non-oscillating solutions for two-phase flow calculations. The scheme was applied both to shock tube problems and to standard tests for two-fluid codes. (author)
Wetting phase transition of two segregated Bose–Einstein condensates restricted by a hard wall
Energy Technology Data Exchange (ETDEWEB)
Thu, Nguyen Van [Department of Physics, Hanoi Pedagogical University No. 2, Hanoi (Viet Nam); Phat, Tran Huu [Vietnam Atomic Energy Commission, 59 Ly Thuong Kiet, Hanoi (Viet Nam); Song, Pham The, E-mail: thesong80@icloud.com [Tay Bac University, Son La (Viet Nam)
2016-04-01
Highlights: • System of two segregated Bose–Einstein condensates limited by a wall is studied. • Double-parabola approximation is applied to Gross–Pitaevskii theory. • Interface tension and wetting phase diagram are established. - Abstract: The wetting phase transition in the system of two segregated Bose–Einstein condensates (BECs) restricted by a hard wall is studied by means of the double-parabola approximation (DPA) applied to the Gross–Pitaevskii (GP) theory. We found the interfacial tension and the wetting phase diagram which depend weakly on the spatial restriction.
Does the Berry phase in a quantum optical system originate from the rotating wave approximation?
International Nuclear Information System (INIS)
Wang, Minghao; Wei, L.F.; Liang, J.Q.
2015-01-01
The Berry phase (BP) in a quantized light field demonstrated more than a decade ago (Fuentes-Guridi et al., 2002 [9]) has attracted considerable attention, since it plays an important role in the cavity quantum electrodynamics. However, it is argued in Larson (2012) [15] that such a BP is just due to the rotating wave approximation (RWA) and the relevant BP should vanish beyond this approximation. Based on a consistent analysis we conclude in this letter that the BP in a generic Rabi model actually exists, no matter whether the RWA is applied. The existence of BP is also generalized to a three-level atom in the quantized cavity field. - Highlights: • Non-zero Berry phases for the Rabi model (without rotating wave approximation) are verified. • A general formulation of Berry phases for both the JC model and the Rabi model is presented. • The claim of vanishing Berry phase in the Rabi model is a result of improper semiclassical approximation. • Analytic solutions for the Rabi model is presented in the semiclassical approximation
The use of wavelet transforms in the solution of two-phase flow problems
International Nuclear Information System (INIS)
Moridis, G.J.; Nikolaou, M.; You, Yong
1994-10-01
In this paper we present the use of wavelets to solve the nonlinear Partial Differential.Equation (PDE) of two-phase flow in one dimension. The wavelet transforms allow a drastically different approach in the discretization of space. In contrast to the traditional trigonometric basis functions, wavelets approximate a function not by cancellation but by placement of wavelets at appropriate locations. When an abrupt chance, such as a shock wave or a spike, occurs in a function, only local coefficients in a wavelet approximation will be affected. The unique feature of wavelets is their Multi-Resolution Analysis (MRA) property, which allows seamless investigational any spatial resolution. The use of wavelets is tested in the solution of the one-dimensional Buckley-Leverett problem against analytical solutions and solutions obtained from standard numerical models. Two classes of wavelet bases (Daubechies and Chui-Wang) and two methods (Galerkin and collocation) are investigated. We determine that the Chui-Wang, wavelets and a collocation method provide the optimum wavelet solution for this type of problem. Increasing the resolution level improves the accuracy of the solution, but the order of the basis function seems to be far less important. Our results indicate that wavelet transforms are an effective and accurate method which does not suffer from oscillations or numerical smearing in the presence of steep fronts
Real-time dynamics of matrix quantum mechanics beyond the classical approximation
Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas
2018-03-01
We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.
Study of nonequilibrium dispersed two phase flow
International Nuclear Information System (INIS)
Reyes, J.N. Jr.
1986-01-01
Understanding the behavior of liquid droplets in a superheated steam environment is essential to the accurate prediction of nuclear fuel rod surface temperatures during the blowdown and reflood phase of a loss-of-coolant-accident (LOCA). In response to this need, this treatise presents several original and significant contributions to the field of thermofluid physics. The research contained herein presents a statistical derivation of the two-phase mass, momentum, and energy-conservation equations using a droplet continuity equation analogous to that used in the Kinetic Theory of Gases. Unlike the Eulerian volume and time-averaged conservation equations generally used to describe dispersed two-phase flow behavior, this statistical averaging approach results in an additional mass momentum or energy term in each of the respective conservation equations. Further, this study demonstrates that current definitions of the volumetric vapor generation rate used in the mass conservation equation are inappropriate results under certain circumstances. The mass conservation equation derived herein is used to obtain a new definition for the volumetric vapor-generation rate. Last, a simple two phase phenomenological model, based on the statistically averaged conservation equations, is presented and solved analytically. It is shown that the actual quality and vapor temperature, under these circumstances, depend on a single dimensionless group
Numerical approach of multi-field two-phase flow models in the OVAP code
International Nuclear Information System (INIS)
Anela Kumbaro
2005-01-01
Full text of publication follows: A significant progress has been made in modeling the complexity of vapor-liquid two-phase flow. Different three-dimensional models exist in order to simulate the evolution of parameters which characterize a two-phase model. These models can be classified into various groups depending on the inter-field coupling. A hierarchy of increasing physical complexity can be defined. The simplest group corresponds to the homogeneous mixture models where no interactions are taken into account. Another group is constituted by the two-fluid models employing physically important interfacial forces between two-phases, liquid, and water. The last group is multi-field modeling where inter-field couplings can be taken into account at different degrees, such as the MUltiple Size Group modeling [2], the consideration of separate equations for the transport and generation of mass and momentum for each field under the assumption of the same energy for all the fields of the same phase, and a full multi-field two-phase model [1]. The numerical approach of the general three-dimensional two-phase flow is by complexity of the phenomena a very challenging task; the ideal numerical method should be at the same time simple in order to apply to any model, from equilibrium to multi-field model and conservative in order to respect the fundamental conservation physical laws. The approximate Riemann solvers have the good properties of conservation of mass, momentum and energy balance and have been extended successfully to two-fluid models [3]- [5]. But, the up-winding of the flux is based on the Eigen-decomposition of the two-phase flow model and the computation of the Eigen-structure of a multi-field model can be a high cost procedure. Our contribution will present a short review of the above two-phase models, and show numerical results obtained for some of them with an approximate Riemann solver and with lower-complexity alternative numerical methods that do not
A Gaussian Approximation Potential for Silicon
Bernstein, Noam; Bartók, Albert; Kermode, James; Csányi, Gábor
We present an interatomic potential for silicon using the Gaussian Approximation Potential (GAP) approach, which uses the Gaussian process regression method to approximate the reference potential energy surface as a sum of atomic energies. Each atomic energy is approximated as a function of the local environment around the atom, which is described with the smooth overlap of atomic environments (SOAP) descriptor. The potential is fit to a database of energies, forces, and stresses calculated using density functional theory (DFT) on a wide range of configurations from zero and finite temperature simulations. These include crystalline phases, liquid, amorphous, and low coordination structures, and diamond-structure point defects, dislocations, surfaces, and cracks. We compare the results of the potential to DFT calculations, as well as to previously published models including Stillinger-Weber, Tersoff, modified embedded atom method (MEAM), and ReaxFF. We show that it is very accurate as compared to the DFT reference results for a wide range of properties, including low energy bulk phases, liquid structure, as well as point, line, and plane defects in the diamond structure.
Application of the resonating Hartree-Fock random phase approximation to the Lipkin model
International Nuclear Information System (INIS)
Nishiyama, S.; Ishida, K.; Ido, M.
1996-01-01
We have applied the resonating Hartree-Fock (Res-HF) approximation to the exactly solvable Lipkin model by utilizing a newly developed orbital-optimization algorithm. The Res-HF wave function was superposed by two Slater determinants (S-dets) which give two corresponding local energy minima of monopole ''deformations''. The self-consistent Res-HF calculation gives an excellent ground-state correlation energy. There exist excitations due to small vibrational fluctuations of the orbitals and mixing coefficients around their stationary values. They are described by a new approximation called the resonating Hartree-Fock random phase approximation (Res-HF RPA). Matrices of the second-order variation of the Res-HF energy have the same structures as those of the Res-HF RPA's matrices. The quadratic steepest descent of the Res-HF energy in the orbital optimization is considered to include certainly both effects of RPA-type fluctuations up to higher orders and their mode-mode couplings. It is a very important and interesting task to apply the Res-HF RPA to the Lipkin model with the use of the stationary values and to prove the above argument. It turns out that the Res-HF RPA works far better than the usual HF RPA and the renormalized one. We also show some important features of the Res-HF RPA. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Kotelnikova, O.A.; Prudnikov, V.N. [Physical Faculty, Lomonosov State University, Department of Magnetism, Moscow (Russian Federation); Rudoy, Yu.G., E-mail: rudikar@mail.ru [People' s Friendship University of Russia, Department of Theoretical Physics, Moscow (Russian Federation)
2015-06-01
The aim of this paper is to generalize the microscopic approach to the description of the magnetocaloric effect (MCE) started by Kokorina and Medvedev (E.E. Kokorina, M.V. Medvedev, Physica B 416 (2013) 29.) by applying it to the anisotropic ferromagnet of the “easy axis” type in two settings—with external magnetic field parallel and perpendicular to the axis of easy magnetization. In the last case there appears the field induced (or spin-reorientation) phase transition which occurs at the critical value of the external magnetic field. This value is proportional to the exchange anisotropy constant at low temperatures, but with the rise of temperature it may be renormalized (as a rule, proportional to the magnetization). We use the explicit form of the Hamiltonian of the anisotropic ferromagnet and apply widely used random phase approximation (RPA) (known also as Tyablikov approximation in the Green function method) which is more accurate than the well known molecular field approximation (MFA). It is shown that in the first case the magnitude of MCE is raised whereas in the second one the MCE disappears due to compensation of the critical field renormalized with the magnetization.
Localization and stationary phase approximation on supermanifolds
Zakharevich, Valentin
2017-08-01
Given an odd vector field Q on a supermanifold M and a Q-invariant density μ on M, under certain compactness conditions on Q, the value of the integral ∫Mμ is determined by the value of μ on any neighborhood of the vanishing locus N of Q. We present a formula for the integral in the case where N is a subsupermanifold which is appropriately non-degenerate with respect to Q. In the process, we discuss the linear algebra necessary to express our result in a coordinate independent way. We also extend the stationary phase approximation and the Morse-Bott lemma to supermanifolds.
Fast and accurate computation of projected two-point functions
Grasshorn Gebhardt, Henry S.; Jeong, Donghui
2018-01-01
We present the two-point function from the fast and accurate spherical Bessel transformation (2-FAST) algorithm1Our code is available at https://github.com/hsgg/twoFAST. for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum P (k ) onto the configuration space, ξℓν(r ), or spherical harmonic space, Cℓ(χ ,χ'). First, we employ the FFTLog transformation of the power spectrum to divide the calculation into P (k )-dependent coefficients and P (k )-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.
The phase transition lines in pair approximation for the basic reinfection model SIRI
International Nuclear Information System (INIS)
Stollenwerk, Nico; Martins, Jose; Pinto, Alberto
2007-01-01
For a spatial stochastic epidemic model we investigate in the pair approximation scheme the differential equations for the moments. The basic reinfection model of susceptible-infected-recovered-reinfected or SIRI type is analysed, its phase transition lines calculated analytically in this pair approximation
Random phase approximation in relativistic approach
International Nuclear Information System (INIS)
Ma Zhongyu; Yang Ding; Tian Yuan; Cao Ligang
2009-01-01
Some special issues of the random phase approximation(RPA) in the relativistic approach are reviewed. A full consistency and proper treatment of coupling to the continuum are responsible for the successful application of the RPA in the description of dynamical properties of finite nuclei. The fully consistent relativistic RPA(RRPA) requires that the relativistic mean filed (RMF) wave function of the nucleus and the RRPA correlations are calculated in a same effective Lagrangian and the consistent treatment of the Dirac sea of negative energy states. The proper treatment of the single particle continuum with scattering asymptotic conditions in the RMF and RRPA is discussed. The full continuum spectrum can be described by the single particle Green's function and the relativistic continuum RPA is established. A separable form of the paring force is introduced in the relativistic quasi-particle RPA. (authors)
Geometric convergence of some two-point Pade approximations
International Nuclear Information System (INIS)
Nemeth, G.
1983-01-01
The geometric convergences of some two-point Pade approximations are investigated on the real positive axis and on certain infinite sets of the complex plane. Some theorems concerning the geometric convergence of Pade approximations are proved, and bounds on geometric convergence rates are given. The results may be interesting considering the applications both in numerical computations and in approximation theory. As a specific case, the numerical calculations connected with the plasma dispersion function may be performed. (D.Gy.)
Correlated random-phase approximation from densities and in-medium matrix elements
Energy Technology Data Exchange (ETDEWEB)
Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)
2016-07-01
The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.
Self-consistent random phase approximation - application to systems of strongly correlated fermions
International Nuclear Information System (INIS)
Jemai, M.
2004-07-01
In the present thesis we have applied the self consistent random phase approximation (SCRPA) to the Hubbard model with a small number of sites (a chain of 2, 4, 6,... sites). Earlier SCRPA had produced very good results in other models like the pairing model of Richardson. It was therefore interesting to see what kind of results the method is able to produce in the case of a more complex model like the Hubbard model. To our great satisfaction the case of two sites with two electrons (half-filling) is solved exactly by the SCRPA. This may seem a little trivial but the fact is that other respectable approximations like 'GW' or the approach with the Gutzwiller wave function yield results still far from exact. With this promising starting point, the case of 6 sites at half filling was considered next. For that case, evidently, SCRPA does not any longer give exact results. However, they are still excellent for a wide range of values of the coupling constant U, covering for instance the phase transition region towards a state with non zero magnetisation. We consider this as a good success of the theory. Non the less the case of 4 sites (a plaquette), as indeed all cases with 4n sites at half filling, turned out to have a problem because of degeneracies at the Hartree Fock level. A generalisation of the present method, including in addition to the pairs, quadruples of Fermions operators (called second RPA) is proposed to also include exactly the plaquette case in our approach. This is therefore a very interesting perspective of the present work. (author)
An approximate analysis of expected cycle time in business process execution
Ha, B.H.; Reijers, H.A.; Bae, J.; Bae, H.; Eder, J.; Dustdar, S
2006-01-01
The accurate prediction of business process performance during its design phase can facilitate the assessment of existing processes and the generation of alternatives. In this paper, an approximation method to estimate the cycle time of a business process is introduced. First, we propose a process
Effects of two-phase flow in a model for nitramine deflagration
International Nuclear Information System (INIS)
Li, S.C.; Williams, F.A.; Margolis, S.B.
1990-01-01
Methods of asymptotic analysis are employed to extend an earlier model for the deflagration of nitramines to account for the presence of bubbles and droplets in a two-phase layer at the propellant surface during combustion. Two zones are identified in the two-phase region: one, at higher liquid volume fractions, maintains evaporative equilibrium, whereas the other, at lower liquid volume fractions, exhibits nonequilibrium vaporization. By introducing the most reasonable estimates for two-phase behavior of nitramines, the steady burning rates are found to be close to those obtained for models with a sharp liquid-gas interface. Good agreement with measured burning rates and pressure and temperature sensitivities are achieved through reasonable approximations concerning overall chemical-kinetic parameters
Random-phase approximation and its extension for the O(2) anharmonic oscillator
International Nuclear Information System (INIS)
Aouissat, Z.; Martin, C.
2004-01-01
We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogolyubov equation. We draw the parallel between the two approaches. (orig.)
Random-phase approximation and its extension for the O(2) anharmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Aouissat, Z. [Institut fuer Kernphysik, Technische Hochschule Darmstadt, Schlossgarten 9, D-64289, Darmstadt (Germany); Martin, C. [Groupe de Physique Theorique, Institut de Physique Nucleaire, F-91406, Orsay Cedex (France)
2004-02-01
We apply the random-phase approximation (RPA) and its extension called renormalized RPA to the quantum anharmonic oscillator with an O(2) symmetry. We first obtain the equation for the RPA frequencies in the standard and in the renormalized RPAs using the equation-of-motion method. In the case where the ground state has a broken symmetry, we check the existence of a zero frequency in the standard and in the renormalized RPAs. Then we use a time-dependent approach where the standard-RPA frequencies are obtained as small oscillations around the static solution in the time-dependent Hartree-Bogolyubov equation. We draw the parallel between the two approaches. (orig.)
Right unitarity triangles, stable CP-violating phases and approximate quark-lepton complementarity
International Nuclear Information System (INIS)
Xing Zhizhong
2009-01-01
Current experimental data indicate that two unitarity triangles of the CKM quark mixing matrix V are almost the right triangles with α∼90 deg. We highlight a very suggestive parametrization of V and show that its CP-violating phase φ is nearly equal to α (i.e., φ-α∼1.1 deg.). Both φ and α are stable against the renormalizaton-group evolution from the electroweak scale M Z to a superhigh energy scale M X or vice versa, and thus it is impossible to obtain α=90 deg. at M Z from φ=90 deg. at M X . We conjecture that there might also exist a maximal CP-violating phase φ∼90 deg. in the MNS lepton mixing matrix U. The approximate quark-lepton complementarity relations, which hold in the standard parametrizations of V and U, can also hold in our particular parametrizations of V and U simply due to the smallness of |V ub | and |V e3 |.
Interfacial area measurements in two-phase flow
International Nuclear Information System (INIS)
Veteau, J.-M.
1979-08-01
A thorough understanding of two-phase flow requires the accurate measurement of the time-averaged interfacial area per unit volume (also called the time-averaged integral specific area). The so-called 'specific area' can be estimated by several techniques described in the literature. These different methods are reviewed and the flow conditions which lead to a rigourous determination of the time-averaged integral specific area are clearly established. The probe technique, involving local measurements seems very attractive because of its large range of application [fr
Two-Phase Algorithm for Optimal Camera Placement
Directory of Open Access Journals (Sweden)
Jun-Woo Ahn
2016-01-01
Full Text Available As markers for visual sensor networks have become larger, interest in the optimal camera placement problem has continued to increase. The most featured solution for the optimal camera placement problem is based on binary integer programming (BIP. Due to the NP-hard characteristic of the optimal camera placement problem, however, it is difficult to find a solution for a complex, real-world problem using BIP. Many approximation algorithms have been developed to solve this problem. In this paper, a two-phase algorithm is proposed as an approximation algorithm based on BIP that can solve the optimal camera placement problem for a placement space larger than in current studies. This study solves the problem in three-dimensional space for a real-world structure.
Measurement of Two-Phase Flow Characteristics Under Microgravity Conditions
Keshock, E. G.; Lin, C. S.; Edwards, L. G.; Knapp, J.; Harrison, M. E.; Xhang, X.
1999-01-01
This paper describes the technical approach and initial results of a test program for studying two-phase annular flow under the simulated microgravity conditions of KC-135 aircraft flights. A helical coil flow channel orientation was utilized in order to circumvent the restrictions normally associated with drop tower or aircraft flight tests with respect to two-phase flow, namely spatial restrictions preventing channel lengths of sufficient size to accurately measure pressure drops. Additionally, the helical coil geometry is of interest in itself, considering that operating in a microgravity environment vastly simplifies the two-phase flows occurring in coiled flow channels under 1-g conditions for virtually any orientation. Pressure drop measurements were made across four stainless steel coil test sections, having a range of inside tube diameters (0.95 to 1.9 cm), coil diameters (25 - 50 cm), and length-to-diameter ratios (380 - 720). High-speed video photographic flow observations were made in the transparent straight sections immediately preceding and following the coil test sections. A transparent coil of tygon tubing of 1.9 cm inside diameter was also used to obtain flow visualization information within the coil itself. Initial test data has been obtained from one set of KC-135 flight tests, along with benchmark ground tests. Preliminary results appear to indicate that accurate pressure drop data is obtainable using a helical coil geometry that may be related to straight channel flow behavior. Also, video photographic results appear to indicate that the observed slug-annular flow regime transitions agree quite reasonably with the Dukler microgravity map.
An acoustic-convective splitting-based approach for the Kapila two-phase flow model
Energy Technology Data Exchange (ETDEWEB)
Eikelder, M.F.P. ten, E-mail: m.f.p.teneikelder@tudelft.nl [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands); Daude, F. [EDF R& D, AMA, 7 boulevard Gaspard Monge, 91120 Palaiseau (France); IMSIA, UMR EDF-CNRS-CEA-ENSTA 9219, Université Paris Saclay, 828 Boulevard des Maréchaux, 91762 Palaiseau (France); Koren, B.; Tijsseling, A.S. [Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven (Netherlands)
2017-02-15
In this paper we propose a new acoustic-convective splitting-based numerical scheme for the Kapila five-equation two-phase flow model. The splitting operator decouples the acoustic waves and convective waves. The resulting two submodels are alternately numerically solved to approximate the solution of the entire model. The Lagrangian form of the acoustic submodel is numerically solved using an HLLC-type Riemann solver whereas the convective part is approximated with an upwind scheme. The result is a simple method which allows for a general equation of state. Numerical computations are performed for standard two-phase shock tube problems. A comparison is made with a non-splitting approach. The results are in good agreement with reference results and exact solutions.
International Nuclear Information System (INIS)
Hsu, Y.Y.
1974-01-01
The following papers related to two-phase flow are summarized: current assumptions made in two-phase flow modeling; two-phase unsteady blowdown from pipes, flow pattern in Laval nozzle and two-phase flow dynamics; dependence of radial heat and momentum diffusion; transient behavior of the liquid film around the expanding gas slug in a vertical tube; flooding phenomena in BWR fuel bundles; and transient effects in bubble two-phase flow. (U.S.)
Is 2D impedance tomography a reliable technique for two-phase flow?
International Nuclear Information System (INIS)
Lemonnier, H.; Peytraud, J.F.
1998-01-01
Impedance tomography consists in reconstructing the conductivity distribution from electrical data which characterize the electrical response of a medium to arbitrary excitations. Impedance tomography is an ill-conditioned problem and designing a tomograph therefore requires the quantitative knowledge of the sensitivity of the reconstruction to the measurements noise. The numerical conditioning of an original and accurate algorithm has been studied. This algorithm does not suffer from the shortcomings already identified in the literature. It is shown that for media encompassing inclusions which is a typical situation in two-phase flows, the necessary accuracy for the measurements if far beyond any technological reach. Moreover, within these high requirements for accuracy, some side effects must be carefully controlled or compensated and relevant procedures arc provided. Furthermore. reconstruction artifacts are shown and they are found to derive from the unavoidable tridimensional nature of the electric field. For all these reasons, it is concluded that impedance tomography has very low potentialities as an accurate phase fraction distribution measuring technique in any arbitrary two-phase flows. (author)
A Rotational Pressure-Correction Scheme for Incompressible Two-Phase Flows with Open Boundaries
Dong, S.; Wang, X.
2016-01-01
Two-phase outflows refer to situations where the interface formed between two immiscible incompressible fluids passes through open portions of the domain boundary. We present several new forms of open boundary conditions for two-phase outflow simulations within the phase field framework, as well as a rotational pressure correction based algorithm for numerically treating these open boundary conditions. Our algorithm gives rise to linear algebraic systems for the velocity and the pressure that involve only constant and time-independent coefficient matrices after discretization, despite the variable density and variable viscosity of the two-phase mixture. By comparing simulation results with theory and the experimental data, we show that the method produces physically accurate results. We also present numerical experiments to demonstrate the long-term stability of the method in situations where large density contrast, large viscosity contrast, and backflows occur at the two-phase open boundaries. PMID:27163909
Two-phase flow models in unbounded two-phase critical flows
International Nuclear Information System (INIS)
Celata, G.P.; Cumo, M.; Farello, G.E.
1985-01-01
With reference to a Loss-of-Coolant Accident in Light Water Reactors, an analysis of the unbounded two-phase critical flow (i.e. the issuing two-phase jet) has been accomplished. Considering jets external shape, obtained by means of photographic pictures; pressure profiles inside the jet, obtained by means of a movable ''Pitot;'' and jet phases distribution information, obtained by means of X-rays pictures; a characterization of the flow pattern in the unbounded region of a two-phase critical flow is given. Jets X-ray pictures show the existence of a central high density ''core'' gradually evaporating all around, which gives place to a characteristic ''dartflow'' the length of which depends on stagnation thermodynamic conditions
Development of a large-scale general purpose two-phase flow analysis code
International Nuclear Information System (INIS)
Terasaka, Haruo; Shimizu, Sensuke
2001-01-01
A general purpose three-dimensional two-phase flow analysis code has been developed for solving large-scale problems in industrial fields. The code uses a two-fluid model to describe the conservation equations for two-phase flow in order to be applicable to various phenomena. Complicated geometrical conditions are modeled by FAVOR method in structured grid systems, and the discretization equations are solved by a modified SIMPLEST scheme. To reduce computing time a matrix solver for the pressure correction equation is parallelized with OpenMP. Results of numerical examples show that the accurate solutions can be obtained efficiently and stably. (author)
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
Central upwind scheme for a compressible two-phase flow model.
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.
Accurately bi-orthogonal direct and adjoint lambda modes via two-sided Eigen-solvers
International Nuclear Information System (INIS)
Roman, J.E.; Vidal, V.; Verdu, G.
2005-01-01
This work is concerned with the accurate computation of the dominant l-modes (Lambda mode) of the reactor core in order to approximate the solution of the neutron diffusion equation in different situations such as the transient modal analysis. In a previous work, the problem was already addressed by implementing a parallel program based on SLEPc (Scalable Library for Eigenvalue Problem Computations), a public domain software for the solution of eigenvalue problems. Now, the proposed solution is extended by incorporating also the computation of the adjoint l-modes in such a way that the bi-orthogonality condition is enforced very accurately. This feature is very desirable in some types of analyses, and in the proposed scheme it is achieved by making use of two-sided eigenvalue solving software. Current implementations of some of these software, while still susceptible of improvement, show that they can be competitive in terms of response time and accuracy with respect to other types of eigenvalue solving software. The code developed by the authors has parallel capabilities in order to be able to analyze reactors with a great level of detail in a short time. (authors)
Accurately bi-orthogonal direct and adjoint lambda modes via two-sided Eigen-solvers
Energy Technology Data Exchange (ETDEWEB)
Roman, J.E.; Vidal, V. [Valencia Univ. Politecnica, D. Sistemas Informaticos y Computacion (Spain); Verdu, G. [Valencia Univ. Politecnica, D. Ingenieria Quimica y Nuclear (Spain)
2005-07-01
This work is concerned with the accurate computation of the dominant l-modes (Lambda mode) of the reactor core in order to approximate the solution of the neutron diffusion equation in different situations such as the transient modal analysis. In a previous work, the problem was already addressed by implementing a parallel program based on SLEPc (Scalable Library for Eigenvalue Problem Computations), a public domain software for the solution of eigenvalue problems. Now, the proposed solution is extended by incorporating also the computation of the adjoint l-modes in such a way that the bi-orthogonality condition is enforced very accurately. This feature is very desirable in some types of analyses, and in the proposed scheme it is achieved by making use of two-sided eigenvalue solving software. Current implementations of some of these software, while still susceptible of improvement, show that they can be competitive in terms of response time and accuracy with respect to other types of eigenvalue solving software. The code developed by the authors has parallel capabilities in order to be able to analyze reactors with a great level of detail in a short time. (authors)
Phase diagram of two-color QCD in a Dyson-Schwinger approach
Energy Technology Data Exchange (ETDEWEB)
Buescher, Pascal Joachim
2014-04-28
We investigate two-color QCD with N{sub f}=2 at finite temperatures and chemical potentials using a Dyson-Schwinger approach. We employ two different truncations for the quark loop in the gluon DSE: one based on the Hard-Dense/Hard-Thermal Loop (HDTL) approximation of the quark loop and one based on the back-coupling of the full, self-consistent quark propagator (SCQL). We compare results for the different truncations with each other as well as with other approaches. As expected, we find a phase dominated by the condensation of quark-quark pairs. This diquark condensation phase overshadows the critical end point and first-order phase transition which one finds if diquark condensation is neglected. The phase transition from the phase without diquark condensation to the diquark-condensation phase is of second order. We observe that the dressing with massless quarks in the HDTL approximation leads to a significant violation of the Silver Blaze property and to a too small diquark condensate. The SCQL truncation, on the other hand, is found to reproduce all expected features of the μ-dependent quark condensates. Moreover, with parameters adapted to the situation in other approaches, we also find good to very good agreement with model and lattice calculations in all quark quantities. We find indictions that the physics in recent lattice calculations is likely to be driven solely by the explicit chiral symmetry breaking. Discrepancies w.r.t. the lattice are, however, observed in two quantities that are very sensitive to the screening of the gluon propagator, the dressed gluon propagator itself and the phase-transition line at high temperatures.
Adaptive moving grid methods for two-phase flow in porous media
Dong, Hao; Qiao, Zhonghua; Sun, Shuyu; Tang, Tao
2014-01-01
In this paper, we present an application of the moving mesh method for approximating numerical solutions of the two-phase flow model in porous media. The numerical schemes combine a mixed finite element method and a finite volume method, which can
International Nuclear Information System (INIS)
Park, Chan Wook; Lee, Sung Su
2008-01-01
Two-phase compressible flow fields of air-water are investigated numerically in the fixed Eulerian grid framework. The phase interface is captured via volume fractions of ech phase. A way to model two phase compressible flows as a single phase one is found based on an equivalent equation of states of Tait's type for a multiphase cell. The equivalent single phase field is discretized using the Roe's approximate Riemann solver. Two approaches are tried to suppress the pressure oscillation phenomena at the phase interface, a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. In discretizing the compressible form of volume fraction equation, phase interfaces are geometrically reconstructed to minimize the numerical diffusion of volume fraction and relevant variables. The motion of a projectile in a water-filled tube which is fired by the release of highly pressurized air is simulated presuming the flow field as a two dimensional one, and several design factors affecting the projectile movement are investigated
Joshi, Vaibhav; Jaiman, Rajeev K.
2018-05-01
We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase
Relativistic quasiparticle random phase approximation in deformed nuclei
Energy Technology Data Exchange (ETDEWEB)
Pena Arteaga, D.
2007-06-25
Covariant density functional theory is used to study the influence of electromagnetic radiation on deformed superfluid nuclei. The relativistic Hartree-Bogolyubov equations and the resulting diagonalization problem of the quasiparticle random phase approximation are solved for axially symmetric systems in a fully self-consistent way by a newly developed parallel code. Three different kinds of high precision energy functionals are investigated and special care is taken for the decoupling of the Goldstone modes. This allows the microscopic investigation of Pygmy and scissor resonances in electric and magnetic dipole fields. Excellent agreement with recent experiments is found and new types of modes are predicted for deformed systems with large neutron excess. (orig.)
Photons in dense nuclear matter: Random-phase approximation
Stetina, Stephan; Rrapaj, Ermal; Reddy, Sanjay
2018-04-01
We present a comprehensive and pedagogic discussion of the properties of photons in cold and dense nuclear matter based on the resummed one-loop photon self-energy. Correlations among electrons, muons, protons, and neutrons in β equilibrium that arise as a result of electromagnetic and strong interactions are consistently taken into account within the random phase approximation. Screening effects, damping, and collective excitations are systematically studied in a fully relativistic setup. Our study is relevant to the linear response theory of dense nuclear matter, calculations of transport properties of cold dense matter, and investigations of the production and propagation of hypothetical vector bosons such as the dark photons.
International Nuclear Information System (INIS)
Bates, J.M.; Stewart, C.W.
1979-08-01
Laser-Doppler anemometry (LDA) was used to measure local mean axial velocities and turbulence intnsities at selected locations within a study model dimensionally protypic of an existing PWR steam generator design. The model tube bundle with support plate was installed in a special flow housing that formed part of an isothermal recirculating water flow loop. Flow conditions for this experiment were intended to simulate only typical single-phase flow velocities and were not an attempt to completely model actual steam generator, boiling, two-phase flow conditions. The measurements were performed in water at approximately 85 0 F with test section average velocities of approximately 0.55 and 1.1 fps. These conditions corresponded to Reynolds numbers of approximately 7,000 and approximately 14,000, respectively. Normalized velocity and turbulence intensity ratios are graphically reported. Additional qualitative, photographic investigations of air-water two-phase flows in a PWR steam generator study model were also performed
Modeling and numerical analysis of non-equilibrium two-phase flows
International Nuclear Information System (INIS)
Rascle, P.; El Amine, K.
1997-01-01
We are interested in the numerical approximation of two-fluid models of nonequilibrium two-phase flows described by six balance equations. We introduce an original splitting technique of the system of equations. This technique is derived in a way such that single phase Riemann solvers may be used: moreover, it allows a straightforward extension to various and detailed exchange source terms. The properties of the fluids are first approached by state equations of ideal gas type and then extended to real fluids. For the construction of numerical schemes , the hyperbolicity of the full system is not necessary. When based on suitable kinetic unwind schemes, the algorithm can compute flow regimes evolving from mixture to single phase flows and vice versa. The whole scheme preserves the physical features of all the variables which remain in the set of physical states. Several stiff numerical tests, such as phase separation and phase transition are displayed in order to highlight the efficiency of the proposed method. The document is a PhD thesis divided in 6 chapters and two annexes. They are entitled: 1. - Introduction (in French), 2. - Two-phase flow, modelling and hyperbolicity (in French), 3. - A numerical method using upwind schemes for the resolution of two-phase flows without exchange terms (in English), 4. - A numerical scheme for one-phase flow of real fluids (in English), 5. - An upwind numerical for non-equilibrium two-phase flows (in English), 6. - The treatment of boundary conditions (in English), A.1. The Perthame scheme (in English) and A.2. The Roe scheme (in English)
Modelling of two-phase flow based on separation of the flow according to velocity
International Nuclear Information System (INIS)
Narumo, T.
1997-01-01
The thesis concentrates on the development work of a physical one-dimensional two-fluid model that is based on Separation of the Flow According to Velocity (SFAV). The conventional way to model one-dimensional two-phase flow is to derive conservation equations for mass, momentum and energy over the regions occupied by the phases. In the SFAV approach, the two-phase mixture is divided into two subflows, with as distinct average velocities as possible, and momentum conservation equations are derived over their domains. Mass and energy conservation are treated equally with the conventional model because they are distributed very accurately according to the phases, but momentum fluctuations follow better the flow velocity. Submodels for non-uniform transverse profile of velocity and density, slip between the phases within each subflow and turbulence between the subflows have been derived. The model system is hyperbolic in any sensible flow conditions over the whole range of void fraction. Thus, it can be solved with accurate numerical methods utilizing the characteristics. The characteristics agree well with the used experimental data on two-phase flow wave phenomena Furthermore, the characteristics of the SFAV model are as well in accordance with their physical counterparts as of the best virtual-mass models that are typically optimized for special flow regimes like bubbly flow. The SFAV model has proved to be applicable in describing two-phase flow physically correctly because both the dynamics and steady-state behaviour of the model has been considered and found to agree well with experimental data This makes the SFAV model especially suitable for the calculation of fast transients, taking place in versatile form e.g. in nuclear reactors
Mapping moveout approximations in TI media
Stovas, Alexey; Alkhalifah, Tariq Ali
2013-01-01
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
Mapping moveout approximations in TI media
Stovas, Alexey
2013-11-21
Moveout approximations play a very important role in seismic modeling, inversion, and scanning for parameters in complex media. We developed a scheme to map one-way moveout approximations for transversely isotropic media with a vertical axis of symmetry (VTI), which is widely available, to the tilted case (TTI) by introducing the effective tilt angle. As a result, we obtained highly accurate TTI moveout equations analogous with their VTI counterparts. Our analysis showed that the most accurate approximation is obtained from the mapping of generalized approximation. The new moveout approximations allow for, as the examples demonstrate, accurate description of moveout in the TTI case even for vertical heterogeneity. The proposed moveout approximations can be easily used for inversion in a layered TTI medium because the parameters of these approximations explicitly depend on corresponding effective parameters in a layered VTI medium.
An Effective Method to Accurately Calculate the Phase Space Factors for β"-β"- Decay
International Nuclear Information System (INIS)
Horoi, Mihai; Neacsu, Andrei
2016-01-01
Accurate calculations of the electron phase space factors are necessary for reliable predictions of double-beta decay rates and for the analysis of the associated electron angular and energy distributions. We present an effective method to calculate these phase space factors that takes into account the distorted Coulomb field of the daughter nucleus, yet it allows one to easily calculate the phase space factors with good accuracy relative to the most exact methods available in the recent literature.
Approximate solution of space and time fractional higher order phase field equation
Shamseldeen, S.
2018-03-01
This paper is concerned with a class of space and time fractional partial differential equation (STFDE) with Riesz derivative in space and Caputo in time. The proposed STFDE is considered as a generalization of a sixth-order partial phase field equation. We describe the application of the optimal homotopy analysis method (OHAM) to obtain an approximate solution for the suggested fractional initial value problem. An averaged-squared residual error function is defined and used to determine the optimal convergence control parameter. Two numerical examples are studied, considering periodic and non-periodic initial conditions, to justify the efficiency and the accuracy of the adopted iterative approach. The dependence of the solution on the order of the fractional derivative in space and time and model parameters is investigated.
Calculation of thermodynamic properties using the random-phase approximation: alpha-N2
Jansen, A.P.J.; Schoorl, R.
1988-01-01
The random-phase approximation (RPA) for molecular crystals is extended in order to calculate thermodynamic properties. A recursion formula for thermodynamic averages of products of mean-field excitation and deexcitation operators is derived. With this formula the thermodynamic average of any
Numerical methods for limit problems in two-phase flow models
International Nuclear Information System (INIS)
Cordier, F.
2011-01-01
Numerical difficulties are encountered during the simulation of two-phase flows. Two issues are studied in this thesis: the simulation of phase transitions on one hand, and the simulation of both compressible and incompressible flows in the other hand. Un asymptotic study has shown that the loss of hyperbolicity of the bi fluid model was responsible for the difficulties encountered by the Roe scheme during the simulation of phase transitions. Robust and accurate polynomial schemes have thus been developed. To tackle the occasional lack of positivity of the solution, a numerical treatment based on adaptive diffusion was proposed and allowed to simulate with accuracy the test-cases of a boiling channel with creation of vapor and a tee-junction with separation of the phases. In a second part, an all-speed scheme for compressible and incompressible flows have been proposed. This pressure-based semi-implicit asymptotic preserving scheme is conservative, solves an elliptic equation on the pressure, and has been designed for general equations of state. The scheme was first developed for the full Euler equations and then extended to the Navier-Stokes equations. The good behaviour of the scheme in both compressible and incompressible regimes have been investigated. An extension of the scheme to the two-phase mixture model was implemented and demonstrated the ability of the scheme to simulate two-phase flows with phase change and a water-steam equation of state. (author) [fr
Comparison between wire mesh sensor and gamma densitometry void measurements in two-phase flows
Sharaf, S.; Da Silva, M.; Hampel, U.; Zippe, C.; Beyer, M.; Azzopardi, B.
2011-10-01
Wire mesh sensors (WMS) are fast imaging instruments that are used for gas-liquid and liquid-liquid two-phase flow measurements and experimental investigations. Experimental tests were conducted at Helmholtz-Zentrum Dresden-Rossendorf to test both the capacitance and conductance WMS against a gamma densitometer (GD). A small gas-liquid test facility was utilized. This consisted of a vertical round pipe approximately 1 m in length, and 50 mm internal diameter. A 16 × 16 WMS was used with high spatial and temporal resolutions. Air-deionized water was the two-phase mixture. The gas superficial velocity was varied between 0.05 m s-1 and 1.4 m s-1 at two liquid velocities of 0.2 and 0.7 m s-1. The GD consisted of a collimated source and a collimated detector. The GD was placed on a moving platform close to the plane of wires of the sensor, in order to align it accurately using a counter mechanism, with each of the wires of the WMS, and the platform could scan the full section of the pipe. The WMS was operated as a conductivity WMS for a half-plane with eight wires and as a capacitance WMS for the other half. For the cross-sectional void (time and space averaged), along each wire, there was good agreement between WMS and the GD chordal void fraction near the centre of the pipe.
Comparison between wire mesh sensor and gamma densitometry void measurements in two-phase flows
International Nuclear Information System (INIS)
Sharaf, S; Azzopardi, B; Da Silva, M; Hampel, U; Zippe, C; Beyer, M
2011-01-01
Wire mesh sensors (WMS) are fast imaging instruments that are used for gas–liquid and liquid–liquid two-phase flow measurements and experimental investigations. Experimental tests were conducted at Helmholtz-Zentrum Dresden-Rossendorf to test both the capacitance and conductance WMS against a gamma densitometer (GD). A small gas–liquid test facility was utilized. This consisted of a vertical round pipe approximately 1 m in length, and 50 mm internal diameter. A 16 × 16 WMS was used with high spatial and temporal resolutions. Air–deionized water was the two-phase mixture. The gas superficial velocity was varied between 0.05 m s −1 and 1.4 m s −1 at two liquid velocities of 0.2 and 0.7 m s −1 . The GD consisted of a collimated source and a collimated detector. The GD was placed on a moving platform close to the plane of wires of the sensor, in order to align it accurately using a counter mechanism, with each of the wires of the WMS, and the platform could scan the full section of the pipe. The WMS was operated as a conductivity WMS for a half-plane with eight wires and as a capacitance WMS for the other half. For the cross-sectional void (time and space averaged), along each wire, there was good agreement between WMS and the GD chordal void fraction near the centre of the pipe
Two-phase velocity measurements around cylinders using particle image velocimetry
Energy Technology Data Exchange (ETDEWEB)
Hassan, Y.A.; Philip, O.G.; Schmidl, W.D. [Texas A& M Univ., College Station, TX (United States)] [and others
1995-09-01
The particle Image Velocimetry flow measurement technique was used to study both single-phase flow and two-phase flow across a cylindrical rod inserted in a channel. First, a flow consisting of only a single-phase fluid was studied. The experiment consisted of running a laminar flow over four rods inserted in a channel. The water flow rate was 126 cm{sup 3}/s. Then a two-phase flow was studied. A mixture of water and small air bubbles was used. The water flow rate was 378 cm{sup 3}/s and the air flow rate was approximately 30 cm{sup 3}/s. The data are analyzed to obtain the velocity fields for both experiments. After interpretation of the velocity data, forces acting on a bubble entrained by the vortex were calculated successfully. The lift and drag coefficients were calculated using the velocity measurements and the force data.
Aspects of the Color Flavor Locking phase of QCD in the Nambu-Jona Lasinio approximation
Casalbuoni, Roberto; Nardulli, Giuseppe; Ruggieri, Marco
2003-01-01
We study two aspects of the CFL phase of QCD in the NJL approximation. The first one is the issue of the dependence on \\mu of the ultraviolet cutoff in the gap equation, which is solved allowing a running coupling constant. The second one is the dependence of the gap on the strange quark mass; using the high density effective theory we perform an expansion in the parameter (m_s/\\mu)^2 after checking that its numerical validity is very good already at first order.
Synchronization effects in two coupled one-dimensional lattices of phase oscillators
International Nuclear Information System (INIS)
Pando L, Carlos L.
2001-03-01
We study synchronization effects in a model consisting of two identical unidirectionally coupled 1-D arrays of phase oscillators. The master array is in the spatio-temporal chaos regime and the coupling across the two arrays is not strong enough in order to reach complete synchronization. The time series of the distance between the arrays is the main object of our study and this shows on-off intermittency. We can approximate the dynamics of the aforementioned time series with that of a first-order Markov process with two symbols. This model can be implemented in arrays of phase-locked loops (PPL) and Josephson junctions. (author)
International Nuclear Information System (INIS)
Leavell, W.H.; Mullens, J.A.
1981-01-01
A computational algorithm has been developed to measure transient, phase-interface velocity in two-phase, steam-water systems. The algorithm will be used to measure the transient velocity of steam-water mixture during simulated PWR reflood experiments. By utilizing signals produced by two, spatially separated impedance probes immersed in a two-phase mixture, the algorithm computes the average transit time of mixture fluctuations moving between the two probes. This transit time is computed by first, measuring the phase shift between the two probe signals after transformation to the frequency domain and then computing the phase shift slope by a weighted least-squares fitting technique. Our algorithm, which has been tested with both simulated and real data, is able to accurately track velocity transients as fast as 4 m/s/s
International Nuclear Information System (INIS)
Peng, Degao; Yang, Yang; Zhang, Peng; Yang, Weitao
2014-01-01
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N 4 ). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S ^2 〉 are also developed and tested
Energy Technology Data Exchange (ETDEWEB)
Peng, Degao; Yang, Yang; Zhang, Peng [Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States); Yang, Weitao, E-mail: weitao.yang@duke.edu [Department of Chemistry and Department of Physics, Duke University, Durham, North Carolina 27708 (United States)
2014-12-07
In this article, we develop systematically second random phase approximations (RPA) and Tamm-Dancoff approximations (TDA) of particle-hole and particle-particle channels for calculating molecular excitation energies. The second particle-hole RPA/TDA can capture double excitations missed by the particle-hole RPA/TDA and time-dependent density-functional theory (TDDFT), while the second particle-particle RPA/TDA recovers non-highest-occupied-molecular-orbital excitations missed by the particle-particle RPA/TDA. With proper orbital restrictions, these restricted second RPAs and TDAs have a formal scaling of only O(N{sup 4}). The restricted versions of second RPAs and TDAs are tested with various small molecules to show some positive results. Data suggest that the restricted second particle-hole TDA (r2ph-TDA) has the best overall performance with a correlation coefficient similar to TDDFT, but with a larger negative bias. The negative bias of the r2ph-TDA may be induced by the unaccounted ground state correlation energy to be investigated further. Overall, the r2ph-TDA is recommended to study systems with both single and some low-lying double excitations with a moderate accuracy. Some expressions on excited state property evaluations, such as 〈S{sup ^2}〉 are also developed and tested.
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
Modelling of two-phase flow based on separation of the flow according to velocity
Energy Technology Data Exchange (ETDEWEB)
Narumo, T. [VTT Energy, Espoo (Finland). Nuclear Energy
1997-12-31
The thesis concentrates on the development work of a physical one-dimensional two-fluid model that is based on Separation of the Flow According to Velocity (SFAV). The conventional way to model one-dimensional two-phase flow is to derive conservation equations for mass, momentum and energy over the regions occupied by the phases. In the SFAV approach, the two-phase mixture is divided into two subflows, with as distinct average velocities as possible, and momentum conservation equations are derived over their domains. Mass and energy conservation are treated equally with the conventional model because they are distributed very accurately according to the phases, but momentum fluctuations follow better the flow velocity. Submodels for non-uniform transverse profile of velocity and density, slip between the phases within each subflow and turbulence between the subflows have been derived. The model system is hyperbolic in any sensible flow conditions over the whole range of void fraction. Thus, it can be solved with accurate numerical methods utilizing the characteristics. The characteristics agree well with the used experimental data on two-phase flow wave phenomena Furthermore, the characteristics of the SFAV model are as well in accordance with their physical counterparts as of the best virtual-mass models that are typically optimized for special flow regimes like bubbly flow. The SFAV model has proved to be applicable in describing two-phase flow physically correctly because both the dynamics and steady-state behaviour of the model has been considered and found to agree well with experimental data This makes the SFAV model especially suitable for the calculation of fast transients, taking place in versatile form e.g. in nuclear reactors. 45 refs. The thesis includes also five previous publications by author.
Zhao, Xiao-mei; Xie, Dong-fan; Li, Qi
2015-02-01
With the development of intelligent transport system, advanced information feedback strategies have been developed to reduce traffic congestion and enhance the capacity. However, previous strategies provide accurate information to travelers and our simulation results show that accurate information brings negative effects, especially in delay case. Because travelers prefer to the best condition route with accurate information, and delayed information cannot reflect current traffic condition but past. Then travelers make wrong routing decisions, causing the decrease of the capacity and the increase of oscillations and the system deviating from the equilibrium. To avoid the negative effect, bounded rationality is taken into account by introducing a boundedly rational threshold BR. When difference between two routes is less than the BR, routes have equal probability to be chosen. The bounded rationality is helpful to improve the efficiency in terms of capacity, oscillation and the gap deviating from the system equilibrium.
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
A Time--Independent Born--Oppenheimer Approximation with Exponentially Accurate Error Estimates
Hagedorn, G A
2004-01-01
We consider a simple molecular--type quantum system in which the nuclei have one degree of freedom and the electrons have two levels. The Hamiltonian has the form \\[ H(\\epsilon)\\ =\\ -\\,\\frac{\\epsilon^4}2\\, \\frac{\\partial^2\\phantom{i}}{\\partial y^2}\\ +\\ h(y), \\] where $h(y)$ is a $2\\times 2$ real symmetric matrix. Near a local minimum of an electron level ${\\cal E}(y)$ that is not at a level crossing, we construct quasimodes that are exponentially accurate in the square of the Born--Oppenheimer parameter $\\epsilon$ by optimal truncation of the Rayleigh--Schr\\"odinger series. That is, we construct $E_\\epsilon$ and $\\Psi_\\epsilon$, such that $\\|\\Psi_\\epsilon\\|\\,=\\,O(1)$ and \\[ \\|\\,(H(\\epsilon)\\,-\\,E_\\epsilon))\\,\\Psi_\\epsilon\\,\\|\\ 0. \\
Directory of Open Access Journals (Sweden)
Xin Chen
2015-01-01
Full Text Available Adaptive Dynamic Programming (ADP with critic-actor architecture is an effective way to perform online learning control. To avoid the subjectivity in the design of a neural network that serves as a critic network, kernel-based adaptive critic design (ACD was developed recently. There are two essential issues for a static kernel-based model: how to determine proper hyperparameters in advance and how to select right samples to describe the value function. They all rely on the assessment of sample values. Based on the theoretical analysis, this paper presents a two-phase simultaneous learning method for a Gaussian-kernel-based critic network. It is able to estimate the values of samples without infinitively revisiting them. And the hyperparameters of the kernel model are optimized simultaneously. Based on the estimated sample values, the sample set can be refined by adding alternatives or deleting redundances. Combining this critic design with actor network, we present a Gaussian-kernel-based Adaptive Dynamic Programming (GK-ADP approach. Simulations are used to verify its feasibility, particularly the necessity of two-phase learning, the convergence characteristics, and the improvement of the system performance by using a varying sample set.
Contribution to the theory of the two phase blowdown phenomenon
International Nuclear Information System (INIS)
Hutcherson, M.N.
1975-12-01
In order to accurately model the two phase portion of a pressure vessel blowdown, it becomes necessary to understand the bubble growth mechanism within the vessel during the early period of the decompression, the two phase flow behavior within the vessel, and the applicability of the available two phase critical flow models to the blowdown transient. To aid in providing answers to such questions, a small scale, separate effects, isothermal blowdown experiment has been conducted in a small pressure vessel. The tests simulated a full open, double ended, guillotine break in a large diameter, short exhaust duct from the vessel. The vaporization process at the initiation of the decompression is apparently that of thermally dominated bubble growth originating from the surface cavities inside the system. Thermodynamic equilibrium of the remaining fluid within the vessel existed in the latter portion of the decompression. A nonuniform distribution of fluid quality within the vessel was also detected in this experiment. By comparison of the experimental results from this and other similar transient, two phase critical flow studies with steady state, small duct, two phase critical flow data, it is shown that transient, two phase critical flow in large ducts appears to be similar to steady state, two phase critical flow in small ducts. Analytical models have been developed to predict the blowdown characteristics of a system during subcooled decompression, the bubble growth regime of blowdown, and also in the nearly dispersed period of depressurization. This analysis indicates that the system pressure history early in the blowdown is dependent on the internal vessel surface area, the internal vessel volume, and also on the exhaust flow area from the system. This analysis also illustrates that the later period of decompression can be predicted based on thermodynamic equilibrium
Stability of icosahedral quasicrystals in a simple model with two-length scales
International Nuclear Information System (INIS)
Jiang, Kai; Zhang, Pingwen; Shi, An-Chang
2017-01-01
The phase behaviour of a free energy functional with two length scales is examined by comparing the free energy of different candidate phases including three-dimensional icosahedral quasicrystals. Accurate free energy of the quasicrystals has been obtained using the recently developed projection method. The results reveal that the icosahedral quasicrystal and body-centred-cubic spherical phase are the stable ordered phases of the model. Furthermore, the difference between the results obtained from the projection method and the one-mode approximation has been analyzed in detail. The present study extends previous results on two-dimensional systems, demonstrating that the interactions between density waves at two length scales can stabilize two- and three-dimensional quasicrystals. (paper)
Daude, F.; Galon, P.
2018-06-01
A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.
Leveraging Two Kinect Sensors for Accurate Full-Body Motion Capture
Directory of Open Access Journals (Sweden)
Zhiquan Gao
2015-09-01
Full Text Available Accurate motion capture plays an important role in sports analysis, the medical field and virtual reality. Current methods for motion capture often suffer from occlusions, which limits the accuracy of their pose estimation. In this paper, we propose a complete system to measure the pose parameters of the human body accurately. Different from previous monocular depth camera systems, we leverage two Kinect sensors to acquire more information about human movements, which ensures that we can still get an accurate estimation even when significant occlusion occurs. Because human motion is temporally constant, we adopt a learning analysis to mine the temporal information across the posture variations. Using this information, we estimate human pose parameters accurately, regardless of rapid movement. Our experimental results show that our system can perform an accurate pose estimation of the human body with the constraint of information from the temporal domain.
Energy Technology Data Exchange (ETDEWEB)
Zwick, D; Balachandar, S [Department of Mechanical and Aerospace Engineering, University of Florida, FL, United States of America (United States); Sakhaee, E; Entezari, A, E-mail: dpzwick@ufl.edu [Department of Computer and Information Science and Engineering, University of Florida, FL, United States of America (United States)
2017-10-15
Multiphase flow simulation serves a vital purpose in applications as diverse as engineering design, natural disaster prediction, and even study of astrophysical phenomena. In these scenarios, it can be very difficult, expensive, or even impossible to fully represent the physical system under consideration. Even still, many such real-world applications can be modeled as a two-phase flow containing both continuous and dispersed phases. Consequentially, the continuous phase is thought of as a fluid and the dispersed phase as particles. The continuous phase is typically treated in the Eulerian frame of reference and represented on a fixed grid, while the dispersed phase is treated in the Lagrangian frame and represented by a sample distribution of Lagrangian particles that approximate a cloud. Coupling between the phases requires interpolation of the continuous phase properties at the locations of the Lagrangian particles. This interpolation step is straightforward and can be performed at higher order accuracy. The reverse process of projecting the Lagrangian particle properties from the sample points to the Eulerian grid is complicated by the time-dependent non-uniform distribution of the Lagrangian particles. In this paper we numerically examine three reconstruction, or projection, methods: (i) direct summation (DS), (ii) least-squares, and (iii) sparse approximation. We choose a continuous representation of the dispersed phase property that is systematically varied from a simple single mode periodic signal to a more complex artificially constructed turbulent signal to see how each method performs in reconstruction. In these experiments, we show that there is a link between the number of dispersed Lagrangian sample points and the number of structured grid points to accurately represent the underlying functional representation to machine accuracy. The least-squares method outperforms the other methods in most cases, while the sparse approximation method is able to
Ahmad, Zahoor; Hanif, Muhammad
2013-01-01
The development of estimators of population parameters based on two-phase sampling schemes has seen a dramatic increase in the past decade. Various authors have developed estimators of population using either one or two auxiliary variables. The present volume is a comprehensive collection of estimators available in single and two phase sampling. The book covers estimators which utilize information on single, two and multiple auxiliary variables of both quantitative and qualitative nature. Th...
Random phase approximation: from Giant to Intra-doublet resonances
International Nuclear Information System (INIS)
Amusia, M.Ya.
2004-01-01
We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms
Random phase approximation: from Giant to Intra-doublet resonances
Energy Technology Data Exchange (ETDEWEB)
Amusia, M.Ya. E-mail: amusia@vms.huji.ac.il
2004-06-01
We discuss here the history and current achievements of one of the most powerful approaches of 20th century physics--the random phase approximation (RPA) that permits us to study collective or multiparticle effects in atoms, nuclei, molecules and clusters, as well as in quantum liquids. We concentrate on RPA application to studies of isolated atoms where it permits one to disclose the collective multielectron nature of so-called Giant resonances and predict a number of others, like Interference and Intra-doublet resonances. We present general theory as well as results of concrete calculations for a number of atoms.
Frydel, Derek; Ma, Manman
2016-06-01
Using the adiabatic connection, we formulate the free energy in terms of the correlation function of a fictitious system, h_{λ}(r,r^{'}), in which interactions λu(r,r^{'}) are gradually switched on as λ changes from 0 to 1. The function h_{λ}(r,r^{'}) is then obtained from the inhomogeneous Ornstein-Zernike equation and the two equations constitute a general liquid-state framework for treating inhomogeneous fluids. The two equations do not yet constitute a closed set. In the present work we use the closure c_{λ}(r,r^{'})≈-λβu(r,r^{'}), known as the random-phase approximation (RPA). We demonstrate that the RPA is identical with the variational Gaussian approximation derived within the field-theoretical framework, originally derived and used for charged particles. We apply our generalized RPA approximation to the Gaussian core model and Coulomb charges.
An Approximate Approach to Automatic Kernel Selection.
Ding, Lizhong; Liao, Shizhong
2016-02-02
Kernel selection is a fundamental problem of kernel-based learning algorithms. In this paper, we propose an approximate approach to automatic kernel selection for regression from the perspective of kernel matrix approximation. We first introduce multilevel circulant matrices into automatic kernel selection, and develop two approximate kernel selection algorithms by exploiting the computational virtues of multilevel circulant matrices. The complexity of the proposed algorithms is quasi-linear in the number of data points. Then, we prove an approximation error bound to measure the effect of the approximation in kernel matrices by multilevel circulant matrices on the hypothesis and further show that the approximate hypothesis produced with multilevel circulant matrices converges to the accurate hypothesis produced with kernel matrices. Experimental evaluations on benchmark datasets demonstrate the effectiveness of approximate kernel selection.
Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.
2016-01-01
The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.
International Nuclear Information System (INIS)
Barnes, D.C.; Cayton, T.E.
1980-01-01
The ideal magnetohydrodynamic stability of the diffuse linear pinch is studied in the special case when the poloidal magnetic field component is small compared with the axial field component. A two-term approximation for growth rates is derived by straightforward asymptotic expansion in terms of a small parameter that is proportional to (B/sub theta//rB/sub z/). Evaluation of the second term in the expansion requires only a trivial amount of additional computation after the leading-order eigenvalue and eigenfunction are determined. For small, but finite, values of the expansion parameter the second term is found to be non-negligible compared with the leading term. The approximate solution is compared with exact solutions and the range of validity of the approximation is investigated. Implications of these results to a wide class of problems involving weakly unstable near theta-pinch configurations are discussed
Insight into organic reactions from the direct random phase approximation and its corrections
Energy Technology Data Exchange (ETDEWEB)
Ruzsinszky, Adrienn [Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 (United States); Zhang, Igor Ying; Scheffler, Matthias [Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin (Germany)
2015-10-14
The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges.
Insight into organic reactions from the direct random phase approximation and its corrections
International Nuclear Information System (INIS)
Ruzsinszky, Adrienn; Zhang, Igor Ying; Scheffler, Matthias
2015-01-01
The performance of the random phase approximation (RPA) and beyond-RPA approximations for the treatment of electron correlation is benchmarked on three different molecular test sets. The test sets are chosen to represent three typical sources of error which can contribute to the failure of most density functional approximations in chemical reactions. The first test set (atomization and n-homodesmotic reactions) offers a gradually increasing balance of error from the chemical environment. The second test set (Diels-Alder reaction cycloaddition = DARC) reflects more the effect of weak dispersion interactions in chemical reactions. Finally, the third test set (self-interaction error 11 = SIE11) represents reactions which are exposed to noticeable self-interaction errors. This work seeks to answer whether any one of the many-body approximations considered here successfully addresses all these challenges
Efficient and Accurate Log-Levy Approximations of Levy-Driven LIBOR Models
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Schoenmakers, John; Skovmand, David
2012-01-01
The LIBOR market model is very popular for pricing interest rate derivatives but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term grows exponentially fast (as a function of the tenor length). We consider a Lévy-driven ...... ratchet caps show that the approximations perform very well. In addition, we also consider the log-Lévy approximation of annuities, which offers good approximations for high-volatility regimes....
Some issues in the simulation of two-phase flows: The relative velocity
International Nuclear Information System (INIS)
Gräbel, J.; Hensel, S.; Ueberholz, P.; Farber, P.; Zeidan, D.
2016-01-01
In this paper we compare numerical approximations for solving the Riemann problem for a hyperbolic two-phase flow model in two-dimensional space. The model is based on mixture parameters of state where the relative velocity between the two-phase systems is taken into account. This relative velocity appears as a main discontinuous flow variable through the complete wave structure and cannot be recovered correctly by some numerical techniques when simulating the associated Riemann problem. Simulations are validated by comparing the results of the numerical calculation qualitatively with OpenFOAM software. Simulations also indicate that OpenFOAM is unable to resolve the relative velocity associated with the Riemann problem.
Some issues in the simulation of two-phase flows: The relative velocity
Energy Technology Data Exchange (ETDEWEB)
Gräbel, J.; Hensel, S.; Ueberholz, P.; Farber, P. [Niederrhein University of Applied Sciences, Institute for Modelling and High Performance Computing, Reinarzstraße 49, 47805 Krefeld (Germany); Zeidan, D. [School of Basic Sciences and Humanities, German Jordanian University, Amman (Jordan)
2016-06-08
In this paper we compare numerical approximations for solving the Riemann problem for a hyperbolic two-phase flow model in two-dimensional space. The model is based on mixture parameters of state where the relative velocity between the two-phase systems is taken into account. This relative velocity appears as a main discontinuous flow variable through the complete wave structure and cannot be recovered correctly by some numerical techniques when simulating the associated Riemann problem. Simulations are validated by comparing the results of the numerical calculation qualitatively with OpenFOAM software. Simulations also indicate that OpenFOAM is unable to resolve the relative velocity associated with the Riemann problem.
Experimental investigations of two-phase flow measurement using ultrasonic sensors
Abbagoni, Baba Musa
2016-01-01
This thesis presents the investigations conducted in the use of ultrasonic technology to measure two-phase flow in both horizontal and vertical pipe flows which is important for the petroleum industry. However, there are still key challenges to measure parameters of the multiphase flow accurately. Four methods of ultrasonic technologies were explored. The Hilbert-Huang transform (HHT) was first applied to the ultrasound signals of air-water flow on horizontal flow for measur...
Computer analysis of an adiabatic Stirling cryocooler using a two-phase two-component working fluid
International Nuclear Information System (INIS)
Renfroe, D.A.; Cheung, C.M.
1992-01-01
This paper describes the performance and behavior of a Stirling cyrocooler incorporating a working fluid composed of helium and nitrogen. At the operating temperature of the cryocooler (80 K), the nitrogen component will condense in the freezer section. It is shown that the phase change in the working fluid increased the heat lifted for a given size and weight of machine and the coefficient of performance. The magnitude of these effects was dependent on the mass ratio of nitrogen to helium, phase angle between the compression and expansion processes, and the ratio of the compression space volume to the expansion space volume. The optimum heat lifted performance was obtained for a mass ratio of four parts of nitrogen to one part of helium, a phase angle of approximately 100 degrees, and a volume ratio of two which resulted in a heat lifted increase of 75% over the single phase, 90 degree phase angle configuration. The coefficient of performance showed a 20% improvement
Isoscalar compression modes in relativistic random phase approximation
International Nuclear Information System (INIS)
Ma, Zhong-yu; Van Giai, Nguyen.; Wandelt, A.; Vretenar, D.; Ring, P.
2001-01-01
Monopole and dipole compression modes in nuclei are analyzed in the framework of a fully consistent relativistic random phase approximation (RRPA), based on effective mean-field Lagrangians with nonlinear meson self-interaction terms. The large effect of Dirac sea states on isoscalar strength distribution functions is illustrated for the monopole mode. The main contribution of Fermi and Dirac sea pair states arises through the exchange of the scalar meson. The effect of vector meson exchange is much smaller. For the monopole mode, RRPA results are compared with constrained relativistic mean-field calculations. A comparison between experimental and calculated energies of isoscalar giant monopole resonances points to a value of 250-270 MeV for the nuclear matter incompressibility. A large discrepancy remains between theoretical predictions and experimental data for the dipole compression mode
Generalized network modeling of capillary-dominated two-phase flow.
Raeini, Ali Q; Bijeljic, Branko; Blunt, Martin J
2018-02-01
We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network-described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312]-which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature.
Generalized network modeling of capillary-dominated two-phase flow
Raeini, Ali Q.; Bijeljic, Branko; Blunt, Martin J.
2018-02-01
We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network—described in a companion paper [A. Q. Raeini, B. Bijeljic, and M. J. Blunt, Phys. Rev. E 96, 013312 (2017), 10.1103/PhysRevE.96.013312]—which comprises pores that are divided into smaller elements called half-throats and subsequently into corners. Half-throats define the connectivity of the network at the coarsest level, connecting each pore to half-throats of its neighboring pores from their narrower ends, while corners define the connectivity of pore crevices. The corners are discretized at different levels for accurate calculation of entry pressures, fluid volumes, and flow conductivities that are obtained using direct simulation of flow on the underlying image. This paper discusses the two-phase flow model that is used to compute the averaged flow properties of the generalized network, including relative permeability and capillary pressure. We validate the model using direct finite-volume two-phase flow simulations on synthetic geometries, and then present a comparison of the model predictions with a conventional pore-network model and experimental measurements of relative permeability in the literature.
International Nuclear Information System (INIS)
Toumi, I.
1990-04-01
This thesis is devoted to the study of the Riemann problem and the construction of Godunov type numerical schemes for one or two dimensional two-phase flow models. In the first part, we study the Riemann problem for the well-known Drift-Flux, model which has been widely used for the analysis of thermal hydraulics transients. Then we use this study to construct approximate Riemann solvers and we describe the corresponding Godunov type schemes for simplified equation of state. For computation of complex two-phase flows, a weak formulation of Roe's approximate Riemann solver, which gives a method to construct a Roe-averaged jacobian matrix with a general equation of state, is proposed. For two-dimensional flows, the developed methods are based upon an approximate solver for a two-dimensional Riemann problem, according to Harten-Lax-Van Leer principles. The numerical results for standard test problems show the good behaviour of these numerical schemes for a wide range of flow conditions [fr
International Nuclear Information System (INIS)
Girardin, Mathieu
2014-01-01
Two-phase flows in Pressurized Water Reactors belong to a wide range of Mach number flows. Computing accurate approximate solutions of those flows may be challenging from a numerical point of view as classical finite volume methods are too diffusive in the low Mach regime. In this thesis, we are interested in designing and studying some robust numerical schemes that are stable for large time steps and accurate even on coarse meshes for a wide range of flow regimes. An important feature is the strategy to construct those schemes. We use a mixed implicit-explicit strategy based on an operator splitting to solve fast and slow phenomena separately. Then, we introduce a modification of a Suliciu type relaxation scheme to improve the accuracy of the numerical scheme in some regime of interest. Two approaches have been used to assess the ability of our numerical schemes to deal with a wide range of flow regimes. The first approach, based on the asymptotic preserving property, has been used for the gas dynamics equations with stiff source terms. The second approach, based on the all-regime property, has been used for the gas dynamics equations and the homogeneous two-phase flows models HRM and HEM in the low Mach regime. We obtained some robustness and stability properties for our numerical schemes. In particular, some discrete entropy inequalities are shown. Numerical evidences, in 1D and in 2D on unstructured meshes, assess the gain in term of accuracy and CPU time of those asymptotic preserving and all-regime numerical schemes in comparison with classical finite volume methods. (author) [fr
Stochastic modelling of two-phase flows including phase change
International Nuclear Information System (INIS)
Hurisse, O.; Minier, J.P.
2011-01-01
Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)
Moerk, J. Steven (Inventor); Youngquist, Robert C. (Inventor); Werlink, Rudy J. (Inventor)
1999-01-01
A quality and/or flow meter employs a capacitance probe assembly for measuring the dielectric constant of flow stream, particularly a two-phase flow stream including liquid and gas components.ne dielectric constant of the flow stream varies depending upon the volume ratios of its liquid and gas components, and capacitance measurements can therefore be employed to calculate the quality of the flow, which is defined as the volume ratio of liquid in the flow to the total volume ratio of gas and liquid in the flow. By using two spaced capacitance sensors, and cross-correlating the time varying capacitance values of each, the velocity of the flow stream can also be determined. A microcontroller-based processing circuit is employed to measure the capacitance of the probe sensors.The circuit employs high speed timer and counter circuits to provide a high resolution measurement of the time interval required to charge each capacitor in the probe assembly. In this manner, a high resolution, noise resistant, digital representation of each of capacitance value is obtained without the need for a high resolution A/D converter, or a high frequency oscillator circuit. One embodiment of the probe assembly employs a capacitor with two ground plates which provide symmetry to insure that accurate measurements are made thereby.
Calculation of the MSD two-step process with the sudden approximation
Energy Technology Data Exchange (ETDEWEB)
Yoshida, Shiro [Tohoku Univ., Sendai (Japan). Dept. of Physics; Kawano, Toshihiko [Kyushu Univ., Advanced Energy Engineering Science, Kasuga, Fukuoka (Japan)
2000-03-01
A calculation of the two-step process with the sudden approximation is described. The Green's function which connects the one-step matrix element to the two-step one is represented in {gamma}-space to avoid the on-energy-shell approximation. Microscopically calculated two-step cross sections are averaged together with an appropriate level density to give a two-step cross section. The calculated cross sections are compared with the experimental data, however the calculation still contains several simplifications at this moment. (author)
Energy Technology Data Exchange (ETDEWEB)
Botvinick, E.H.; Frais, M.A.; Shosa, D.W.; O' Connell, J.W.; Pacheco-Alvarez, J.A.; Scheinman, M.; Hattner, R.S.; Morady, F.; Faulkner, D.B.
1982-08-01
The ability of scintigraphic phase image analysis to characterize patterns of abnormal ventricular activation was investigated. The pattern of phase distribution and sequential phase changes over both right and left ventricular regions of interest were evaluated in 16 patients with normal electrical activation and wall motion and compared with those in 8 patients with an artificial pacemaker and 4 patients with sinus rhythm with the Wolff-Parkinson-White syndrome and delta waves. Normally, the site of earliest phase angle was seen at the base of the interventricular septum, with sequential change affecting the body of the septum and the cardiac apex and then spreading laterally to involve the body of both ventricles. The site of earliest phase angle was located at the apex of the right ventricle in seven patients with a right ventricular endocardial pacemaker and on the lateral left ventricular wall in one patient with a left ventricular epicardial pacemaker. In each case the site corresponded exactly to the position of the pacing electrode as seen on posteroanterior and left lateral chest X-ray films, and sequential phase changes spread from the initial focus to affect both ventricles. In each of the patients with the Wolff-Parkinson-White syndrome, the site of earliest ventricular phase angle was located, and it corresponded exactly to the site of the bypass tract as determined by endocardial mapping. In this way, four bypass pathways, two posterior left paraseptal, one left lateral and one right lateral, were correctly localized scintigraphically. On the basis of the sequence of mechanical contraction, phase image analysis provides an accurate noninvasive method of detecting abnormal foci of ventricular activation.
International Nuclear Information System (INIS)
Botvinick, E.H.; Frais, M.A.; Shosa, D.W.; O'Connell, J.W.; Pacheco-Alvarez, J.A.; Scheinman, M.; Hattner, R.S.; Morady, F.; Faulkner, D.B.
1982-01-01
The ability of scintigraphic phase image analysis to characterize patterns of abnormal ventricular activation was investigated. The pattern of phase distribution and sequential phase changes over both right and left ventricular regions of interest were evaluated in 16 patients with normal electrical activation and wall motion and compared with those in 8 patients with an artificial pacemaker and 4 patients with sinus rhythm with the Wolff-Parkinson-White syndrome and delta waves. Normally, the site of earliest phase angle was seen at the base of the interventricular septum, with sequential change affecting the body of the septum and the cardiac apex and then spreading laterally to involve the body of both ventricles. The site of earliest phase angle was located at the apex of the right ventricle in seven patients with a right ventricular endocardial pacemaker and on the lateral left ventricular wall in one patient with a left ventricular epicardial pacemaker. In each case the site corresponded exactly to the position of the pacing electrode as seen on posteroanterior and left lateral chest X-ray films, and sequential phase changes spread from the initial focus to affect both ventricles. In each of the patients with the Wolff-Parkinson-White syndrome, the site of earliest ventricular phase angle was located, and it corresponded exactly to the site of the bypass tract as determined by endocardial mapping. In this way, four bypass pathways, two posterior left paraseptal, one left lateral and one right lateral, were correctly localized scintigraphically. On the basis of the sequence of mechanical contraction, phase image analysis provides an accurate noninvasive method of detecting abnormal foci of ventricular activation
Energy Technology Data Exchange (ETDEWEB)
Shulenburger, Luke [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mattsson, Thomas Kjell Rene [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Desjarlais, Michael Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-01-01
Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.
Random signal tomographical analysis of two-phase flow
International Nuclear Information System (INIS)
Han, P.; Wesser, U.
1990-01-01
This paper reports on radiation tomography which is a useful tool for studying the internal structures of two-phase flow. However, general tomography analysis gives only time-averaged results, hence much information is lost. As a result, it is sometimes difficult to identify the flow regime; for example, the time-averaged picture does not significantly change as an annual flow develops from a slug flow. A two-phase flow diagnostic technique based on random signal tomographical analysis is developed. It extracts more information by studying the statistical variation of the measured signal with time. Local statistical parameters, including mean value, variance, skewness and flatness etc., are reconstructed from the information obtained by a general tomography technique. More important information are provided by the results. Not only the void fraction can be easily calculated, but also the flow pattern can be identified more objectively and more accurately. The experimental setup is introduced. It consisted of a two-phase flow loop, an X-ray system, a fan-like five-beam detector system and a signal acquisition and processing system. In the experiment, for both horizontal and vertical test sections (aluminum and steel tube with Di/Do = 40/45 mm), different flow situations are realized by independently adjusting air and water mass flow. Through a glass tube connected with the test section, some typical flow patterns are visualized and used for comparing with the reconstruction results
Development of highly accurate approximate scheme for computing the charge transfer integral
Energy Technology Data Exchange (ETDEWEB)
Pershin, Anton; Szalay, Péter G. [Laboratory for Theoretical Chemistry, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest (Hungary)
2015-08-21
The charge transfer integral is a key parameter required by various theoretical models to describe charge transport properties, e.g., in organic semiconductors. The accuracy of this important property depends on several factors, which include the level of electronic structure theory and internal simplifications of the applied formalism. The goal of this paper is to identify the performance of various approximate approaches of the latter category, while using the high level equation-of-motion coupled cluster theory for the electronic structure. The calculations have been performed on the ethylene dimer as one of the simplest model systems. By studying different spatial perturbations, it was shown that while both energy split in dimer and fragment charge difference methods are equivalent with the exact formulation for symmetrical displacements, they are less efficient when describing transfer integral along the asymmetric alteration coordinate. Since the “exact” scheme was found computationally expensive, we examine the possibility to obtain the asymmetric fluctuation of the transfer integral by a Taylor expansion along the coordinate space. By exploring the efficiency of this novel approach, we show that the Taylor expansion scheme represents an attractive alternative to the “exact” calculations due to a substantial reduction of computational costs, when a considerably large region of the potential energy surface is of interest. Moreover, we show that the Taylor expansion scheme, irrespective of the dimer symmetry, is very accurate for the entire range of geometry fluctuations that cover the space the molecule accesses at room temperature.
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
Investigation of Power Losses of Two-Stage Two-Phase Converter with Two-Phase Motor
Directory of Open Access Journals (Sweden)
Michal Prazenica
2011-01-01
Full Text Available The paper deals with determination of losses of two-stage power electronic system with two-phase variable orthogonal output. The simulation is focused on the investigation of losses in the converter during one period in steady-state operation. Modeling and simulation of two matrix converters with R-L load is shown in the paper. The simulation results confirm a very good time-waveform of the phase current and the system seems to be suitable for low-cost application in automotive/aerospace industries and in application with high frequency voltage sources.
Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model
Shuard, Adrian M.; Mahmud, Hisham B.; King, Andrew J.
2016-03-01
Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ɷ turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model.
Cihan, Abdullah; Birkholzer, Jens; Trevisan, Luca; Gonzalez-Nicolas, Ana; Illangasekare, Tissa
2017-01-01
Incorporating hysteresis into models is important to accurately capture the two phase flow behavior when porous media systems undergo cycles of drainage and imbibition such as in the cases of injection and post-injection redistribution of CO2 during geological CO2 storage (GCS). In the traditional model of two-phase flow, existing constitutive models that parameterize the hysteresis associated with these processes are generally based on the empirical relationships. This manuscript presents development and testing of mathematical hysteretic capillary pressure—saturation—relative permeability models with the objective of more accurately representing the redistribution of the fluids after injection. The constitutive models are developed by relating macroscopic variables to basic physics of two-phase capillary displacements at pore-scale and void space distribution properties. The modeling approach with the developed constitutive models with and without hysteresis as input is tested against some intermediate-scale flow cell experiments to test the ability of the models to represent movement and capillary trapping of immiscible fluids under macroscopically homogeneous and heterogeneous conditions. The hysteretic two-phase flow model predicted the overall plume migration and distribution during and post injection reasonably well and represented the postinjection behavior of the plume more accurately than the nonhysteretic models. Based on the results in this study, neglecting hysteresis in the constitutive models of the traditional two-phase flow theory can seriously overpredict or underpredict the injected fluid distribution during post-injection under both homogeneous and heterogeneous conditions, depending on the selected value of the residual saturation in the nonhysteretic models.
Simulation of the catalyst layer in PEMFC based on a novel two-phase lattice model
Energy Technology Data Exchange (ETDEWEB)
Zhang Jiejing; Yang Wei; Xu Li [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China); Wang Yuxin, E-mail: yxwang@tju.edu.cn [School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, Tianjin Key Laboratory of Membrane Science and Desalination Technology, Tianjin University, Tianjin 300072 (China)
2011-08-01
Highlights: > We propose a novel two phase lattice model of catalyst layer in PEMFC. > The model features a catalyst phase and a mixed ionomer and pores phase. > Transport and electrochemical reaction in the lattice are simulated. > The model enables more accurate results than pore-solid two phase model. > Profiles of oxygen level and reaction rate across catalyst layer vary with cell current. - Abstract: A lattice model of catalyst layer in proton exchange membrane fuel cells (PEMFCs), consisting of randomly distributed catalyst phase (C phase) and mixed ionomer-pore phase (IP phase), was established by means of Monte Carlo method. Transport and electrochemical reactions in the model catalyst layer were calculated. The newly proposed C-IP model was compared with previously established pore-solid two phase model. The variation of oxygen level and reaction rate along the thickness of catalyst layer with cell current was discussed. The effect of ionomer distribution across catalyst layer was studied by comparing profiles of oxygen level, reaction rate and overpotential, as well as corresponding polarization curves.
