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Exact solution to the nonlinear Boltzmann equation for the diffusion of test particles in a host medium

Точное решение нелинейного уравнения Болыцмана для диффузии пробных частиц в среде

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Il Nuovo Cimento B (1971-1996)

Summary

An exact analytical solution to the scalar nonlinear Boltzmann equation governing the diffusion of some test particles in an unbounded background of certain other field particles is presented. A moment method is used to reconstruct then via a Fourier transform technique the sought solution for the isotropic distribution function of the test particles considered. Coupling and removal effects are finally commented in some detail.

Riassunto

In questo lavoro si presenta una soluzione analitica esatta dell’equazione scalare di Boltzmann non lineare per lo studio della diffusione di certe particelle «di prova» in un mezzo ospite infinito costituito da certe altre particelle «di campo». Si fa ricorso ad un metodo di momenti per ricostruire quindi, tramite una tecnica di trasformata di Fourier, la cercata soluzione per la funzione di distribuzione isotropa delle particelle «di prova» considerate. Effetti di accoppiamento e di rimozione sono infine discussi in dettaglio.

Резюме

Предлагается точное аналитическое решение скалярного нелинейного уравнения Болыцмана для диффузии пробных частиц в неограниченной среде других полевых частиц. Используя метод моментов для реконструкции, затем с помощью метода Фурье-преобразования получается искомое решение для изотропной функции распределения пробных частиц. В заключение подробно рассматриваются эффекты связи и удаления.

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Author notes

  1. T. F. Nonnenmacher

    Present address: Abteilung für Mathematische Physik, Universität Ulm, D-7900, Ulm, BRD

Authors and Affiliations

  1. Laboratorio di Ingegneria Nucleare dell’Università, Via dei Colli 16, 40136, Bologna, Italia

    V. C. Boffi & T. F. Nonnenmacher

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  1. V. C. Boffi
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  2. T. F. Nonnenmacher
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Boffi, V.C., Nonnenmacher, T.F. Exact solution to the nonlinear Boltzmann equation for the diffusion of test particles in a host medium. Nuov Cim B 85, 165–181 (1985). https://doi.org/10.1007/BF02721558

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