Macroscopic models of collective motion and self-organization

Pierre Degond (1) , Amic Frouvelle (2) , Jian-Guo Liu (3) , Sébastien Motsch (4) , Laurent Navoret (5)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Duke Physics
4 CSCAMM - Center for Scientific Computation and Mathematical Modeling
5 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Physique mathématique [math-ph]

Pierre Degond, Amic Frouvelle, Jian-Guo Liu, Sébastien Motsch, Laurent Navoret. Macroscopic models of collective motion and self-organization. Séminaire Laurent Schwartz - EDP et applications, 2013, Année 2012-2013, Exp. No. 1, 27 p. ⟨hal-00816752⟩