Diffusion in a continuum model of self-propelled particles with alignment interaction

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)1459-1490
Journal / PublicationMathematical Models and Methods in Applied Sciences
Issue numberSUPPL. 1
Publication statusPublished - Sept 2010


In this paper, we provide the O(ε) corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological agents. The parameter ε stands for the ratio of the microscopic to the macroscopic scales. The O(ε) corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first-order derivatives of the density and velocity. The derivation method is based on the standard ChapmanEnskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation. © 2010 World Scientific Publishing Company.

Research Area(s)

  • alignment interaction, asymptotic analysis, ChapmanEnskog expansion, Flocking, hydrodynamic limit, Vicsek model