摘要:

Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations.

ISSN:0041-1450    

DOI:10.1080/00411459608203544

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The time dependent transport equation with periodic boundary conditions is discussed in the space of continuous functions. A suitable subspace is constructed and it is shown that the corresponding operatorAgenerates a strongly continuous semigroupTF(t) inF=D(A). By virtue of Trotter's approximation theorem of strongly continuous semigroups, the convergence of the discrete ordinates approximation for the time dependent transport equation is rigorously obtained.

ISSN:0041-1450    

DOI:10.1080/00411459608203545

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The time dependent transport equation with periodic boundary conditions is discussed in the space of continuous functions. Some aspects of the spectral properties of the corresponding transport operatorAandTF(t) (which is the strongly continuous semigroup generated byAin the subspaceF=D(A)) are studied, and it is shown that σ(TF(t)){λ:∣λ∣ exp (β1t)}, where β1is any real constant greater than the infimum of the total collision frequency, contains only finitely many elements, each of which is an eigenvalue ofTF(t) with finite algebraic multiplicity. Consequently, the asymptotic behavior of the time dependent solution is obtained.

ISSN:0041-1450    

DOI:10.1080/00411459608203546

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

A way to derive consistently kinetic models for vehicular traffic from microscopic follow the leader models is presented. The obtained class of kinetic equations is investigated. Explicit examples for kinetic models are developed with a particular emphasis on obtaining models that give realistic results. For space homogeneous traffic flow situations numerical examples are given including stationary distributions and fundamental diagrams.

ISSN:0041-1450    

DOI:10.1080/00411459608203547

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The purpose of this paper is two fold. First, we shed some light on the slow convergence behaviour of a certain iterative procedure for solving the reflection matrix in a nonmultiplying half-space. In particular, we show that the asymptotic convergence rate of the iterative procedure of Shimiju and Aoki is 1 – □1–c. Herec, 0 ≤c≤ 1. the expected number of particles emerging from a collision. Second, a convergence accerelation procedure is proposed. The asymptotic convergence rate of the accerelation procedure is given. Some very satisfactory numerical results are also presented.

ISSN:0041-1450    

DOI:10.1080/00411459608203548

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

This paper discusses the spectrum of the energy-dependent neutron transport opertor in the anisotropic nonhomogeneous slab geometry with generalized boundary conditions. We prove the existence of a strictly dominant eigenavalue for this operator.

ISSN:0041-1450    

DOI:10.1080/00411459608203549

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

The work analyzes the temporal variation of mean current and mean square current for Gaussian fluctuations of conductivity. The relaxation times for the mean current and mean square current are determined. The correlation between the fluctuations of electric current and conductivity is derived. The limits of validity of white noise approximation are discussed.

ISSN:0041-1450    

DOI:10.1080/00411459608203550

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

摘要:

Discrete ordinates radiation transport problems in two-dimensional geometry that have curvilinear (or inclined) surfaces are not accurately represented with rectangular cells. Some such problems do not have the symmetry necessary for cylindrical (r,) geometry. We have developed various spatial quadratures for arbitrarily-shaped triangular cells, and an algorithm for tracking the flow from cell to cell through an unstructured grid of such cells. Such a grid can accurately approximate curved or inclined surfaces. Furthermore, unstructured grids can increase efficiency by providing mesh refinement only where needed. By splitting each cell along the streaming direction, into two triangular subcells, each of which has only one inflow edge and one outflow edge, a wide variety of spatial quadratures can be readily adapted to these grids. We present split-cell versions of the step, step characteristic, diamond difference, and linear characteristic spatial quadratures and necessary details of implementation of the flow-tracking algorithm. Test results, also presented here, demonstrate advantages of unstructured triangular grids and show the robustness of the method for grids formed by Delaunay triangulation of randomly-chosen vertices. Indeed, randomness of the mesh is observed to ameliorate the systematic accumulation of spatial truncation errors, thus decreasing numerical diffusion.

ISSN:0041-1450    

DOI:10.1080/00411459608203551

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459608203552

出版商:Taylor & Francis Group    

年代:1996

数据来源: Taylor