PHASE TRANSITIONS IN A KINETIC FLOCKING MODEL OF CUCKER-SMALE TYPE

被引：52

作者：

Barbaro, Alethea B. T. ^{[1
]}

Canizo, Jose A. ^{[2
]}

Carrillo, Jose A. ^{[3
]}

Degond, Pierre ^{[3
]}

机构：

[1] Case Western Reserve Univ, Dept Math Appl Math & Stat, Cleveland, OH 44106 USA

[2] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Campus Fuentenueva, E-18071 Granada, Spain

[3] Imperial Coll London, Dept Math, London SW7 2AZ, England

来源：

MULTISCALE MODELING & SIMULATION | 2016年 / 14卷 / 03期

基金：

美国国家科学基金会; 英国工程与自然科学研究理事会;

关键词：

flocking model; phase transition; Cucker-Smale model; Vicsek model; SELF-STABILIZING PROCESSES; MEAN-FIELD LIMIT; MULTI-WELLS LANDSCAPE; DRIVEN PARTICLES; DYNAMICS; EQUATIONS; FISH; CONVERGENCE; SYSTEM; ORDER;

D O I：

10.1137/15M1043637

中图分类号：

O1 [数学];

学科分类号：

070101 [基础数学];

摘要：

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a "disordered" to an "ordered" state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition.

引用

页码：1063 / 1088

页数：26

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