An approximate solution of the two-group critical problem for reflected slabs
International Nuclear Information System (INIS)
Ishiguro, Y.; Garcia, R.D.M.
1977-01-01
A new approximation is developed to solve two group slab problems involving two media where one of the media is infinite. The method consists in combining the P sub(L) approximation with invariance principles. Several numerical results are reported for the critical slab problem [pt
First-order corrections to random-phase approximation GW calculations in silicon and diamond
Ummels, R.T.M.; Bobbert, P.A.; van Haeringen, W.
1998-01-01
We report on ab initio calculations of the first-order corrections in the screened interaction W to the random-phase approximation polarizability and to the GW self-energy, using a noninteracting Green's function, for silicon and diamond. It is found that the first-order vertex and self-consistency
International Nuclear Information System (INIS)
Lahey, Richard T.; Drew, Donald A.
2001-01-01
This paper reviews the state-of-the-art in the prediction of multidimensional multiphase flow and heat transfer phenomena using a four field, two-fluid model. It is shown that accurate mechanistic computational fluid dynamic (CFD) predictions are possible for a wide variety of adiabatic and diabatic flows using this computational model. In particular, the model is able to predict the bubbly air/water upflow data of Serizawa (Serizawa, A., 1974. Fluid dynamic characteristics of two-phase flow. Ph.D. thesis, (Nuclear Engineering), Kyoto University, Japan), the downflow data of Wang et al. (Wang, S.K., Lee, S.J., Lahey Jr., R.T., Jones, O.C., 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13 (3), 327-343), the isosceles triangle upflow data of Lopez de Bertodano et al. (Lopez de Bertodano, M., Lahey Jr., R.T., Jones, O.C., 1994b. Phase distribution in bubbly two-phase flow in vertical ducts. Int. J. Multiphase Flow 20 (5), 805-818), the heated annular R-113 subcooled boiling data of Velidandala, et al. (Velidandla, V., Pulta, S., Roy, P., Kaira, S.P., 1995. Velocity field in turbulent subcooled boiling flow. ASME Preprint HTD-314, 107-123) and the R-113 CHF data of Hino and Ueda (Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled boiling-part 2, flow characteristics. Int. J. Multiphase Flow 11, 283-297). It can also predict external two-phase flows, such as those for spreading two-phase jets (Bonetto, F., Lahey Jr., R.T., 1993. An experimental study on air carryunder due to a plunging liquid jet. Int. J. Multiphase Flow 19 (2), 281-294) and multiphase flows around the hull of naval surface ships (Carrica, P.M., Bonetto, F., Drew, D.A., Lahey, R.T., 1999. A polydispersed model for bubbly two-phase flow around a surface ship. Int. J. Multiphase Flow 25 (2), 257-305)
Estimation of the sugar cane cultivated area from LANDSAT images using the two phase sampling method
Parada, N. D. J. (Principal Investigator); Cappelletti, C. A.; Mendonca, F. J.; Lee, D. C. L.; Shimabukuro, Y. E.
1982-01-01
A two phase sampling method and the optimal sampling segment dimensions for the estimation of sugar cane cultivated area were developed. This technique employs visual interpretations of LANDSAT images and panchromatic aerial photographs considered as the ground truth. The estimates, as a mean value of 100 simulated samples, represent 99.3% of the true value with a CV of approximately 1%; the relative efficiency of the two phase design was 157% when compared with a one phase aerial photographs sample.
Importance of self-consistency in relativistic continuum random-phase approximation calculations
International Nuclear Information System (INIS)
Yang Ding; Cao Ligang; Tian Yuan; Ma Zhongyu
2010-01-01
A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.
Directory of Open Access Journals (Sweden)
Giorgos Minas
2017-07-01
Full Text Available In order to analyse large complex stochastic dynamical models such as those studied in systems biology there is currently a great need for both analytical tools and also algorithms for accurate and fast simulation and estimation. We present a new stochastic approximation of biological oscillators that addresses these needs. Our method, called phase-corrected LNA (pcLNA overcomes the main limitations of the standard Linear Noise Approximation (LNA to remain uniformly accurate for long times, still maintaining the speed and analytically tractability of the LNA. As part of this, we develop analytical expressions for key probability distributions and associated quantities, such as the Fisher Information Matrix and Kullback-Leibler divergence and we introduce a new approach to system-global sensitivity analysis. We also present algorithms for statistical inference and for long-term simulation of oscillating systems that are shown to be as accurate but much faster than leaping algorithms and algorithms for integration of diffusion equations. Stochastic versions of published models of the circadian clock and NF-κB system are used to illustrate our results.
Vapor Compressor Driven Hybrid Two-Phase Loop, Phase I
National Aeronautics and Space Administration — This Small Business Innovation Research Phase I project will demonstrate a vapor compressor driven hybrid two-phase loop technology. The hybrid two-phase loop...
Modified random phase approximation for multipole excitations at finite temperature
International Nuclear Information System (INIS)
Nguyen Dinh Dang
1991-01-01
The modified finite temperature random phase approximation (modified FT-RPA) has been constructed with taking the influence of thermostat on the structure of quansiparticles into account. The modified FT-RPA linear response for electric quadrupole (λ π = 2 + ) and octupole (λ π = 3 - ) excitations in 5 8Ni has been calculated as a function of the nuclear temperature. As compared to the conventional FT-RPA the modified FT-RPA has given a stronger spreading for the strength distribution of quandrupole excitations at finite temperature T ≤ 3MeV. (author). 22 refs; 4 figs; 2 tabs
Developing two-phase flow modelling concepts for rock fractures
Energy Technology Data Exchange (ETDEWEB)
Keto, V. (Fortum Nuclear Services Oy, Espoo (Finland))
2010-01-15
The Finnish nuclear waste disposal company, Posiva Oy, is planning an underground repository for spent nuclear fuel to be constructed on the island of Olkiluoto on the south-west coast of Finland. One element of the site investigations conducted at Olkiluoto is the excavation of the underground rock characterisation facility (ONKALO) that will be extended to the final disposal depth (approximately -400 m). The bedrock around the excavated tunnel volume is fully saturated with groundwater, which water commonly contains a mixture of dissolved gases. These gases remain dissolved due to the high hydrostatic pressure. During tunnel excavation work the natural hydrostatic pressure field is disturbed and the water pressure will decrease close to the atmospheric pressure in the immediate vicinity of the tunnel. During this pressure drop two-phase flow conditions (combined flow of both water and gas) may develop in the vicinity of the underground opening, as the dissolved gas is exsoluted under the low pressure (the term exsolution refers here to release of the dissolved gas molecules from the water phase into a separate gas phase). This report steers towards concept development for numerical two-phase flow modeling for fractured rock. The focus is on the description of gas phase formation process under disturbed hydraulic conditions by exsolution of dissolved gases from groundwater, and on understanding the effects of a possibly formed gas phase on groundwater flow conditions in rock fractures. A mathematical model of three mutually coupled nonlinear partial differential equations for two-phase flow is presented and corresponding constitutional relationships are introduced and discussed. Illustrative numerical simulations are performed in a simplified setting using COMSOL Multiphysics 3.5a - software package. Shortcomings and conceptual problems are discussed. (orig.)
Developing two-phase flow modelling concepts for rock fractures
International Nuclear Information System (INIS)
Keto, V.
2010-01-01
The Finnish nuclear waste disposal company, Posiva Oy, is planning an underground repository for spent nuclear fuel to be constructed on the island of Olkiluoto on the south-west coast of Finland. One element of the site investigations conducted at Olkiluoto is the excavation of the underground rock characterisation facility (ONKALO) that will be extended to the final disposal depth (approximately -400 m). The bedrock around the excavated tunnel volume is fully saturated with groundwater, which water commonly contains a mixture of dissolved gases. These gases remain dissolved due to the high hydrostatic pressure. During tunnel excavation work the natural hydrostatic pressure field is disturbed and the water pressure will decrease close to the atmospheric pressure in the immediate vicinity of the tunnel. During this pressure drop two-phase flow conditions (combined flow of both water and gas) may develop in the vicinity of the underground opening, as the dissolved gas is exsoluted under the low pressure (the term exsolution refers here to release of the dissolved gas molecules from the water phase into a separate gas phase). This report steers towards concept development for numerical two-phase flow modeling for fractured rock. The focus is on the description of gas phase formation process under disturbed hydraulic conditions by exsolution of dissolved gases from groundwater, and on understanding the effects of a possibly formed gas phase on groundwater flow conditions in rock fractures. A mathematical model of three mutually coupled nonlinear partial differential equations for two-phase flow is presented and corresponding constitutional relationships are introduced and discussed. Illustrative numerical simulations are performed in a simplified setting using COMSOL Multiphysics 3.5a - software package. Shortcomings and conceptual problems are discussed. (orig.)
High-velocity two-phase flow two-dimensional modeling
International Nuclear Information System (INIS)
Mathes, R.; Alemany, A.; Thilbault, J.P.
1995-01-01
The two-phase flow in the nozzle of a LMMHD (liquid metal magnetohydrodynamic) converter has been studied numerically and experimentally. A two-dimensional model for two-phase flow has been developed including the viscous terms (dragging and turbulence) and the interfacial mass, momentum and energy transfer between the phases. The numerical results were obtained by a finite volume method based on the SIMPLE algorithm. They have been verified by an experimental facility using air-water as a simulation pair and a phase Doppler particle analyzer for velocity and droplet size measurement. The numerical simulation of a lithium-cesium high-temperature pair showed that a nearly homogeneous and isothermal expansion of the two phases is possible with small pressure losses and high kinetic efficiencies. In the throat region a careful profiling is necessary to reduce the inertial effects on the liquid velocity field
Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method
Directory of Open Access Journals (Sweden)
Yunfeng Dai
2017-01-01
Full Text Available To describe accurately the flow characteristic of fracture scale displacements of immiscible fluids, an incompressible two-phase (crude oil and water flow model incorporating interfacial forces and nonzero contact angles is developed. The roughness of the two-dimensional synthetic rough-walled fractures is controlled with different fractal dimension parameters. Described by the Navier–Stokes equations, the moving interface between crude oil and water is tracked using level set method. The method accounts for differences in densities and viscosities of crude oil and water and includes the effect of interfacial force. The wettability of the rough fracture wall is taken into account by defining the contact angle and slip length. The curve of the invasion pressure-water volume fraction is generated by modeling two-phase flow during a sudden drainage. The volume fraction of water restricted in the rough-walled fracture is calculated by integrating the water volume and dividing by the total cavity volume of the fracture while the two-phase flow is quasistatic. The effect of invasion pressure of crude oil, roughness of fracture wall, and wettability of the wall on two-phase flow in rough-walled fracture is evaluated.
Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits
Energy Technology Data Exchange (ETDEWEB)
Yang, Ping; Zou, Ping [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China); Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China)
2012-10-01
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. -- Highlights: ► Our work shows that the adiabatic approximations may work also in the ultrastrong coupling limit. ► Both of the approximation methods are valid in a large range of coupling strength, including the ultrastrong coupling regime. ► The results of the approximate formula meet well the exact numerical solution.
New realisation of Preisach model using adaptive polynomial approximation
Liu, Van-Tsai; Lin, Chun-Liang; Wing, Home-Young
2012-09-01
Modelling system with hysteresis has received considerable attention recently due to the increasing accurate requirement in engineering applications. The classical Preisach model (CPM) is the most popular model to demonstrate hysteresis which can be represented by infinite but countable first-order reversal curves (FORCs). The usage of look-up tables is one way to approach the CPM in actual practice. The data in those tables correspond with the samples of a finite number of FORCs. This approach, however, faces two major problems: firstly, it requires a large amount of memory space to obtain an accurate prediction of hysteresis; secondly, it is difficult to derive efficient ways to modify the data table to reflect the timing effect of elements with hysteresis. To overcome, this article proposes the idea of using a set of polynomials to emulate the CPM instead of table look-up. The polynomial approximation requires less memory space for data storage. Furthermore, the polynomial coefficients can be obtained accurately by using the least-square approximation or adaptive identification algorithm, such as the possibility of accurate tracking of hysteresis model parameters.
Collective excitations in the Penson-Kolb model: A generalized random-phase-approximation study
International Nuclear Information System (INIS)
Roy, G.K.; Bhattacharyya, B.
1997-01-01
The evolution of the superconducting ground state of the half-filled Penson-Kolb model is examined as a function of the coupling constant using a mean-field approach and the generalized random phase approximation (RPA) in two and three dimensions. On-site singlet pairs hop to compete against single-particle motion in this model, giving the coupling constant a strong momentum dependence. There is a pronounced bandwidth enhancement effect that converges smoothly to a finite value in the strong-coupling (Bose) regime. The low-lying collective excitations evaluated in generalized RPA show a linear dispersion and a gradual crossover from the weak-coupling (BCS) limit to the Bose regime; the mode velocity increases monotonically in sharp contrast to the attractive Hubbard model. Analytical results are derived in the asymptotic limits. copyright 1997 The American Physical Society
Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media
Chen, J.
2014-06-03
This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow. 2014 Jie Chen et al.
Coupling Two-Phase Fluid Flow with Two-Phase Darcy Flow in Anisotropic Porous Media
Directory of Open Access Journals (Sweden)
Jie Chen
2014-06-01
Full Text Available This paper reports a numerical study of coupling two-phase fluid flow in a free fluid region with two-phase Darcy flow in a homogeneous and anisotropic porous medium region. The model consists of coupled Cahn-Hilliard and Navier-Stokes equations in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition on the interface between the free flow and the porous media regions. Obtained results have shown the anisotropic properties effect on the velocity and pressure of the two-phase flow.
Two-phase flow field simulation of horizontal steam generators
Energy Technology Data Exchange (ETDEWEB)
Rabiee, Ataollah; Kamalinia, Amir Hossein; Hadad, Kamal [School of Mechanical Engineering, Shiraz University, Shiraz (Iran, Islamic Republic of)
2017-02-15
The analysis of steam generators as an interface between primary and secondary circuits in light water nuclear power plants is crucial in terms of safety and design issues. VVER-1000 nuclear power plants use horizontal steam generators which demand a detailed thermal hydraulics investigation in order to predict their behavior during normal and transient operational conditions. Two phase flow field simulation on adjacent tube bundles is important in obtaining logical numerical results. However, the complexity of the tube bundles, due to geometry and arrangement, makes it complicated. Employment of porous media is suggested to simplify numerical modeling. This study presents the use of porous media to simulate the tube bundles within a general-purpose computational fluid dynamics code. Solved governing equations are generalized phase continuity, momentum, and energy equations. Boundary conditions, as one of the main challenges in this numerical analysis, are optimized. The model has been verified and tuned by simple two-dimensional geometry. It is shown that the obtained vapor volume fraction near the cold and hot collectors predict the experimental results more accurately than in previous studies.
Nonequilibrium dynamics of spin-boson models from phase-space methods
Piñeiro Orioli, Asier; Safavi-Naini, Arghavan; Wall, Michael L.; Rey, Ana Maria
2017-09-01
An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase-space methods such as the truncated Wigner approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [J. Schachenmayer, A. Pikovski, and A. M. Rey, Phys. Rev. X 5, 011022 (2015), 10.1103/PhysRevX.5.011022]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations to our coupled spin-boson model. This allows us, in principle, to study how systematically adding higher-order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model, which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for an arbitrary number of bosonic modes.
Calculating beta decay in the deformed self-consistent quasiparticle random phase approximation
Energy Technology Data Exchange (ETDEWEB)
Engel, Jonathan, E-mail: engelj@physics.unc.edu [Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 (United States); Mustonen, M. T., E-mail: mika.mustonen@yale.edu [Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255 (United States); Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06052 (United States)
2016-06-21
We discuss a recent global calculation of beta-decay rates in the self-consistent Skyrme quasiparticle random phase approximation (QRPA), with axially symmetric nuclear deformation treated explicitly. The calculation makes makes use of the finite-amplitude method, first proposed by Nakatsukasa and collaborators, to reduce computation time. The results are comparable in quality to those of several other global QRPA calculations. The QRPA may have reached the limit of its accuracy.
Neutrino-nucleus reaction rates based on the relativistic quasiparticle random phase approximation
International Nuclear Information System (INIS)
Paar, N.; Vretenar, D.; Marketin, T.; Ring, P.
2008-01-01
Neutrino-nucleus cross sections are described in a novel theoretical framework where the weak interaction of leptons with hadrons is expressed in the standard current-current form, the nuclear ground state is described in the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited states are calculated in the relativistic quasiparticle random phase approximation. The model is employed in studies of neutrino-nucleus reactions in several test cases
Dynamical Mean Field Approximation Applied to Quantum Field Theory
Akerlund, Oscar; Georges, Antoine; Werner, Philipp
2013-12-04
We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar phi^4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents nu and beta. We also map out the phase diagram in four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice phi^4-theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behaviour away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is sec...
Improvement of Tone's method with two-term rational approximation
International Nuclear Information System (INIS)
Yamamoto, Akio; Endo, Tomohiro; Chiba, Go
2011-01-01
An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method. (author)
Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows
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.
Frictional pressure drop of gas liquid two-phase flow in pipes
International Nuclear Information System (INIS)
Shannak, Benbella A.
2008-01-01
Experiments of air water two-phase flow frictional pressure drop of vertical and horizontal smooth and relatively rough pipes were conducted, respectively. The result demonstrated that the frictional pressure drop increases with increasing relative roughness of the pipe. However, the influence of the relative roughness becomes more evident at higher vapour quality and higher mass flux. A new prediction model for frictional pressure drop of two-phase flow in pipes is proposed. The model includes a new definition of the Reynolds number and the friction factor of two-phase flow. The proposed model fits the presented experimental data very well, for vertical, horizontal, smooth and rough pipes. Therefore, the reproductive accuracy of the model is tested on the experimental data existing in the open literature and compared with the most common models. The statistical comparison, based on the Friedel's Data-Bank containing of about 16,000 measured data, demonstrated that the proposed model is the best overall agreement with the data. The model was tested for a wide range of flow types, fluid systems, physical properties and geometrical parameters, typically encountered in industrial piping systems. Hence, calculating based on the new approach is sufficiently accurate for engineering purposes
The design of a two-phase radiolabelled meal for gastric emptying studies
International Nuclear Information System (INIS)
Mather, S.J.; Ellison, D.; Nightingale, J.; Kamm, M.; Britton, K.E.
1991-01-01
A meal intended for use in gastric emptying studies must be highly reproducible, must provide a normal physiological stimulus in terms of bulk, calorie content and composition and must employ stable radiotracers which accurately reflect in their biodistribution, the fate of the two-phases. This is particularly important in a field, such as gastric emptying, where so many variables may influence the results. A conventional pancake and orange juice were chosen as suitable vehicles for the solid and liquid phases. 111 In-labelled resin beads were used as the solid-phase marker and a variety of 99 Tc m -labelled radiopharmaceuticals including pertechnetate, DTPA and colloid forms were investigated as liquid-phase markers. Prior to administration to patients, the stability of the phases and their interactions in vitro were investigated. The use of 99 Tc m -DTPA resulted in a loss of 111 In from solid to liquid phase. All non-colloidal markers exhibited a tendency for adsorption onto solid phase. Colloidal markers including rhenium and antimony sulphide colloids showed the truest delineation of the liquid phase. (author)
Propagation of small disturbances in two phases, one component flow (1963)
International Nuclear Information System (INIS)
Boure, J.
1963-01-01
A small disturbance is, shown to give rise to two waves: a pressure (sonic) wave and a continuity wave. Their propagation velocities are calculated. These velocities are independent of the disturbance amplitude. The sonic velocity is primarily a function of that one corresponding to the same medium with no flow and of the liquid phase velocity. It is also a function of the physical properties of the phases on the saturation line, of the slip laws and of the void fraction. The continuity wave velocity is only a function of the slip laws, of the void fraction and of the velocity of either phase. It appears two kinds of critical flow rates which are calculated. The void fraction and the liquid and gas velocities variations are calculated. These results are extended to the case of a real loop and an approximative method is given for the treatment of this case. (author) [fr
Comparison of Two-Phase Pipe Flow in OpenFOAM with a Mechanistic Model
International Nuclear Information System (INIS)
Shuard, Adrian M; Mahmud, Hisham B; King, Andrew J
2016-01-01
Two-phase pipe flow is a common occurrence in many industrial applications such as power generation and oil and gas transportation. Accurate prediction of liquid holdup and pressure drop is of vast importance to ensure effective design and operation of fluid transport systems. In this paper, a Computational Fluid Dynamics (CFD) study of a two-phase flow of air and water is performed using OpenFOAM. The two-phase solver, interFoam is used to identify flow patterns and generate values of liquid holdup and pressure drop, which are compared to results obtained from a two-phase mechanistic model developed by Petalas and Aziz (2002). A total of 60 simulations have been performed at three separate pipe inclinations of 0°, +10° and -10° respectively. A three dimensional, 0.052m diameter pipe of 4m length is used with the Shear Stress Transport (SST) k - ω turbulence model to solve the turbulent mixtures of air and water. Results show that the flow pattern behaviour and numerical values of liquid holdup and pressure drop compare reasonably well to the mechanistic model. (paper)
Analytical prediction of the electromagnetic torques in single-phase and two-phase ac motors
Energy Technology Data Exchange (ETDEWEB)
Popescu, M.
2004-07-01
mathematical models can be used in preliminary design for further optimisation and accurate estimation in complex numerical models. Another important feature of the analytical models for single-phase and two-phase AC motors, is that they can be directly implemented in any suitable electrical drives control strategy. (orig.)
Phase transitions in nonequilibrium traffic theory
Energy Technology Data Exchange (ETDEWEB)
Zhang, H.M.
2000-02-01
This paper uses the center difference scheme of Lax-Friedrichs to numerically solve a newly developed continuum traffic flow theory and the kinematic theory of Lighthill and Whitham, and Richards, and it studies the flow-concentration phase transitions in flow containing both shock and rarefaction waves. A homogeneous road with finite length was modeled by both theories. Numerical simulations show that both theories yield nearly identical results for two representative Riemann problems--one has a shock solution and the other a rarefaction wave solution. Their phase transition curves, however, are different: those derived from the new theory have two branches--one for acceleration flow and one for deceleration flow, whereas those derived from the LWR theory comprise a single curve--the equilibrium curve. The phase transition curves in the shock case agree well with certain experimental observations but disagree with others. This disagreement may be resolved by studying transitions among nonequilibrium states, which awaits further development of a more accurate finite difference approximation of the nonequilibrium theory.
Stratified steady and unsteady two-phase flows between two parallel plates
International Nuclear Information System (INIS)
Sim, Woo Gun
2006-01-01
To understand fluid dynamic forces acting on a structure subjected to two-phase flow, it is essential to get detailed information about the characteristics of two-phase flow. Stratified steady and unsteady two-phase flows between two parallel plates have been studied to investigate the general characteristics of the flow related to flow-induced vibration. Based on the spectral collocation method, a numerical approach has been developed for the unsteady two-phase flow. The method is validated by comparing numerical result to analytical one given for a simple harmonic two-phase flow. The flow parameters for the steady two-phase flow, such as void fraction and two-phase frictional multiplier, are evaluated. The dynamic characteristics of the unsteady two-phase flow, including the void fraction effect on the complex unsteady pressure, are illustrated
Grima, Ramon
2011-11-01
The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
Energy Technology Data Exchange (ETDEWEB)
Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)
2015-01-15
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming.
Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.
Approximating high-dimensional dynamics by barycentric coordinates with linear programming
International Nuclear Information System (INIS)
Hirata, Yoshito; Aihara, Kazuyuki; Suzuki, Hideyuki; Shiro, Masanori; Takahashi, Nozomu; Mas, Paloma
2015-01-01
The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data
Bridge density functional approximation for non-uniform hard core repulsive Yukawa fluid
International Nuclear Information System (INIS)
Zhou Shiqi
2008-01-01
In this work, a bridge density functional approximation (BDFA) (J. Chem. Phys. 112, 8079 (2000)) for a non-uniform hard-sphere fluid is extended to a non-uniform hard-core repulsive Yukawa (HCRY) fluid. It is found that the choice of a bulk bridge functional approximation is crucial for both a uniform HCRY fluid and a non-uniform HCRY fluid. A new bridge functional approximation is proposed, which can accurately predict the radial distribution function of the bulk HCRY fluid. With the new bridge functional approximation and its associated bulk second order direct correlation function as input, the BDFA can be used to well calculate the density profile of the HCRY fluid subjected to the influence of varying external fields, and the theoretical predictions are in good agreement with the corresponding simulation data. The calculated results indicate that the present BDFA captures quantitatively the phenomena such as the coexistence of solid-like high density phase and low density gas phase, and the adsorption properties of the HCRY fluid, which qualitatively differ from those of the fluids combining both hard-core repulsion and an attractive tail. (condensed matter: structure, thermal and mechanical properties)
Collapse of the random-phase approximation: Examples and counter-examples from the shell model
International Nuclear Information System (INIS)
Johnson, Calvin W.; Stetcu, Ionel
2009-01-01
The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a 'phase transition' in the literature). The order of the transition is important when one applies the random-phase approximation (RPA) to the of the Hartree-Fock wave function: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as 'collapse' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time nontrivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.
Unsteady interfacial coupling of two-phase flow models
International Nuclear Information System (INIS)
Hurisse, O.
2006-01-01
The primary coolant circuit in a nuclear power plant contains several distinct components (vessel, core, pipes,...). For all components, specific codes based on the discretization of partial differential equations have already been developed. In order to obtain simulations for the whole circuit, the interfacial coupling of these codes is required. The approach examined within this work consists in coupling codes by providing unsteady information through the coupling interface. The numerical technique relies on the use of an interface model, which is combined with the basic strategy that was introduced by Greenberg and Leroux in order to compute approximations of steady solutions of non-homogeneous hyperbolic systems. Three different coupling cases have been examined: (i) the coupling of a one-dimensional Euler system with a two-dimensional Euler system; (ii) the coupling of two distinct homogeneous two-phase flow models; (iii) the coupling of a four-equation homogeneous model with the standard two-fluid model. (author)
International Nuclear Information System (INIS)
Tong Yunxian; Wang Wenran
1992-03-01
The mass flowrate and steam quality measuring of two phase flowrate is an essential issue in the tests of loss-of-coolant accident (LOCA). The spatial stochastic distribution of phase concentration would cause a differential pressure noise when two phase flow is crossing a throttling set. Under the assumption of that the variance of disperse phase concentration is proportional to its mean phase concentration and by using the separated flow model of two phase flow, it has demonstrated that the variance of noise of differential pressure square root is approximately proportional to the flowrate of disperse phase. Thus, a theoretical model for measuring mass flowrate and quality of two phase flow by noise measurement is developed. It indicates that there is a possibility to measure two phase flowrate and steam quality by using the simple theoretical model and a single throttling set
Counter-current gas-liquid two-phase flow in a narrow rectangular channel
International Nuclear Information System (INIS)
Sohn, Byung Hu; Kim, Byong Joo
2000-01-01
A study of counter-current two-phase flow in a narrow rectangular channel has been performed. Two-phase flow patterns and void fractions were experimentally studied in a 760 mm long and 100 mm wide test section with 3.0 mm gap. The resulting data have been compared to previous transition criteria and empirical correlations. The comparison of experimental data to the transition criteria developed by Taitel and Barnea showed good agreement for the bubbly-to-slug transition. For the criteria of Mishima and Ishii to be applicable to the slug to churn transition, a new model seems to be needed for the accurate prediction of the distribution parameter for the counter-current flow in narrow rectangular channels. For the churn-to-annular transition the model of Taitel and Barnea was found to be close to the experimental data. However the model should be improved in conjunction with the channel geometry to accurately predict the counter-current flow limitation and flow transition. It was verified the distribution parameter was well-correlated by the drift-flux model. The distribution parameter for the present study was found to be about 1.2 for all flow regimes except 1.0 for an annular flow. (author)
On the use of nuclear magnetic resonance to characterize vertical two-phase bubbly flows
International Nuclear Information System (INIS)
Lemonnier, H.; Jullien, P.
2011-01-01
Research highlights: → We provide a complete theory of the PGSE measurement in single and two-phase flow. → Friction velocity can be directly determinated from measured velocity distributions. → Fast determination of moments shorten PGSE process with small loss of accuracy. → Turbulent diffusion measurements agree well with known trends and existing models. → We think NMR can be a tool to benchmark thermal anemometry in two-phase flow. - Abstract: Since the pioneering work of who showed that NMR can be used to measure accurately the mean liquid velocity and void fraction in two-phase pipe flow, it has been shown that NMR signal can also characterize the turbulent eddy diffusivity and velocity fluctuations. In this paper we provide an in depth validation of these statements together with a clarification of the nature of the mean velocity that is actually measured by NMR PFGSE sequence. The analysis shows that the velocity gradient at the wall is finely space-resolved and allows the determination of the friction velocity in single-phase flows. Next turbulent diffusion measurements in two-phase flows are presented, analyzed and compared to existing data and models. It is believed that NMR velocity measurement is sufficiently understood that it can be utilized to benchmark thermal anemometry in two-phase flows. Theoretical results presented in this paper also show how this can be undertaken.
Three-dimensional multi-relaxation-time lattice Boltzmann front-tracking method for two-phase flow
International Nuclear Information System (INIS)
Xie Hai-Qiong; Zeng Zhong; Zhang Liang-Qi
2016-01-01
We developed a three-dimensional multi-relaxation-time lattice Boltzmann method for incompressible and immiscible two-phase flow by coupling with a front-tracking technique. The flow field was simulated by using an Eulerian grid, an adaptive unstructured triangular Lagrangian grid was applied to track explicitly the motion of the two-fluid interface, and an indicator function was introduced to update accurately the fluid properties. The surface tension was computed directly on a triangular Lagrangian grid, and then the surface tension was distributed to the background Eulerian grid. Three benchmarks of two-phase flow, including the Laplace law for a stationary drop, the oscillation of a three-dimensional ellipsoidal drop, and the drop deformation in a shear flow, were simulated to validate the present model. (paper)
Quantum mechanics of the fractional-statistics gas: Random-phase approximation
International Nuclear Information System (INIS)
Dai, Q.; Levy, J.L.; Fetter, A.L.; Hanna, C.B.; Laughlin, R.B.
1992-01-01
A description of the fractional-statistics gas based on the complete summation of Hartree, Fock, ladder and bubble diagrams is presented. The superfluid properties identified previously in the random-phase-approximation (RPA) calculation of Fetter, Hanna, and Laughlin [Phys. Rev. B 39, 9679 (1989)] are substantially confirmed. The discrepancy between the RPA sound speed and the Hartree-Fock bulk modulus is found to be eliminated. The unusual Hall-effect behavior is found to vanish for the Bose gas test case but not for the fractional-statistics gas, implying that it is physically correct. Excellent agreement is obtained with the collective-mode dispersion obtained numerically by Xie, He, and Das Sarma [Phys. Rev. Lett. 65, 649 (1990)
Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Samier, Pierre
2018-03-01
In this work, we extend, to two-phase flow, the single-phase Darcy flow model proposed in [26], [12] in which the (d - 1)-dimensional flow in the fractures is coupled with the d-dimensional flow in the matrix. Three types of so called hybrid-dimensional two-phase Darcy flow models are proposed. They all account for fractures acting either as drains or as barriers, since they allow pressure jumps at the matrix-fracture interfaces. The models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces. The three models differ by their transmission conditions at matrix fracture interfaces: while the first model accounts for the nonlinear two-phase Darcy flux conservations, the second and third ones are based on the linear single phase Darcy flux conservations combined with different approximations of the mobilities. We adapt the Vertex Approximate Gradient (VAG) scheme to this problem, in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes. Several test cases are presented to compare our hybrid-dimensional models to the generic equi-dimensional model, in which fractures have the same dimension as the matrix, leading to deep insight about the quality of the proposed reduced models.
Broglia, Riccardo; Durante, Danilo
2017-11-01
This paper focuses on the analysis of a challenging free surface flow problem involving a surface vessel moving at high speeds, or planing. The investigation is performed using a general purpose high Reynolds free surface solver developed at CNR-INSEAN. The methodology is based on a second order finite volume discretization of the unsteady Reynolds-averaged Navier-Stokes equations (Di Mascio et al. in A second order Godunov—type scheme for naval hydrodynamics, Kluwer Academic/Plenum Publishers, Dordrecht, pp 253-261, 2001; Proceedings of 16th international offshore and polar engineering conference, San Francisco, CA, USA, 2006; J Mar Sci Technol 14:19-29, 2009); air/water interface dynamics is accurately modeled by a non standard level set approach (Di Mascio et al. in Comput Fluids 36(5):868-886, 2007a), known as the single-phase level set method. In this algorithm the governing equations are solved only in the water phase, whereas the numerical domain in the air phase is used for a suitable extension of the fluid dynamic variables. The level set function is used to track the free surface evolution; dynamic boundary conditions are enforced directly on the interface. This approach allows to accurately predict the evolution of the free surface even in the presence of violent breaking waves phenomena, maintaining the interface sharp, without any need to smear out the fluid properties across the two phases. This paper is aimed at the prediction of the complex free-surface flow field generated by a deep-V planing boat at medium and high Froude numbers (from 0.6 up to 1.2). In the present work, the planing hull is treated as a two-degree-of-freedom rigid object. Flow field is characterized by the presence of thin water sheets, several energetic breaking waves and plungings. The computational results include convergence of the trim angle, sinkage and resistance under grid refinement; high-quality experimental data are used for the purposes of validation, allowing to
International Nuclear Information System (INIS)
Tamura, R.; Shibata, K.; Nishimoto, K.; Takeuchi, S.; Edagawa, K.; Saitoh, K.; Isobe, M.; Ueda, Y.
2005-01-01
An antiparallel orientational transition is reported for an intermetallic compound, i.e., Cd 6 Ca crystal, which is a 1/1-1/1-1/1 crystalline approximant to the icosahedral quasicrystal Cd 5.7 Ca. A group theoretical analysis based on the Landau theory predicts that the space group of the low-temperature phase is either C2/c or C2/m, in good agreement with the observations. Accordingly, two types of orientational orderings of Cd 4 tetrahedra, which are located in the center of icosahedral clusters, may occur below 100 K: In both cases, the Cd 4 tetrahedra are orientationally ordered in an antiparallel fashion along the [110] direction of the high temperature body-centered-cubic phase. Such a transition in a metal is reminiscent of orientational transitions in molecular solids
Using function approximation to determine neural network accuracy
International Nuclear Information System (INIS)
Wichman, R.F.; Alexander, J.
2013-01-01
Many, if not most, control processes demonstrate nonlinear behavior in some portion of their operating range and the ability of neural networks to model non-linear dynamics makes them very appealing for control. Control of high reliability safety systems, and autonomous control in process or robotic applications, however, require accurate and consistent control and neural networks are only approximators of various functions so their degree of approximation becomes important. In this paper, the factors affecting the ability of a feed-forward back-propagation neural network to accurately approximate a non-linear function are explored. Compared to pattern recognition using a neural network for function approximation provides an easy and accurate method for determining the network's accuracy. In contrast to other techniques, we show that errors arising in function approximation or curve fitting are caused by the neural network itself rather than scatter in the data. A method is proposed that provides improvements in the accuracy achieved during training and resulting ability of the network to generalize after training. Binary input vectors provided a more accurate model than with scalar inputs and retraining using a small number of the outlier x,y pairs improved generalization. (author)
DEFF Research Database (Denmark)
Ratkovich, Nicolas Rios; Bentzen, Thomas Ruby; Majumder, S.
Gas-liquid two-phase flows are presented everywhere in industrial processes (i.e. gas-oil pipelines). In spite of the common occurrence of these two-phase flows, their understanding is limited compared to single-phase flows. Different studies on two-phase flow have focus on developing empirical...... in the literature but none of them is enough robust and suitable for different conditions (i.e. flow patterns, gas-liquid combinations, pipe inclination angles, etc.). This clearly represents a drawback and more research in required on this field....... correlations based on large sets of experiment data for void fraction [1,2] and pressure drop [3,4] which have proven to be accurate for the specific condition that their where developed for. Currently, dozens of void fraction and pressure drop correlations for different flow patterns are available...
Garza, Alejandro J.; Bulik, Ireneusz W.; Alencar, Ana G. Sousa; Sun, Jianwei; Perdew, John P.; Scuseria, Gustavo E.
2016-04-01
Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add - without introducing double counting, self-interaction, or increase in cost - the missing correlation to these methods via meta-GGA (generalised gradient approximation) density functionals (Tao-Perdew-Staroverov-Scuseria and strongly constrained and appropriately normed). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with density functional theory and the direct random phase approximation, respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.
Two-phase flow characteristics in BWRs
International Nuclear Information System (INIS)
Katono, Kenichi; Aoyama, Goro; Nagayoshi, Takuji; Yasuda, Kenichi; Nishida, Koji
2014-01-01
Reliable prediction of two-phase flow characteristics is important for safety and economy improvements of BWR plants. We have been developing two-phase flow measurement tools and techniques for BWR thermal hydraulic conditions, such as a 3D time-averaged X-ray CT system, an ultrasonic liquid film sensor and a wire-mesh sensor. We applied the developed items in experiments using the multi-purpose steam-water test facility known as HUSTLE, which can simulate two-phase thermal-hydraulic conditions in a BWR reactor pressure vessel, and we constructed a detailed instrumentation database. We validated a 3D two-phase flow simulator using the database and developed the reactor internal two-phase flow analysis system. (author)
Finite-temperature random-phase approximation for spectroscopic properties of neon plasmas
International Nuclear Information System (INIS)
Colgan, J.; Collins, L. A.; Fontes, C. J.; Csanak, G.
2007-01-01
A finite-temperature random-phase approximation (FTRPA) is applied to calculate oscillator strengths for excitations in hot and dense plasmas. Application of the FTRPA provides a convenient, self-consistent method with which to explore coupled-channel effects of excited electrons in a dense plasma. We present FTRPA calculations that include coupled-channel effects. The inclusion of these effects is shown to cause significant differences in the oscillator strength for a prototypical case of 1 P excitation in neon when compared with single-channel and with average-atom calculations. Trends as a function of temperature and density are also discussed
International Nuclear Information System (INIS)
Almbladh, C.-O.; Ekenberg, U.; Pedroza, A.C.
1983-01-01
The authors compare the electron densities and Hartree potentials in the local density and the Hartree-Fock approximations to the corresponding quantities obtained from more accurate correlated wavefunctions. The comparison is made for a number of two-electron atoms, Li, and for Be. The Hartree-Fock approximation is more accurate than the local density approximation within the 1s shell and for the spin polarization in Li, while the local density approximation is slightly better than the Hartree-Fock approximation for charge densities in the 2s shell. The inaccuracy of the Hartree-Fock and local density approximations to the Hartree potential is substantially smaller than the inaccuracy of the local density approximation to the ground-state exchange-correlation potential. (Auth.)
