https://doi.org/10.1140/epjst/e2014-02193-y
Regular Article
Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models
1 Physique et Mécanique des Milieux Hétérogènes, CNRS UMR 7636, Ecole Supérieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75005 Paris, France
2 Laboratoire Interdisciplinaire de Physique, Université Joseph Fourier Grenoble, CNRS UMR 5588, BP. 87, 38402 Saint-Martin-d'Hères, France
3 Université de Lyon, Laboratoire de Physique, ENS Lyon, CNRS, 46 allée d'Italie, 69007 Lyon, France
4 SUPA, Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, UK
5 Service de Physique de l'Etat Condensé, CNRS URA 2464, CEA-Saclay, 91191 Gif-sur-Yvette, France
6 LPTMC, CNRS UMR 7600, Université Pierre et Marie Curie, 75252 Paris, France
Received: 27 February 2014
Revised: 14 April 2014
Published online: 12 June 2014
We describe a generic theoretical framework, denoted as the Boltzmann-Ginzburg-Landau approach, to derive continuous equations for the polar and/or nematic order parameters describing the large scale behavior of assemblies of point-like active particles interacting through polar or nematic alignment rules. Our study encompasses three main classes of dry active systems, namely polar particles with ‘ferromagnetic' alignment (like the original Vicsek model), nematic particles with nematic alignment (“active nematics”), and polar particles with nematic alignment (“self-propelled rods”). The Boltzmann-Ginzburg-Landau approach combines a low-density description in the form of a Boltzmann equation, with a Ginzburg-Landau-type expansion close to the instability threshold of the disordered state. We provide the generic form of the continuous equations obtained for each class, and comment on the relationships and differences with other approaches.
© EDP Sciences, Springer-Verlag, 2014
