TY - JOUR
T1 - Macroscopic limit of self-driven particles with orientation interaction
AU - Degond, Pierre
AU - Motsch, Sébastien
PY - 2007/11/15
Y1 - 2007/11/15
N2 - The discrete Couzin-Vicsek algorithm (CVA) has been proposed to model the interactions of individuals among animal societies such as schools of fish. In this Note, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity. The result is based on the introduction of a non-conventional concept of a collisional invariant of the collision operator. To cite this article: P. Degond, S. Motsch, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
AB - The discrete Couzin-Vicsek algorithm (CVA) has been proposed to model the interactions of individuals among animal societies such as schools of fish. In this Note, we propose a kinetic (mean-field) version of the CVA model and provide its formal macroscopic limit. The final macroscopic model involves a conservation equation for the density of the individuals and a non-conservative equation for the director of the mean velocity. The result is based on the introduction of a non-conventional concept of a collisional invariant of the collision operator. To cite this article: P. Degond, S. Motsch, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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U2 - 10.1016/j.crma.2007.10.024
DO - 10.1016/j.crma.2007.10.024
M3 - Article
AN - SCOPUS:36148999055
SN - 1631-073X
VL - 345
SP - 555
EP - 560
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
IS - 10
ER -