The design of a two-phase radiolabelled meal for gastric emptying studies
Energy Technology Data Exchange (ETDEWEB)
Mather, S.J.; Ellison, D.; Nightingale, J.; Kamm, M.; Britton, K.E. (Saint Bartholomew' s Hospital, London (UK) St. Marks Hospital, London (UK))
1991-05-01
A meal intended for use in gastric emptying studies must be highly reproducible, must provide a normal physiological stimulus in terms of bulk, calorie content and composition and must employ stable radiotracers which accurately reflect in their biodistribution, the fate of the two-phases. This is particularly important in a field, such as gastric emptying, where so many variables may influence the results. A conventional pancake and orange juice were chosen as suitable vehicles for the solid and liquid phases. {sup 111}In-labelled resin beads were used as the solid-phase marker and a variety of {sup 99}Tc{sup m}-labelled radiopharmaceuticals including pertechnetate, DTPA and colloid forms were investigated as liquid-phase markers. Prior to administration to patients, the stability of the phases and their interactions in vitro were investigated. The use of {sup 99}Tc{sup m}-DTPA resulted in a loss of {sup 111}In from solid to liquid phase. All non-colloidal markers exhibited a tendency for adsorption onto solid phase. Colloidal markers including rhenium and antimony sulphide colloids showed the truest delineation of the liquid phase. (author).
International Nuclear Information System (INIS)
Senatore, G.; Tosi, M.P.; Trieste Univ.
1981-08-01
The purpose of this letter is to stress that the way towards an unconventional optimized-random-phase-approximation (ORPA) approach to the structure of liquid metals is indicated, and in fact already a good first-order solution for such an approach is provided
Czech Academy of Sciences Publication Activity Database
DeSimone, A.; Kružík, Martin
2013-01-01
Roč. 8, č. 2 (2013), s. 481-499 ISSN 1556-1801 R&D Projects: GA ČR(CZ) GAP201/12/0671 Institutional support: RVO:67985556 Keywords : hysteresis * shape memory Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2013 http://library.utia.cas.cz/separaty/2013/MTR/kruzik-domain patterns and hysteresis in phase-transforming solids analysis and numerical simulations of a sharp interface dissipative model via phase-field approximation.pdf
On intermittent flow characteristics of gas–liquid two-phase flow
Energy Technology Data Exchange (ETDEWEB)
Thaker, Jignesh; Banerjee, Jyotirmay, E-mail: jbaner@gmail.com
2016-12-15
Highlights: • Unified correlations for intermittent flow characteristics are developed. • Influence of inflow conditions on intermittent flow characteristics is analysed. • Developed correlations can be used for effective design of piping components. - Abstract: Flow visualisation experiments are reported for intermittent regime of gas–liquid two-phase flow. Intermittent flow characteristics, which include plug/slug frequency, liquid plug/slug velocity, liquid plug/slug length, and plug/slug bubble length are determined by image processing of flow patterns captured at a rate of 1600 frames per second (FPS). Flow characteristics are established as a function of inlet superficial velocity of both the phases (in terms of Re{sub SL} and Re{sub SG}). The experimental results are first validated with the existing correlations for slug flow available in literature. It is observed that the correlations proposed in literature for slug flow do not accurately predict the flow characteristics in the plug flow regime. The differences are clearly highlighted in this paper. Based on the measured database for both plug and slug flow regime, modified correlations for the intermittent flow regime are proposed. The correlations reported in the present paper, which also include plug flow characteristics will aid immensely to the effective design and optimization of operating conditions for safer operation of two-phase flow piping systems.
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (author)
Prestack wavefield approximations
Alkhalifah, Tariq
2013-01-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
Reference Determinant Dependence of the Random Phase Approximation in 3d Transition Metal Chemistry.
Bates, J E; Mezei, P D; Csonka, G I; Sun, J; Ruzsinszky, A
2017-01-10
Without extensive fitting, accurate prediction of transition metal chemistry is a challenge for semilocal and hybrid density funcitonals. The Random Phase Approximation (RPA) has been shown to yield superior results to semilocal functionals for main group thermochemistry, but much less is known about its performance for transition metals. We have therefore analyzed the behavior of reaction energies, barrier heights, and ligand dissociation energies obtained with RPA and compare our results to several semilocal and hybrid functionals. Particular attention is paid to the reference determinant dependence of RPA. We find that typically the results do not vary much between semilocal or hybrid functionals as a reference, as long as the fraction of exact exchange (EXX) mixing in the hybrid functional is small. For large fractions of EXX mixing, however, the Hartree-Fock-like nature of the determinant can severely degrade the performance. Overall, RPA systematically reduces the errors of semilocal functionals and delivers excellent performance from a single reference determinant for inherently multireference reactions. The behavior of dual hybrids that combine RPA correlation with a hybrid exchange energy was also explored, but ultimately did not lead to a systematic improvement compared to traditional RPA for these systems. We rationalize this conclusion by decomposing the contributions to the reaction energies, and briefly discuss the possible implications for double-hybrid functionals based on RPA. The correlation between EXX mixing and spin-symmetry breaking is also discussed.
System identification on two-phase flow stability
International Nuclear Information System (INIS)
Wu Shaorong; Zhang Youjie; Wang Dazhong; Bo Jinghai; Wang Fei
1996-01-01
The theoretical principle, experimental method and results of interrelation analysis identification for the instability of two-phase flow are described. A completely new concept of test technology and method on two-phase flow stability was developed by using he theory of information science on system stability and system identification for two-phase flow stability in thermo-physics field. Application of this method would make it possible to identify instability boundary of two-phase flow under stable operation conditions of two-phase flow system. The experiment was carried out on the thermohydraulic test system HRTL-5. Using reverse repeated pseudo-random sequences of heating power as input signal sources and flow rate as response function in the test, the two-phase flow stability and stability margin of the natural circulation system are investigated. The effectiveness and feasibility of identifying two-phase flow stability by using this system identification method were experimentally demonstrated. Basic data required for mathematics modeling of two-phase flow and analysis of two-phase flow stability were obtained, which are useful for analyzing, monitoring of the system operation condition, and forecasting of two-phase flow stability in engineering system
Gaussian and 1/N approximations in semiclassical cosmology
International Nuclear Information System (INIS)
Mazzitelli, F.D.; Paz, J.P.
1989-01-01
We study the λphi 4 theory and the interacting O(N) model in a curved background using the Gaussian approximation for the former and the large-N approximation for the latter. We obtain the renormalized version of the semiclassical Einstein equations having in mind a future application of these models to investigate the physics of the very early Universe. We show that, while the Gaussian approximation has two different phases, in the large-N limit only one is present. The different features of the two phases are analyzed at the level of the effective field equations. We discuss the initial-value problem and find the initial conditions that make the theory renormalizable. As an example, we study the de Sitter self-consistent solutions of the semiclassical Einstein equations. Finally, for an identically zero mean value of the field we find the evolution equations for the classical field Ω(x) = (λ 2 >)/sup 1/2/ and the spacetime metric. They are very similar to the ones obtained by replacing the classical potential by the one-loop effective potential in the classical equations but do not have the drawbacks of the one-loop approximation
International Nuclear Information System (INIS)
LaJohn, L A; Pratt, R H
2009-01-01
We discuss the increase in error with increasing nuclear charge Z in the use of the relativistic impulse approximation (RIA) for the calculation of Compton K-shell scattering doubly differential cross sections (DDCS). We also show that nonrelativistic (nr) expressions can be used to obtain accurate peak region DDCS at scattering angles less than about 35 0 even at incident photon energies ω i exceeding 1 MeV, if Z<30. This is possible because in the Compton peak region, as θ→0, a low momentum transfer limit is being approached.
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Dynamic Modeling Strategy for Flow Regime Transition in Gas-Liquid Two-Phase Flows
Directory of Open Access Journals (Sweden)
Xia Wang
2012-12-01
Full Text Available In modeling gas-liquid two-phase flows, the concept of flow regimes has been widely used to characterize the global interfacial structure of the flows. Nearly all constitutive relations that provide closures to the interfacial transfers in two-phase flow models, such as the two-fluid model, are flow regime dependent. Current nuclear reactor safety analysis codes, such as RELAP5, classify flow regimes using flow regime maps or transition criteria that were developed for steady-state, fully-developed flows. As two-phase flows are dynamic in nature, it is important to model the flow regime transitions dynamically to more accurately predict the two-phase flows. The present work aims to develop a dynamic modeling strategy to determine flow regimes in gas-liquid two-phase flows through introduction of interfacial area transport equations (IATEs within the framework of a two-fluid model. The IATE is a transport equation that models the interfacial area concentration by considering the creation of the interfacial area, fluid particle (bubble or liquid droplet disintegration, boiling and evaporation, and the destruction of the interfacial area, fluid particle coalescence and condensation. For flow regimes beyond bubbly flows, a two-group IATE has been proposed, in which bubbles are divided into two groups based on their size and shapes, namely group-1 and group-2 bubbles. A preliminary approach to dynamically identify the flow regimes is discussed, in which discriminators are based on the predicted information, such as the void fraction and interfacial area concentration. The flow regime predicted with this method shows good agreement with the experimental observations.
International Nuclear Information System (INIS)
Fraser, D.W.H.; Abdelmessih, A.H.
1995-01-01
A general unified model is developed to predict one-component critical two-phase pipe flow. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the results of an experimental study of the critical two-phase flow of saturated and subcooled water through long tubes. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass flux occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. Available data since 1970 for both short and long tubes over a wide range of conditions are compared with the model predictions. This includes test section L/D ratios from 25 to 300 and covers a temperature and pressure range of 110 to 280 degrees C and 0.16 to 6.9 MPa. respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data
Energy Technology Data Exchange (ETDEWEB)
Fraser, D.W.H. [Univ. of British Columbia (Canada); Abdelmessih, A.H. [Univ. of Toronto, Ontario (Canada)
1995-09-01
A general unified model is developed to predict one-component critical two-phase pipe flow. Modelling of the two-phase flow is accomplished by describing the evolution of the flow between the location of flashing inception and the exit (critical) plane. The model approximates the nonequilibrium phase change process via thermodynamic equilibrium paths. Included are the relative effects of varying the location of flashing inception, pipe geometry, fluid properties and length to diameter ratio. The model predicts that a range of critical mass fluxes exist and is bound by a maximum and minimum value for a given thermodynamic state. This range is more pronounced at lower subcooled stagnation states and can be attributed to the variation in the location of flashing inception. The model is based on the results of an experimental study of the critical two-phase flow of saturated and subcooled water through long tubes. In that study, the location of flashing inception was accurately controlled and adjusted through the use of a new device. The data obtained revealed that for fixed stagnation conditions, the maximum critical mass flux occurred with flashing inception located near the pipe exit; while minimum critical mass fluxes occurred with the flashing front located further upstream. Available data since 1970 for both short and long tubes over a wide range of conditions are compared with the model predictions. This includes test section L/D ratios from 25 to 300 and covers a temperature and pressure range of 110 to 280{degrees}C and 0.16 to 6.9 MPa. respectively. The predicted maximum and minimum critical mass fluxes show an excellent agreement with the range observed in the experimental data.
Directory of Open Access Journals (Sweden)
Sheila K Patterson
Full Text Available Salmonella enterica serovar Typhimurium strain 798 has previously been shown to undergo phenotypic phase variation. One of the phenotypes expresses virulence traits such as adhesion, while the other phenotype does not. Phenotypic phase variation appears to correlate with the ability of this strain to cause persistent, asymptomatic infections of swine. A new method to detect cells in either phenotypic phase was developed using Evans Blue-Uranine agar plates. Using this new assay, rates of phenotypic phase variation were obtained. The rate of phase variation from non-adhesive to adhesive phenotype was approximately 10(-4 per cell per generation while phase variation from the adhesive to the non-adhesive phenotype was approximately 10(-6 per cell per generation. Two highly virulent S. Typhimurium strains, SL1344 and ATCC 14028, were also shown to undergo phase variation. However, while the rate from adhesive to non-adhesive phenotype was approximately the same as for strain 798, the non-adhesive to adhesive phenotype shift was 37-fold higher. Differential gene expression was measured using RNA-Seq. Eighty-three genes were more highly expressed by 798 cells in the adhesive phenotype compared to the non-adhesive cells. Most of the up-regulated genes were in virulence genes and in particular all genes in the Salmonella pathogenicity island 1 were up-regulated. When compared to the virulent strain SL1344, expression of the virulence genes was approximately equal to those up-regulated in the adhesive phenotype of strain 798. A comparison of invasive ability demonstrated that strain SL1344 was the most invasive followed by the adhesive phenotype of strain 798, then the non-adhesive phenotype of strain 798. The least invasive strain was ATCC 14028. The genome of strain 798 was sequenced and compared to SL1344. Both strains had very similar genome sequences and gene deletions could not readily explain differences in the rates of phase variation from non
Pressure loss in two-phase flow through a microchannel rod bundle
International Nuclear Information System (INIS)
Smith, A.C.; Hamm, L.L.; Qureshi, Z.; Steeper, T.J.
1998-01-01
The purpose of the microchannel rod bundle two-phase flow test described here was to provide data for benchmarking safety analyses for the accelerator production of tritium (APT). The objective was to obtain pressure loss data for a typical accelerator target rod bundle over a wide range of two-phase flow conditions. The test rod bundle assembly was fabricated for single-phase pressure drop tests conducted at Los Alamos National Laboratory (LANL) and subsequently used for the two-phase flow testing described here. The results for a typical case are given. These results fall generally in the slug flow regime for the horizontal flow results of Fukano and Kariyasaki for a 1.0-mm circular channel. Fukano and Kariyasaki found that surface tension effects were dominant in the 1-mm channel and report no churn regime. The results were also compared with the flow regime maps given by Triplett et al. for flow in discrete microchannels. Triplett employed both circular and trapezoidal channels, the latter to approximate the rod bundle interstitial flow channel shape. It was found that the rod bundle flow fell across the slug-to-churn flow regime transition reported by Triplett. This is consistent with the expectation that cross flow among channels would result in turbulent mixing and would suppress the formation of large discrete bubbles
The Validity of a Paraxial Approximation in the Simulation of Laser Plasma Interactions
International Nuclear Information System (INIS)
Hyole, E. M.
2000-01-01
The design of high-power lasers such as those used for inertial confinement fusion demands accurate modeling of the interaction between lasers and plasmas. In inertial confinement fusion, initial laser pulses ablate material from the hohlraum, which contains the target, creating a plasma. Plasma density variations due to plasma motion, ablating material and the ponderomotive force exerted by the laser on the plasma disrupt smooth laser propagation, undesirably focusing and scattering the light. Accurate and efficient computational simulations aid immensely in developing an understanding of these effects. In this paper, we compare the accuracy of two methods for calculating the propagation of laser light through plasmas. A full laser-plasma simulation typically consists of a fluid model for the plasma motion and a laser propagation model. These two pieces interact with each other as follows. First, given the plasma density, one propagates the laser with a refractive index determined by this density. Then, given the laser intensities, the calculation of one time step of the plasma motion provides a new density for the laser propagation. Because this procedure repeats over many time steps, each piece must be performed accurately and efficiently. In general, calculation of the light intensities necessitates the solution of the Helmholtz equation with a variable index of refraction. The Helmholtz equation becomes extremely difficult and time-consuming to solve as the problem size increases. The size of laser-plasma problems of present interest far exceeds current capabilities. To avoid solving the full Helmholtz equation one may use a partial approximation. Generally speaking the partial approximation applies when one expects negligible backscattering of the light and only mild scattering transverse to the direction of light propagation. This approximation results in a differential equation that is first-order in the propagation direction that can be integrated
Zero-range approximation for two-component boson systems
International Nuclear Information System (INIS)
Sogo, T.; Fedorov, D.V.; Jensen, A.S.
2005-01-01
The hyperspherical adiabatic expansion method is combined with the zero-range approximation to derive angular Faddeev-like equations for two-component boson systems. The angular eigenvalues are solutions to a transcendental equation obtained as a vanishing determinant of a 3 x 3 matrix. The eigenfunctions are linear combinations of Jacobi functions of argument proportional to the distance between pairs of particles. We investigate numerically the influence of two-body correlations on the eigenvalue spectrum, the eigenfunctions and the effective hyperradial potential. Correlations decrease or increase the distance between pairs for effectively attractive or repulsive interactions, respectively. New structures appear for non-identical components. Fingerprints can be found in the nodal structure of the density distributions of the condensates. (author)
Efficient and accurate log-Lévy approximations to Lévy driven LIBOR models
DEFF Research Database (Denmark)
Papapantoleon, Antonis; Schoenmakers, John; Skovmand, David
2011-01-01
The LIBOR market model is very popular for pricing interest rate derivatives, but is known to have several pitfalls. In addition, if the model is driven by a jump process, then the complexity of the drift term is growing exponentially fast (as a function of the tenor length). In this work, we con...... ratchet caps show that the approximations perform very well. In addition, we also consider the log-L\\'evy approximation of annuities, which offers good approximations for high volatility regimes....
Approximate analytical solution of two-dimensional multigroup P-3 equations
International Nuclear Information System (INIS)
Matausek, M.V.; Milosevic, M.
1981-01-01
Iterative solution of multigroup spherical harmonics equations reduces, in the P-3 approximation and in two-dimensional geometry, to a problem of solving an inhomogeneous system of eight ordinary first order differential equations. With appropriate boundary conditions, these equations have to be solved for each energy group and in each iteration step. The general solution of the corresponding homogeneous system of equations is known in analytical form. The present paper shows how the right-hand side of the system can be approximated in order to derive a particular solution and thus an approximate analytical expression for the general solution of the inhomogeneous system. This combined analytical-numerical approach was shown to have certain advantages compared to the finite-difference method or the Lie-series expansion method, which have been used to solve similar problems. (orig./RW) [de
Research on one-dimensional two-phase flow
International Nuclear Information System (INIS)
Adachi, Hiromichi
1988-10-01
In Part I the fundamental form of the hydrodynamic basic equations for a one-dimensional two-phase flow (two-fluid model) is described. Discussions are concentrated on the treatment of phase change inertial force terms in the equations of motion and the author's equations of motion which have a remarkable uniqueness on the following three points. (1) To express force balance of unit mass two-phase fluid instead of that of unit volume two-phase fluid. (2) To pick up the unit existing mass and the unit flowing mass as the unit mass of two-phase fluid. (3) To apply the kinetic energy principle instead of the momentum low in the evaluation of steady inertial force term. In these three, the item (1) is for excluding a part of momentum change or kinetic energy change due to mass change of the examined part of fluid, which is independent of force. The item (2) is not to introduce a phenomenological physical model into the evaluation of phase change inertial force term. And the item (3) is for correctly applying the momentum law taking into account the difference of representative velocities between the main flow fluid (vapor phase or liquid phase) and the phase change part of fluid. In Part II, characteristics of various kinds of high speed two-phase flow are clarified theoretically by the basic equations derived. It is demonstrated that the steam-water two-phase critical flow with violent flashing and the airwater two-phase critical flow without phase change can be described with fundamentally the same basic equations. Furthermore, by comparing the experimental data from the two-phase critical discharge test and the theoretical prediction, the two-phase discharge coefficient, C D , for large sharp-edged orifice is determined as the value which is not affected by the experimental facility characteristics, etc. (author)
Energy Technology Data Exchange (ETDEWEB)
Freeze, G.A.; Larson, K.W. [INTERA, Inc., Albuquerque, NM (United States); Davies, P.B. [Sandia National Labs., Albuquerque, NM (United States)
1995-10-01
Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time.
International Nuclear Information System (INIS)
Freeze, G.A.; Larson, K.W.; Davies, P.B.
1995-10-01
Eight alternative methods for approximating salt creep and disposal room closure in a multiphase flow model of the Waste Isolation Pilot Plant (WIPP) were implemented and evaluated: Three fixed-room geometries three porosity functions and two fluid-phase-salt methods. The pressure-time-porosity line interpolation method is the method used in current WIPP Performance Assessment calculations. The room closure approximation methods were calibrated against a series of room closure simulations performed using a creep closure code, SANCHO. The fixed-room geometries did not incorporate a direct coupling between room void volume and room pressure. The two porosity function methods that utilized moles of gas as an independent parameter for closure coupling. The capillary backstress method was unable to accurately simulate conditions of re-closure of the room. Two methods were found to be accurate enough to approximate the effects of room closure; the boundary backstress method and pressure-time-porosity line interpolation. The boundary backstress method is a more reliable indicator of system behavior due to a theoretical basis for modeling salt deformation as a viscous process. It is a complex method and a detailed calibration process is required. The pressure lines method is thought to be less reliable because the results were skewed towards SANCHO results in simulations where the sequence of gas generation was significantly different from the SANCHO gas-generation rate histories used for closure calibration. This limitation in the pressure lines method is most pronounced at higher gas-generation rates and is relatively insignificant at lower gas-generation rates. Due to its relative simplicity, the pressure lines method is easier to implement in multiphase flow codes and simulations have a shorter execution time
Luenser, Arne; Schurkus, Henry F; Ochsenfeld, Christian
2017-04-11
A reformulation of the random phase approximation within the resolution-of-the-identity (RI) scheme is presented, that is competitive to canonical molecular orbital RI-RPA already for small- to medium-sized molecules. For electronically sparse systems drastic speedups due to the reduced scaling behavior compared to the molecular orbital formulation are demonstrated. Our reformulation is based on two ideas, which are independently useful: First, a Cholesky decomposition of density matrices that reduces the scaling with basis set size for a fixed-size molecule by one order, leading to massive performance improvements. Second, replacement of the overlap RI metric used in the original AO-RPA by an attenuated Coulomb metric. Accuracy is significantly improved compared to the overlap metric, while locality and sparsity of the integrals are retained, as is the effective linear scaling behavior.
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)
An angularly refineable phase space finite element method with approximate sweeping procedure
International Nuclear Information System (INIS)
Kophazi, J.; Lathouwers, D.
2013-01-01
An angularly refineable phase space finite element method is proposed to solve the neutron transport equation. The method combines the advantages of two recently published schemes. The angular domain is discretized into small patches and patch-wise discontinuous angular basis functions are restricted to these patches, i.e. there is no overlap between basis functions corresponding to different patches. This approach yields block diagonal Jacobians with small block size and retains the possibility for S n -like approximate sweeping of the spatially discontinuous elements in order to provide efficient preconditioners for the solution procedure. On the other hand, the preservation of the full FEM framework (as opposed to collocation into a high-order S n scheme) retains the possibility of the Galerkin interpolated connection between phase space elements at arbitrary levels of discretization. Since the basis vectors are not orthonormal, a generalization of the Riemann procedure is introduced to separate the incoming and outgoing contributions in case of unstructured meshes. However, due to the properties of the angular discretization, the Riemann procedure can be avoided at a large fraction of the faces and this fraction rapidly increases as the level of refinement increases, contributing to the computational efficiency. In this paper the properties of the discretization scheme are studied with uniform refinement using an iterative solver based on the S 2 sweep order of the spatial elements. The fourth order convergence of the scalar flux is shown as anticipated from earlier schemes and the rapidly decreasing fraction of required Riemann faces is illustrated. (authors)
Evaluation of Gaussian approximations for data assimilation in reservoir models
Iglesias, Marco A.
2013-07-14
implementation of the MCMC method provides the gold standard against which the aforementioned Gaussian approximations are assessed. We present numerical synthetic experiments where we quantify the capability of each of the ad hoc Gaussian approximation in reproducing the mean and the variance of the posterior distribution (characterized via MCMC) associated to a data assimilation problem. Both single-phase and two-phase (oil-water) reservoir models are considered so that fundamental differences in the resulting forward operators are highlighted. The main objective of our controlled experiments was to exhibit the substantial discrepancies of the approximation properties of standard ad hoc Gaussian approximations. Numerical investigations of the type we present here will lead to the greater understanding of the cost-efficient, but ad hoc, Bayesian techniques used for data assimilation in petroleum reservoirs and hence ultimately to improved techniques with more accurate uncertainty quantification. © 2013 Springer Science+Business Media Dordrecht.
Revisiting low-fidelity two-fluid models for gas–solids transport
Energy Technology Data Exchange (ETDEWEB)
Adeleke, Najeem, E-mail: najm@psu.edu; Adewumi, Michael, E-mail: m2a@psu.edu; Ityokumbul, Thaddeus
2016-08-15
Two-phase gas–solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas–solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe–Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
Revisiting low-fidelity two-fluid models for gas–solids transport
International Nuclear Information System (INIS)
Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus
2016-01-01
Two-phase gas–solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas–solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe–Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
Revisiting low-fidelity two-fluid models for gas-solids transport
Adeleke, Najeem; Adewumi, Michael; Ityokumbul, Thaddeus
2016-08-01
Two-phase gas-solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas-solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of Roe-Pike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.
S-wave pion-nucleon phase shifts in PADE approximation
International Nuclear Information System (INIS)
Achuthan, P.; Chandramohan, T.; Venkatesan, K.
1978-01-01
The two S-wave pion nucleon pahse shifts delta( 1 ) (I = 1/2) and delta( 3 ) (I = 3/2) have been calculated in the Pade approximation using epsilon(700), rho(770), f(1260), Δ(1236) and N(938) for the energy range W = 1085 MeV - 1820 MeV in the centre of mass. Contributions from suitable resonance combinations which agree nearest with the delta( 3 ) experimental values are given. (orig.) [de
Identification of two-phase flow regimes under variable gravity conditions
International Nuclear Information System (INIS)
Kamiel S Gabriel; Huawei Han
2005-01-01
Full text of publication follows: Two-phase flow is becoming increasingly important as we move into new and more aggressive technologies in the twenty-first century. Some of its many applications include the design of efficient heat transport systems, the transfer and storage of cryogenic fluids, and condensation and flow boiling processes in heat exchangers and energy transport systems. Two-phase flow has many applications in reduced gravity environments experienced in orbiting spacecraft and earth observation satellites. Examples are heat transport systems, the transfer and storage of cryogenic fluids, and condensation and flow boiling processes in heat exchangers. A concave parallel plate capacitance sensor has been developed to measure void fraction for the purpose of objectively identifying flow regimes. The sensor has been used to collect void-fraction data at microgravity conditions aboard the NASA and ESA zero-gravity aircraft. It is shown that the flow regimes can be objectively determined from the probability density functions of the void fraction signals. It was shown that under microgravity conditions four flow regimes exist: bubbly flow, characterized by discrete gas bubbles flowing in the liquid; slug flow, consisting of Taylor bubbles separated by liquid slugs which may or may not contain several small gas bubbles; transitional flow, characterized by the liquid flowing as a film at the tube wall, and the gas phase flowing in the center with the frequent appearance of chaotic, unstable slugs; and annular flow in which the liquid flows as a film along the tube wall and the gas flows uninterrupted through the center. Since many two-phase flow models are flow regime dependent, a method that can accurately and objectively determine flow regimes is required. (authors)
Identification of two-phase flow regimes under variable gravity conditions
Energy Technology Data Exchange (ETDEWEB)
Kamiel S Gabriel [University of Ontario Institute of Technology 2000 Simcoe Street North, Oshawa, ON L1H 7K4 (Canada); Huawei Han [Mechanical Engineering Department, University of Saskatchewan 57 Campus Dr., Saskatoon, Saskatchewan, S7N 5A9 (Canada)
2005-07-01
Full text of publication follows: Two-phase flow is becoming increasingly important as we move into new and more aggressive technologies in the twenty-first century. Some of its many applications include the design of efficient heat transport systems, the transfer and storage of cryogenic fluids, and condensation and flow boiling processes in heat exchangers and energy transport systems. Two-phase flow has many applications in reduced gravity environments experienced in orbiting spacecraft and earth observation satellites. Examples are heat transport systems, the transfer and storage of cryogenic fluids, and condensation and flow boiling processes in heat exchangers. A concave parallel plate capacitance sensor has been developed to measure void fraction for the purpose of objectively identifying flow regimes. The sensor has been used to collect void-fraction data at microgravity conditions aboard the NASA and ESA zero-gravity aircraft. It is shown that the flow regimes can be objectively determined from the probability density functions of the void fraction signals. It was shown that under microgravity conditions four flow regimes exist: bubbly flow, characterized by discrete gas bubbles flowing in the liquid; slug flow, consisting of Taylor bubbles separated by liquid slugs which may or may not contain several small gas bubbles; transitional flow, characterized by the liquid flowing as a film at the tube wall, and the gas phase flowing in the center with the frequent appearance of chaotic, unstable slugs; and annular flow in which the liquid flows as a film along the tube wall and the gas flows uninterrupted through the center. Since many two-phase flow models are flow regime dependent, a method that can accurately and objectively determine flow regimes is required. (authors)
Energy Technology Data Exchange (ETDEWEB)
Hou, Guangjin, E-mail: hou@udel.edu, E-mail: tpolenov@udel.edu; Lu, Xingyu, E-mail: luxingyu@udel.edu, E-mail: lexvega@comcast.net; Vega, Alexander J., E-mail: luxingyu@udel.edu, E-mail: lexvega@comcast.net; Polenova, Tatyana, E-mail: hou@udel.edu, E-mail: tpolenov@udel.edu [Department of Chemistry and Biochemistry, University of Delaware, Newark, Delaware 19716, USA and Pittsburgh Center for HIV Protein Interactions, University of Pittsburgh School of Medicine, 1051 Biomedical Science Tower 3, 3501 Fifth Ave., Pittsburgh, Pennsylvania 15261 (United States)
2014-09-14
We report a Phase-Alternating R-Symmetry (PARS) dipolar recoupling scheme for accurate measurement of heteronuclear {sup 1}H-X (X = {sup 13}C, {sup 15}N, {sup 31}P, etc.) dipolar couplings in MAS NMR experiments. It is an improvement of conventional C- and R-symmetry type DIPSHIFT experiments where, in addition to the dipolar interaction, the {sup 1}H CSA interaction persists and thereby introduces considerable errors in the dipolar measurements. In PARS, phase-shifted RN symmetry pulse blocks applied on the {sup 1}H spins combined with π pulses applied on the X spins at the end of each RN block efficiently suppress the effect from {sup 1}H chemical shift anisotropy, while keeping the {sup 1}H-X dipolar couplings intact. Another advantage over conventional DIPSHIFT experiments, which require the signal to be detected in the form of a reduced-intensity Hahn echo, is that the series of π pulses refocuses the X chemical shift and avoids the necessity of echo formation. PARS permits determination of accurate dipolar couplings in a single experiment; it is suitable for a wide range of MAS conditions including both slow and fast MAS frequencies; and it assures dipolar truncation from the remote protons. The performance of PARS is tested on two model systems, [{sup 15}N]-N-acetyl-valine and [U-{sup 13}C,{sup 15}N]-N-formyl-Met-Leu-Phe tripeptide. The application of PARS for site-resolved measurement of accurate {sup 1}H-{sup 15}N dipolar couplings in the context of 3D experiments is presented on U-{sup 13}C,{sup 15}N-enriched dynein light chain protein LC8.
Separable pairing force for relativistic quasiparticle random-phase approximation
International Nuclear Information System (INIS)
Tian Yuan; Ma Zhongyu; Ring, Peter
2009-01-01
We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random-Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited 2 + states for the chain of Sn isotopes with Z=50 and the chain of isotones with N=82 isotones are calculated in RQRPA together with the 3 - states of Sn isotopes. By comparing our results with experimental data and with the results of the original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.
Optimized implementations of rational approximations for the Voigt and complex error function
International Nuclear Information System (INIS)
Schreier, Franz
2011-01-01
Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued functions. For the complex error function w(x+iy), whose real part is the Voigt function K(x,y), code optimizations of rational approximations are investigated. An assessment of requirements for atmospheric radiative transfer modeling indicates a y range over many orders of magnitude and accuracy better than 10 -4 . Following a brief survey of complex error function algorithms in general and rational function approximations in particular the problems associated with subdivisions of the x, y plane (i.e., conditional branches in the code) are discussed and practical aspects of Fortran and Python implementations are considered. Benchmark tests of a variety of algorithms demonstrate that programming language, compiler choice, and implementation details influence computational speed and there is no unique ranking of algorithms. A new implementation, based on subdivision of the upper half-plane in only two regions, combining Weideman's rational approximation for small |x|+y<15 and Humlicek's rational approximation otherwise is shown to be efficient and accurate for all x, y.
ENTROPY PRODUCTION IN COLLISIONLESS SYSTEMS. II. ARBITRARY PHASE-SPACE OCCUPATION NUMBERS
International Nuclear Information System (INIS)
Barnes, Eric I.; Williams, Liliya L. R.
2012-01-01
We present an analysis of two thermodynamic techniques for determining equilibria of self-gravitating systems. One is the Lynden-Bell (LB) entropy maximization analysis that introduced violent relaxation. Since we do not use the Stirling approximation, which is invalid at small occupation numbers, our systems have finite mass, unlike LB's isothermal spheres. (Instead of Stirling, we utilize a very accurate smooth approximation for ln x!.) The second analysis extends entropy production extremization to self-gravitating systems, also without the use of the Stirling approximation. In addition to the LB statistical family characterized by the exclusion principle in phase space, and designed to treat collisionless systems, we also apply the two approaches to the Maxwell-Boltzmann (MB) families, which have no exclusion principle and hence represent collisional systems. We implicitly assume that all of the phase space is equally accessible. We derive entropy production expressions for both families and give the extremum conditions for entropy production. Surprisingly, our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy, in both LB and MB statistics. In other words, both thermodynamic approaches lead to the same equilibrium structures.
International Nuclear Information System (INIS)
Bruk, Yulii M; Voloshchuk, Aleksandr N
2012-01-01
The functional Pais equation for scattering phases with nonzero orbital momenta is solved in the case of low-energy particles. For short-range screened potentials, in particular, Yukawa or Thomas-Fermi potentials, the Pais equation is shown to reduce to transcendental equations. For the potentials varying ∼r - n , n > 0, simple algebraic equations are obtained for determining the phases δ l , l≠0. Possible applications of the Pais approximation to the problem of finding resonance regimes in the scattering of low-energy particles with nonzero orbital momenta are discussed. (methodological notes)
Czech Academy of Sciences Publication Activity Database
Veis, Libor; Višňák, Jakub; Nishizawa, H.; Nakai, H.; Pittner, Jiří
2016-01-01
Roč. 116, č. 18 (2016), s. 1328-1336 ISSN 0020-7608 R&D Projects: GA ČR GA203/08/0626 Institutional support: RVO:61388955 Keywords : Born-Oppenheimer approximation * nuclear orbital plus molecular orbital method * phase estimation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.920, year: 2016
Arbogast, Todd
2012-01-01
Motivated by possible generalizations to more complex multiphase multicomponent systems in higher dimensions, we develop an Eulerian-Lagrangian numerical approximation for a system of two conservation laws in one space dimension modeling a simplified two-phase flow problem in a porous medium. The method is based on following tracelines, so it is stable independent of any CFL constraint. The main difficulty is that it is not possible to follow individual tracelines independently. We approximate tracing along the tracelines by using local mass conservation principles and self-consistency. The two-phase flow problem is governed by a system of equations representing mass conservation of each phase, so there are two local mass conservation principles. Our numerical method respects both of these conservation principles over the computational mesh (i.e., locally), and so is a fully conservative traceline method. We present numerical results that demonstrate the ability of the method to handle problems with shocks and rarefactions, and to do so with very coarse spatial grids and time steps larger than the CFL limit. © 2012 Society for Industrial and Applied Mathematics.
Post Analysis of Two Phase Natural Circulation Mass Flow Rate for CE-PECS
Energy Technology Data Exchange (ETDEWEB)
Park, R. J.; Ha, K. S.; Rhee, B. W.; Kim, H. Y. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
The coolant in the inclined channel absorbs the decay heat and sensible heat transferred from the corium through the structure of the core catcher body and flows up to the pool as a two phase mixture. On the other hand, some of the pool water will flow into the inlet of the downcomer piping, and will flow into the inclined cooling channel of the core catcher by gravity. The engineered cooling channel is designed to provide effective long-term cooling and stabilization of the corium mixture in the core catcher body while facilitating steam venting. To maintain the integrity of the ex-vessel core catcher, however, it is required that the coolant be circulated at a rate along the inclined cooling channel sufficient to avoid CHF (Critical Heat Flux) on the heating surface of the cooling channel. In this study, post simulations of two phase natural circulation in the CEPECS have been performed to evaluate two phase flow characteristics and the natural circulation mass flow rate in the flow channel using the RELAP5/MOD3 computer code. Post simulations of two phase natural circulation in the CE-PECS have been conducted to evaluate two phase flow characteristics and the natural circulation mass flow rate in the flow channel using the RELAP5/MOD3 computer code. The RELAP5/MOD3 results have shown that the water circulation mass flow rate is approximately 8.7 kg/s in the base case.
Post Analysis of Two Phase Natural Circulation Mass Flow Rate for CE-PECS
International Nuclear Information System (INIS)
Park, R. J.; Ha, K. S.; Rhee, B. W.; Kim, H. Y.
2015-01-01
The coolant in the inclined channel absorbs the decay heat and sensible heat transferred from the corium through the structure of the core catcher body and flows up to the pool as a two phase mixture. On the other hand, some of the pool water will flow into the inlet of the downcomer piping, and will flow into the inclined cooling channel of the core catcher by gravity. The engineered cooling channel is designed to provide effective long-term cooling and stabilization of the corium mixture in the core catcher body while facilitating steam venting. To maintain the integrity of the ex-vessel core catcher, however, it is required that the coolant be circulated at a rate along the inclined cooling channel sufficient to avoid CHF (Critical Heat Flux) on the heating surface of the cooling channel. In this study, post simulations of two phase natural circulation in the CEPECS have been performed to evaluate two phase flow characteristics and the natural circulation mass flow rate in the flow channel using the RELAP5/MOD3 computer code. Post simulations of two phase natural circulation in the CE-PECS have been conducted to evaluate two phase flow characteristics and the natural circulation mass flow rate in the flow channel using the RELAP5/MOD3 computer code. The RELAP5/MOD3 results have shown that the water circulation mass flow rate is approximately 8.7 kg/s in the base case
Two-phase wall function for modeling of turbulent boundary layer in subcooled boiling flow
International Nuclear Information System (INIS)
Bostjan Koncar; Borut Mavko; Yassin A Hassan
2005-01-01
Full text of publication follows: The heat transfer and phase-change mechanisms in the subcooled flow boiling are governed mainly by local multidimensional mechanisms near the heated wall, where bubbles are generated. The structure of such 'wall boiling flow' is inherently non-homogeneous and is further influenced by the two-phase flow turbulence, phase-change effects in the bulk, interfacial forces and bubble interactions (collisions, coalescence, break-up). In this work the effect of two-phase flow turbulence on the development of subcooled boiling flow is considered. Recently, the modeling of two-phase flow turbulence has been extensively investigated. A notable progress has been made towards deriving reliable models for description of turbulent behaviour of continuous (liquid) and dispersed phase (bubbles) in the bulk flow. However, there is a lack of investigation considering the modeling of two-phase flow boundary layer. In most Eulerian two-fluid models standard single-phase wall functions are used for description of turbulent boundary layer of continuous phase. That might be a good approximation at adiabatic flows, but their use for boundary layers with high concentration of dispersed phase is questionable. In this work, the turbulent boundary layer near the heated wall will be modeled with the so-called 'two-phase' wall function, which is based on the assumption of additional turbulence due to bubble-induced stirring in the boundary layer. In the two-phase turbulent boundary layer the wall function coefficients strongly depend on the void fraction. Moreover, in the turbulent boundary layer with nucleating bubbles, the bubble size variation also has a significant impact on the liquid phase. As a basis, the wall function of Troshko and Hassan (2001), developed for adiabatic bubbly flows will be used. The simulations will be performed by a general-purpose CFD code CFX-4.4 using additional models provided by authors. The results will be compared to the boiling
Approximation in two-stage stochastic integer programming
W. Romeijnders; L. Stougie (Leen); M. van der Vlerk
2014-01-01
htmlabstractApproximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value.
