摘要:

We deal with the Dirac equation with time-dependent, non-homogeneous electro-magnetic potential, in particular with its approximation in the limit of infinite speed of light.

ISSN:0041-1450    

DOI:10.1080/00411450008205884

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The hydrodynamical scalings of many discrete-velocity kinetic models lead to a small-relaxation time behavior governed by the corresponding Euler type hyperbolic equations or Navier-Stokes type parabolic equations. Using as a prototype a simple discrete-velocity model of the Boltzmann equation we develop a class of central schemes with the correct asymptotic limit that work with uniform second order accuracy with respect to the scaling parameter. Numerical results for both the fluid-dynamic limit and the diffusive limit show the robustness of the present approach.

ISSN:0041-1450    

DOI:10.1080/00411450008205885

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

This paper contains the description of a hierachy of mathematical models for the simulation of vehicular traffic. A microscopic, kinetic and macroscopic model is discussed. It is shown how the kinetic model can be derived from the microscopic one and how the macroscopic model is derived from the underlying kinetic model. Connections between the different types of models are presented and numerical methods and simulations are shown for all types of models.

ISSN:0041-1450    

DOI:10.1080/00411450008205886

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

High accuracy of the time-differencing method for the spatially non-homogeneous Boltzmann equation, recently developed in [T. Ohwada, Journal of Compt. Phys., 139, 1 (1998)] as the second order approximation of the integral form of the equation along its characteristic line, is demonstrated numerically in both deterministic and stochastic computations of the standard Boltzmann equation for hard-sphere molecules. Comparisons are made with the results by the conventional splitting method and those by the splitting method with second order accurate collision step. Although the error of splitting method is reduced by the improvement of accuracy of the collision step, however, the accuracy is still first order because of the intrinsic error of the method. The intrinsic error is observed clearly in the stochastic computation of an initial value problem with a steep initial function, where the modified direct simulation Monte-Carlo proposed in the previous study is shown to work well.

ISSN:0041-1450    

DOI:10.1080/00411450008205887

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Dysthe's nonlinear Schrädinger equation is a correction to the well-known cubic nonlinear Schrädinger equation of the theory of deep water waves; it describes the modulation of the wave envelope with third order accuracy. We consider the well-posedness problem with physically adequate periodic boundary conditions, and study the convergence of Galerkin's method for the numerical computation of solutions including error estimates.

ISSN:0041-1450    

DOI:10.1080/00411450008205888

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

A mesoscopic/macroscopic model for self-consistent charged transport under high field scaling conditions corresponding to drift-collisions balance was derived by Cercignani, Gamba, and Lever-more in [4]. The model was summarized in relationship to semiconductors in [2]. In [3], a conceptual domain decomposition method was implemented, based upon use of the drift-diffusion model in highly-doped regions of the device, and use of the high-field model in the channel, which represents a (relatively) lightly-doped region. The hydrodynamic model was used to calibrate interior boundary conditions. The material parameters of GaAs were employed in [3].

ISSN:0041-1450    

DOI:10.1080/00411450008205889

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We apply the method of time-dependent rescalings which has been developed by G. Rein and the author to a model kinetic equation, to the Euler equations for a perfect polytropic gas and to a model with friction and heat transfer. We build Lyapunov functionals which are in the case of the fluid models improved versions of the estimates which have been found by J.-Y. Chemin and D. Serre (see [2],[14]).

ISSN:0041-1450    

DOI:10.1080/00411450008205890

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Starting from a kinetic model for electrons in a weakly ionized plasma, a spherical harmonic expansion (SHE-) model is derived by a formal asymptotic analysis for strongly disparate masses of electrons and ions. The macroscopic limit of the SHE-model for high fields gives a high field extension of standard macroscopic models for ionization.

ISSN:0041-1450    

DOI:10.1080/00411450008205891

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The “smooth” quantum hydrodynamic (QHD) model is an extension of the classical hydrodynamic model for semiconductor devices which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. Smooth QHD model simulations of the resonant tunneling diode exhibit negative differential resistance—the experimental signal for quantum resonance effects. Resonant tunneling is analyzed in fluid dynamical terms from the point of view of the smooth QHD transport equations.

ISSN:0041-1450    

DOI:10.1080/00411450008205892

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this paper we analyze the convergence rate of solutions of certain drift-diffusion-Poisson systems to their unique steady state. These bi-polar equations model the transport of two populations of charged particles and have applications for semiconductor devices and plasmas.

ISSN:0041-1450    

DOI:10.1080/00411450008205893

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor