Communications in Mathematical Sciences
Volume 13 (2015)
Macroscopic models of collective motion with repulsion
Pages: 1615 – 1638
We study a system of self-propelled particles which interact with their neighbors via alignment and repulsion. The particle velocities result from self-propulsion and repulsion by close neighbors. The direction of self-propulsion is continuously aligned to that of the neighbors, up to some noise. A continuum model is derived starting from a mean-field kinetic description of the particle system. It leads to a set of non conservative hydrodynamic equations. We provide a numerical validation of the continuum model by comparison with the particle model. We also provide comparisons with other self-propelled particle models with alignment and repulsion.
Fokker–Planck equation, macroscopic limit, Von Mises–Fisher distribution, generalized collision invariants, non-conservative equations, self-organized hydrodynamics, self-propelled particles, alignment, repulsion
2010 Mathematics Subject Classification
35L60, 35Qxx, 82C22, 82C70, 92D50