Approximation in two-stage stochastic integer programming
Romeijnders, W.; Stougie, L.; van der Vlerk, M.H.
2014-01-01
Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value. However,
Analysis of phase dynamics in two-phase flow using latticegas automata
International Nuclear Information System (INIS)
Ohashi, H.; Hashimoto, Y.; Tsumaya, A.; Chen, Y.; Akiyama, M.
1998-01-01
In this paper, we describe lattice gas automaton models appropriate for two-phase flow simulation and their applications to study various phase dynamics of two-fluid mixtures. Several algorithms are added to the original immiscible Lattice Gas model to adjust surface tension and to introduce density difference between two fluids. Surface tension is controlled by the collision rules an difference in density is due to nonlocal forces between automaton particles. We simulate the relative motion of the dispersed phase in another continuous fluid. Deformation and disintegration of rising drops are reproduced. The interaction between multiple drops is also observed in calculations. Furutre, we obtain the transition of the two-phase flow pattern from bubbly, slug to annular flow. Density difference of two phase is one of the key ingredients to generate the annular flow pattern
International Nuclear Information System (INIS)
Kleinig, W.; Nesterenko, V.O.; Reinhard, P.-G.; Serra, Ll.
1998-01-01
The systematics of the plasmon response in spherical K, Na and Li clusters in a wide size region (8≤N≤440) is studied. We have considered two simplifying approximations whose validity has been established previously. First, a separable approach to the random-phase approximation is used. This involves an expansion of the residual interaction into a sum of separable terms until convergence is reached. Second, the electron-ion interaction is modelled by using the pseudo-Hamiltonian jellium model (MHJM) which includes nonlocal effects by means of realistic atomic pseudo-Hamiltonians. In cases where nonlocal effects are negligible the Structure Averaged Jellium Model (SAJM) has been used. Good agreement with available experimental data is achieved for K, Na (using the SAJM) and small Li clusters (invoking the PHJM). The trends for peak position and width are generally well reproduced, even up to details of the Landau fragmentation in several clusters. Less good agreement, however, is found for large Li clusters. This remains an open question
Development of a two-phase SPH model for sediment laden flows
Shi, Huabin; Yu, Xiping; Dalrymple, Robert A.
2017-12-01
A SPH model based on a general formulation for solid-fluid two-phase flows is proposed for suspended sediment motion in free surface flows. The water and the sediment are treated as two miscible fluids, and the multi-fluid system is discretized by a single set of SPH particles, which move with the water velocity and carry properties of the two phases. Large eddy simulation (LES) is introduced to deal with the turbulence effect, and the widely used Smagorinsky model is modified to take into account the influence of sediment particles on the turbulence. The drag force is accurately formulated by including the hindered settling effect. In the model, the water is assumed to be weakly compressible while the sediment is incompressible, and a new equation of state is proposed for the pressure in the sediment-water mixture. Dynamic boundary condition is employed to treat wall boundaries, and a new strategy of Shepard filtering is adopted to damp the pressure oscillation. The developed two-phase SPH model is validated by comparing the numerical results with analytical solutions for idealized cases of still water containing both neutrally buoyant and naturally settling sand and for plane Poiseuille flows carrying neutrally buoyant particles, and is then applied to sand dumping from a line source into a water tank, where the sand cloud settles with a response of the free water surface. It is shown that the numerical results are in good agreement with the experimental data as well as the empirical formulas. The characteristics of the settling sand cloud, the pressure field, and the flow vortices are studied. The motion of the free water surface is also discussed. The proposed two-phase SPH model is proven to be effective for numerical simulation of sand dumping into waters.
Rossi, Mariana; Liu, Hanchao; Paesani, Francesco; Bowman, Joel; Ceriotti, Michele
2014-11-14
Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.
Gambacurta, D.; Grasso, M.; Vasseur, O.
2018-02-01
The second random-phase-approximation model corrected by a subtraction procedure designed to cure double counting, instabilities, and ultraviolet divergences, is employed for the first time to analyze the dipole strength and polarizability in 48Ca. All the terms of the residual interaction are included, leading to a fully self-consistent scheme. Results are illustrated with two Skyrme parametrizations, SGII and SLy4. Those obtained with the SGII interaction are particularly satisfactory. In this case, the low-lying strength below the neutron threshold is well reproduced and the giant dipole resonance is described in a very satisfactory way especially in its spreading and fragmentation. Spreading and fragmentation are produced in a natural way within such a theoretical model by the coupling of 1 particle-1 hole and 2 particle-2 hole configurations. Owing to this feature, we may provide for the electric polarizability as a function of the excitation energy a curve with a similar slope around the centroid energy of the giant resonance compared to the corresponding experimental results. This represents a considerable improvement with respect to previous theoretical predictions obtained with the random-phase approximation or with several ab-initio models. In such cases, the spreading width of the excitation cannot be reproduced and the polarizability as a function of the excitation energy displays a stiff increase around the predicted centroid energy of the giant resonance.
Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models
Vignal, Philippe
2016-02-11
Phase-field models are emerging as a promising strategy to simulate interfacial phenomena. Rather than tracking interfaces explicitly as done in sharp interface descriptions, these models use a diffuse order parameter to monitor interfaces implicitly. This implicit description, as well as solid physical and mathematical footings, allow phase-field models to overcome problems found by predecessors. Nonetheless, the method has significant drawbacks. The phase-field framework relies on the solution of high-order, nonlinear partial differential equations. Solving these equations entails a considerable computational cost, so finding efficient strategies to handle them is important. Also, standard discretization strategies can many times lead to incorrect solutions. This happens because, for numerical solutions to phase-field equations to be valid, physical conditions such as mass conservation and free energy monotonicity need to be guaranteed. In this work, we focus on the development of thermodynamically consistent algorithms for time integration of phase-field models. The first part of this thesis focuses on an energy-stable numerical strategy developed for the phase-field crystal equation. This model was put forward to model microstructure evolution. The algorithm developed conserves, guarantees energy stability and is second order accurate in time. The second part of the thesis presents two numerical schemes that generalize literature regarding energy-stable methods for conserved and non-conserved phase-field models. The time discretization strategies can conserve mass if needed, are energy-stable, and second order accurate in time. We also develop an adaptive time-stepping strategy, which can be applied to any second-order accurate scheme. This time-adaptive strategy relies on a backward approximation to give an accurate error estimator. The spatial discretization, in both parts, relies on a mixed finite element formulation and isogeometric analysis. The codes are
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yijie [ORNL; Lim, Hyun-Kyung [ORNL; de Almeida, Valmor F [ORNL; Navamita, Ray [State University of New York, Stony Brook; Wang, Shuqiang [State University of New York, Stony Brook; Glimm, James G [ORNL; Li, Xiao-lin [State University of New York, Stony Brook; Jiao, Xiangmin [ORNL
2012-06-01
This progress report describes the development of a front tracking method for the solution of the governing equations of motion for two-phase micromixing of incompressible, viscous, liquid-liquid solvent extraction processes. The ability to compute the detailed local interfacial structure of the mixture allows characterization of the statistical properties of the two-phase mixture in terms of droplets, filaments, and other structures which emerge as a dispersed phase embedded into a continuous phase. Such a statistical picture provides the information needed for building a consistent coarsened model applicable to the entire mixing device. Coarsening is an undertaking for a future mathematical development and is outside the scope of the present work. We present here a method for accurate simulation of the micromixing dynamics of an aqueous and an organic phase exposed to intense centrifugal force and shearing stress. The onset of mixing is the result of the combination of the classical Rayleigh- Taylor and Kelvin-Helmholtz instabilities. A mixing environment that emulates a sector of the annular mixing zone of a centrifugal contactor is used for the mathematical domain. The domain is small enough to allow for resolution of the individual interfacial structures and large enough to allow for an analysis of their statistical distribution of sizes and shapes. A set of accurate algorithms for this application requires an advanced front tracking approach constrained by the incompressibility condition. This research is aimed at designing and implementing these algorithms. We demonstrate verification and convergence results for one-phase and unmixed, two-phase flows. In addition we report on preliminary results for mixed, two-phase flow for realistic operating flow parameters.
International Nuclear Information System (INIS)
Bonetto, Paola; Qi, Jinyi; Leahy, Richard M.
1999-01-01
We describe a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, we derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. We show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow us to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm
Approximating the Ising model on fractal lattices of dimension less than two
DEFF Research Database (Denmark)
Codello, Alessandro; Drach, Vincent; Hietanen, Ari
2015-01-01
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained...... with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also...
Prediction of two-phase mixture density using artificial neural networks
International Nuclear Information System (INIS)
Lombardi, C.; Mazzola, A.
1997-01-01
In nuclear power plants, the density of boiling mixtures has a significant relevance due to its influence on the neutronic balance, the power distribution and the reactor dynamics. Since the determination of the two-phase mixture density on a purely analytical basis is in fact impractical in many situations of interest, heuristic relationships have been developed based on the parameters describing the two-phase system. However, the best or even a good structure for the correlation cannot be determined in advance, also considering that it is usually desired to represent the experimental data with the most compact equation. A possible alternative to empirical correlations is the use of artificial neural networks, which allow one to model complex systems without requiring the explicit formulation of the relationships existing among the variables. In this work, the neural network methodology was applied to predict the density data of two-phase mixtures up-flowing in adiabatic channels under different experimental conditions. The trained network predicts the density data with a root-mean-square error of 5.33%, being ∼ 93% of the data points predicted within 10%. When compared with those of two conventional well-proven correlations, i.e. the Zuber-Findlay and the CISE correlations, the neural network performances are significantly better. In spite of the good accuracy of the neural network predictions, the 'black-box' characteristic of the neural model does not allow an easy physical interpretation of the knowledge integrated in the network weights. Therefore, the neural network methodology has the advantage of not requiring a formal correlation structure and of giving very accurate results, but at the expense of a loss of model transparency. (author)
Multijet final states: exact results and the leading pole approximation
International Nuclear Information System (INIS)
Ellis, R.K.; Owens, J.F.
1984-09-01
Exact results for the process gg → ggg are compared with those obtained using the leading pole approximation. Regions of phase space where the approximation breaks down are discussed. A specific example relevant for background estimates to W boson production is presented. It is concluded that in this instance the leading pole approximation may underestimate the standard QCD background by more than a factor of two in certain kinematic regions of physical interest
Can phenological models predict tree phenology accurately under climate change conditions?
Chuine, Isabelle; Bonhomme, Marc; Legave, Jean Michel; García de Cortázar-Atauri, Inaki; Charrier, Guillaume; Lacointe, André; Améglio, Thierry
2014-05-01
The onset of the growing season of trees has been globally earlier by 2.3 days/decade during the last 50 years because of global warming and this trend is predicted to continue according to climate forecast. The effect of temperature on plant phenology is however not linear because temperature has a dual effect on bud development. On one hand, low temperatures are necessary to break bud dormancy, and on the other hand higher temperatures are necessary to promote bud cells growth afterwards. Increasing phenological changes in temperate woody species have strong impacts on forest trees distribution and productivity, as well as crops cultivation areas. Accurate predictions of trees phenology are therefore a prerequisite to understand and foresee the impacts of climate change on forests and agrosystems. Different process-based models have been developed in the last two decades to predict the date of budburst or flowering of woody species. They are two main families: (1) one-phase models which consider only the ecodormancy phase and make the assumption that endodormancy is always broken before adequate climatic conditions for cell growth occur; and (2) two-phase models which consider both the endodormancy and ecodormancy phases and predict a date of dormancy break which varies from year to year. So far, one-phase models have been able to predict accurately tree bud break and flowering under historical climate. However, because they do not consider what happens prior to ecodormancy, and especially the possible negative effect of winter temperature warming on dormancy break, it seems unlikely that they can provide accurate predictions in future climate conditions. It is indeed well known that a lack of low temperature results in abnormal pattern of bud break and development in temperate fruit trees. An accurate modelling of the dormancy break date has thus become a major issue in phenology modelling. Two-phases phenological models predict that global warming should delay
Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results
Liu, Li; Mishchenko, Michael I.
2016-01-01
We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.
Chiral NNLOsat descriptions of nuclear multipole resonances within the random-phase approximation
Wu, Q.; Hu, B. S.; Xu, F. R.; Ma, Y. Z.; Dai, S. J.; Sun, Z. H.; Jansen, G. R.
2018-05-01
We study nuclear multipole resonances in the framework of the random-phase approximation by using the chiral potential NNLOsat. This potential includes two- and three-body terms that have been simultaneously optimized to low-energy nucleon-nucleon scattering data and selected nuclear structure data. Our main focuses have been the isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of the closed-shell nuclei, 4He, O 16 ,22 ,24 , and Ca,4840. These resonance modes have been widely observed in experiment. In addition, we use a renormalized chiral potential Vlow-k, based on the N3LO two-body potential by Entem and Machleidt [Phys. Rev. C 68, 041001 (2011), 10.1103/PhysRevC.68.041001]. This introduces a dependency on the cutoff parameter used in the normalization procedure as reported in previous works by other groups. While NNLOsat can reasonably reproduce observed multipole resonances, it is not possible to find a single cutoff parameter for the Vlow-k potential that simultaneously describes the different types of resonance modes. The sensitivity to the cutoff parameter can be explained by missing induced three-body forces in the calculations. Our results for neutron-rich O,2422 show a mixing nature of isoscalar and isovector resonances in the dipole channel at low energies. We predict that 22O and 24O have low-energy isoscalar quadrupole resonances at energies lower than 5 MeV.
Phase transitions in two dimensions
International Nuclear Information System (INIS)
Henderson, D.
1980-01-01
Although a two-dimensional solid with long-range translational order cannot existin the thermodynamic limit (N → ∞, V →∞, N/V finite) macroscopic samples of two-dimensional solids can exist. In this work, stability of the phase was determined by the usuar method of equating the pressure and chemical potential of the phases. (A.C.A.S.) [pt
Rosolen, A.; Peco, C.; Arroyo, M.
2013-01-01
We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp i...
Syntrophic acetate oxidation in two-phase (acid-methane) anaerobic digesters.
Shimada, T; Morgenroth, E; Tandukar, M; Pavlostathis, S G; Smith, A; Raskin, L; Kilian, R E
2011-01-01
The microbial processes involved in two-phase anaerobic digestion were investigated by operating a laboratory-scale acid-phase (AP) reactor and analyzing two full-scale, two-phase anaerobic digesters operated under mesophilic (35 °C) conditions. The digesters received a blend of primary sludge and waste activated sludge (WAS). Methane levels of 20% in the laboratory-scale reactor indicated the presence of methanogenic activity in the AP. A phylogenetic analysis of an archaeal 16S rRNA gene clone library of one of the full-scale AP digesters showed that 82% and 5% of the clones were affiliated with the orders Methanobacteriales and Methanosarcinales, respectively. These results indicate that substantial levels of aceticlastic methanogens (order Methanosarcinales) were not maintained at the low solids retention times and acidic conditions (pH 5.2-5.5) of the AP, and that methanogenesis was carried out by hydrogen-utilizing methanogens of the order Methanobacteriales. Approximately 43, 31, and 9% of the archaeal clones from the methanogenic phase (MP) digester were affiliated with the orders Methanosarcinales, Methanomicrobiales, and Methanobacteriales, respectively. A phylogenetic analysis of a bacterial 16S rRNA gene clone library suggested the presence of acetate-oxidizing bacteria (close relatives of Thermacetogenium phaeum, 'Syntrophaceticus schinkii,' and Clostridium ultunense). The high abundance of hydrogen consuming methanogens and the presence of known acetate-oxidizing bacteria suggest that acetate utilization by acetate oxidizing bacteria in syntrophic interaction with hydrogen-utilizing methanogens was an important pathway in the second-stage of the two-phase digestion, which was operated at high ammonium-N concentrations (1.0 and 1.4 g/L). A modified version of the IWA Anaerobic Digestion Model No. 1 (ADM1) with extensions for syntrophic acetate oxidation and weak-acid inhibition adequately described the dynamic profiles of volatile acid production
Dynamic of Ising model with transverse field for two coupled sublattices in disordered phase
International Nuclear Information System (INIS)
Sa Motta, C.E.H. de.
1984-02-01
The dynamics of the two coupled sublattices tridimensional Ising model in a transverse field was studied by means of a continued fraction expansion for coupled operators. The static Correlation Functions necessary for studying the dynamics were calculated with the Green's Functions Method in the Random Phase Approximation (RPA). The spectral function was calculated in the region T c → . (Author) [pt
The pdf approach to turbulent polydispersed two-phase flows
Minier, Jean-Pierre; Peirano, Eric
2001-10-01
The purpose of this paper is to develop a probabilistic approach to turbulent polydispersed two-phase flows. The two-phase flows considered are composed of a continuous phase, which is a turbulent fluid, and a dispersed phase, which represents an ensemble of discrete particles (solid particles, droplets or bubbles). Gathering the difficulties of turbulent flows and of particle motion, the challenge is to work out a general modelling approach that meets three requirements: to treat accurately the physically relevant phenomena, to provide enough information to address issues of complex physics (combustion, polydispersed particle flows, …) and to remain tractable for general non-homogeneous flows. The present probabilistic approach models the statistical dynamics of the system and consists in simulating the joint probability density function (pdf) of a number of fluid and discrete particle properties. A new point is that both the fluid and the particles are included in the pdf description. The derivation of the joint pdf model for the fluid and for the discrete particles is worked out in several steps. The mathematical properties of stochastic processes are first recalled. The various hierarchies of pdf descriptions are detailed and the physical principles that are used in the construction of the models are explained. The Lagrangian one-particle probabilistic description is developed first for the fluid alone, then for the discrete particles and finally for the joint fluid and particle turbulent systems. In the case of the probabilistic description for the fluid alone or for the discrete particles alone, numerical computations are presented and discussed to illustrate how the method works in practice and the kind of information that can be extracted from it. Comments on the current modelling state and propositions for future investigations which try to link the present work with other ideas in physics are made at the end of the paper.
Numerical analysis of gas-liquid two-phase flow in secondary side of steam generator
Energy Technology Data Exchange (ETDEWEB)
Murase, Michio; Nakamura, Akira; Yagi, Yoshinori [Inst. of Nuclear Safety System Inc., Mihama, Fukui (Japan)
2002-09-01
The steam generator (SG) in a pressurized water reactor (PWR) is an important two-phase flow component as the boundary between the primary loop and the secondary loop. In this study, we performed gas-liquid two-phase flow analyses for SG reliability tests conduced by Nuclear Power Engineering Corporation (NUPEC) using the two-fluid model of a thermal-hydraulic computer code PHOENICS. In order to calculate the location of the boiling initiation accurately, detailed inputs were required for the friction coefficients affecting the velocity distribution and the heat transfer distribution. However, the velocity and heat transfer distributions did not greatly affect the void fractions in the upper region of the heat transfer tubes. The calculated void fractions agreed with the measured values within 4% as the local average and within 2% as an average in a cross-section, except the region of low void fractions. (author)
Kou, Jisheng; Sun, Shuyu
2013-01-01
A class of discontinuous Galerkin methods with interior penalties is presented for incompressible two-phase flow in heterogeneous porous media with capillary pressures. The semidiscrete approximate schemes for fully coupled system of two-phase flow are formulated. In highly heterogeneous permeable media, the saturation is discontinuous due to different capillary pressures, and therefore, the proposed methods incorporate the capillary pressures in the pressure equation instead of saturation equation. By introducing a coupling approach for stability and error estimates instead of the conventional separate analysis for pressure and saturation, the stability of the schemes in space and time and a priori hp error estimates are presented in the L2(H 1) for pressure and in the L∞(L2) and L2(H1) for saturation. Two time discretization schemes are introduced for effectively computing the discrete solutions. © 2013 Societ y for Industrial and Applied Mathematics.
Rapid yet accurate measurement of mass diffusion coefficients by phase shifting interferometer
Guo Zhi Xiong; Komiya, A
1999-01-01
The technique of using a phase-shifting interferometer is applied to the study of diffusion in transparent liquid mixtures. A quick method is proposed for determining the diffusion coefficient from the measurements of the location of fringes on a grey level picture. The measurement time is very short (within 100 s) and a very small transient diffusion field can be observed and recorded accurately with a rate of 30 frames per second. The measurement can be completed using less than 0.12 cc of solutions. The influence of gravity on the measurement of the diffusion coefficient is eliminated in the present method. Results on NaCl-water diffusion systems are presented and compared with the reference data. (author)
Investigation for vertical, two-phase steam-water flow of three turbine models
International Nuclear Information System (INIS)
Silverman, S.; Goodrich, L.D.
1977-01-01
One of the basic quantities of interest during a loss-of-coolant experiment (LOCE) is the primary system mass flow rate. Presently, there are no transducers commercially available which continuously measure this parameter. Therefore, a transducer was designed at EG and G Idaho, Inc. which combines a drag-disc and turbine into a single unit. The basis for the design was that the drag-disc would measure momentum flux (rhoV 2 ), the turbine would measure velocity and the mass flow rate could then be calculated from the two quantities by assuming a flow profile. For two-phase flow, the outputs are approximately proportional to the desired parameter, but rather large errors can be expected under those assumptions. Preliminary evaluation of the experimental two- and single-phase calibration data has resulted in uncertainty estimates of +-8% of range for the turbine and +-20% of range for the drag-disc. In an effort to reduce the errors, further investigations were made to determine what the drag-disc and turbine really measure. In the present paper, three turbine models for vertical, two-phase, steam/water flow are investigated; the Aya Model, the Rouhani Model, and a volumetric flow model. Theoretical predictions are compared with experimental data for vertical, two-phase steam/water flow. For the purposes of the mass flow calculation, velocity profiles were assumed to be flat for the free-field condition. It is appreciated that this may not be true for all cases investigated, but for an initial inspection, flat profiles were assumed
Vibrationally inelastic electron scattering in a two-channel approximation
Czech Academy of Sciences Publication Activity Database
Čársky, Petr; Čurík, Roman
2008-01-01
Roč. 41, č. 5 (2008), , , 055203-1-6 ISSN 0953-4075 R&D Projects: GA AV ČR IAA100400501; GA AV ČR 1ET400400413; GA AV ČR KJB400400803; GA ČR GA202/08/0631; GA MŠk ME 857 Institutional research plan: CEZ:AV0Z40400503 Keywords : inelastic electron scattering * two-channel approximation Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.089, year: 2008
Thermo-fluid dynamics of two-phase flow
Ishii, Mamoru; Ishii, Mamoru; Ishii, M
2006-01-01
Provides a very systematic treatment of two phase flow problems from a theoretical perspectiveProvides an easy to follow treatment of modeling and code devlopemnt of two phase flow related phenomenaCovers new results of two phase flow research such as coverage of fuel cells technology.
Two-phase flow in refrigeration systems
Gu, Junjie; Gan, Zhongxue
2013-01-01
Two-Phase Flow in Refrigeration Systems presents recent developments from the authors' extensive research programs on two-phase flow in refrigeration systems. This book covers advanced mass and heat transfer and vapor compression refrigeration systems and shows how the performance of an automotive air-conditioning system is affected through results obtained experimentally and theoretically, specifically with consideration of two-phase flow and oil concentration. The book is ideal for university postgraduate students as a textbook, researchers and professors as an academic reference book, and b
Approximate Riemann solver for the two-fluid plasma model
International Nuclear Information System (INIS)
Shumlak, U.; Loverich, J.
2003-01-01
An algorithm is presented for the simulation of plasma dynamics using the two-fluid plasma model. The two-fluid plasma model is more general than the magnetohydrodynamic (MHD) model often used for plasma dynamic simulations. The two-fluid equations are derived in divergence form and an approximate Riemann solver is developed to compute the fluxes of the electron and ion fluids at the computational cell interfaces and an upwind characteristic-based solver to compute the electromagnetic fields. The source terms that couple the fluids and fields are treated implicitly to relax the stiffness. The algorithm is validated with the coplanar Riemann problem, Langmuir plasma oscillations, and the electromagnetic shock problem that has been simulated with the MHD plasma model. A numerical dispersion relation is also presented that demonstrates agreement with analytical plasma waves
Goal-oriented error estimation for Cahn-Hilliard models of binary phase transition
van der Zee, Kristoffer G.
2010-10-27
A posteriori estimates of errors in quantities of interest are developed for the nonlinear system of evolution equations embodied in the Cahn-Hilliard model of binary phase transition. These involve the analysis of wellposedness of dual backward-in-time problems and the calculation of residuals. Mixed finite element approximations are developed and used to deliver numerical solutions of representative problems in one- and two-dimensional domains. Estimated errors are shown to be quite accurate in these numerical examples. © 2010 Wiley Periodicals, Inc.
International Nuclear Information System (INIS)
Albayrak, Erhan; Keskin, Mustafa
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made
Albayrak, E
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.
Baek, Sunghye
2017-07-01
For more efficient and accurate computation of radiative flux, improvements have been achieved in two aspects, integration of the radiative transfer equation over space and angle. First, the treatment of the Monte Carlo-independent column approximation (MCICA) is modified focusing on efficiency using a reduced number of random samples ("G-packed") within a reconstructed and unified radiation package. The original McICA takes 20% of CPU time of radiation in the Global/Regional Integrated Model systems (GRIMs). The CPU time consumption of McICA is reduced by 70% without compromising accuracy. Second, parameterizations of shortwave two-stream approximations are revised to reduce errors with respect to the 16-stream discrete ordinate method. Delta-scaled two-stream approximation (TSA) is almost unanimously used in Global Circulation Model (GCM) but contains systematic errors which overestimate forward peak scattering as solar elevation decreases. These errors are alleviated by adjusting the parameterizations of each scattering element—aerosol, liquid, ice and snow cloud particles. Parameterizations are determined with 20,129 atmospheric columns of the GRIMs data and tested with 13,422 independent data columns. The result shows that the root-mean-square error (RMSE) over the all atmospheric layers is decreased by 39% on average without significant increase in computational time. Revised TSA developed and validated with a separate one-dimensional model is mounted on GRIMs for mid-term numerical weather forecasting. Monthly averaged global forecast skill scores are unchanged with revised TSA but the temperature at lower levels of the atmosphere (pressure ≥ 700 hPa) is slightly increased (< 0.5 K) with corrected atmospheric absorption.
Bonetto, P.; Qi, Jinyi; Leahy, R. M.
2000-08-01
Describes a method for computing linear observer statistics for maximum a posteriori (MAP) reconstructions of PET images. The method is based on a theoretical approximation for the mean and covariance of MAP reconstructions. In particular, the authors derive here a closed form for the channelized Hotelling observer (CHO) statistic applied to 2D MAP images. The theoretical analysis models both the Poission statistics of PET data and the inhomogeneity of tracer uptake. The authors show reasonably good correspondence between these theoretical results and Monte Carlo studies. The accuracy and low computational cost of the approximation allow the authors to analyze the observer performance over a wide range of operating conditions and parameter settings for the MAP reconstruction algorithm.
A Complex Solar Coronal Jet with Two Phases
Energy Technology Data Exchange (ETDEWEB)
Chen, Jie; Su, Jiangtao; Deng, Yuanyong [Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012 (China); Priest, E. R., E-mail: chenjie@bao.ac.cn [Mathematical Institute, University of St Andrews, North Haugh, St Andrews, KY16 9SS (United Kingdom)
2017-05-01
Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an opposite-polarity fragment between them.
Potvin, Guy
2015-10-01
We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
Simple and Accurate Analytical Solutions of the Electrostatically Actuated Curled Beam Problem
Younis, Mohammad I.
2014-08-17
We present analytical solutions of the electrostatically actuated initially deformed cantilever beam problem. We use a continuous Euler-Bernoulli beam model combined with a single-mode Galerkin approximation. We derive simple analytical expressions for two commonly observed deformed beams configurations: the curled and tilted configurations. The derived analytical formulas are validated by comparing their results to experimental data in the literature and numerical results of a multi-mode reduced order model. The derived expressions do not involve any complicated integrals or complex terms and can be conveniently used by designers for quick, yet accurate, estimations. The formulas are found to yield accurate results for most commonly encountered microbeams of initial tip deflections of few microns. For largely deformed beams, we found that these formulas yield less accurate results due to the limitations of the single-mode approximations they are based on. In such cases, multi-mode reduced order models need to be utilized.
Xie, Beibei; Kong, Lingfu; Kong, Deming; Kong, Weihang; Li, Lei; Liu, Xingbin; Chen, Jiliang
2017-11-01
In order to accurately measure the flow rate under the low yield horizontal well conditions, an auto-cumulative flowmeter (ACF) was proposed. Using the proposed flowmeter, the oil flow rate in horizontal oil-water two-phase segregated flow can be finely extracted. The computational fluid dynamics software Fluent was used to simulate the fluid of the ACF in oil-water two-phase flow. In order to calibrate the simulation measurement of the ACF, a novel oil flow rate measurement method was further proposed. The models of the ACF were simulated to obtain and calibrate the oil flow rate under different total flow rates and oil cuts. Using the finite-element method, the structure of the seven conductance probes in the ACF was simulated. The response values for the probes of the ACF under the conditions of oil-water segregated flow were obtained. The experiments for oil-water segregated flow under different heights of the oil accumulation in horizontal oil-water two-phase flow were carried out to calibrate the ACF. The validity of the oil flow rate measurement in horizontal oil-water two-phase flow was verified by simulation and experimental results.
International Nuclear Information System (INIS)
Sanchez, Richard.
1980-11-01
This work is divided into two parts: the first part deals with the solution of complex two-dimensional transport problems, the second one (note CEA-N-2166) treats the critically mixed methods of resolution. A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the interface current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding, and water, or homogenized structural material. The cells are divided into zones that are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is effected by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: CALLIOPE uses a cylindrical cell model and one or three terms for the flux expansion, and NAUSICAA uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes, one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark problems and by calculations performed in the APOLLO multigroup code [fr
Qin, Feifei; Mazloomi Moqaddam, Ali; Kang, Qinjun; Derome, Dominique; Carmeliet, Jan
2018-03-01
An entropic multiple-relaxation-time lattice Boltzmann approach is coupled to a multirange Shan-Chen pseudopotential model to study the two-phase flow. Compared with previous multiple-relaxation-time multiphase models, this model is stable and accurate for the simulation of a two-phase flow in a much wider range of viscosity and surface tension at a high liquid-vapor density ratio. A stationary droplet surrounded by equilibrium vapor is first simulated to validate this model using the coexistence curve and Laplace's law. Then, two series of droplet impact behavior, on a liquid film and a flat surface, are simulated in comparison with theoretical or experimental results. Droplet impact on a liquid film is simulated for different Reynolds numbers at high Weber numbers. With the increase of the Sommerfeld parameter, onset of splashing is observed and multiple secondary droplets occur. The droplet spreading ratio agrees well with the square root of time law and is found to be independent of Reynolds number. Moreover, shapes of simulated droplets impacting hydrophilic and superhydrophobic flat surfaces show good agreement with experimental observations through the entire dynamic process. The maximum spreading ratio of a droplet impacting the superhydrophobic flat surface is studied for a large range of Weber numbers. Results show that the rescaled maximum spreading ratios are in good agreement with a universal scaling law. This series of simulations demonstrates that the proposed model accurately captures the complex fluid-fluid and fluid-solid interfacial physical processes for a wide range of Reynolds and Weber numbers at high density ratios.
Qualitative behaviour of incompressible two-phase flows with phase ...
Indian Academy of Sciences (India)
Jan Prüss
2017-11-07
Nov 7, 2017 ... Qualitative behaviour of incompressible two-phase flows with phase ... Germany. 2Graduate School of Human and Environmental Studies, Kyoto University, ... Note that j is a dummy variable as it can be eliminated from the ...
Phase separation and shape deformation of two-phase membranes
International Nuclear Information System (INIS)
Jiang, Y.; Lookman, T.; Saxena, A.
2000-01-01
Within a coupled-field Ginzburg-Landau model we study analytically phase separation and accompanying shape deformation on a two-phase elastic membrane in simple geometries such as cylinders, spheres, and tori. Using an exact periodic domain wall solution we solve for the shape and phase separating field, and estimate the degree of deformation of the membrane. The results are pertinent to preferential phase separation in regions of differing curvature on a variety of vesicles. (c) 2000 The American Physical Society
Energy Technology Data Exchange (ETDEWEB)
Sim, Woo Gun; Dagdan, Banzragch [Hannam Univ., Daejeon (Korea, Republic of)
2017-03-15
Two-phase cross flow exists in many shell-and-tube heat exchangers such as condensers, evaporators, and nuclear steam generators. The drag force acting on a tube bundle subjected to air/water flow is evaluated experimentally. The cylinders subjected to two-phase flow are arranged in a normal square array. The ratio of pitch to diameter is 1.35, and the diameter of the cylinder is 18 mm. The drag force along the flow direction on the tube bundles is measured to calculate the drag coefficient and the two-phase damping ratio. The two-phase damping ratios, given by the analytical model for a homogeneous two-phase flow, are compared with experimental results. The correlation factor between the frictional pressure drop and the hydraulic drag coefficient is determined from the experimental results. The factor is used to calculate the drag force analytically. It is found that with an increase in the mass flux, the drag force, and the drag coefficients are close to the results given by the homogeneous model. The result shows that the damping ratio can be calculated using the homogeneous model for bubbly flow of sufficiently large mass flux.
The random phase approximation
International Nuclear Information System (INIS)
Schuck, P.
1985-01-01
RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more
International Nuclear Information System (INIS)
Kocifaj, Miroslav
2016-01-01
The study of diffuse light of a night sky is undergoing a renaissance due to the development of inexpensive high performance computers which can significantly reduce the time needed for accurate numerical simulations. Apart from targeted field campaigns, numerical modeling appears to be one of the most attractive and powerful approaches for predicting the diffuse light of a night sky. However, computer-aided simulation of night-sky radiances over any territory and under arbitrary conditions is a complex problem that is difficult to solve. This study addresses three concepts for modeling the artificial light propagation through a turbid stratified atmosphere. Specifically, these are two-stream approximation, iterative approach to Radiative Transfer Equation (RTE) and Method of Successive Orders of Scattering (MSOS). The principles of the methods, their strengths and weaknesses are reviewed with respect to their implications for night-light modeling in different environments. - Highlights: • Three methods for modeling nightsky radiance are reviewed. • The two-stream approximation allows for rapid calculation of radiative fluxes. • The above approach is convenient for modeling large uniformly emitting areas. • SOS is applicable to heterogeneous deployment of well-separated cities or towns. • MSOS is generally CPU less-intensive than traditional 3D RTE.
International Nuclear Information System (INIS)
Liu, Yinyan; Deng, Yuchi; Zhang, Maomao; Yu, Peining; Li, Yi
2017-01-01
Oil–water two-phase flows are commonly found in the production processes of the petroleum industry. Accurate online measurement of flow rates is crucial to ensure the safety and efficiency of oil exploration and production. A research team from Tsinghua University has developed an experimental apparatus for multiphase flow measurement based on an electrical capacitance tomography (ECT) sensor, an electrical resistance tomography (ERT) sensor, and a venturi tube. This work presents the phase fraction and flow rate measurements of oil–water two-phase flows based on the developed apparatus. Full-range phase fraction can be obtained by the combination of the ECT sensor and the ERT sensor. By data fusion of differential pressures measured by venturi tube and the phase fraction, the total flow rate and single-phase flow rate can be calculated. Dynamic experiments were conducted on the multiphase flow loop in horizontal and vertical pipelines and at various flow rates. (paper)
DEFF Research Database (Denmark)
Kaasgaard, Thomas; Leidy, Chad; Crowe, J.H.
2003-01-01
Temperature-controlled atomic force microscopy (AFM) has been used to visualize and study the structure and kinetics of ripple phases in one-component dipalmitoylphosphaticlylcholine (DPPC) and two-component dimyristoylphosphatidylcholine-distearoylphosphatidylcholine (DMPC-DSPC) lipid bilayers....... The lipid bilayers are mica-supported double bilayers in which ripple-phase formation occurs in the top bilayer. In one-component DPPC lipid bilayers, the stable and metastable ripple phases were observed. In addition, a third ripple structure with approximately twice the wavelength of the metastable...... ripples was seen. From height profiles of the AFM images, estimates of the amplitudes of the different ripple phases are reported. To elucidate the processes of ripple formation and disappearance, a ripple-phase DPPC lipid bilayer was taken through the pretransition in the cooling and the heating...
Investigation of two-phase bubbly flows using laser doppler anemometry
Marié , Jean-Louis
1983-01-01
International audience; The present work is devoted to the development of an accurate and reliable laser Doppler anemometer technique (L.D.A.) meant for the measurement of the characteristics of twoephase bubbly flows. Most of these characteristics are the various statistical moments of the velocity fluctuations and the Reynolds stress tensor components within the continuous phase but also, under well defined conditions, the mean slip velocity of the dispersed phase. Although this technique w...
Popov approximation for composite bosons in the BCS-BEC crossover
International Nuclear Information System (INIS)
Pieri, P.; Strinati, G.C.
2005-01-01
Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for pointlike bosons. This work bears on the recent experimental advances on the BCS-BEC crossover with trapped Fermi atoms, which show the need for accurate theoretical descriptions of the BEC side of the crossover
An energy-stable time-integrator for phase-field models
Vignal, Philippe
2016-12-27
We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.
An energy-stable time-integrator for phase-field models
Vignal, Philippe; Collier, N.; Dalcin, Lisandro; Brown, D.L.; Calo, V.M.
2016-01-01
We introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.
Numerical simulation of gas-liquid two-phase flow and convective heat transfer in a micro tube
International Nuclear Information System (INIS)
Fukagata, Koji; Kasagi, Nobuhide; Ua-arayaporn, Poychat; Himeno, Takehiro
2007-01-01
Numerical simulation of an air and water two-phase flow in a 20 μm ID tube is carried out. A focus is laid upon the flow and heat transfer characteristics in bubble-train flows. An axisymmetric two-dimensional flow is assumed. The finite difference method is used to solve the governing equations, while the level set method is adopted for capturing the interface of gas and liquid. In each simulation, the mean pressure gradient and the wall heat flux are kept constant. The simulation is repeated under different conditions of pressure gradient and void fraction. The superficial Reynolds numbers of gas and liquid phases studied are 0.34-13 and 16-490, respectively, and the capillary number is 0.0087-0.27. Regardless of the flow conditions, the gas-phase velocity is found approximately 1.2 times higher than the liquid-phase velocity. This is in accordance with the Armand correlation valid for two-phase flows in macro-sized tubes. The two-phase friction coefficient is found to be scaled with the Reynolds number based on the effective viscosity of the Einstein type. The computed wall temperature distribution is qualitatively similar to that observed experimentally in a mini channel. The local Nusselt number beneath the bubble is found notably higher than that of single-phase flow
Validation of Friction Models in MARS-MultiD Module with Two-Phase Cross Flow Experiment
International Nuclear Information System (INIS)
Choi, Chi-Jin; Yang, Jin-Hwa; Cho, Hyoung-Kyu; Park, Goon-Cher; Euh, Dong-Jin
2015-01-01
In the downcomer of Advanced Power Reactor 1400 (APR1400) which has direct vessel injection (DVI) lines as an emergency core cooling system, multidimensional two-phase flow may occur due to the Loss-of-Coolant-Accident (LOCA). The accurate prediction about that is high relevance to evaluation of the integrity of the reactor core. For this reason, Yang performed an experiment that was to investigate the two-dimensional film flow which simulated the two-phase cross flow in the upper downcomer, and obtained the local liquid film velocity and thickness data. From these data, it could be possible to validate the multidimensional modules of system analysis codes. In this study, MARS-MultiD was used to simulate the Yang's experiment, and obtained the local variables. Then, the friction models used in MARS-MultiD were validated by comparing the two-phase flow experimental results with the calculated local variables. In this study, the two-phase cross flow experiment was modeled by the MARS-MultiD. Compared with the experimental results, the calculated results by the code properly presented mass conservation which could be known from the relation between the liquid film velocity and thickness at the same flow rate. The magnitude and direction of the liquid film, however, did not follow well with experimental results. According to the results of Case-2, wall friction should be increased, and interfacial friction should be decreased in MARS-MultiD. These results show that it is needed to modify the friction models in the MARS-MultiD to simulate the two-phase cross flow
Accuracy of the ''decoupled l-dominant'' approximation for atom--molecule scattering
International Nuclear Information System (INIS)
Green, S.
