摘要:

Some rigorous results obtained in the study of two nonlinear problems arising in particle transporf theory are illustrated and appropriately reviewed. The relevant existence theory and convergence of the associated iterative schemes are in particular considered.

ISSN:0041-1450    

DOI:10.1080/00411458408211648

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Progress made in the past two years on deriving inverse scattering methods for the transport equation is reviewed. The developments include new results for both monoenergetic and multigroup transport in plane-geometry media that are uniformly illuminated, and for targets that are not uniformly illuminated or not necessarily of plane geometry. New inverse equations for determining multigroup cross sections are also derived for plane geometry, as well as those for a target containing a spatially-uniform isotropic source.

ISSN:0041-1450    

DOI:10.1080/00411458408211649

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Since Hangelbroek's11study of non-conservative neutron transport with isotropic scattering considerable effort has been made towards the solution of abstract half-space problems of the from

ISSN:0041-1450    

DOI:10.1080/00411458408211650

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Let us consider the stationary one-dimensional Fokker-Planck equation

ISSN:0041-1450    

DOI:10.1080/00411458408211651

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Ever since K. M. Case's famous 1960 paper,1transport theorists have been studying the questions of full- and half-range completeness for various transport type equations. The purpose of this note is to try to define exactly what is meant by “Completeness” as it is needed, and used, in solving transport equations and to discuss some of the various techniques which have been, or might be, used to verify completeness.

ISSN:0041-1450    

DOI:10.1080/00411458408211652

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The generalized function solution of Kramers' equation describing Brownian motion is shown to be valid in type S function spaces of entire functions for at least a finite time.

ISSN:0041-1450    

DOI:10.1080/00411458408211653

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A variation of the FN method for which convergence is known is applied to calculation of Chandrasekhar's H-function and to exit distribution problems in multi-group neutron transport.

ISSN:0041-1450    

DOI:10.1080/00411458408211654

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A certain monotonically increasing nonlinear iterative procedure, first employed systematically by Shimizu and Aoki, has proven quite effective for computing the reflection matrix for a spatially homogeneous half-space, where the direction and energy variables are treated by suitable discrete approximations. In this paper it is shown that this procedure converges, provided only that the underlying half-space is nonmultiplying. (“Nonmultiplying” means that the maximum expected number of particles emerging from a collision does not exceed unity, where the maximum is taken over all energies and directions of the incident particles.) Furthermore, in this case it is shown that a certain norm of the approximate reflection matrices produced by the iterative process is bounded above by the maximum secondary scattering ratio.

ISSN:0041-1450    

DOI:10.1080/00411458408211655

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The diffusion-synthetic acceleration (DSA) method is an iterative procedure for obtaining numerical solutions of discrete-ordinates problems. The DSA method is operationally more complicated than the standard source-iteration (SI) method, but if encoded properly it converges much more rapidly, especially for problems with diffusion-like regions. In this article we describe the basic ideas behind the DSA method and give a (roughly chronological) review of its long development. We conclude with a discussion which covers additional topics, including some remaining open problems and the status of current efforts aimed at solving these problems.

ISSN:0041-1450    

DOI:10.1080/00411458408211656

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Problems in transport theory have long presented difficulties to the numerical analyst; a great diversity of methods have been spawned by the efforts of many who have attempted to deal with these difficulties, each usually successful only used in production codes for time independent linear transport problems is the source iteration method. This method consists of iterating the particle density in the transport equation using the result of the previous iteration in the scattering integral term thus reducing the computation at each step to a much simpler streaming calculation. This method generally gives good results when the criticality constant, c, is bounded below one; however, the spectral radius of the iteration map approaches one as c does.

ISSN:0041-1450    

DOI:10.1080/00411458408211657

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor