Macroscopic models of collective motion and self-organization

Navoret, Laurent; Motsch, Sébastien; Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre

Navoret, Laurent; Motsch, Sébastien; Liu, Jian-Guo; Frouvelle, Amic; Degond, Pierre (2013), Macroscopic models of collective motion and self-organization, p. 27. https://basepub.dauphine.fr/handle/123456789/11238

Type

Rapport

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http://hal.archives-ouvertes.fr/hal-00816752

Date

2013

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Auteur(s)

Navoret, Laurent
Motsch, Sébastien
Liu, Jian-Guo
Frouvelle, Amic

Degond, Pierre

Résumé (EN)

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.

Mots-clés

self - organized hydrodynamics; von Mises-Fisher distribution; macroscopic limit; Fokker - Planck equation; mean-ﬁeld kinetic model; Vicsek model; self-alignment; self-propelled particles; Individual-Based Models