1976-01-01
Cross sections for rotational excitation and spectral pressure broadening of HD, HCl, CO, and HCN due to collisions with low energy He atoms have been computed within the ''decoupled l-dominant'' (DLD) approximation recently suggested by DePristo and Alexander. These are compared with accurate close coupling results and also with two similar approximations, the effective potential of Rabitz and the coupled states of McGuire and Kouri. These collision systems are all dominated by short-range repulsive interactions although they have varying degrees of anisotropy and inelasticity. The coupled states method is expected to be valid for such systems, but they should be a severe test to the DLD approximation which is expected to be better for long-range interactions. Nonetheless, DLD predictions of state-to-state cross sections are rather good, being only slightly less accurate than coupled states results. DLD is far superior to either the coupled states or effective potential methods for pressure broadening calculations, although it may not be uniformly of the quantitative accuracy desirable for obtaining intermolecular potentials from experimental data
An Efficient and Packing-Resilient Two-Phase Android Cloned Application Detection Approach
Directory of Open Access Journals (Sweden)
Fang Lyu
2017-01-01
Full Text Available The huge benefit of mobile application industry has attracted a large number of developers and attendant attackers. Application repackaging provides help for the distribution of most Android malware. It is a serious threat to the entire Android ecosystem, as it not only compromises the security and privacy of the app users but also plunders app developers’ income. Although massive approaches have been proposed to address this issue, plagiarists try to fight back through packing their malicious code with the help of commercial packers. Previous works either do not consider the packing issue or rely on time-consuming computations, which are not scalable for large-scale real-world scenario. In this paper, we propose FUIDroid, a novel two-phase app clones detection system that can detect the packed cloned app. FUIDroid includes a function-based fast selection phase to quickly select suspicious apps by analyzing apps’ description and a further UI-based accurate detection phase to refine the detection result. We evaluate our system on two sets of apps. The result from experiment on 320 packed samples demonstrates that FUIDroid is resilient to packed apps. The evaluation on more than 150,000 real-world apps shows the efficiency of FUIDroid in large-scale scenario.
Directory of Open Access Journals (Sweden)
Mergheni Ali Mohamed
2008-01-01
Full Text Available For simultaneous measurement of size and velocity distributions of continuous and dispersed phases in a two-phase flow a technique phase-Doppler anemometry was used. Spherical glass particles with a particle diameter range from 102 up to 212 µm were used. In this two-phase flow an experimental results are presented which indicate a significant influence of the solid particles on the flow characteristics. The height of influence of these effects depends on the local position in the jet. Near the nozzle exit high gas velocity gradients exist and therefore high turbulence production in the shear layer of the jet is observed. Here the turbulence intensity in the two-phase jet is decreased compared to the single-phase jet. In the developed zone the velocity gradient in the shear layer is lower and the turbulence intensity reduction is higher. .
Roles of antinucleon degrees of freedom in the relativistic random phase approximation
Kurasawa, Haruki; Suzuki, Toshio
2015-11-01
The roles of antinucleon degrees of freedom in the relativistic random phase approximation (RPA) are investigated. The energy-weighted sum of the RPA transition strengths is expressed in terms of the double commutator between the excitation operator and the Hamiltonian, as in nonrelativistic models. The commutator, however, should not be calculated in the usual way in the local field theory, because, otherwise, the sum vanishes. The sum value obtained correctly from the commutator is infinite, owing to the Dirac sea. Most of the previous calculations take into account only some of the nucleon-antinucleon states, in order to avoid divergence problems. As a result, RPA states with negative excitation energy appear, which make the sum value vanish. Moreover, disregarding the divergence changes the sign of nuclear interactions in the RPA equation that describes the coupling of the nucleon particle-hole states with the nucleon-antinucleon states. Indeed, the excitation energies of the spurious state and giant monopole states in the no-sea approximation are dominated by these unphysical changes. The baryon current conservation can be described without touching the divergence problems. A schematic model with separable interactions is presented, which makes the structure of the relativistic RPA transparent.
Thermo-Fluid Dynamics of Two-Phase Flow
Ishii, Mamrou
2011-01-01
"Thermo-fluid Dynamics of Two-Phase Flow, Second Edition" is focused on the fundamental physics of two-phase flow. The authors present the detailed theoretical foundation of multi-phase flow thermo-fluid dynamics as they apply to: Nuclear reactor transient and accident analysis; Energy systems; Power generation systems; Chemical reactors and process systems; Space propulsion; Transport processes. This edition features updates on two-phase flow formulation and constitutive equations and CFD simulation codes such as FLUENT and CFX, new coverage of the lift force model, which is of part
Padé approximant for normal stress differences in large-amplitude oscillatory shear flow
Poungthong, P.; Saengow, C.; Giacomin, A. J.; Kolitawong, C.; Merger, D.; Wilhelm, M.
2018-04-01
Analytical solutions for the normal stress differences in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the inexact form of the first few terms of a series expansion in the shear rate amplitude. Here, we improve the accuracy of these truncated expansions by replacing them with rational functions called Padé approximants. The recent advent of exact solutions in LAOS presents an opportunity to identify accurate and useful Padé approximants. For this identification, we replace the truncated expansion for the corotational Jeffreys fluid with its Padé approximants for the normal stress differences. We uncover the most accurate and useful approximant, the [3,4] approximant, and then test its accuracy against the exact solution [C. Saengow and A. J. Giacomin, "Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow," Phys. Fluids 29, 121601 (2017)]. We use Ewoldt grids to show the stunning accuracy of our [3,4] approximant in LAOS. We quantify this accuracy with an objective function and then map it onto the Pipkin space. Our two applications illustrate how to use our new approximant reliably. For this, we use the Spriggs relations to generalize our best approximant to multimode, and then, we compare with measurements on molten high-density polyethylene and on dissolved polyisobutylene in isobutylene oligomer.
Finite rank separable approximation for Skyrme interactions: spin-isospin excitations
International Nuclear Information System (INIS)
Severyukhin, A.P.; Voronov, V.V.; Borzov, I.N.; Nguyen Van Giai
2012-01-01
A finite rank separable approximation for the quasiparticle random phase approximation with the Skyrme interactions is applied for the case of charge-exchange nuclear modes. The coupling between one- and two-phonon terms in the wave functions is taken into account. It has been shown that the approximation reproduces reasonably well the full charge-exchange RPA results for the spin-dipole resonances in 132 Sn. As an illustration of the method, the phonon-phonon coupling effect on the β-decay half-life of 78 Ni is considered
'LTE-diffusion approximation' for arc calculations
International Nuclear Information System (INIS)
Lowke, J J; Tanaka, M
2006-01-01
This paper proposes the use of the 'LTE-diffusion approximation' for predicting the properties of electric arcs. Under this approximation, local thermodynamic equilibrium (LTE) is assumed, with a particular mesh size near the electrodes chosen to be equal to the 'diffusion length', based on D e /W, where D e is the electron diffusion coefficient and W is the electron drift velocity. This approximation overcomes the problem that the equilibrium electrical conductivity in the arc near the electrodes is almost zero, which makes accurate calculations using LTE impossible in the limit of small mesh size, as then voltages would tend towards infinity. Use of the LTE-diffusion approximation for a 200 A arc with a thermionic cathode gives predictions of total arc voltage, electrode temperatures, arc temperatures and radial profiles of heat flux density and current density at the anode that are in approximate agreement with more accurate calculations which include an account of the diffusion of electric charges to the electrodes, and also with experimental results. Calculations, which include diffusion of charges, agree with experimental results of current and heat flux density as a function of radius if the Milne boundary condition is used at the anode surface rather than imposing zero charge density at the anode
Approximate anlysis of an unreliable $M/M/c$ retrial queue with phase merging algorithm.
Directory of Open Access Journals (Sweden)
faiza BELARBI
2016-06-01
Full Text Available In this paper, we investigate an approximate analysis of unreliable $M/M/c$ retrial queue with $c\\geq 3$ in which all servers are subject to breakdowns and repairs. Arriving customers that are unable to access a server due to congestion or failure can choose to enter a retrial orbit for an exponentially distributed amount of time and persistently attempt to gain access to a server, or abandon their request and depart the system. Once a customer is admitted to a service station, they remain there for a random duration until service is complete and then depart the system. However, if the server fails during service, i.e., an active breakdown, the customer may choose to abandon the system or proceed directly to the retrial orbit while the server begins repair immediately. In the unreliable model, there are no exact solutions when the number of servers exceeds one. Therefore, we seek to approximate the steady-state joint distribution of the number of customers in orbit and the status of the $c$ servers for the case of Markovian arrival and service times. Our approach to deriving the approximate steady-state probabilities employs a phase-merging algorithm.
Nonlinear dynamics of two-phase flow
International Nuclear Information System (INIS)
Rizwan-uddin
1986-01-01
Unstable flow conditions can occur in a wide variety of laboratory and industry equipment that involve two-phase flow. Instabilities in industrial equipment, which include boiling water reactor (BWR) cores, steam generators, heated channels, cryogenic fluid heaters, heat exchangers, etc., are related to their nonlinear dynamics. These instabilities can be of static (Ledinegg instability) or dynamic (density wave oscillations) type. Determination of regions in parameters space where these instabilities can occur and knowledge of system dynamics in or near these regions is essential for the safe operation of such equipment. Many two-phase flow engineering components can be modeled as heated channels. The set of partial differential equations that describes the dynamics of single- and two-phase flow, for the special case of uniform heat flux along the length of the channel, can be reduced to a set of two coupled ordinary differential equations [in inlet velocity v/sub i/(t) and two-phase residence time tau(t)] involving history integrals: a nonlinear ordinary functional differential equation and an integral equation. Hence, to solve these equations, the dependent variables must be specified for -(nu + tau) ≤ t ≤ 0, where nu is the single-phase residence time. This system of nonlinear equations has been solved analytically using asymptotic expansion series for finite but small perturbations and numerically using finite difference techniques
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
Application of the random phase approximation to some atoms with ns2 ground state configurations
International Nuclear Information System (INIS)
Wright, L.A.
1975-01-01
Atomic bound state properties such as excitation energies and oscillator strengths were calculated by the Random Phase Approximation (RPA), also known as the Time Dependent Hartree-Fock Approximation (TDHFA). The RPA is equivalent to describing excited states as the creation of particle-hole pairs and the application to atoms is important for two reasons: the wide range of densities in an atom will cause the physical interpretation and mathematical approximations to be much different than with a uniform density system, such as an electron gas; this method could detect the existence of collective states in atoms similar to those responsible for the giant dipole resonances in nuclei. The method is shown to be superior to the H-F method in three basic ways: (1) The RPA contains explicit correlations between the excited and ground states. These are not included in the H-F theory. One can apply this method to large atoms since only these correlations are explicitly included. (2) The RPA calculates excitation energies directly without recourse to highly correlated ground state wavefunctions. This is in contrast to the method of configuration mixing which is known to have slow convergence properties. (3) Oscillator strengths and photoionization cross sections can be calculated by finding the eigenvectors corresponding excitation energy eigenvalues. The strength of the RPA is that the excitation energies and oscillator strengths, which are relative quantities, are calculated directly. The results for the oscillator strengths show an improvement of up to 45 percent over the H-F values and an improvement over the RPA done with Hartree wavefunctions by as much as 65 percent. The work was limited to atoms with an ns 2 ground state configuration. These atoms were He, Be, Mg and Ca
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
Vibration response of a pipe subjected to two-phase flow: Analytical formulations and experiments
Energy Technology Data Exchange (ETDEWEB)
Ortiz-Vidal, L. Enrique, E-mail: leortiz@sc.usp.br [Department of Mechanical Engineering, Sao Carlos School of Engineering, University of Sao Paulo (USP), Av., Trabalhador São-carlense, 400, 13566-970 São Carlos, SP (Brazil); Mureithi, Njuki W., E-mail: njuki.mureithi@polymtl.ca [Department of Mechanical Engineering, Polytechnique Montreal, Département de Géniemécanique 2900, H3T 1J7 Montreal, QC (Canada); Rodriguez, Oscar M.H., E-mail: oscarmhr@sc.usp.br [Department of Mechanical Engineering, Sao Carlos School of Engineering, University of Sao Paulo (USP), Av., Trabalhador São-carlense, 400, 13566-970 São Carlos, SP (Brazil)
2017-03-15
Highlights: • Analytical formulations for two-phase flow-induced vibration (2-FIV) are presented. • Standard deviation of acceleration pipe response is a function of the square of shear velocity. • Peak frequency is correlated to hydrodynamic mass and consequently to void fraction. • Dynamic pipe response increases with increasing mixture velocity and void fraction. • Hydrodynamic mass in 2-FIV in horizontal pipe is proportional to mixture density. - Abstract: This paper treats the two-phase flow-induced vibration in pipes. A broad range of two-phase flow conditions, including bubbly, dispersed and slug flow, were tested in a clamped-clamped straight horizontal pipe. The vibration response of both transversal directions for two span lengths was measured. From experimental results, an in-depth discussion on the nature of the flow excitation and flow-parameters influence is presented. The hydrodynamic mass parameter is also studied. Experimental results suggest that it is proportional to mixture density. On the other hand, two analytical formulations were developed and tested against experimental results. One formulation predicts the quadratic trend between standard deviation of acceleration and shear velocity found in experiments. The other formulation indicates that the peak-frequency of vibration response depends strongly on void fraction. It provides accurate predictions of peak-frequency, predicting 97.6% of the data within ±10% error bands.
International Nuclear Information System (INIS)
Soysal, A.O.; Semlyen, A.
1994-01-01
A general methodology is presented for the state equation approximation of a multiple input-output linear system from transfer matrix data. A complex transformation matrix, obtained by eigen analysis at a fixed frequency, is used for diagonalization of the transfer matrix over the whole frequency range. A scalar estimation procedure is applied for identification of the modal transfer functions. The state equations in the original coordinates are obtained by inverse transformation. An iterative Gauss-Newton refinement process is used to reduce the overall error of the approximation. The developed methodology is applied to the phase domain modeling of untransposed transmission lines. The approach makes it possible to perform EMTP calculations directly in the phase domain. This results in conceptual simplification and savings in computation time since modal transformations are not needed in the sequences of the transient analysis. The presented procedure is compared with the conventional modal approach in terms of accuracy and computation time
A review of damping of two-phase flows
International Nuclear Information System (INIS)
Hara, Fumio
1993-01-01
Damping of two-phase flows has been recognized as one of the most unknown parameters in analyzing vibrational characteristics of structures subjected to two-phase flows since it seems to be influenced by many physical parameters involved in the physics of dynamic energy dissipation of a vibrating structure, for example, liquid viscosity, surface tension, flow velocity, mass ratio, frequency, void fraction, flow regime and so forth. This paper deals with a review of scientific works done to date on the damping of two phase flows and discussions about what has been clarified and what has not been known to us, or what kinds of research are needed about two-phase flow damping. The emphasis is put on the definition of two-phase fluid damping, damping measurement techniques, damping characteristics in relation to two phase flow configurations, and damping generation mechanisms
Mergheni Ali Mohamed; Ben Ticha Hmaied; Sautet Jen-Charles; Godard Gille; Ben Nasrallah Sassi
2008-01-01
For simultaneous measurement of size and velocity distributions of continuous and dispersed phases in a two-phase flow a technique phase-Doppler anemometry was used. Spherical glass particles with a particle diameter range from 102 up to 212 µm were used. In this two-phase flow an experimental results are presented which indicate a significant influence of the solid particles on the flow characteristics. The height of influence of these effects depends on the local position in the jet. Near t...
Two-phase systems. Fundamentals and industrial applications
International Nuclear Information System (INIS)
Woillez, Jacques
2014-01-01
Two-phase flows are omnipresent in industrial processes in different sectors with the behaviour and control of non-mixing mixtures of gas and liquids, of several liquids, of solids and fluids which are present in the production of raw materials, in the environment, in energy production, in chemistry, in pharmaceutical or food industry. The author presents the fundamentals elements which are needed to perform hardware predictive calculations and to understand typical phenomena associated with these flows. The chapters address fluids mechanics (movement equations, Bernoulli equation, load losses, turbulence, heat exchange coefficients, thermodynamics, compressible flows), two-phase systems (characteristic values, modes of appearance of two-phase flows, conduct flows, suspension mechanics, mass transfers, similarity, numerical simulation), the applications (energy production, agitation and mixing, phase separation, sprays), and peculiar phenomena (Marangoni effect, the tea cup effect, entry jets, water hammer effect, sound speed, two-phase pumping, fluidization)
Two-dimensional phase fraction charts
International Nuclear Information System (INIS)
Morral, J.E.
1984-01-01
A phase fraction chart is a graphical representation of the amount of each phase present in a system as a function of temperature, composition or other variable. Examples are phase fraction versus temperature charts used to characterize specific alloys and as a teaching tool in elementary texts, and Schaeffler diagrams used to predict the amount of ferrite in stainless steel welds. Isothermal-transformation diagrams (TTT diagrams) are examples that give phase (or microconstituent) amount versus temperature and time. The purpose of this communication is to discuss the properties of two-dimensional phase fraction charts in more general terms than have been reported before. It is shown that they can represent multi-component, multiphase equilibria in a way which is easier to read and which contains more information than the isotherms and isopleths of multi-component phase diagrams
Thermal hydraulics-II. 2. Benchmarking of the TRIO Two-Phase-Flow Module
International Nuclear Information System (INIS)
Helton, Donald; Kumbaro, Anela; Hassan, Yassin
2001-01-01
The Commissariat a l'Energie Atomique (CEA) is currently developing a two-phase-flow module for the Trio-U CFD computer program. Work in the area of advanced numerical technique application to two-phase flow is being carried out by the SYSCO division at the CEA Saclay center. Recently, this division implemented several advanced numerical solvers, including approximate Riemann solvers and flux vector splitting schemes. As a test of these new advances, several benchmark tests were executed. This paper describes the pertinent results of this study. The first benchmark problem was the Ransom faucet problem. This problem consists of a vertical column of water acting under the gravity force. The appeal of this problem is that it tests the program's handling of the body force term and it has an analytical solution. The Trio results [based on a two-fluid, two-dimensional (2-D) simulation] for this problem were very encouraging. The two-phase-flow module was able to reproduce the analytical velocity and void fraction profiles. A reasonable amount of numerical diffusion was observed, and the numerical solution converged to the analytical solution as the grid size was refined, as shown in Fig. 1. A second series of benchmark problems is concerned with the employment of a drag force term. In a first approach, we test the capability of the code to take account of this source term, using a flux scheme solution technique. For this test, a rectangular duct was utilized. As shown in Fig. 2, mesh refinement results in an approach to the analytical solution. Next, a convergent/divergent nozzle problem is proposed. The nozzle is characterized by a brief contraction section and a long expansion section. A two-phase, 2-D, non-condensing model is used in conjunction with the Rieman solver. Figure 3 shows a comparison of the pressure profile for the experimental case and for the values calculated by the TRIO U two-phase-flow module. Trio was able to handle the drag force term and
An approximate fractional Gaussian noise model with computational cost
Sørbye, Sigrunn H.
2017-09-18
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length $n$ using a likelihood-based approach is ${\\\\mathcal O}(n^{2})$, exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to ${\\\\mathcal O}(n^{3})$. This paper presents an approximate fGn model of ${\\\\mathcal O}(n)$ computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved by approximating fGn with a weighted sum of independent first-order autoregressive processes, fitting the parameters of the approximation to match the autocorrelation function of the fGn model. The resulting approximation is stationary despite being Markov and gives a remarkably accurate fit using only four components. The performance of the approximate fGn model is demonstrated in simulations and two real data examples.
Surface wake in the random-phase approximation
International Nuclear Information System (INIS)
Garcia de Abajo, F.J.; Echenique, P.M.
1993-01-01
The scalar-electric-potential distribution set up by an ion traveling in the vicinity of a plane solid-vacuum interface, that is, the surface-wake potential, is investigated with the specular-reflection model to describe the response of the surface and with the random-phase approximation for the dielectric function of the bulk material. This permits us to address the study of the low-velocity surface wake: the static potential is found to have a dip at the position of the ion; that dip is shifted towards the direction opposite to the velocity vector for velocities smaller than the threshold of creation of plasmons (∼1.3v F ). Extensive numerical calculations are presented for an ion both inside and outside aluminum. Comparison to the results obtained with the plasmon-pole dielectric function indicates excellent agreement for velocities larger than ∼1.3v F . On the other side, the possibility of surface-wake riding is suggested, by analogy with bulk-wake riding postulated in the past. In it, the electron would be bound in the first trough of the surface-wake potential set up when the ion describes a grazing trajectory. The main feature introduced by the surface with respect to the bulk consists of allowing the use of ions of higher charge, reducing in this way the relative importance of the electron self-energy, and in addition, giving rise to larger binding energies. When the ion beam is directed along a special direction of an oriented crystal surface, the mechanism of resonant coherent excitation could provide a way for experimentally detecting this phenomenon through the emission of the bound electron with well-defined energy and around a preferential direction
Two-Phase Acto-Cytosolic Fluid Flow in a Moving Keratocyte: A 2D Continuum Model.
Nikmaneshi, M R; Firoozabadi, B; Saidi, M S
2015-09-01
The F-actin network and cytosol in the lamellipodia of crawling cells flow in a centripetal pattern and spout-like form, respectively. We have numerically studied this two-phase flow in the realistic geometry of a moving keratocyte. Cytosol has been treated as a low viscosity Newtonian fluid flowing through the high viscosity porous medium of F-actin network. Other involved phenomena including myosin activity, adhesion friction, and interphase interaction are also discussed to provide an overall view of this problem. Adopting a two-phase coupled model by myosin concentration, we have found new accurate perspectives of acto-cytosolic flow and pressure fields, myosin distribution, as well as the distribution of effective forces across the lamellipodia of a keratocyte with stationary shape. The order of magnitude method is also used to determine the contribution of forces in the internal dynamics of lamellipodia.
Relativistic continuum random phase approximation in spherical nuclei
International Nuclear Information System (INIS)
Daoutidis, Ioannis
2009-01-01
Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)
Relativistic continuum random phase approximation in spherical nuclei
Energy Technology Data Exchange (ETDEWEB)
Daoutidis, Ioannis
2009-10-01
Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)
When Density Functional Approximations Meet Iron Oxides.
Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-Dong
2016-10-11
Three density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
Ren, Xinguo; Rinke, Patrick; Tkatchenko, Alexandre; Scheffler, Matthias
2010-01-01
The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice-evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals-leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior ca...
Review of two-phase instabilities
Energy Technology Data Exchange (ETDEWEB)
Kang, Han Ok; Seo, Han Ok; Kang, Hyung Suk; Cho, Bong Hyun; Lee, Doo Jeong
1997-06-01
KAERI is carrying out a development of the design for a new type of integral reactors. The once-through helical steam generator is important design features. The study on designs and operating conditions which prevent flow instability should precede the introduction of one-through steam generator. Experiments are currently scheduled to understand two-phase instability, evaluate the effect of each design parameter on the critical point, and determine proper inlet throttling for the prevention of instability. This report covers general two-phase instability with review of existing studies on this topics. The general classification of two phase flow instability and the characteristics of each type of instability are first described. Special attention is paid to BWR core flow instability and once-through steam generator instability. The reactivity feedback and the effect of system parameters are treated mainly for BWR. With relation to once-through steam generators, the characteristics of convective heating and dryout point oscillation are first investigated and then the existing experimental studies are summarized. Finally chapter summarized the proposed correlations for instability boundary conditions. (author). 231 refs., 5 tabs., 47 figs
Cheng, Lixin; Bandarra Filho, Enio P; Thome, John R
2008-07-01
Nanofluids are a new class of fluids engineered by dispersing nanometer-size solid particles in base fluids. As a new research frontier, nanofluid two-phase flow and thermal physics have the potential to improve heat transfer and energy efficiency in thermal management systems for many applications, such as microelectronics, power electronics, transportation, nuclear engineering, heat pipes, refrigeration, air-conditioning and heat pump systems. So far, the study of nanofluid two-phase flow and thermal physics is still in its infancy. This field of research provides many opportunities to study new frontiers but also poses great challenges. To summarize the current status of research in this newly developing interdisciplinary field and to identify the future research needs as well, this paper focuses on presenting a comprehensive review of nucleate pool boiling, flow boiling, critical heat flux, condensation and two-phase flow of nanofluids. Even for the limited studies done so far, there are some controversies. Conclusions and contradictions on the available nanofluid studies on physical properties, two-phase flow, heat transfer and critical heat flux (CHF) are presented. Based on a comprehensive analysis, it has been realized that the physical properties of nanofluids such as surface tension, liquid thermal conductivity, viscosity and density have significant effects on the nanofluid two-phase flow and heat transfer characteristics but the lack of the accurate knowledge of these physical properties has greatly limited the study in this interdisciplinary field. Therefore, effort should be made to contribute to the physical property database of nanofluids as a first priority. Secondly, in particular, research on nanofluid two-phase flow and heat transfer in microchannels should be emphasized in the future.
Analysis of water hammer in two-component two-phase flows
International Nuclear Information System (INIS)
Warde, H.; Marzouk, E.; Ibrahim, S.
1989-01-01
The water hammer phenomena caused by a sudden valve closure in air-water two-phase flows must be clarified for the safety analysis of LOCA in reactors and further for the safety of boilers, chemical plants, pipe transport of fluids such as petroleum and natural gas. In the present work water hammer phenomena caused by sudden valve closure in two-component two-phase flows are investigated theoretically and experimentally. The phenomena are more complicated than in single phase-flows due to the fact of the presence of compressible component. Basic partial differential equations based on a one-dimensional homogeneous flow model are solved by the method of characteristic. The analysis is extended to include friction in a two-phase mixture depending on the local flow pattern. The profiles of the pressure transients, the propagation velocity of pressure waves and the effect of valve closure on the transient pressure are found. Different two-phase flow pattern and frictional pressure drop correlations were used including Baker, Chesholm and Beggs and Bril correlations. The effect of the flow pattern on the characteristic of wave propagation is discussed primarily to indicate the effect of void fraction on the velocity of wave propagation and on the attenuation of pressure waves. Transient pressure in the mixture were recorded at different air void fractions, rates of uniform valve closure and liquid flow velocities with the aid of pressure transducers, transient wave form recorders interfaced with an on-line pc computer. The results are compared with computation, and good agreement was obtained within experimental accuracy
Magnetic liquid metal two-phase flow research. Phase 1. Final report
International Nuclear Information System (INIS)
Graves, R.D.
1983-04-01
The Phase I research demonstrates the feasibility of the magnetic liquid metal (MLM) two-phase flow concept. A dispersion analysis is presented based on a complete set of two-phase-flow equations augmented to include stresses due to magnetic polarization of the fluid. The analysis shows that the stability of the MLM two-phase flow is determined by the magnetic Mach number, the slip ratio, geometry of the flow relative to the applied magnetic field, and by the voidage dependence of the interfacial forces. Results of a set of experiments concerned with magnetic effects on the dynamics of single bubble motion in an aqueous-based, viscous, conducting magnetic fluid are presented. Predictions in the theoretical literature are qualitatively verified using a bench-top experimental apparatus. In particular, applied magnetic fields are seen to lead to reduced bubble size at fixed generating orifice pressure
International Nuclear Information System (INIS)
Numano, M.
1976-01-01
The growth rates for the ionization instability obtained using the Saha and temperature relaxation approximations are compared with those obtained from an exact treatment, and the requirements for validity of these two approximations are obtained analytically. For the range of plasma parameters pertinent to MHD power generation it is found that the Saha approximation is valid for relatively high electron temperature, which it becomes inapplicable as the electron temperature is decreased. On the other hand, the temperature relaxation approximation is accurate over a wide range of electron temperature. It is found also that the marginal condition for the ionization instability is correctly obtained from both approximations. (author)
Legendre-tau approximations for functional differential equations
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Two-phase flow in fractured rock
International Nuclear Information System (INIS)
Davies, P.; Long, J.; Zuidema, P.
1993-11-01
This report gives the results of a three-day workshop on two-phase flow in fractured rock. The workshop focused on two-phase flow processes that are important in geologic disposal of nuclear waste as experienced in a variety of repository settings. The goals and objectives of the workshop were threefold: exchange information; describe the current state of understanding; and identify research needs. The participants were divided into four subgroups. Each group was asked to address a series of two-phase flow processes. The following groups were defined to address these processes: basic flow processes; fracture/matrix interactions; complex flow processes; and coupled processes. For each process, the groups were asked to address these four issues: (1) describe the two-phase flow processes that are important with respect to repository performance; (2) describe how this process relates to the specific driving programmatic issues given above for nuclear waste storage; (3) evaluate the state of understanding for these processes; and (4) suggest additional research to address poorly understood processes relevant to repository performance. The reports from each of the four working groups are given here
A two-fluid approximation for calculating the cosmic microwave background anisotropies
Seljak, Uros
1994-01-01
We present a simplified treatment for calculating the cosmic microwave background anisotropy power spectrum in adiabatic models. It consists of solving for the evolution of a two-fluid model until the epoch of recombination and then integrating over the sources to obtain the cosmic microwave background (CMB) anisotropy power spectrum. The approximation is useful both for a physical understanding of CMB anisotropies as well as for a quantitative analysis of cosmological models. Comparison with exact calculations shows that the accuracy is typically 10%-20% over a large range of angles and cosmological models, including those with curvature and cosmological constant. Using this approximation we investigate the dependence of the CMB anisotropy on the cosmological parameters. We identify six dimensionless parameters that uniquely determine the anisotropy power spectrum within our approximation. CMB experiments on different angular scales could in principle provide information on all these parameters. In particular, mapping of the Doppler peaks would allow an independent determination of baryon mass density, matter mass density, and the Hubble constant.
Industrial aspects of gas-liquid two-phase flow
International Nuclear Information System (INIS)
Hewitt, G.F.
1977-01-01
The lecture begins by reviewing the various types of plant in which two phase flow occurs. Specifically, boiling plant, condensing plant and pipelines are reviewed, and the various two phase flow problems occurring in them are described. Of course, many other kinds of chemical engineering plant involve two phase flow, but are somewhat outside the scope of this lecture. This would include distillation columns, vapor-liquid separators, absorption towers etc. Other areas of industrial two phase flow which have been omitted for space reasons from this lecture are those concerned with gas/solids, liquid/solid and liquid/liquid flows. There then follows a description of some of the two phase flow processes which are relevant in industrial equipment and where special problems occur. The topics chosen are as follows: (1) pressure drop; (2) horizontal tubes - separation effects non-uniformites in heat transfer coefficient, effect of bends on dryout; (3) multicomponent mixtures - effects in pool boiling, mass transfer effects in condensation and Marangoni effects; (4) flow distribution - manifold problems in single phase flow, separation effects at a single T-junction in two phase flow and distribution in manifolds in two phase flow; (5) instability - oscillatory instability, special forms of instability in cryogenic systems; (6) nucleate boiling - effect of variability of surface, unresolved problems in forced convective nucleate boiling; and (7) shell side flows - flow patterns, cross flow boiling, condensation in cross flow
Relativistic quasiparticle random phase approximation with a separable pairing force
International Nuclear Information System (INIS)
Tian Yuan; Ma Zhongyu; Ring Peter
2009-01-01
In our previous work, we introduced a separable pairing force for relativistic Hartree-Bogoliubov calculations. This force was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. By using the well known techniques of Talmi and Moshinsky it can be expanded in a series of separable terms and converges quickly after a few terms. It was found that the pairing properties can be depicted on almost the same footing as the original pairing interaction, not only in nuclear matter, but also in finite nuclei. In this study, we construct a relativistic quasiparticle random phase approximation (RQRPA) with this separable pairing interaction and calculate the excitation energies of the first excited 2 + states and reduced B(E2; 0 + →2 + ) transition rates for a chain of Sn isotopes in RQRPA. Compared with the results of the full Gogny force, we find that this simple separable pairing interaction can describe the pairing properties of the excited vibrational states as well as the original pairing interaction. (authors)
Wheeler, M.F.
2010-09-06
For many years there have been formulations considered for modeling single phase ow on general hexahedra grids. These include the extended mixed nite element method, and families of mimetic nite di erence methods. In most of these schemes either no rate of convergence of the algorithm has been demonstrated both theoret- ically and computationally or a more complicated saddle point system needs to be solved for an accurate solution. Here we describe a multipoint ux mixed nite element (MFMFE) method [5, 2, 3]. This method is motivated from the multipoint ux approximation (MPFA) method [1]. The MFMFE method is locally conservative with continuous ux approximations and is a cell-centered scheme for the pressure. Compared to the MPFA method, the MFMFE has a variational formulation, since it can be viewed as a mixed nite element with special approximating spaces and quadrature rules. The framework allows han- dling of hexahedral grids with non-planar faces by applying trilinear mappings from physical elements to reference cubic elements. In addition, there are several multi- scale and multiphysics extensions such as the mortar mixed nite element method that allows the treatment of non-matching grids [4]. Extensions to the two-phase oil-water ow are considered. We reformulate the two- phase model in terms of total velocity, capillary velocity, water pressure, and water saturation. We choose water pressure and water saturation as primary variables. The total velocity is driven by the gradient of the water pressure and total mobility. Iterative coupling scheme is employed for the coupled system. This scheme allows treatments of di erent time scales for the water pressure and water saturation. In each time step, we rst solve the pressure equation using the MFMFE method; we then Center for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; mfw@ices.utexas.edu. yCenter for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; gxue
Linear-scaling implementation of the direct random-phase approximation
International Nuclear Information System (INIS)
Kállay, Mihály
2015-01-01
We report the linear-scaling implementation of the direct random-phase approximation (dRPA) for closed-shell molecular systems. As a bonus, linear-scaling algorithms are also presented for the second-order screened exchange extension of dRPA as well as for the second-order Møller–Plesset (MP2) method and its spin-scaled variants. Our approach is based on an incremental scheme which is an extension of our previous local correlation method [Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The approach extensively uses local natural orbitals to reduce the size of the molecular orbital basis of local correlation domains. In addition, we also demonstrate that using natural auxiliary functions [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], the size of the auxiliary basis of the domains and thus that of the three-center Coulomb integral lists can be reduced by an order of magnitude, which results in significant savings in computation time. The new approach is validated by extensive test calculations for energies and energy differences. Our benchmark calculations also demonstrate that the new method enables dRPA calculations for molecules with more than 1000 atoms and 10 000 basis functions on a single processor
Dynamic Modeling of Phase Crossings in Two-Phase Flow
DEFF Research Database (Denmark)
Madsen, Søren; Veje, Christian; Willatzen, Morten
2012-01-01
by a high resolution finite difference scheme due to Kurganov and Tadmore. The homogeneous formulation requires a set of thermodynamic relations to cover the entire range from liquid to gas state. This leads a number of numerical challenges since these relations introduce discontinuities in the derivative...... of the variables and are usually very slow to evaluate. To overcome these challenges, we use an interpolation scheme with local refinement. The simulations show that the method handles crossing of the saturation lines for both liquid to two-phase and two-phase to gas regions. Furthermore, a novel result obtained...
Second-law analysis of a two-phase self-pumping solar water heater
International Nuclear Information System (INIS)
Walker, H.A.; Davidson, J.H.
1992-01-01
In this paper entropy generated by operation of a two-phase self-pumping solar water heater under Solar Rating and Certification Corporation rating conditions is computed numerically in a methodology based on an exergy cascade. An order of magnitude analysis shows that entropy generation is dominated by heat transfer across temperature differences. Conversion of radiant solar energy incident on the collector to thermal energy within the collector accounts for 87.1 percent of total entropy generation. Thermal losses are responsible for 9.9 percent of total entropy generation, and heat transfer across the condenser accounts for 2.4 percent of the total entropy generation. Mixing in the tempering valve is responsible for 0.7 percent of the total entropy generation. Approximately one half of the entropy generated by thermal losses is attributable to the self-pumping process. The procedure to determine total entropy generation can be used in a parametric study to evaluate the performance of two-phase hot water heating systems relative to other solar water heating options
Random phase approximations for the screening function in high Tc superconductors
International Nuclear Information System (INIS)
Lopez-Aguilar, F.; Costa-Quintana, J.; Sanchez, A.; Puig, T.; Aurell, M.T.; Martinez, L.M.; Munoz, J.S.
1990-01-01
This paper reports on the electronic transferences from the CuO 2 sheets toward the CuO 3 linear chain, which locate electrons in the orbitals p y /p z of O4/O1 and d z 2 -y 2 of Cu1, and holes in the orbitals d x 2 -y 2 - P z /p y of Cu2 - P2/O3. These holes states present large interatomic overlapping. In this paper, we determine the screening function within the random phase approximation applied to the high-T c superconductors. This screening function is vanishing for determined values of the frequency which correspond to renormalized plasmon frequencies. These frequencies depends on the band parameters and their knowledge is essential for determining the self energy. This self energy is deduced and it contain independent terms for each of the channels for the localization
Relativistic quasiparticle random-phase approximation calculation of total muon capture rates
International Nuclear Information System (INIS)
Marketin, T.; Paar, N.; Niksic, T.; Vretenar, D.
2009-01-01
The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from 12 C to 244 Pu, for which experimental values are available. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the pn-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value g A =1.262 by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.
Multilevel Monte Carlo in Approximate Bayesian Computation
Jasra, Ajay
2017-02-13
In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.
The geometric phase in two-level atomic systems
International Nuclear Information System (INIS)
Tian Mingzhen; Barber, Zeb W.; Fischer, Joe A.; Randall Babbitt, Wm.
2004-01-01
We report the observation of the geometric phase in a closed two-level atomic system using stimulated photon echoes. The two-level system studied consists of the two-electronic energy levels ( 3 H 4 and 3 H 6 ) of Tm 3+ doped in YAG crystal. When a two-level atom at an arbitrary superposition state is excited by a pair of specially designed laser pulses, the excited state component gains a relative phase with respect to the ground state component. We identified the phase shift to be of pure geometric nature. The dynamic phase associated to the driving Hamiltonian is unchanged. The experiment results of the phase change agree with the theory to the extent of the measurement limit
Semiclassical initial value approximation for Green's function.
Kay, Kenneth G
2010-06-28
A semiclassical initial value approximation is obtained for the energy-dependent Green's function. For a system with f degrees of freedom the Green's function expression has the form of a (2f-1)-dimensional integral over points on the energy surface and an integral over time along classical trajectories initiated from these points. This approximation is derived by requiring an integral ansatz for Green's function to reduce to Gutzwiller's semiclassical formula when the integrations are performed by the stationary phase method. A simpler approximation is also derived involving only an (f-1)-dimensional integral over momentum variables on a Poincare surface and an integral over time. The relationship between the present expressions and an earlier initial value approximation for energy eigenfunctions is explored. Numerical tests for two-dimensional systems indicate that good accuracy can be obtained from the initial value Green's function for calculations of autocorrelation spectra and time-independent wave functions. The relative advantages of initial value approximations for the energy-dependent Green's function and the time-dependent propagator are discussed.
