2017/01/13 by Mihaï Bostan, M. Bostan, J. A. Carrillo +3
Computer Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Distributed Control Multi-Agent Systems #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Micro and Nano Robotics #math.AP
paper · pdf · doi:10.48550/arxiv.1701.03560
arxiv created 2017/01/13 · openalex publication_date 2017/01/13 · arxiv updated 2017/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The asymptotic analysis of kinetic models describing the behavior of particles interacting through alignment is performed. We will analyze the asymptotic regime corresponding to large alignment frequency where the alignment effects are dominated by the self propulsion and friction forces. The former hypothesis leads to a macroscopic fluid model due to the fast averaging in velocity, while the second one imposes a fixed speed in the limit, and thus a reduction of the dynamics to a sphere in the velocity space. The analysis relies on averaging techniques successfully used in the magnetic confinement of charged particles. The limiting particle distribution is supported on a sphere, and therefore we are forced to work with measures in velocity. As for the Euler-type equations, the fluid model comes by integrating the kinetic equation against the collision invariants and its generalizations in the velocity space. The main difficulty is their identification for the averaged alignment kernel in our functional setting of measures in velocity.