期刊
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
卷 20, 期 -, 页码 1459-1490出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202510004659
关键词
Flocking; Vicsek model; alignment interaction; asymptotic analysis; hydrodynamic limit; Chapman-Enskog expansion
资金
- European Commission [MEST-CT-2005-021122]
- French Agence Nationale pour la Recherche (ANR) [ANR-07-BLAN-0208-03]
- General Research Fund of Hong Kong [CityU 103109]
In this paper, we provide the O(epsilon) 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 epsilon stands for the ratio of the microscopic to the macroscopic scales. The O(epsilon) 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 Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.
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