Geodesic
Macroscopic models of collective motion and self-organization
Degond, Pierre1, 2 idref; Frouvelle, Amic3 idref; Liu, Jian-Guo4; Motsch, Sebastien5 idref; Navoret, Laurent6 idref
1Université de Toulouse; UPS, INSA, UT1, UTM Institut de Mathématiques de Toulouse F-31062 Toulouse France
2CNRS; Institut de Mathématiques de Toulouse UMR 5219 F-31062 Toulouse France
3CEREMADE, UMR CNRS 7534 Université Paris-Dauphine 75775 Paris Cedex 16 France
4Department of Physics and Department of Mathematics Duke University Durham, NC 27708 USA
5Center for Scientific Computation and Mathematical Modeling (CSCAMM) University of Maryland College Park, MD 20742 USA
6Institut de Recherche Mathématique Avancée de Strasbourg CNRS UMR 7501 and Université de Strasbourg 7 rue René Descartes, 67084 Strasbourg Cedex France
Séminaire Laurent Schwartz — EDP et applications (2012-2013), Talk no. 1, 27 p.

See the original proceeding notice from the Numdam source

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.

DOI: 10.5802/slsedp.32

Degond, Pierre  1 , 2 ; Frouvelle, Amic  3 ; Liu, Jian-Guo  4 ; Motsch, Sebastien  5 ; Navoret, Laurent  6

1 Université de Toulouse; UPS, INSA, UT1, UTM Institut de Mathématiques de Toulouse F-31062 Toulouse France
2 CNRS; Institut de Mathématiques de Toulouse UMR 5219 F-31062 Toulouse France
3 CEREMADE, UMR CNRS 7534 Université Paris-Dauphine 75775 Paris Cedex 16 France
4 Department of Physics and Department of Mathematics Duke University Durham, NC 27708 USA
5 Center for Scientific Computation and Mathematical Modeling (CSCAMM) University of Maryland College Park, MD 20742 USA
6 Institut de Recherche Mathématique Avancée de Strasbourg CNRS UMR 7501 and Université de Strasbourg 7 rue René Descartes, 67084 Strasbourg Cedex France 
Degond, Pierre; Frouvelle, Amic; Liu, Jian-Guo; Motsch, Sebastien; Navoret, Laurent. Macroscopic models of collective motion and self-organization. Séminaire Laurent Schwartz — EDP et applications (2012-2013), Talk no. 1, 27 p.. doi: 10.5802/slsedp.32
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     author = {Degond, Pierre and Frouvelle, Amic and Liu, Jian-Guo and Motsch, Sebastien and Navoret, Laurent},
     title = {Macroscopic models of collective motion and self-organization},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:1},
     pages = {1--27},
     year = {2012-2013},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     doi = {10.5802/slsedp.32},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/slsedp.32/}
}
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