摘要:

A functional equation arising firom kinetic theory of dense gases is considered. The solutions to this equation represent the quillbrium distniutions for the revised Enskog Equation. Indeed, they make the Rdsiiois-Polewczak Liapounov fUncti0∼1 constant m time. The class of all the above mentioned distriiutions is completely characterized. This class is wider than that characterized by Risibois only consisting of the distributions which are periodic with respect to the space variable.

ISSN:0041-1450    

DOI:10.1080/00411459708229328

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In the paper we consider a kinetic model that can be considered as a generalization of the Boltzmann equation. The model is formally derived from the BBGKY hierarchy for hard spheres system by introducing a variable diameter r in the domain [0,R] and then, by averaging the two-particle distribution function over this domain. For this model we prove global existence, uniqueness, and exponential convergence to equilibrium.

ISSN:0041-1450    

DOI:10.1080/00411459708229329

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In order to develop ICF reactors a model is needed for the anisotropic transport of neutral and charged particles inside a high density hot plasma generated at the centre of a DT pellet by a laser-driven implosion. Two BFF equations in cascade for the F-transformed angular flux(0) (B, E, μ), unperturbed by the continuous deviation tern, and for its correction(1) (B, E, μ), talcing this effect into account, are solved via FPN-BNmethod, once an appropriate closed-form, but of infinite anisotropy order, expression is found for(0) (B, E, μ). The introduction of suitably generalized F-transformed kernel functions, with respect to the classical ones for usual anisotropic transport integral formulation, and of projections, of both FPNand BNequations, onto a suitable sequence of Paley-Wiener spaces, leads finally to FPNrecurrences reducing the two first BNequations to a couple of F-transformed integral equations for the zero-th order moments only of the two unknowns, talcing nevertheless into account the whole flux and scattering anisotropy of the problem. Finally easily computable polynomial series expansions, of such zero-th order moments of the unknowns, with Fourier coefficients solving appropriate infinite algebraic linear systems, are derived, once appropriate relations are found, between boundary angular flux moments, substantially correspondent to the boundary conditions for the problem.

ISSN:0041-1450    

DOI:10.1080/00411459708229330

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The transcendental method for finding the analytical closed-form solution to the dispersive equation in the Linear Transport Theory is studied in some detail. The mathematical genesis of general form of the analytical solution is presented. This solution is exact according to the new closed-form representation of the numbers with desired accuracy in the transcendental method theory. This approach implies the qualitative improvement of the more conventional method such as successive approximations. The numerical results, obtained for different magnitudes of the cross section parameterc, support the validity and basic principles of the transcendental method. The conditions for the existence of the exact solution are discussed.

ISSN:0041-1450    

DOI:10.1080/00411459708229331

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

Singular integral equations with Cauchy type kernels are considered on a real interval. It is assumed that near the end points of the interval the solution of the Riemann-Hilbert problem diverges at most logarithmically. By using such an “end-point condition” in a simple case of neutron transport in a infinite medium, the evaluation of the continuum coefficients of the singular eigenfunction expansion is carried out easily. Moreover, it results that such coefficients have a structure completely analogous to that of the discrete coefficients, showing the intimate relationship between Case's continuum and dis crete modes.

ISSN:0041-1450    

DOI:10.1080/00411459708229332

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor