摘要:

We prove L2-error estimates for the discrete ordinates method for the angular discretization of the three-dimensional neutron transport equation. The analysis is for monoenergetic three-dimensional transport of neutrons in a homogeneous uniform media and isotropic scattering is assumed. A special quadrature rule with relatively uniformly distributed discrete directions is considered.

ISSN:0041-1450    

DOI:10.1080/00411458808230852

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We consider the linearized Roltzmann equation with special reflecting boundary conditions. Both the Soltzmann operator and the reflecting conditions are time dependent. It seems to be adequate to use locally convex spaces. The basic idea is a transformation of the boundary value problem into an initial data problem. Our aim is the formulation of an existence and uniqueness theorem. In this paper we describe the problem in a space of continuous functions.

ISSN:0041-1450    

DOI:10.1080/00411458808230853

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The diffusion and maximum anisotropy approximations are compared in the calculation of the electron distribution function for steady-state polar optical scattering in III-V semiconductors. An expansion of the steady-state Boltzmann equation in powers of (EO/E) is made for a high electric field E where EOis the characteristic critical electric field. This expansion is a fairly good approximation for certain ternary III-V semiconductors. The electron distribution function found by the diffusion approximation is useful only as a functional; a modified maximum anisotropy approximation gives a valid electron distribution function.

ISSN:0041-1450    

DOI:10.1080/00411458808230854

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

This paper deals with the problem of estimating the order of discretization error in finite difference approximation to the transport equation. We conider S2 approximation in slab geometry and show rigorously that the global error is one order less than the cell edge errors in a single mesh problem.

ISSN:0041-1450    

DOI:10.1080/00411458808230855

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The one dimensional, linear, half space, abstract transport equation with an accretive, invertible collision operator is shown to be uniquely solvable. An example from multigroup neutron transport is given.

ISSN:0041-1450    

DOI:10.1080/00411458808230856

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

The unique solvability of a class of abstract kinetic equations with applications to multigroup neutron transport and polarized light transfer is established for the case when the collision operator differs from the identity by an operator of spectral radius <1 for a semi-infinite medium and ≤1 for a finite slab medium. Some applications to the critical slab problem are discussed.

ISSN:0041-1450    

DOI:10.1080/00411458808230857

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

A NATO Advanced Study Institute on “Non-Linear Evolution and Chaotic Phenomena” was held in Noto, Sicily, June 8–19, 1987. The director was Giovanni Gallavotti (Roma) with co-directors Marcello Anile (Catania) and your author. Other members of the scientific organizing committee included Mitchell Feigenbaum (Rockefeller University) and David Ruelle (IHES). The attendance consisted of 23 invited speakers and about 80 “students”. In this report, I have summarized the talks of the invited speakers who gave between one and three lectures each. In addition, there were contributed seminars, presented during the two-hour afternoon “tutorials” organized by Gallavotti to assist the students' assimilation of the material presented by the principal lecturers. (These students, incidentally, ranged from graduate students through recent Ph.D.'s all the way to an endowed chair professor from the University of Virginia and the former chairman of the mathematics department at Rutgers University!) The contributed seminars are listed by title and author at the end of this report, but here I should mention the special efforts of Jack Dorning (the previously mentioned participant from U.Va.) who contributed four hours' worth of talks on non-linear phenomena and chaos at an introductory level. (He spoke about fixed points, bifurcations, attractors, Poincare maps, return maps, self-similarity, etc.) These lectures, to a large extent, helped overcome the difficulties inherent in a school with students of such widely differing backgrounds and in no little way contributed to a successful learning experience for all concerned.

ISSN:0041-1450    

DOI:10.1080/00411458808230858

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458808230859

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor