具有远距离相互作用的相互作用粒子系统:随机场中标记粒子的近似

IF 0.6 4区 数学 Q3 MATHEMATICS
A. Nota, J. Vel'azquez, Raphael Winter
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引用次数: 4

摘要

在本文中,我们继续研究由相互作用粒子系统的标度极限产生的不同类型的动力学方程的推导。我们在[16]开始了这项研究。更确切地说,我们考虑了具有长程相互作用系统的动力学方程的推导。特别强调的是,所有的动力学状态都可以通过单个粒子的随机Langevin型动力学近似相互作用粒子系统的动力学以及瑞利气体的动力学来获得。我们将详细介绍这种近似,并将获得出现在极限福克-普朗克方程中的扩散系数和摩擦系数的精确公式,用于标记粒子f(x,v,t)的概率密度,用于三类不同的势。将详细考虑在大距离处表现为库仑势的相互作用势的情况。特别是,我们将讨论所谓库伦对数的起始点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Interacting particle systems with long-range interactions: Approximation by tagged particles in random fields
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in [16]. More precisely, we consider the derivation of the kinetic equations for systems with long range interaction. Particular emphasis is put on the fact that all the kinetic regimes can be obtained approximating the dynamics of interacting particle systems, as well as the dynamics of Rayleigh Gases, by a stochastic Langevin-type dynamics for a single particle. We will present this approximation in detail and we will obtain precise formulas for the diffusion and friction coefficients appearing in the limit Fokker-Planck equation for the probability density of the tagged particle f (x, v, t), for three different classes of potentials. The case of interaction potentials behaving as Coulombian potentials at large distances will be considered in detail. In particular, we will discuss the onset of the the so-called Coulombian logarithm.
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来源期刊
Rendiconti Lincei-Matematica e Applicazioni
Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.30
自引率
0.00%
发文量
27
审稿时长
>12 weeks
期刊介绍: The journal is dedicated to the publication of high-quality peer-reviewed surveys, research papers and preliminary announcements of important results from all fields of mathematics and its applications.
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