DEFF Research Database (Denmark)
Patrick, Christopher; Thygesen, Kristian Sommer
2016-01-01
In non-self-consistent calculations of the total energy within the random-phase approximation (RPA) for electronic correlation, it is necessary to choose a single-particle Hamiltonian whose solutions are used to construct the electronic density and noninteracting response function. Here we...... investigate the effect of including a Hubbard-U term in this single-particle Hamiltonian, to better describe the on-site correlation of 3d electrons in the transitionmetal compounds ZnS, TiO2, and NiO.We find that the RPA lattice constants are essentially independent of U, despite large changes...... in the underlying electronic structure. We further demonstrate that the non-selfconsistent RPA total energies of these materials have minima at nonzero U. Our RPA calculations find the rutile phase of TiO2 to be more stable than anatase independent of U, a result which is consistent with experiments...
Phase separation and pressure drop of two-phase flow in vertical manifolds
International Nuclear Information System (INIS)
Zetzmann, K.
1982-01-01
The splitting of a two-phase mass flow in a tube manifold results in a separation between liquid and gas phase. A study is presented of the phase distribution and the related two-phase pressure drop for vertical manifolds in the technically relevant geometry and flow parameter region of an air-water-flow. At the outlet changes in the gas/fluid-radio are observed which are proportional to this ratio at the inlet. The separation characteristic strongly depends on the massflow through the junction. Empirical equations are given to calculate the separation. Measuring the pressure drop at main- and secondary tube of the manifold the additional pressure drop can be obtained. If these results are related with the dynamic pressure at the inlet, two-phase resistance coefficients can be deduced, which may be tested by empirical relations. (orig.) [de
Eshuis, Henk; Yarkony, Julian; Furche, Filipp
2010-06-01
The random phase approximation (RPA) is an increasingly popular post-Kohn-Sham correlation method, but its high computational cost has limited molecular applications to systems with few atoms. Here we present an efficient implementation of RPA correlation energies based on a combination of resolution of the identity (RI) and imaginary frequency integration techniques. We show that the RI approximation to four-index electron repulsion integrals leads to a variational upper bound to the exact RPA correlation energy if the Coulomb metric is used. Auxiliary basis sets optimized for second-order Møller-Plesset (MP2) calculations are well suitable for RPA, as is demonstrated for the HEAT [A. Tajti et al., J. Chem. Phys. 121, 11599 (2004)] and MOLEKEL [F. Weigend et al., Chem. Phys. Lett. 294, 143 (1998)] benchmark sets. Using imaginary frequency integration rather than diagonalization to compute the matrix square root necessary for RPA, evaluation of the RPA correlation energy requires O(N4 log N) operations and O(N3) storage only; the price for this dramatic improvement over existing algorithms is a numerical quadrature. We propose a numerical integration scheme that is exact in the two-orbital case and converges exponentially with the number of grid points. For most systems, 30-40 grid points yield μH accuracy in triple zeta basis sets, but much larger grids are necessary for small gap systems. The lowest-order approximation to the present method is a post-Kohn-Sham frequency-domain version of opposite-spin Laplace-transform RI-MP2 [J. Jung et al., Phys. Rev. B 70, 205107 (2004)]. Timings for polyacenes with up to 30 atoms show speed-ups of two orders of magnitude over previous implementations. The present approach makes it possible to routinely compute RPA correlation energies of systems well beyond 100 atoms, as is demonstrated for the octapeptide angiotensin II.
A Phase-Controlled Optical Parametric Amplifier Pumped by Two Phase-Distorted Laser Beams
International Nuclear Information System (INIS)
Hong-Yan, Ren; Lie-Jia, Qian; Peng, Yuan; He-Yuan, Zhu; Dian-Yuan, Fan
2010-01-01
We theoretically study the phase characteristic of optical parametric amplification (OPA) or chirped pulse OPA (OPCPA) pumped by two phase-distorted laser beams. In the two-beam-pumped optical parametric amplification (TBOPA), due to spatial walk-off, both of the pump phase distortions will be partly transferred to signal in a single crystal so as to degrade the signal beam-quality, which will be more serious in high-energy OPCPA. An OPA configuration with a walkoff-compensated crystal pair is demonstrated for reducing the signal phase distortion experienced in the first stage and ensuring the signal phase independent of two pump phase distortions through the second crystal, hence maintaining the signal beam-quality. Such a TBOPA is similar to the conventional quantum laser amplifier by means of eliminating its sensitivity to the phase and number of the pump beams
Kerner, Boris S; Klenov, Sergey L; Schreckenberg, Michael
2014-05-01
Physical features of induced phase transitions in a metastable free flow at an on-ramp bottleneck in three-phase and two-phase cellular automaton (CA) traffic-flow models have been revealed. It turns out that at given flow rates at the bottleneck, to induce a moving jam (F → J transition) in the metastable free flow through the application of a time-limited on-ramp inflow impulse, in both two-phase and three-phase CA models the same critical amplitude of the impulse is required. If a smaller impulse than this critical one is applied, neither F → J transition nor other phase transitions can occur in the two-phase CA model. We have found that in contrast with the two-phase CA model, in the three-phase CA model, if the same smaller impulse is applied, then a phase transition from free flow to synchronized flow (F → S transition) can be induced at the bottleneck. This explains why rather than the F → J transition, in the three-phase theory traffic breakdown at a highway bottleneck is governed by an F → S transition, as observed in real measured traffic data. None of two-phase traffic-flow theories incorporates an F → S transition in a metastable free flow at the bottleneck that is the main feature of the three-phase theory. On the one hand, this shows the incommensurability of three-phase and two-phase traffic-flow theories. On the other hand, this clarifies why none of the two-phase traffic-flow theories can explain the set of fundamental empirical features of traffic breakdown at highway bottlenecks.
Models for assessing the relative phase velocity in a two-phase flow. Status report
International Nuclear Information System (INIS)
Schaffrath, A.; Ringel, H.
2000-06-01
The knowledge of slip or drift flux in two phase flow is necessary for several technical processes (e.g. two phase pressure losses, heat and mass transfer in steam generators and condensers, dwell period in chemical reactors, moderation effectiveness of two phase coolant in BWR). In the following the most important models for two phase flow with different phase velocities (e.g. slip or drift models, analogy between pressure loss and steam quality, ε - ε models and models for the calculation of void distribution in reposing fluids) are classified, described and worked up for a further comparison with own experimental data. (orig.)
International Nuclear Information System (INIS)
Sanchez, Richard
1977-01-01
A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr
Two phase cooling for superconducting magnets
International Nuclear Information System (INIS)
Eberhard, P.H.; Gibson, G.A.; Green, M.A.; Ross, R.R.; Smits, R.G.
1986-01-01
Comments on the use of two phase helium in a closed circuit tubular cooling system and some results obtained with the TPC superconducting magnet are given. Theoretical arguments and experimental evidence are given against a previously suggested method to determine helium two phase flow regimes. Two methods to reduce pressure in the magnet cooling tubes during quenches are discussed; 1) lowering the density of helium in the magnet cooling tubes and 2) proper location of pressure relief valves. Some techniques used to protect the refrigerator from too much cold return gas are also mentioned
Experimental study of flow monitoring instruments in air-water, two-phase downflow
International Nuclear Information System (INIS)
Sheppard, J.D.; Hayes, P.H.; Wynn, M.C.
1976-01-01
The performance of a turbine meter, target flow meter (drag disk), and a gamma densitometer was studied in air-water, two-phase vertical downflow. Air and water were metered into an 0.0889-m-ID (3.5-in.) piping system; air flows ranged from 0.007 to 0.3 m 3 /sec (16 to 500 scfm) and water flows ranged from 0.0006 to 0.03 m 3 /sec (10 to 500 gpm). The study included effects of flow rate, quality, flow regime, and flow dispersion on the mean and fluctuating components of the instrument signals. Wire screen flow dispersers located at the inlet to the test section had a significant effect on the readings of the drag disk and gamma densitometer, but had little effect on the turbine. Further, when flow dispersers were used, mass flow rates determined from the three instrument readings and a two-velocity, slip flow model showed good agreement with actual mass flow rate over a three-fold range in quality; mass flows determined with the drag disk and densitometer readings assuming homogeneous flow were nearly as accurate. However, when mass flows were calculated using the turbine and densitometer or turbine and drag disk readings assuming homogeneous flow, results were scattered and relatively inaccurate compared to the actual mass flows. Turbine meter data were used with a two-velocity turbine model and continuity relationships for each phase to determine the void fraction and mean phase velocities in the test section. The void fraction was compared with single beam gamma densitometer results and fluid momentum calculated from a two-velocity model was compared with drag disk readings
Approximate analytic theory of the multijunction grill
International Nuclear Information System (INIS)
Hurtak, O.; Preinhaelter, J.
1991-03-01
An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs
Equivalence of two models in single-phase multicomponent flow simulations
Wu, Yuanqing
2016-02-28
In this work, two models to simulate the single-phase multicomponent flow in reservoirs are introduced: single-phase multicomponent flow model and two-phase compositional flow model. Because the single-phase multicomponent flow is a special case of the two-phase compositional flow, the two-phase compositional flow model can also simulate the case. We compare and analyze the two models when simulating the single-phase multicomponent flow, and then demonstrate the equivalence of the two models mathematically. An experiment is also carried out to verify the equivalence of the two models.
Equivalence of two models in single-phase multicomponent flow simulations
Wu, Yuanqing; Sun, Shuyu
2016-01-01
In this work, two models to simulate the single-phase multicomponent flow in reservoirs are introduced: single-phase multicomponent flow model and two-phase compositional flow model. Because the single-phase multicomponent flow is a special case of the two-phase compositional flow, the two-phase compositional flow model can also simulate the case. We compare and analyze the two models when simulating the single-phase multicomponent flow, and then demonstrate the equivalence of the two models mathematically. An experiment is also carried out to verify the equivalence of the two models.
Ivliev, S. V.
2017-12-01
For calculation of short laser pulse absorption in metal the imaginary part of permittivity, which is simply related to the conductivity, is required. Currently to find the static and dynamic conductivity the Kubo-Greenwood formula is most commonly used. It describes the electromagnetic energy absorption in the one-electron approach. In the present study, this formula is derived directly from the expression for the permittivity expression in the random phase approximation, which in fact is equivalent to the method of the mean field. The detailed analysis of the role of electron-electron interaction in the calculation of the matrix elements of the velocity operator is given. It is shown that in the one-electron random phase approximation the single-particle conductive electron wave functions in the field of fixed ions should be used. The possibility of considering the exchange and correlation effects by means of an amendment to a local function field is discussed.
A practical method for accurate quantification of large fault trees
International Nuclear Information System (INIS)
Choi, Jong Soo; Cho, Nam Zin
2007-01-01
This paper describes a practical method to accurately quantify top event probability and importance measures from incomplete minimal cut sets (MCS) of a large fault tree. The MCS-based fault tree method is extensively used in probabilistic safety assessments. Several sources of uncertainties exist in MCS-based fault tree analysis. The paper is focused on quantification of the following two sources of uncertainties: (1) the truncation neglecting low-probability cut sets and (2) the approximation in quantifying MCSs. The method proposed in this paper is based on a Monte Carlo simulation technique to estimate probability of the discarded MCSs and the sum of disjoint products (SDP) approach complemented by the correction factor approach (CFA). The method provides capability to accurately quantify the two uncertainties and estimate the top event probability and importance measures of large coherent fault trees. The proposed fault tree quantification method has been implemented in the CUTREE code package and is tested on the two example fault trees
Two-phase flow patterns and their relationship to two-phase heat transfer
International Nuclear Information System (INIS)
Hewitt, G.F.
1977-01-01
The objective of this lecture was to discuss the general nature of two phase flows, to define the various regimes of flow and to discuss the influence of these regimes on the heat transfer processes taking place. The methods of regime delineation are briefly described and regime descriptions introduced for both vertical and horizontal flows in tubes. ''Flow regime maps'' have been widely used as an aid to determination of the regime which occurs in a given situation. Some of the more widely used maps are described and the limitations of this approach discussed. There have been many attempts to obtain a better phenomenological description of two phase flow patterns. In this lecture, these attempts will be reviewed in the context of the bubble/plug, plug/churn and churn/annular flow transitions in vertical flow. The latter two transitions are related to the flooding/flow reversal phenomena. For horizontal flows, recent work on the onset of slugging will be reviewed. In flows with evaporation or condensation, the situation is influenced by departures from thermodynamic equilibrium and the types of departure observed are discuss briefly. Flow patterns and their relationships with heat transfer regimes are then reviewed for the case of condensation in horizontal tubes and evaporation in vertical tubes
Approximation of functions in two variables by some linear positive operators
Directory of Open Access Journals (Sweden)
Mariola Skorupka
1995-12-01
Full Text Available We introduce some linear positive operators of the Szasz-Mirakjan type in the weighted spaces of continuous functions in two variables. We study the degree of the approximation of functions by these operators. The similar results for functions in one variable are given in [5]. Some operators of the Szasz-Mirakjan type are examined also in [3], [4].
Mussard, Bastien; Rocca, Dario; Jansen, Georg; Ángyán, János G
2016-05-10
Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case, the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed, and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental for improvement over direct RPA results.
International Nuclear Information System (INIS)
Spinato, Giulia; Borhani, Navid; Thome, John R.
2015-01-01
In the framework of efficient thermal management schemes, pulsating heat pipes (PHPs) represent a breakthrough solution for passive on-chip two-phase flow cooling of micro-electronics. Unfortunately, the unique coupling of thermodynamics, hydrodynamics and heat transfer, responsible for the self-sustained pulsating two-phase flow in such devices, presents many challenges to the understanding of the underlying physical phenomena which have so far eluded accurate prediction. In this experimental study, the novel time-strip image processing technique was used to investigate the thermo-flow dynamics of a single-turn channel CLPHP (closed loop pulsating heat pipe) charged with R245fa and tested under different operating conditions. The resulting frequency data confirmed the effect of flow pattern, and thus operating conditions, on the oscillating behavior. Dominant frequencies from 1.2 Hz for the oscillating regime to 0.6 Hz for the unidirectional flow circulation regime were measured, whilst wide spectral bands were observed for the unstable circulation regime. In order to analytically assess the observed trends in the spectral behavior, a spring-mass-damper system model was developed for the two-phase flow motion. As well as showing that system stiffness and mass have an effect on the two-phase flow dynamics, further insights into the flow pattern transition mechanism were also gained. - Highlights: • A novel synchronized thermal and visual investigation technique was applied to a CLPHP. • Thermal and hydrodynamic behaviors were analyzed by means of spectral analysis. • 3D frequency spectra for temperature and flow data show significant trends. • A spring-mass-damper system model was developed for the two-phase flow motion. • System stiffness and mass have an effect on the two-phase flow dynamics.
International Nuclear Information System (INIS)
Easterday, O.T.; Wang, C.Y.; Cheng, P.
1995-01-01
Understanding and predicting two-phase flow and heat transfer in porous media is of fundamental interest for a number of engineering applications. Examples include thermal technologies for remediation of contaminated subsurfaces, the extraction of geothermal energy from vapor-dominated reservoirs, and the assessment of high-level nuclear waste repositories. A numerical and experimental study is reported for two-phase flow and heat transfer in a horizontal porous formation with water through flow and partial heating from below. Based on a newly developed two-phase mixture model, numerical results of the temperature distribution, liquid saturation, liquid and vapor phase velocity fields are presented for three representative cases with varying inlet velocities. It is found that the resulting two-phase structure and flow patterns are strongly dependent upon the water inlet velocity and the bottom heat flux. The former parameter measures the flow along the horizontal direction, while the latter creates a relative motion between the phases in the vertical direction. Experiments are also performed to measure temperature distributions and to visualize the two-phase flow patterns. Qualitative agreement between experiments and numerical predictions is achieved. Overall, this combined experimental and numerical study has provided new insight into conjugate single- and two-phase flow and heat transfer in porous media, although future research is required if accurate modeling of these complex problems is to be accomplished
Numerical calculation of two-phase turbulent jets
Energy Technology Data Exchange (ETDEWEB)
Saif, A.A.
1995-05-01
Two-phase turbulent round jets were numerically simulated using a multidimensional two-phase CFD code based on the two-fluid model. The turbulence phenomena were treated with the standard k-{epsilon} model. It was modified to take into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-fluid model it is more appropriate and physically justified to treat the diffusion by an interfacial force in the momentum equation. In this work, the diffusion force and the additional dissipation effect by the dispersed phase were modeled starting from the classical turbulent energy spectrum analysis. A cut-off frequency was proposed to decrease the dissipation effect by the dispersed phase when large size particles are introduced in the flow. The cut-off frequency combined with the bubble-induced turbulence effect allows for an increase in turbulence for large particles. Additional care was taken in choosing the right kind of experimental data from the literature so that a good separate effect test was possible for their models. The models predicted the experimental data very closely and they were general enough to predict extreme limit cases: water-bubble and air-droplet jets.
A Schur complement method for compressible two-phase flow models
International Nuclear Information System (INIS)
Dao, Thu-Huyen; Ndjinga, Michael; Magoules, Frederic
2014-01-01
In this paper, we will report our recent efforts to apply a Schur complement method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver. With the interface variable introduced in [4] in the context of single phase flows, we are able to simulate two-fluid models ([12]) with various schemes such as upwind, centered or Rusanov. Moreover, we introduce a scaling strategy to improve the condition number of both the interface system and the local systems. Numerical results for the isentropic two-fluid model and the compressible Navier-Stokes equations in various 2D and 3D configurations and various schemes show that our method is robust and efficient. The scaling strategy considerably reduces the number of GMRES iterations in both interface system and local system resolutions. Comparisons of performances with classical distributed computing with up to 218 processors are also reported. (authors)
Regularized lattice Boltzmann model for immiscible two-phase flows with power-law rheology
Ba, Yan; Wang, Ningning; Liu, Haihu; Li, Qiang; He, Guoqiang
2018-03-01
In this work, a regularized lattice Boltzmann color-gradient model is developed for the simulation of immiscible two-phase flows with power-law rheology. This model is as simple as the Bhatnagar-Gross-Krook (BGK) color-gradient model except that an additional regularization step is introduced prior to the collision step. In the regularization step, the pseudo-inverse method is adopted as an alternative solution for the nonequilibrium part of the total distribution function, and it can be easily extended to other discrete velocity models no matter whether a forcing term is considered or not. The obtained expressions for the nonequilibrium part are merely related to macroscopic variables and velocity gradients that can be evaluated locally. Several numerical examples, including the single-phase and two-phase layered power-law fluid flows between two parallel plates, and the droplet deformation and breakup in a simple shear flow, are conducted to test the capability and accuracy of the proposed color-gradient model. Results show that the present model is more stable and accurate than the BGK color-gradient model for power-law fluids with a wide range of power-law indices. Compared to its multiple-relaxation-time counterpart, the present model can increase the computing efficiency by around 15%, while keeping the same accuracy and stability. Also, the present model is found to be capable of reasonably predicting the critical capillary number of droplet breakup.
The time-dependent relativistic mean-field theory and the random phase approximation
International Nuclear Information System (INIS)
Ring, P.; Ma, Zhong-yu; Van Giai, Nguyen; Vretenar, D.; Wandelt, A.; Cao, Li-gang
2001-01-01
The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116 Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained
Two phase cooling for superconducting magnets
International Nuclear Information System (INIS)
Eberhard, P.H.; Gibson, G.A.; Green, M.A.; Ross, R.R.; Smits, R.G.; Taylor, J.D.; Watt, R.D.
1986-01-01
Comments on the use of two phase helium in a closed circuit tubular cooling system and some results obtained with the TPC superconducting magnet are given. Theoretical arguments and experimental evidence are given against a previously suggested method to determine helium two phase flow regimes. Two methods to reduce pressure in the magnet cooling tubes during quenches are discussed; (1) lowering the density of helium in the magnet cooling tubes and (2) proper location of pressure relief valves. Some techniques used to protect the refrigerator from too much cold return gas are also mentioned. 10 refs., 1 fig., 5 tabs
Application of non-equilibrium thermodynamics to two-phase flows with a change of phase
International Nuclear Information System (INIS)
Delhaye, J.M.
1969-01-01
In this report we use the methods of non-equilibrium thermodynamics in two-phase flows. This paper follows a prior one in which we have studied the conservation laws and derived the general equations of two-phase flow. In the first part the basic ideas of thermodynamics of irreversible systems are given. We follow the classical point of view. The second part is concerned with the derivation of a closed set of equations for the two phase elementary volume model. In this model we assume that the elementary volume contains two phases and that it is possible to define a volumetric local concentration. To obtain the entropy balance we can choose either the reversibility of the barycentric motion or the reversibility of each phase. We adopt the last assumption and our derivation is the same as this of I.Prigogine and P. Mazur about the hydrodynamics of liquid helium. The scope of this work is not to find a general solution to the problems of two phase flows but to obtain a new set of equations which may be used to explain some characteristic phenomena of two-phase flow such as wave propagation or critical states. (author) [fr
Kim, Minsoo; Jung, Na Young; Park, Chang Kyu; Chang, Won Seok; Jung, Hyun Ho; Chang, Jin Woo
2018-06-01
Stereotactic procedures are image guided, often using magnetic resonance (MR) images limited by image distortion, which may influence targets for stereotactic procedures. The aim of this work was to assess methods of identifying target coordinates for stereotactic procedures with MR in multiple phase-encoding directions. In 30 patients undergoing deep brain stimulation, we acquired 5 image sets: stereotactic brain computed tomography (CT), T2-weighted images (T2WI), and T1WI in both right-to-left (RL) and anterior-to-posterior (AP) phase-encoding directions. Using CT coordinates as a reference, we analyzed anterior commissure and posterior commissure coordinates to identify any distortion relating to phase-encoding direction. Compared with CT coordinates, RL-directed images had more positive x-axis values (0.51 mm in T1WI, 0.58 mm in T2WI). AP-directed images had more negative y-axis values (0.44 mm in T1WI, 0.59 mm in T2WI). We adopted 2 methods to predict CT coordinates with MR image sets: parallel translation and selective choice of axes according to phase-encoding direction. Both were equally effective at predicting CT coordinates using only MR; however, the latter may be easier to use in clinical settings. Acquiring MR in multiple phase-encoding directions and selecting axes according to the phase-encoding direction allows identification of more accurate coordinates for stereotactic procedures. © 2018 S. Karger AG, Basel.
Two-Phase Induction Motor Drives
Directory of Open Access Journals (Sweden)
Gholam Reza Arab Markadeh
2010-10-01
Full Text Available The lack of variable-speed drives for two (single induction motor is a reality. This article attempts mainly to investigate the reasons for this lack of variable – speed drives. This paper deals with literature survey of various existing converter topologies, which have been proposed for adjustable speed single phase induction motor drives. Various converter topologies have been compared in this paper. Among these converter topologies, the adjustable frequency PWM inverter is the best choice for single-phase induction motor drives. However, adjustable-frequency drives have not been widely used with single-phase Induction motors. The open-loop constant V/F control law cannot be used with the single-phase induction motor drives as it is used with three phase motors. The variation of the operating frequency at lower speed range with constant load torque causes variation in motor's slip. A constant V/F control is suitable only over the upper speed range.
Amrhein, Sven; Schwab, Marie-Luise; Hoffmann, Marc; Hubbuch, Jürgen
2014-11-07
Over the last decade, the use of design of experiment approaches in combination with fully automated high throughput (HTP) compatible screenings supported by robotic liquid handling stations (LHS), adequate fast analytics and data processing has been developed in the biopharmaceutical industry into a strategy of high throughput process development (HTPD) resulting in lower experimental effort, sample reduction and an overall higher degree of process optimization. Apart from HTP technologies, lab-on-a-chip technology has experienced an enormous growth in the last years and allows further reduction of sample consumption. A combination of LHS and lab-on-a-chip technology is highly desirable and realized in the present work to characterize aqueous two phase systems with respect to tie lines. In particular, a new high throughput compatible approach for the characterization of aqueous two phase systems regarding tie lines by exploiting differences in phase densities is presented. Densities were measured by a standalone micro fluidic liquid density sensor, which was integrated into a liquid handling station by means of a developed generic Tip2World interface. This combination of liquid handling stations and lab-on-a-chip technology enables fast, fully automated, and highly accurate density measurements. The presented approach was used to determine the phase diagram of ATPSs composed of potassium phosphate (pH 7) and polyethylene glycol (PEG) with a molecular weight of 300, 400, 600 and 1000 Da respectively in the presence and in the absence of 3% (w/w) sodium chloride. Considering the whole ATPS characterization process, two complete ATPSs could be characterized within 24h, including four runs per ATPS for binodal curve determination (less than 45 min/run), and tie line determination (less than 45 min/run for ATPS preparation and 8h for density determination), which can be performed fully automated over night without requiring man power. The presented methodology provides
Energy Technology Data Exchange (ETDEWEB)
Barlow, Nathaniel S., E-mail: nsbsma@rit.edu [School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623 (United States); Schultz, Andrew J., E-mail: ajs42@buffalo.edu; Kofke, David A., E-mail: kofke@buffalo.edu [Department of Chemical and Biological Engineering, University at Buffalo, State University of New York, Buffalo, New York 14260 (United States); Weinstein, Steven J., E-mail: sjweme@rit.edu [Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623 (United States)
2015-08-21
The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A
2015-08-21
The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.
Reversible, on-demand generation of aqueous two-phase microdroplets
Collier, Charles Patrick; Retterer, Scott Thomas; Boreyko, Jonathan Barton; Mruetusatorn, Prachya
2017-08-15
The present invention provides methods of on-demand, reversible generation of aqueous two-phase microdroplets core-shell microbeads, microparticle preparations comprising the core-shell microbeads, and drug delivery formulation comprising the microparticle preparations. Because these aqueous microdroplets have volumes comparable to those of cells, they provide an approach to mimicking the dynamic microcompartmentation of biomaterial that naturally occurs within the cytoplasm of cells. Hence, the present methods generate femtoliter aqueous two-phase droplets within a microfluidic oil channel using gated pressure pulses to generate individual, stationary two-phase microdroplets with a well-defined time zero for carrying out controlled and sequential phase transformations over time. Reversible phase transitions between single-phase, two-phase, and core-shell microbead states are obtained via evaporation-induced dehydration and water rehydration.
Radiogauging to investigate two phase flow. Graduation report
International Nuclear Information System (INIS)
Corten, G.P.
1992-01-01
New measuring methods are developed and are tested with the small reactor simulator MIDAS (Mini Dodewaard ASsembly). The purpose of this work is to be able to measure accurately as many different properties of the flow as possible in the coming bigger simulator SIDAS (Simulated Dodewaard ASsembly). In SIDAS the flow around a fuel assembly of the Dutch Dodewaard reactor will be simulated. An extensive evaluation of the gamma detection system showed that the detection system could be simplified strongly. The simplified system is used to measure the radial and axial distribution of the void fraction in the core of MIDAS for three different operating conditions. Two new measuring methods have been developed and tested. A method to estimate the probability density of the void fraction in time. Due to the nonlinear relation between transmission and void fraction the determined average value of the void fraction in general will contain a systematic error. In this investigation it is shown that this error can be maximally 7.5% in MIDAS and maximally 25% in SIDAS. Therefore a new measuring method has been developed in which the true probability density of the void fraction in time is approximated by two different values of the void fraction, each with a certain probability. With this new method firstly the average void fraction can be determined much more precisely and secondly it often can be used to determine the flow pattern. (orig./WL)
Radiogauging to investigate two phase flow. Graduation report
Energy Technology Data Exchange (ETDEWEB)
Corten, G P
1992-11-12
New measuring methods are developed and are tested with the small reactor simulator MIDAS (Mini Dodewaard ASsembly). The purpose of this work is to be able to measure accurately as many different properties of the flow as possible in the coming bigger simulator SIDAS (Simulated Dodewaard ASsembly). In SIDAS the flow around a fuel assembly of the Dutch Dodewaard reactor will be simulated. An extensive evaluation of the gamma detection system showed that the detection system could be simplified strongly. The simplified system is used to measure the radial and axial distribution of the void fraction in the core of MIDAS for three different operating conditions. Two new measuring methods have been developed and tested. A method to estimate the probability density of the void fraction in time. Due to the nonlinear relation between transmission and void fraction the determined average value of the void fraction in general will contain a systematic error. In this investigation it is shown that this error can be maximally 7.5% in MIDAS and maximally 25% in SIDAS. Therefore a new measuring method has been developed in which the true probability density of the void fraction in time is approximated by two different values of the void fraction, each with a certain probability. With this new method firstly the average void fraction can be determined much more precisely and secondly it often can be used to determine the flow pattern. (orig./WL).
Forced two phase helium cooling of large superconducting magnets
International Nuclear Information System (INIS)
Green, M.A.; Burns, W.A.; Taylor, J.D.
1979-08-01
A major problem shared by all large superconducting magnets is the cryogenic cooling system. Most large magnets are cooled by some variation of the helium bath. Helium bath cooling becomes more and more troublesome as the size of the magnet grows and as geometric constraints come into play. An alternative approach to cooling large magnet systems is the forced flow, two phase helium system. The advantages of two phase cooling in many magnet systems are shown. The design of a two phase helium system, with its control dewar, is presented. The paper discusses pressure drop of a two phase system, stability of a two phase system and the method of cool down of a two phase system. The results of experimental measurements at LBL are discussed. Included are the results of cool down and operation of superconducting solenoids
Two reactions method for accurate analysis by irradiation with charged particles
International Nuclear Information System (INIS)
Ishii, K.; Sastri, C.S.; Valladon, M.; Borderie, B.; Debrun, J.L.
1978-01-01
In the average stopping power method the formula error itself was negligible but systematic errors could be introduced by the stopping power data used in this formula. A method directly derived from the average stopping power method, but based on the use of two nuclear reactions, is described here. This method has a negligible formula error and does not require the use of any stopping power or range data: accurate and 'self-consistent' analysis by irradiation with charged particles is then possible. (Auth.)
An Accurate Estimate of the Free Energy and Phase Diagram of All-DNA Bulk Fluids
Directory of Open Access Journals (Sweden)
Emanuele Locatelli
2018-04-01
Full Text Available We present a numerical study in which large-scale bulk simulations of self-assembled DNA constructs have been carried out with a realistic coarse-grained model. The investigation aims at obtaining a precise, albeit numerically demanding, estimate of the free energy for such systems. We then, in turn, use these accurate results to validate a recently proposed theoretical approach that builds on a liquid-state theory, the Wertheim theory, to compute the phase diagram of all-DNA fluids. This hybrid theoretical/numerical approach, based on the lowest-order virial expansion and on a nearest-neighbor DNA model, can provide, in an undemanding way, a parameter-free thermodynamic description of DNA associating fluids that is in semi-quantitative agreement with experiments. We show that the predictions of the scheme are as accurate as those obtained with more sophisticated methods. We also demonstrate the flexibility of the approach by incorporating non-trivial additional contributions that go beyond the nearest-neighbor model to compute the DNA hybridization free energy.
Experimental study on interfacial area transport in downward two-phase flow
Wang, Guanyi
In view of the importance of two group interfacial area transport equations and lack of corresponding accurate downward flow database that can reveal two group interfacial area transport, a systematic database for adiabatic, air-water, vertically downward two-phase flow in a round pipe with inner diameter of 25.4 mm was collected to gain an insight of interfacial structure and provide benchmarking data for two-group interfacial area transport models. A four-sensor conductivity probe was used to measure the local two phase flow parameters and data was collected with data sampling frequency much higher than conventional data sampling frequency to ensure the accuracy. Axial development of local flow parameter profiles including void fraction, interfacial area concentration, and Sauter mean diameter were presented. Drastic inter-group transfer of void fraction and interfacial area was observed at bubbly to slug transition flow. And the wall peaked interfacial area concentration profiles were observed in churn-turbulent flow. The importance of local data about these phenomenon on flow structure prediction and interfacial area transport equation benchmark was analyzed. Bedsides, in order to investigate the effect of inlet conditions, all experiments were repeated after installing the flow straightening facility, and the results were briefly analyzed. In order to check the accuracy of current data, the experiment results were cross-checked with rotameter measurement as well as drift-flux model prediction, the averaged error is less than 15%. Current models for two-group interfacial area transport equation were evaluated using these data. The results show that two-group interfacial area transport equations with current models can predict most flow conditions with error less than 20%, except some bubbly to slug transition flow conditions and some churn-turbulent flow conditions. The disagreement between models and experiments could result from underestimate of inter
On an elastic dissipation model as continuous approximation for discrete media
Directory of Open Access Journals (Sweden)
I. V. Andrianov
2006-01-01
Full Text Available Construction of an accurate continuous model for discrete media is an important topic in various fields of science. We deal with a 1D differential-difference equation governing the behavior of an n-mass oscillator with linear relaxation. It is known that a string-type approximation is justified for low part of frequency spectra of a continuous model, but for free and forced vibrations a solution of discrete and continuous models can be quite different. A difference operator makes analysis difficult due to its nonlocal form. Approximate equations can be obtained by replacing the difference operators via a local derivative operator. Although application of a model with derivative of more than second order improves the continuous model, a higher order of approximated differential equation seriously complicates a solution of continuous problem. It is known that accuracy of the approximation can dramatically increase using Padé approximations. In this paper, one- and two-point Padé approximations suitable for justify choice of structural damping models are used.
Dahms, Rainer N.
2016-04-01
A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing
Energy Technology Data Exchange (ETDEWEB)
Dahms, Rainer N., E-mail: Rndahms@sandia.gov [Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551 (United States)
2016-04-15
A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing
van Aggelen, Helen; Yang, Yang; Yang, Weitao
2014-05-14
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H2, and eliminates delocalization errors in H2(+) and other single-bond systems. It gives surprisingly good non-bonded interaction energies--competitive with the ph-RPA--with the correct R(-6) asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations.
International Nuclear Information System (INIS)
Aggelen, Helen van; Yang, Yang; Yang, Weitao
2014-01-01
Despite their unmatched success for many applications, commonly used local, semi-local, and hybrid density functionals still face challenges when it comes to describing long-range interactions, static correlation, and electron delocalization. Density functionals of both the occupied and virtual orbitals are able to address these problems. The particle-hole (ph-) Random Phase Approximation (RPA), a functional of occupied and virtual orbitals, has recently known a revival within the density functional theory community. Following up on an idea introduced in our recent communication [H. van Aggelen, Y. Yang, and W. Yang, Phys. Rev. A 88, 030501 (2013)], we formulate more general adiabatic connections for the correlation energy in terms of pairing matrix fluctuations described by the particle-particle (pp-) propagator. With numerical examples of the pp-RPA, the lowest-order approximation to the pp-propagator, we illustrate the potential of density functional approximations based on pairing matrix fluctuations. The pp-RPA is size-extensive, self-interaction free, fully anti-symmetric, describes the strong static correlation limit in H 2 , and eliminates delocalization errors in H 2 + and other single-bond systems. It gives surprisingly good non-bonded interaction energies – competitive with the ph-RPA – with the correct R −6 asymptotic decay as a function of the separation R, which we argue is mainly attributable to its correct second-order energy term. While the pp-RPA tends to underestimate absolute correlation energies, it gives good relative energies: much better atomization energies than the ph-RPA, as it has no tendency to underbind, and reaction energies of similar quality. The adiabatic connection in terms of pairing matrix fluctuation paves the way for promising new density functional approximations
International Nuclear Information System (INIS)
Yonomoto, Taisuke; Tasaka, Kanji
1988-01-01
A theoretical and experimental study was conducted to understand two-phase flow discharged from a stratified two-phase region through a small break. This problem is important for an analysis of a small break loss-of-coolant accident (LOCA) in a light water reactor (LWR). The present theoretical results show that a break quality is a function of h/h b , where h is the elevation difference between a bulk water level in the upstream region and break and b the suffix for entrainment initiation. This result is consistent with existing eperimental results in literature. An air-water experiment was also conducted changing a break orientation as an experimental parameter to develop and assess the model. Comparisons between the model and the experimental results show that the present model can satisfactorily predict the flow rate and the quality at the break without using any adjusting constant when liquid entrainment occurs in a stratified two-phase region. When gas entrainment occurs, the experimental data are correlated well by using a single empirical constant. (author)
Modelling aspects of two phase flow
International Nuclear Information System (INIS)
Mayinger, F.
1977-01-01
In two phase flow scaling is much more limited to very narrowly defined physical phenomena than in single phase fluids. For complex and combined phenomena it can be achieved not by using dimensionless numbers alone but in addition a detailed mathematical description of the physical problem - usually in the form of a computer program - must be available. An important role plays the scaling of the thermodynamic data of the modelling fluid. From a literature survey and from own scaling experiments the conclusion can be drawn that Freon is a quite suitable modelling fluid for scaling steam-water mixtures. However, whithout a theoretical description of the phenomena nondimensional numbers for scaling two phase flow must be handled very carefully. (orig.) [de
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
Effect of cosine current approximation in lattice cell calculations in cylindrical geometry
International Nuclear Information System (INIS)
Mohanakrishnan, P.
1978-01-01
It is found that one-dimensional cylindrical geometry reactor lattice cell calculations using cosine angular current approximation at spatial mesh interfaces give results surprisingly close to the results of accurate neutron transport calculations as well as experimental measurements. This is especially true for tight light water moderated lattices. Reasons for this close agreement are investigated here. By re-examining the effects of reflective and white cell boundary conditions in these calculations it is concluded that one major reason is the use of white boundary condition necessitated by the approximation of the two-dimensional reactor lattice cell by a one-dimensional one. (orig.) [de
Two-phase flow instrumentation research at RPI
International Nuclear Information System (INIS)
Lahey, R.T. Jr.; Krycuk, G.
1979-01-01
Novel instrumentation for the measurement of void fraction and phase velocity was developed. An optical digital interferometer and a dual beam x-ray equipment were designed for detection of voids. Pitot tube measurements were made to understand two-phase flow phenomena in liquid phase velocity
Studying Suspended Sediment Mechanism with Two-Phase PIV
Matinpour, H.; Atkinson, J. F.; Bennett, S. J.; Guala, M.
2017-12-01
Suspended sediment transport affects soil erosion, agriculture and water resources quality. Turbulent diffusion is the most primary force to maintain sediments in suspension. Although extensive previous literature have been studying the interactions between turbulent motion and suspended sediment, mechanism of sediments in suspension is still poorly understood. In this study, we investigate suspension of sediments as two distinct phases: one phase of sediments and another phase of fluid with turbulent motions. We designed and deployed a state-of-the-art two-phase PIV measurement technique to discriminate these two phases and acquire velocities of each phase separately and simultaneously. The technique that we have developed is employing a computer-vision based method, which enables us to discriminate sediment particles from fluid tracer particles based on two thresholds, dissimilar particle sizes and different particle intensities. Results indicate that fluid turbulence decreases in the presence of suspended sediments. Obtaining only sediment phase consecutive images enable us to compute fluctuation sediment concentration. This result enlightens understanding of complex interaction between the fluctuation velocities and the fluctuation of associated mass and compares turbulent viscosity with turbulent eddy diffusivity experimentally.
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)
A frozen Gaussian approximation-based multi-level particle swarm optimization for seismic inversion
Energy Technology Data Exchange (ETDEWEB)
Li, Jinglai, E-mail: jinglaili@sjtu.edu.cn [Institute of Natural Sciences, Department of Mathematics, and MOE Key Laboratory of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai 200240 (China); Lin, Guang, E-mail: lin491@purdue.edu [Department of Mathematics, School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States); Computational Sciences and Mathematics Division, Pacific Northwest National Laboratory, Richland, WA 99352 (United States); Yang, Xu, E-mail: xuyang@math.ucsb.edu [Department of Mathematics, University of California, Santa Barbara, CA 93106 (United States)
2015-09-01
In this paper, we propose a frozen Gaussian approximation (FGA)-based multi-level particle swarm optimization (MLPSO) method for seismic inversion of high-frequency wave data. The method addresses two challenges in it: First, the optimization problem is highly non-convex, which makes hard for gradient-based methods to reach global minima. This is tackled by MLPSO which can escape from undesired local minima. Second, the character of high-frequency of seismic waves requires a large number of grid points in direct computational methods, and thus renders an extremely high computational demand on the simulation of each sample in MLPSO. We overcome this difficulty by three steps: First, we use FGA to compute high-frequency wave propagation based on asymptotic analysis on phase plane; Then we design a constrained full waveform inversion problem to prevent the optimization search getting into regions of velocity where FGA is not accurate; Last, we solve the constrained optimization problem by MLPSO that employs FGA solvers with different fidelity. The performance of the proposed method is demonstrated by a two-dimensional full-waveform inversion example of the smoothed Marmousi model.
Accurate thermoelastic tensor and acoustic velocities of NaCl
Energy Technology Data Exchange (ETDEWEB)
Marcondes, Michel L., E-mail: michel@if.usp.br [Physics Institute, University of Sao Paulo, Sao Paulo, 05508-090 (Brazil); Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Shukla, Gaurav, E-mail: shukla@physics.umn.edu [School of Physics and Astronomy, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States); Silveira, Pedro da [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Wentzcovitch, Renata M., E-mail: wentz002@umn.edu [Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455 (United States); Minnesota supercomputer Institute, University of Minnesota, Minneapolis, 55455 (United States)
2015-12-15
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
Direct application of Padé approximant for solving nonlinear differential equations.
Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario
2014-01-01
This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.
Mathematical modeling of disperse two-phase flows
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...
Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning
International Nuclear Information System (INIS)
Serna, J I; Monz, M; Kuefer, K H; Thieke, C
2009-01-01
One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.
Trade-off bounds for the Pareto surface approximation in multi-criteria IMRT planning.
Serna, J I; Monz, M; Küfer, K H; Thieke, C
2009-10-21
One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide on the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to ensure that all clinically meaningful plans are covered and that as many clinically irrelevant plans as possible are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that constitutes the first phase. It is possible that two plans on the Pareto surface have a small, clinically insignificant difference in one criterion and a significant difference in another criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, the so-called trade-off bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects. The proposed scheme is applied to two artificial cases and one clinical case of a paraspinal tumor. For all cases, the quality of the Pareto surface approximation is measured with respect to the number of computed plans, and the range of values occurring in the approximation for different criteria is compared. Through enforcing trade-off bounds, the scheme disregards clinically irrelevant plans during the approximation. Thereby, the number of plans necessary to achieve a good approximation quality can be significantly reduced. Thus, trade-off bounds are an effective tool to focus the planning and to reduce computation time.
Two-phase LMMHD mixer-development experiments
International Nuclear Information System (INIS)
Fabris, G.; Dunn, P.F.; Chow, J.C.F.
1978-01-01
The results of a series of experiments conducted to evaluate the fluid mechanical performance of various two-phase LMMHD mixer designs are presented. The results from both flow visualization studies of the local two-phase flows downstream from various mixer-element configurations and local measurements performed to characterize these flows are presented. A conceptual LMMHD mixer design is described that insures the generation of small bubbles, prevents the formation of gas slugs and separated regions, and favors the stabilization of a homogeneous foam flow
Improved deep desulphurisation of middle distillates by a two-phase reactor with pre-saturator
Energy Technology Data Exchange (ETDEWEB)
Wieland Wache; Leonid Datsevich; Andreas Jess; Gerhard Neumann [University of Bayreuth, Bayreuth (Germany). Department of Chemical Engineering, Faculty of Applied Sciences
2006-08-15
Hydrodesulphurisation (HDS) of middle distillates is up to now performed in trickle bed reactors equipped with an expensive H{sub 2}-recycle. To meet future low S-limits, hydrotreating of already pre-desulphurised oils is needed. The H{sub 2}-supply is then far beyond what is chemically consumed. In addition, conventional three-phase HDS-reactors are generally problematic with respect to mass transfer, hydrodynamics, and therefore, scale-up. In this paper, an improved HDS-concept based on a two-phase reactor is discussed. The oil is thereby externally saturated with H{sub 2} and only the liquid is passed over the fixed bed. This concept was proven by experiments with light fuel oils (582 and 2252 ppm S, CoMo-catalyst, 1-6 MPa, 330-400{sup o}C, up to 100 days continuous operation). In addition, kinetic studies were done with model oil consisting of a mixture of n-dodecane and selected S-species such as di-, tri- and tetra-methyl-dibenzothiophenes. In case of the presented two-phase concept, the H{sub 2}-recycle is redundant, the intrinsic reaction rate can be utilised (and accurately measured), and scale-up problems do not occur. 18 refs., 9 figs., 5 tabs.
Experimental on two sensors combination used in horizontal pipe gas-water two-phase flow
International Nuclear Information System (INIS)
Wu, Hao; Dong, Feng
2014-01-01
Gas-water two phase flow phenomenon widely exists in production and living and the measurement of it is meaningful. A new type of long-waist cone flow sensor has been designed to measure two-phase mass flow rate. Six rings structure of conductance probe is used to measure volume fraction and axial velocity. The calibration of them have been made. Two sensors have been combined in horizontal pipeline experiment to measure two-phase flow mass flow rate. Several model of gas-water two-phase flow has been discussed. The calculation errors of total mass flow rate measurement is less than 5% based on the revised homogeneous flow model
DEFF Research Database (Denmark)
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...
DEFF Research Database (Denmark)
Comminal, Raphaël; Spangenberg, Jon; Hattel, Jesper Henri
2014-01-01
Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable...... of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked...
Dynamic Phase Boundary Estimation in Two-phase Flows Based on Electrical Impedance Tomography
International Nuclear Information System (INIS)
Lee, Jeong Seong; Muhammada, Nauman Malik; Kim, Kyung Youn; Kim, Sin
2008-01-01
For the dynamic visualization of the phase boundary in two-phase flows, the electrical impedance tomography (EIT) technique is introduced. In EIT, a set of predetermined electrical currents is injected through the electrodes placed on the boundary of the flow passage and the induced electrical potentials are measured on the electrodes. With the relationship between the injected currents and the induced voltages, the electrical conductivity distribution across the flow domain is estimated through the image reconstruction algorithm where the conductivity distribution corresponds to the phase distribution. In the application of EIT to two-phase flows where there are only two conductivity values, the conductivity distribution estimation problem can be transformed into the boundary estimation problem. This paper considers phase boundary estimation with EIT in annular two-phase flows. As the image reconstruction algorithm, the unscented Kalman filter (UKF) is adopted since from the control theory it is reported that the UKF shows better performance than the extended Kalman filter (EKF) that has been commonly used. For the present problem, the formulation of UKF algorithm involved its incorporation in the adopted image reconstruction algorithm. Also, phantom experiments have been conducted to evaluate the improvement reported by UKF
A multi-scale network method for two-phase flow in porous media
Energy Technology Data Exchange (ETDEWEB)
Khayrat, Karim, E-mail: khayratk@ifd.mavt.ethz.ch; Jenny, Patrick
2017-08-01
Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces within each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver.
Advanced numerical methods for three dimensional two-phase flow calculations in PWR
International Nuclear Information System (INIS)
Toumi, I.; Gallo, D.; Royer, E.
1997-01-01
This paper is devoted to new numerical methods developed for three dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe's approximate Riemann solver to define convective fluxes versus mean cell quantities. To go forward in time, a linearized conservative implicit integrating step is used, together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is widely used for fluid dynamic calculations, is proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three dimensional thermal-hydraulic code FLICA-4 which is mainly dedicated to core thermal-hydraulic transient and steady-state analysis. Hereafter, we will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with 3 pumps out of 4, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow steam-line-break conditions. (author)
A multi-scale network method for two-phase flow in porous media
International Nuclear Information System (INIS)
Khayrat, Karim; Jenny, Patrick
2017-01-01
Pore-network models of porous media are useful in the study of pore-scale flow in porous media. In order to extract macroscopic properties from flow simulations in pore-networks, it is crucial the networks are large enough to be considered representative elementary volumes. However, existing two-phase network flow solvers are limited to relatively small domains. For this purpose, a multi-scale pore-network (MSPN) method, which takes into account flow-rate effects and can simulate larger domains compared to existing methods, was developed. In our solution algorithm, a large pore network is partitioned into several smaller sub-networks. The algorithm to advance the fluid interfaces within each subnetwork consists of three steps. First, a global pressure problem on the network is solved approximately using the multiscale finite volume (MSFV) method. Next, the fluxes across the subnetworks are computed. Lastly, using fluxes as boundary conditions, a dynamic two-phase flow solver is used to advance the solution in time. Simulation results of drainage scenarios at different capillary numbers and unfavourable viscosity ratios are presented and used to validate the MSPN method against solutions obtained by an existing dynamic network flow solver.
Two-Phase Flow in Pipes: Numerical Improvements and Qualitative Analysis for a Refining Process
Directory of Open Access Journals (Sweden)
Teixeira R.G.D.
2015-03-01
Full Text Available Two-phase flow in pipes occurs frequently in refineries, oil and gas production facilities and petrochemical units. The accurate design of such processing plants requires that numerical algorithms be combined with suitable models for predicting expected pressure drops. In performing such calculations, pressure gradients may be obtained from empirical correlations such as Beggs and Brill, and they must be integrated over the total length of the pipe segment, simultaneously with the enthalpy-gradient equation when the temperature profile is unknown. This paper proposes that the set of differential and algebraic equations involved should be solved as a Differential Algebraic Equations (DAE System, which poses a more CPU-efficient alternative to the “marching algorithm” employed by most related work. Demonstrating the use of specific regularization functions in preventing convergence failure in calculations due to discontinuities inherent to such empirical correlations is also a key feature of this study. The developed numerical techniques are then employed to examine the sensitivity to heat-transfer parameters of the results obtained for a typical refinery two-phase flow design problem.
Extension of CFD Codes Application to Two-Phase Flow Safety Problems - Phase 3
International Nuclear Information System (INIS)
Bestion, D.; Anglart, H.; Mahaffy, J.; Lucas, D.; Song, C.H.; Scheuerer, M.; Zigh, G.; Andreani, M.; Kasahara, F.; Heitsch, M.; Komen, E.; Moretti, F.; Morii, T.; Muehlbauer, P.; Smith, B.L.; Watanabe, T.
2014-11-01
The Writing Group 3 on the extension of CFD to two-phase flow safety problems was formed following recommendations made at the 'Exploratory Meeting of Experts to Define an Action Plan on the Application of Computational Fluid Dynamics (CFD) Codes to Nuclear Reactor Safety Problems' held in Aix-en-Provence, in May 2002. Extension of CFD codes to two-phase flow is significant potentiality for the improvement of safety investigations, by giving some access to smaller scale flow processes which were not explicitly described by present tools. Using such tools as part of a safety demonstration may bring a better understanding of physical situations, more confidence in the results, and an estimation of safety margins. The increasing computer performance allows a more extensive use of 3D modelling of two-phase Thermal hydraulics with finer nodalization. However, models are not as mature as in single phase flow and a lot of work has still to be done on the physical modelling and numerical schemes in such two-phase CFD tools. The Writing Group listed and classified the NRS problems where extension of CFD to two-phase flow may bring real benefit, and classified different modelling approaches in a first report (Bestion et al., 2006). First ideas were reported about the specification and analysis of needs in terms of validation and verification. It was then suggested to focus further activity on a limited number of NRS issues with a high priority and a reasonable chance to be successful in a reasonable period of time. The WG3-step 2 was decided with the following objectives: - selection of a limited number of NRS issues having a high priority and for which two-phase CFD has a reasonable chance to be successful in a reasonable period of time; - identification of the remaining gaps in the existing approaches using two-phase CFD for each selected NRS issue; - review of the existing data base for validation of two-phase CFD application to the selected NRS problems
Two-phase flow characteristics analysis code: MINCS
International Nuclear Information System (INIS)
Watanabe, Tadashi; Hirano, Masashi; Akimoto, Masayuki; Tanabe, Fumiya; Kohsaka, Atsuo.
1992-03-01
Two-phase flow characteristics analysis code: MINCS (Modularized and INtegrated Code System) has been developed to provide a computational tool for analyzing two-phase flow phenomena in one-dimensional ducts. In MINCS, nine types of two-phase flow models-from a basic two-fluid nonequilibrium (2V2T) model to a simple homogeneous equilibrium (1V1T) model-can be used under the same numerical solution method. The numerical technique is based on the implicit finite difference method to enhance the numerical stability. The code structure is highly modularized, so that new constitutive relations and correlations can be easily implemented into the code and hence evaluated. A flow pattern can be fixed regardless of flow conditions, and state equations or steam tables can be selected. It is, therefore, easy to calculate physical or numerical benchmark problems. (author)
Coupling two-phase fluid flow with two-phase darcy flow in anisotropic porous media
Chen, J.; Sun, S.; Chen, Z.
2014-01-01
in the free fluid region and the two-phase Darcy law in the anisotropic porous medium region. A Robin-Robin domain decomposition method is used for the coupled Navier-Stokes and Darcy system with the generalized Beavers-Joseph-Saffman condition
Energy Technology Data Exchange (ETDEWEB)
Lu, Z X; Teng, B H; Rong, Y H; Lu, X H; Yang, X [School of Physical Electronics, University of Electronic Science and Technology of China, Chengdu 610054 (China)], E-mail: phytbh@163.com
2010-03-15
Within the framework of effective-field theory with correlations, the phase diagrams of an N-layer ferroelectric thin film with two surface layers are studied by the differential operator technique based on the spin-1/2 transverse Ising model. A general analytical equation for the phase diagram of a ferroelectric thin film with arbitrary layer number as well as exchange interactions and transverse fields is derived, and then the effects of exchange interactions and transverse fields on phase diagrams are discussed for an arbitrary layer number N. Meanwhile, the crossover features, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for various parameters of an N-layer ferroelectric thin film with two surface layers are investigated. As a result, an N-independent common intersection point equation is obtained, and the three-dimensional curved surfaces for the crossover values are constructed. In comparison with the usual mean-field approximation, the differential operator technique with correlations reduces to some extent the ferroelectric features of a ferroelectric thin film.
Analyser-based phase contrast image reconstruction using geometrical optics
International Nuclear Information System (INIS)
Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A
2007-01-01
Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 μm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser
Three-dimensional numerical modeling of turbulent single-phase and two-phase flow in curved pipes
International Nuclear Information System (INIS)
Xin, R.C.; Dong, Z.F.; Ebadian, M.A.
1996-01-01
In this study, three-dimensional single-phase and two-phase flows in curved pipes have been investigated numerically. Two different pipe configurations were computed. When the results of the single-phase flow simulation were compared with the experimental data, a fairly good agreement was achieved. A flow-developing process has been suggested in single-phase flow, in which the turbulence is stronger near the outer tube wall than near the inner tube wall. For two-phase flow, the Eulerian multiphase model was used to simulate the phase distribution of a three-dimensional gas-liquid bubble flow in curved pipe. The RNG/κ-ε turbulence model was used to determine the turbulence field. An inlet gas void fraction of 5 percent was simulated. The gas phase effects on the liquid phase flow velocity have been examined by comparing the results of single-phase flow and two-phase flow. The findings show that for the downward flow in the U bend, the gas concentrates at the inner portion of the cross section at φ = π/18 - π/6 in most cases. The results of the phase distribution simulation are compared to experimental observations qualitatively and topologically
Numerical simulation for two-phase jet problem
International Nuclear Information System (INIS)
Lee, W.H.; Shah, V.L.
1981-01-01
A computer program TWOP was developed for obtaining the numerical solutions of three-dimensional, transient, two-phase flow system with nonequilibrium and nonhomogeneous conditions. TWOP employs two-fluid model and a set of the conservation equations formulated by Harlow and Amsden along with their Implicit Multi-Field (IMF) numerical technique that allows all degrees of couplings between the two fields. We have further extended the procedure of Harlow and Amsden by incorporating the implicit couplings of phase transition and interfacial heat transfer terms in the energy equations. Numerical results of two tested problems are presented to demonstrate the capabilities of the TWOP code. The first problem is the separation of vapor and liquid, showing that the code can handle the computational difficulties such as liquid packing and sharp interface phenomena. The second problem is the high pressure two-phase jet impinged on vertical plate, demonstrating the important role of the interfacial mass and momentum exchange
Visual Analysis of Inclusion Dynamics in Two-Phase Flow.
Karch, Grzegorz Karol; Beck, Fabian; Ertl, Moritz; Meister, Christian; Schulte, Kathrin; Weigand, Bernhard; Ertl, Thomas; Sadlo, Filip
2018-05-01
In single-phase flow visualization, research focuses on the analysis of vector field properties. In two-phase flow, in contrast, analysis of the phase components is typically of major interest. So far, visualization research of two-phase flow concentrated on proper interface reconstruction and the analysis thereof. In this paper, we present a novel visualization technique that enables the investigation of complex two-phase flow phenomena with respect to the physics of breakup and coalescence of inclusions. On the one hand, we adapt dimensionless quantities for a localized analysis of phase instability and breakup, and provide detailed inspection of breakup dynamics with emphasis on oscillation and its interplay with rotational motion. On the other hand, we present a parametric tightly linked space-time visualization approach for an effective interactive representation of the overall dynamics. We demonstrate the utility of our approach using several two-phase CFD datasets.
International Nuclear Information System (INIS)
Ansari, A.; Ring, P.
2006-01-01
The excitation energies and electric multipole decay rates of the lowest lying 2 + and 3 - vibrational states in Pb, Sn, and Ni nuclei are calculated following relativistic quasiparticle random-phase approximation formalism based on the relativistic Hartree-Bogoliubov mean field. Two sets of Lagrangian parameters, NL1 and NL3, are used to investigate the effect of the nuclear force. Overall there is good agreement with the available experimental data for a wide range of mass numbers considered here, and the NL3 set seems to be a better choice. However, strictly speaking, these studies point toward the need of a new set of force parameters that could produce more realistic single-particle levels, at least in vicinity of the Fermi surface, of a wide range of nuclear masses
Accurate Modeling of Advanced Reflectarrays
DEFF Research Database (Denmark)
Zhou, Min
to the conventional phase-only optimization technique (POT), the geometrical parameters of the array elements are directly optimized to fulfill the far-field requirements, thus maintaining a direct relation between optimization goals and optimization variables. As a result, better designs can be obtained compared...... of the incident field, the choice of basis functions, and the technique to calculate the far-field. Based on accurate reference measurements of two offset reflectarrays carried out at the DTU-ESA Spherical NearField Antenna Test Facility, it was concluded that the three latter factors are particularly important...... using the GDOT to demonstrate its capabilities. To verify the accuracy of the GDOT, two offset contoured beam reflectarrays that radiate a high-gain beam on a European coverage have been designed and manufactured, and subsequently measured at the DTU-ESA Spherical Near-Field Antenna Test Facility...
Directory of Open Access Journals (Sweden)
Irina-Carmen ANDREI
2017-09-01
Full Text Available Following the demands of the design and performance analysis in case of liquid fuel propelled rocket engines, as well as the trajectory optimization, the development of efficient codes, which frequently need to call the Fuel Combustion Charts, became an important matter. This paper presents an efficient solution to the issue; the author has developed an original approach to determine the non-linear approximation function of two variables: the chamber pressure and the nozzle exit pressure ratio. The numerical algorithm based on this two variable approximation function is more efficient due to its simplicity, capability to providing numerical accuracy and prospects for an increased convergence rate of the optimization codes.
Modeling two-phase flow in PEM fuel cell channels
Energy Technology Data Exchange (ETDEWEB)
Wang, Yun; Basu, Suman; Wang, Chao-Yang [Electrochemical Engine Center (ECEC), and Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802 (United States)
2008-05-01
This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy's law and the M{sup 2} formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels. (author)
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
International Nuclear Information System (INIS)
Lian-Huang, Li; Fu-Yuan, Guo
2009-01-01
This paper analyzes the characteristic of matching efficiency between the fundamental mode of two kinds of optical waveguides and its Gaussian approximate field. Then, it presents a new method where the mode-field half-width of Gaussian approximation for the fundamental mode should be defined according to the maximal matching efficiency method. The relationship between the mode-field half-width of the Gaussian approximate field obtained from the maximal matching efficiency and normalized frequency is studied; furthermore, two formulas of mode-field half-widths as a function of normalized frequency are proposed
Parallel two-phase-flow-induced vibrations in fuel pin model
International Nuclear Information System (INIS)
Hara, Fumio; Yamashita, Tadashi
1978-01-01
This paper reports the experimental results of vibrations of a fuel pin model -herein meaning the essential form of a fuel pin from the standpoint of vibration- in a parallel air-and-water two-phase flow. The essential part of the experimental apparatus consisted of a flat elastic strip made of stainless steel, both ends of which were firmly supported in a circular channel conveying the two-phase fluid. Vibrational strain of the fuel pin model, pressure fluctuation of the two-phase flow and two-phase-flow void signals were measured. Statistical measures such as power spectral density, variance and correlation function were calculated. The authors obtained (1) the relation between variance of vibrational strain and two-phase-flow velocity, (2) the relation between variance of vibrational strain and two-phase-flow pressure fluctuation, (3) frequency characteristics of variance of vibrational strain against the dominant frequency of the two-phase-flow pressure fluctuation, and (4) frequency characteristics of variance of vibrational strain against the dominant frequency of two-phase-flow void signals. The authors conclude that there exist two kinds of excitation mechanisms in vibrations of a fuel pin model inserted in a parallel air-and-water two-phase flow; namely, (1) parametric excitation, which occurs when the fundamental natural frequency of the fuel pin model is related to the dominant travelling frequency of water slugs in the two-phase flow by the ratio 1/2, 1/1, 3/2 and so on; and (2) vibrational resonance, which occurs when the fundamental frequency coincides with the dominant frequency of the two-phase-flow pressure fluctuation. (auth.)
Approximate Model Checking of PCTL Involving Unbounded Path Properties
Basu, Samik; Ghosh, Arka P.; He, Ru
We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties; or rely on user-specified finite bound on the sample path length. We propose a new method that does not have such restrictions and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for a suitably chosen value of the bound. In essence, our method is a two-phase process: (a) the first phase is concerned with identifying the bound k 0; (b) the second phase computes the probability of satisfying the k 0-bounded until property as an estimate for the probability of satisfying the corresponding unbounded until property. In both phases, it is sufficient to verify bounded until properties which can be effectively done using existing statistical techniques. We prove the correctness of our technique and present its prototype implementations. We empirically show the practical applicability of our method by considering different case studies including a simple infinite-state model, and large finite-state models such as IPv4 zeroconf protocol and dining philosopher protocol modeled as Discrete Time Markov chains.
Fluid dynamics of cryogenic two-phase flows
International Nuclear Information System (INIS)
Verfondern, K.; Jahn, W.
2004-01-01
The objective of this study was to examine the flow behavior of a methane hydrate/methane-liquid hydrogen dispersed two-phase fluid through a given design of a moderator chamber for the ESS target system. The calculations under simplified conditions, e.g., taking no account of heat input from outside, have shown that the computer code used, CFX, was able to simulate the behavior of the two-phase flow through the moderator chamber, producing reasonable results up to a certain level of the solid phase fraction, that allowed a continuous flow process through the chamber. Inlet flows with larger solid phase fractions than 40 vol% were found to be a ''problem'' for the computer code. From the computer runs based on fractions between 20 and 40 vol%, it was observed that with increasing solid phase fraction at the inlet, the resulting flow pattern revealed a strong tendency for blockage within the chamber, supported by the ''heavy weight'' of the pellets compared to the carrying liquid. Locations which are prone to the development of such uneven flow behavior are the areas around the turning points in the semispheres and near the exit of the moderator. The considered moderator chamber with horizontal inlet and outlet flow for a solid-liquid two-phase fluid does not seem to be an appropriate design. (orig.)
Blind sensor calibration using approximate message passing
International Nuclear Information System (INIS)
Schülke, Christophe; Caltagirone, Francesco; Zdeborová, Lenka
2015-01-01
The ubiquity of approximately sparse data has led a variety of communities to take great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them to real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal acquisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measurements. Cal-AMP shares the scalability of approximate message passing, allowing us to treat large sized instances of these problems, and experimentally exhibits a phase transition between domains of success and failure. (paper)
Coupled states approximation for scattering of two diatoms
International Nuclear Information System (INIS)
Heil, T.G.; Green, S.; Kouri, D.J.
1978-01-01
The coupled states (CS) approximation is developed in detail for the general case of two colliding diatomic molecules. The high energy limit of the exact Lippmann-Schwinger equation is used to obtain the CS equations so that the sufficiency conditions of Kouri, Heil, and Shimoni apply. In addition, care is taken to ensure correct treatment of parity in the CS, as well as correct labeling of the CS by an effective orbital angular momentum. The analysis follows that given by Shimoni and Kouri for atom-diatom collisions where the coupled rotor angular momentum j 12 and projection lambda 12 replace the single diatom angular momentum j and projection lambda. The result is an expression for the differential scattering amplitude which is a generalization of the highly successful McGuire-Kouri differential scattering amplitude for atom-diatom collisions. Also, the opacity function is found to be a generalization of the Clebsch-Gordon weight atom-diatom expression of Shimoni and Kouri. The diatom-diatom CS body frame T matrix T/sup J/(j 1 'j 2 'j 12 'lambda 12 'vertical-bar j 1 j 2 j 12 lambda 12 ) is also found to be nondiagonal in lambda' 12 ,lambda 12 , just as in the atom-diatom case. The parity and identical molecule interchange symmetries are also considered in detail in both the exact close coupling and CS approximations. Symmetrized expressions for all relevant quantities are obtained, along with the symmetrized coupled equations one must solve. The properly labeled and symmetrized CS equations have not been derived before this present work. The present correctly labeled CS theory is tested computationally by applications to three different diatom-diatom potentials. First we carry out calculations for para-para, ortho-ortho, and ortho-para H 2 -H 2 collisions using the experimental potential of Farrar and Lee
A new method for ultrasound detection of interfacial position in gas-liquid two-phase flow.
Coutinho, Fábio Rizental; Ofuchi, César Yutaka; de Arruda, Lúcia Valéria Ramos; Neves, Flávio; Morales, Rigoberto E M
2014-05-22
Ultrasonic measurement techniques for velocity estimation are currently widely used in fluid flow studies and applications. An accurate determination of interfacial position in gas-liquid two-phase flows is still an open problem. The quality of this information directly reflects on the accuracy of void fraction measurement, and it provides a means of discriminating velocity information of both phases. The algorithm known as Velocity Matched Spectrum (VM Spectrum) is a velocity estimator that stands out from other methods by returning a spectrum of velocities for each interrogated volume sample. Interface detection of free-rising bubbles in quiescent liquid presents some difficulties for interface detection due to abrupt changes in interface inclination. In this work a method based on velocity spectrum curve shape is used to generate a spatial-temporal mapping, which, after spatial filtering, yields an accurate contour of the air-water interface. It is shown that the proposed technique yields a RMS error between 1.71 and 3.39 and a probability of detection failure and false detection between 0.89% and 11.9% in determining the spatial-temporal gas-liquid interface position in the flow of free rising bubbles in stagnant liquid. This result is valid for both free path and with transducer emitting through a metallic plate or a Plexiglas pipe.
Fluid-elastic vibration in two-phase cross flow
International Nuclear Information System (INIS)
Sasakawa, T.; Serizawa, A.; Kawara, Z.
2003-01-01
The present work aims at clarifying the mechanisms of fluid elastic vibration of tube bundles in two-phase cross flow. The experiment is conducted using air-water two-phase flow under atmospheric pressure. The test section is a 1.03m long transparent acrylic square duct with 128 x 128 mm 2 cross section, which consists of 3 rod-rows with 5 rods in each row. The rods are 125mm long aluminum rods with 22 mm in diameter (p/D=1.45). The natural frequency of rod vibration is about 30Hz. The result indicated a diversion of observed trend in vibration behavior depending on two-phase flow patterns either bubbly flow or churn flow. Specifically, in churn flow, the fluid elastic vibration has been observed to occur when the frequency in void fraction fluctuation approached to the natural frequency of the rods, but this was not the case in fluid elastic vibration in bubbly flow. This fact suggests the existence of mechanisms closely coupled with two-phase flow structures depending on the flow patterns, that is, static two-phase character-controlled mechanism in bubbly flow and dynamic character- controlled in churn flow
Reggeon field theory at D = 2 in two-loop approximation
International Nuclear Information System (INIS)
Eremyan, Sh.S.; Nazaryan, A.E.
1982-01-01
A general method of constructing an explicit representation is developed for the pomeron propagator in the presence of additional parameters, such as the pomeron production threshold xi 0 , momentum transfer K vector or the intercept shift delta 0 . The method is shown to be applicable in both one-loop and two-loop approximations. The obtained general formulae allow to consider the pomeron propagator in both asymptotic region and the region of the perturbation theory applicability. Besides, they provide the smooth matching of both these regions. The observed values are calculated, and the results connected with asymptotically high energies are discussed
Two new constructions of approximately SIC-POVMs from multiplicative characters
Luo, Gaojun; Cao, Xiwang
2017-12-01
In quantum information theory, symmetric informationally complete positive operator-valued measures (SIC-POVMs) are relevant to quantum state tomography [8], quantum cryptography [15], and foundational studies [16]. In general, it is hard to construct SIC-POVMs and only a few classes of them existed, as we know. Moreover, we do not know whether there exists an infinite class of them. Many researchers tried to construct approximately symmetric informationally complete positive operator-valued measures (ASIC-POVMs). In this paper, we propose two new constructions of ASIC-POVMs for prime power dimensions only by using multiplicative characters over finite fields.
Approximate Coulomb effects in the three-body scattering problem
International Nuclear Information System (INIS)
Haftel, M.I.; Zankel, H.
1981-01-01
From the momentum space Faddeev equations we derive approximate expressions which describe the Coulomb-nuclear interference in the three-body elastic scattering, rearrangement, and breakup problems and apply the formalism to p-d elastic scattering. The approximations treat the Coulomb interference as mainly a two-body effect, but we allow for the charge distribution of the deuteron in the p-d calculations. Real and imaginary parts of the Coulomb correction to the elastic scattering phase shifts are described in terms of on-shell quantities only. In the case of pure Coulomb breakup we recover the distorted-wave Born approximation result. Comparing the derived approximation with the full Faddeev p-d elastic scattering calculation, which includes the Coulomb force, we obtain good qualitative agreement in S and P waves, but disagreement in repulsive higher partial waves. The on-shell approximation investigated is found to be superior to other current approximations. The calculated differential cross sections at 10 MeV raise the question of whether there is a significant Coulomb-nuclear interference at backward angles
Theoretical study of titanium phases; Etude theorique des phases du titane
Energy Technology Data Exchange (ETDEWEB)
Trinite, V
2006-10-15
The aim of this work is to obtain a good understanding of the phase diagram of titanium within density functional theory. This diagram is composed of the alpha phase, the high pressure omega phase and the high temperature beta phase. This requires the differences in total energy to be predicted with a great precision, because these differences are around 50 meV. I find the omega phase to be the most stable one by ab initio calculation at zero temperature and pressure, in contradiction to the experimental results. I find this inversion of the stability also appears in titanium dioxide and zirconium. I have analyzed all the approximations brought into play in the ab initio approach. I have estimated the zero point energy and studied the impact of including the semi-core states as well as the effect of the exchange-correlation functionals. The conclusion is that the usual approximations for the exchange-correlation generate the biggest part of the error. A possible correction is to take into account the electronic self-interaction. I have apply this correction to the semi-core states and find a systematic improvement of the cell parameters, but no improvement on the phase stability. So I can conclude that a better description of the exchange interaction on the localized 3d states is needed. Although the standard functionals of exchange-correlation are not accurate enough to predict the phase diagrams of titanium, they perform well in describing physical properties less demanding in terms of precision, like elastic constants. However, I find important that the predicted equilibrium volume must be precise, as these properties are found strongly dependent on the volume. (author)
International Nuclear Information System (INIS)
Zhou, Xinquan; Doup, Benjamin; Sun, Xiaodong
2013-01-01
Liquid-phase turbulence measurements were performed in an air–water two-phase flow loop with a circular test section of 50 mm inner diameter using a particle image velocimetry (PIV) system. An optical phase separation method-–planar laser-induced fluorescence (PLIF) technique—which uses fluorescent particles and an optical filtration technique, was employed to separate the signals of the fluorescent seeding particles from those due to bubbles and other noises. An image pre-processing scheme was applied to the raw PIV images to remove the noise residuals that are not removed by the PLIF technique. In addition, four-sensor conductivity probes were adopted to measure the radial distribution of the void fraction. Two benchmark tests were performed: the first was a comparison of the PIV measurement results with those of similar flow conditions using thermal anemometry from previous studies; the second quantitatively compared the superficial liquid velocities calculated from the local liquid velocity and void fraction measurements with the global liquid flow rate measurements. The differences of the superficial liquid velocity obtained from the two measurements were bounded within ±7% for single-phase flows and two-phase bubbly flows with the area-average void fraction up to 18%. Furthermore, a preliminary uncertainty analysis was conducted to investigate the accuracy of the two-phase PIV measurements. The systematic uncertainties due to the circular pipe curvature effects, bubble surface reflection effects and other potential uncertainty sources of the PIV measurements were discussed. The purpose of this work is to facilitate the development of a measurement technique (PIV-PLIF) combined with image pre-processing for the liquid-phase turbulence in gas–liquid two-phase flows of relatively high void fractions. The high-resolution data set can be used to more thoroughly understand two-phase flow behavior, develop liquid-phase turbulence models, and assess high
Two approximations of the present value distribution of a disability annuity
Spreeuw, Jaap
2006-02-01
The distribution function of the present value of a cash flow can be approximated by means of a distribution function of a random variable, which is also the present value of a sequence of payments, but with a simpler structure. The corresponding random variable has the same expectation as the random variable corresponding to the original distribution function and is a stochastic upper bound of convex order. A sharper upper bound can be obtained if more information about the risk is available. In this paper, it will be shown that such an approach can be adopted for disability annuities (also known as income protection policies) in a three state model under Markov assumptions. Benefits are payable during any spell of disability whilst premiums are only due whenever the insured is healthy. The quality of the two approximations is investigated by comparing the distributions obtained with the one derived from the algorithm presented in the paper by Hesselager and Norberg [Insurance Math. Econom. 18 (1996) 35-42].
International Nuclear Information System (INIS)
Keskin, Mustafa; Erdinc, Ahmet
2004-01-01
As a continuation of the previously published work, the pair approximation of the cluster variation method is applied to study the temperature dependences of the order parameters of the Blume-Emery-Griffiths model with repulsive biquadratic coupling on a body centered cubic lattice. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. We study the dynamics of the model by the path probability method with pair distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagram in addition to the equilibrium phase diagram and also the first-order phase transition line for the unstable branches of the quadrupole order parameter is superimposed on the phase diagrams. It is found that the metastable phase diagram and the first-order phase boundary for the unstable quadrupole order parameter always exist at the low temperatures which are consistent with experimental and theoretical works
Two-phase 1D+1D model of a DMFC: development and validation on extensive operating conditions range
Energy Technology Data Exchange (ETDEWEB)
Casalegno, A.; Marchesi, R.; Parenti, D. [Dipartimento di Energetica, Politecnico di Milano (Italy)
2008-02-15
A two-phase 1D+1D model of a direct methanol fuel cell (DMFC) is developed, considering overall mass balance, methanol transport in gas phase through anode diffusion layer, methanol and water crossover. The model is quantitatively validated on an extensive range of operating conditions, 24 polarisation curves. The model accurately reproduces DMFC performance in the validation range and, outside this, it is able to predict values under feasible operating conditions. Finally, the estimations of methanol crossover flux are qualitatively and quantitatively similar to experimental measures and the main local quantities' trends are coherent with results obtained with more complex models. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
Two-phase flow heat transfer in nuclear reactor systems
International Nuclear Information System (INIS)
Koncar, Bostjan; Krepper, Eckhard; Bestion, Dominique; Song, Chul-Hwa; Hassan, Yassin A.
2013-01-01
occurring in at least two different spatial scales. Uncertainty in modelling of bubble departure diameter at boiling was studied by M. Matkovic and B. Koncar. In this article the propagation of input uncertainties for the simplified model of bubble departure size is evaluated. A methodology for estimating the prediction capability of a given correlation is provided taking into account its range of applicability. Aqueous nanofluids have a great potential for cooling applications, hence they have been studied in the article of P.N. Alekseev et al. as a possible coolant in pressurized water reactor (PWR). The theoretical study presents how a stable formation of nanoparticles in water solution can be established. Formation of fractal nanoparticles with a higher thermal conductivity than water can enhance the heat transfer of water used as a coolant in PWR. Apart from solid particles, also alternative formation of gaseous nanoparticles in density fluctuations of water is discussed. The article of R. Rzehak and E. Krepper provides a comprehensive overview of the state-of-the-art in the field of CFD modelling of subcooled flow boiling. The efficient predictive capability of current models requires calibration of model parameters over a wide range of measured data and operating conditions.The results presented in the article confirmed the great potential of the existing modelling approach for the 3D simulation of subcooled flow boiling in industrial applications but also highlight the need for specific model improvements to achieve highly accurate predictions. Two articles deal with one-dimensional analyses of two phase flows. In the article of O.Costa et al., a rapid depressurization in vertical heated pipe is simulated with the in-house 1D computer code WAHA, which was developed specifically for simulations of two-phase water hammer phenomena. The WAHA results were confronted with the simulations of the well-known system code RELAP5 on the same experimental data. The thermal
Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias
2018-01-22
Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.
Multi-scale diffuse interface modeling of multi-component two-phase flow with partial miscibility
Kou, Jisheng; Sun, Shuyu
2016-08-01
In this paper, we introduce a diffuse interface model to simulate multi-component two-phase flow with partial miscibility based on a realistic equation of state (e.g. Peng-Robinson equation of state). Because of partial miscibility, thermodynamic relations are used to model not only interfacial properties but also bulk properties, including density, composition, pressure, and realistic viscosity. As far as we know, this effort is the first time to use diffuse interface modeling based on equation of state for modeling of multi-component two-phase flow with partial miscibility. In numerical simulation, the key issue is to resolve the high contrast of scales from the microscopic interface composition to macroscale bulk fluid motion since the interface has a nanoscale thickness only. To efficiently solve this challenging problem, we develop a multi-scale simulation method. At the microscopic scale, we deduce a reduced interfacial equation under reasonable assumptions, and then we propose a formulation of capillary pressure, which is consistent with macroscale flow equations. Moreover, we show that Young-Laplace equation is an approximation of this capillarity formulation, and this formulation is also consistent with the concept of Tolman length, which is a correction of Young-Laplace equation. At the macroscopical scale, the interfaces are treated as discontinuous surfaces separating two phases of fluids. Our approach differs from conventional sharp-interface two-phase flow model in that we use the capillary pressure directly instead of a combination of surface tension and Young-Laplace equation because capillarity can be calculated from our proposed capillarity formulation. A compatible condition is also derived for the pressure in flow equations. Furthermore, based on the proposed capillarity formulation, we design an efficient numerical method for directly computing the capillary pressure between two fluids composed of multiple components. Finally, numerical tests