# Macroscopic models of collective motion and self-organization

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

• [1] Université de Toulouse; UPS, INSA, UT1, UTM Institut de Mathématiques de Toulouse F-31062 Toulouse France CNRS; Institut de Mathématiques de Toulouse UMR 5219 F-31062 Toulouse France
• [2] CEREMADE, UMR CNRS 7534 Université Paris-Dauphine 75775 Paris Cedex 16 France
• [3] Department of Physics and Department of Mathematics Duke University Durham, NC 27708 USA
• [4] Center for Scientific Computation and Mathematical Modeling (CSCAMM) University of Maryland College Park, MD 20742 USA
• [5] Institut de Recherche Mathématique Avancée de Strasbourg CNRS UMR 7501 and Université de Strasbourg 7 rue René Descartes, 67084 Strasbourg Cedex France
• Volume: 2012-2013, page 1-27
• ISSN: 2266-0607

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## Abstract

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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.

## How to cite

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Degond, Pierre, et al. "Macroscopic models of collective motion and self-organization." Séminaire Laurent Schwartz — EDP et applications 2012-2013 (2012-2013): 1-27. <http://eudml.org/doc/275795>.

@article{Degond2012-2013,
abstract = {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.},
affiliation = {Université de Toulouse; UPS, INSA, UT1, UTM Institut de Mathématiques de Toulouse F-31062 Toulouse France CNRS; Institut de Mathématiques de Toulouse UMR 5219 F-31062 Toulouse France; CEREMADE, UMR CNRS 7534 Université Paris-Dauphine 75775 Paris Cedex 16 France; Department of Physics and Department of Mathematics Duke University Durham, NC 27708 USA; Center for Scientific Computation and Mathematical Modeling (CSCAMM) University of Maryland College Park, MD 20742 USA; Institut de Recherche Mathématique Avancée de Strasbourg CNRS UMR 7501 and Université de Strasbourg 7 rue René Descartes, 67084 Strasbourg Cedex France},
author = {Degond, Pierre, Frouvelle, Amic, Liu, Jian-Guo, Motsch, Sebastien, Navoret, Laurent},
journal = {Séminaire Laurent Schwartz — EDP et applications},
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},
language = {eng},
pages = {1-27},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Macroscopic models of collective motion and self-organization},
url = {http://eudml.org/doc/275795},
volume = {2012-2013},
year = {2012-2013},
}

TY - JOUR
AU - Degond, Pierre
AU - Frouvelle, Amic
AU - Liu, Jian-Guo
AU - Motsch, Sebastien
AU - Navoret, Laurent
TI - Macroscopic models of collective motion and self-organization
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2012-2013
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2012-2013
SP - 1
EP - 27
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/275795
ER -

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