Boltzmann-Ginzburg-Landau approach for continuous descriptions of generic Vicsek-like models

A. Peshkov, E. Bertin, F. Ginelli, H. Chaté

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87 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1315-1344
Number of pages30
JournalThe European Physical Journal. Special Topics
Issue number7
Publication statusPublished - 12 Jun 2014

Bibliographical note

30 pages, 3 figures, to appear in Eur. Phys. J. Special Topics, in a Discussion and Debate issue on active matter


  • cond-mat.stat-mech
  • cond-mat.soft


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