摘要:

If a potential is spherically symmetric, and satisfies some differential inequalities, then solutions to the Cauchy problem for the linearized Boltzmann equation with the external-force potential have the decay order of an irrational function of the time variable.

ISSN:0041-1450    

DOI:10.1080/00411459408203926

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Methods have been developed to average the transport equation over the energy (spectrum) variable which permit the calculations of particle transport in unhomogeneous and heterogeneous media with high accuracy in an inexpensive way. Proposed averaged equations can be solved by most of the existing Monte Carlo and deterministic transport codes.

ISSN:0041-1450    

DOI:10.1080/00411459408203927

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We put forward three algorithms for computing equations determining asymptotic approximations to solutions of a linear transport equation in the strong scattering asymptote. Applying these algorithms to a one-speed integro-differential linear transport equation in the limit of large scattering cross section, we derive equations that determine various first-, second- and third-order approximations to the scalar flux; one of the first-order approximations satisfies the conventional diffusion equation. We point out a particular diffusion equation that is valid both for large scattering cross sections and for large absorption cross sections.

ISSN:0041-1450    

DOI:10.1080/00411459408203928

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

A numerical algorithm for obtaining the discrete ordinates solution of the time—dependent multigroup neutron and γ–ray transport equation with pulsed sources is discussed. The Adaptive Weighted Diamond Differenced scheme (AWDD scheme) and the S2rebalance method for accelerating inner iterations, consistent with the discretization of the transport equation, are described. The spectral analysis of stability of the WDD scheme is presented. Special tools for correct treatment of the time—dependent problems with pulsed sources are provided. The results of calculations of some benchmark problems given by B. D. Ganopol et al. are presented.

ISSN:0041-1450    

DOI:10.1080/00411459408203929

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Under mild initial assumptions, a functional central limit theorem is obtained for a system of randomly interacting particles regulated by a binomial kernel of interaction. This system is related to a nonlinear Boltzmann-type equation.

ISSN:0041-1450    

DOI:10.1080/00411459408203930

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Nonmonotonic variation of the ‘C’ eigenvalue (average number of secondaries per collision) with increasing α, the strength of forward scattering, has been observed earlier for one-dimensional infinite homogeneous slabs and infinitely long homogeneous cylinders. We have developed the Integral Transform (IT) method, an accurate semi-analytical method to obtain the C eigenvalue for a homogeneous cylinder (two-dimensional system). We are thus able to detect any nonmonotonic variation of C (with α) using the Sahni and Sjöstrand criterion. Along with the IT method, we also present the results obtained by the well-known numerical techniques like the discrete ordinates method using a high quadrature order and the Monte Carlo method for the same problem. The SNresults show disagreement with the other two methods when one of the dimensions is very small (< 0.05λt). We believe that even the 16thorder quadrature set cannot integrate the angular flux accurately in these extreme situations.

ISSN:0041-1450    

DOI:10.1080/00411459408203931

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

Forty-eight scientists from 13 countries participated in this conference, which covered the following three main topics in many-particle systems: the theory and applications of the Boltzmann equation, the nonlinear systems connected with the Vlasov equation (such as the Vlasov-Poisson and Vlasov-Maxwell systems), and the quantum mechanical counterparts of the above (such as the quantum Boltzmann equation, Wigner-Poisson and Schrodinger-Poisson systems). The 43 half-hour talks and the two 20-minute-talks represented latest developments in the following particular research areas: Discrete velocity models and the hydrodynamic limit of the Boltzmann equation, existence theory (with particular emphasis laid on suitable boundary conditions), stability, numerical analysis and modelling, and the diffusion limit of kinetic equations. There were two lectures in the new area of the Vlasov-Einstein equations. The conference was lively and reflected the vivid activity of the research being carried out in important mathematical aspects of many-particle systems. The abstracts below have been prepared on the basis of texts prepared by the authors and edited by us, in order to comply with space limitations. They are given in the chronological order of the talks.

ISSN:0041-1450    

DOI:10.1080/00411459408203932

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor