Mathematical models of collective dynamics and self-organization

TL;DR

This paper reviews mathematical challenges in modeling collective dynamics and self-organization, focusing on deriving fluid equations from particle models and analyzing phase transitions and stability of equilibria.

Contribution

It introduces new insights into deriving fluid equations from particle models and studying phase transitions in collective systems.

Findings

Derivation of fluid equations from particle dynamics

Analysis of phase transitions and stability

Insights into self-organization mechanisms

Abstract

In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from particle dynamics of collective motion and second, the study of phase transitions and the stability of the associated equilibria.