Journal
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
Volume 24, Issue 2, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218202513400095
Keywords
Alignment; Fokker-Planck equation; macroscopic limit; von Mises-Fisher distribution; order parameter; generalized collision invariant; dispersion relation
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Funding
- French Agence Nationale pour la Recherche (ANR) [ANR-11-MONU-009-01]
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We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their rotation motion with their neighbors. It combines the Kuramoto model of synchronization and the Vicsek model of swarm formation. We study the mean-field kinetic and hydrodynamic limits of this system within two different scalings. In the small angular velocity regime, the resulting model is a slight modification of the Self-Organized Hydrodynamic model which has been previously introduced by the first author. In the large angular velocity case, a new type of hydrodynamic model is obtained. A preliminary study of the linearized stability is proposed.
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