arXiv 1809.028082018-09-08math-phcond-mat.stat-mechmath.MP

Mathematical models of collective dynamics and self-organization

Pierre Degond

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Macroscopic models of collective motion and self-organization

In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view of its possible extensions to other kinds of collective motion.

2013-04-22math-phmath.MP

Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints

This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different self-organized patterns from non-locality and anisotropy of the interactions among individuals. A mathematical technique by time-evolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then self-organization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration.

2009-10-24math-phmath.MPnlin.AO

A mean field model for the collective behaviour of interacting multi-species particles. Mathematical results and application to the inverse problem

The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures that the sum with square-root normalization converges toward a Gaussian distribution. The main topic of this thesis is the generalization of the central limit theorem for spin random variable whose interaction is described by a multi-species mean-field Hamiltonian. We found the conditions, in terms of the interaction, that lead in the thermodynamic limit to…

2012-12-15math-phmath.MP

Self-organization in the tornado: the new approach in the tornado description

For the mathematical modeling of highly non-equilibrium and nonlinear processes in a tornado in this paper a new approach based on nonlinear equations of momentum transfer with function of sources and sinks is suggested. In constructing the model thermodynamic description is used, which is not entered before and allows discovering new principles of self-organization in a tornado. This approach gives fairly consistent physical results. This is an attempt to answer some fundamental questions concerning the existence of a tornado based on the created model and numerical results.

2012-04-27math-phmath.MPphysics.ao-ph