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Macroscopic models of collective motion and self-organization

Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo; Motsch, Sébastien; Navoret, Laurent (2013), Macroscopic models of collective motion and self-organization, Séminaire Laurent Schwartz -EDP et applications, 2012-2013, p. 1-27

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Type
Article accepté pour publication ou publié
Date
2013
Journal name
Séminaire Laurent Schwartz -EDP et applications
Volume
2012-2013
Publisher
EUDML (The european Digital mathematics library)
Pages
1-27
Metadata
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Author(s)
Degond, Pierre
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Frouvelle, Amic cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Liu, Jian-Guo
Duke Physics
Motsch, Sébastien
Center for Scientific Computation and Mathematical Modeling [CSCAMM]
Navoret, Laurent
Institut de Recherche Mathématique Avancée [IRMA]
Abstract (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.
Subjects / Keywords
individual-based models; self-propelled particles; self-alignment; Viscek model; mean-field kinetic model; Fokker-Planck equation; macroscopic limit; von Mises-Fisher distribution; self-organized hydrodynamics