TY - JOUR
T1 - Diffusion in a continuum model of self-propelled particles with alignment interaction
AU - Degond, Pierre
AU - Yang, Tong
PY - 2010/9
Y1 - 2010/9
N2 - 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.
AB - 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.
KW - alignment interaction
KW - asymptotic analysis
KW - ChapmanEnskog expansion
KW - Flocking
KW - hydrodynamic limit
KW - Vicsek model
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-77957102842&origin=recordpage
U2 - 10.1142/S0218202510004659
DO - 10.1142/S0218202510004659
M3 - 21_Publication in refereed journal
VL - 20
SP - 1459
EP - 1490
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
SN - 0218-2025
IS - SUPPL. 1
ER -