2019/01/30 by Pedro Aceves-Sánchez, P. Aceves-Sánchez, M. Bostan +9 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical Biology Tumor Growth #Micro and Nano Robotics #math.AP
paper · pdf · doi:10.48550/arxiv.1901.11132
arxiv created 2019/01/30 · openalex publication_date 2019/01/30 · arxiv updated 2019/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The self-propelling and friction forces together with the alignment and the noise are interpreted as a collision/interaction mechanism acting with equal strength. We show that the set of generalized collision invariants, introduced in \citeDM08, is equivalent in our setting to the more classical notion of collision invariants, i.e., the kernel of a suitably linearized collision operator. After identifying these collision invariants, we derive the fluid model, by appealing to the balances for the particle concentration and orientation. We investigate the main properties of the macroscopic model for a general potential with radial symmetry.