具有长程相互作用的相互作用粒子系统：标度极限和动力学方程

IF 0.6 4区数学 Q3 MATHEMATICS

Rendiconti Lincei-Matematica e Applicazioni Pub Date : 2020-12-09 DOI:10.4171/RLM/939

A. Nota, J. Velázquez, Raphael Winter

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引用次数: 5

摘要

本文的目的是描述由相互作用粒子系统的标度极限引起的各种动力学方程。我们提供了一种形式，使我们能够确定给定相互作用势和标度极限的动力学方程。本文的重点是具有长程相互作用的粒子系统。这里的推导是形式化的，但它将粒子系统解释为粒子在随机力场中的运动，该运动具有摩擦项，这是由于与周围粒子的相互作用。该方法的一些技术细节在配套论文[47]中进行了讨论。

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Interacting particle systems with long-range interactions: scaling limits and kinetic equations

The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential and scaling limit. Our focus in this paper is on particle systems with long-range interactions. The derivation here is formal, but it provides an interpretation of particle systems as the motion of a particle in a random force field with a friction term which is due to the interaction with the surrounding particles. Some of the technical details of this method are discussed in the companion paper [47].

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来源期刊

Rendiconti Lincei-Matematica e Applicazioni MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

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.