Macroscopic models of collective motion with repulsion

Pierre Degond (1) , Giacomo Dimarco (2) , Thi Bich Ngoc Mac (3) , Nan Wang (4)

1 Department of Mathematics [Imperial College London]
2 Department of Mathematics
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Department of Mathematics

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.

Domaines: Physique mathématique [math-ph]

Pierre Degond, Giacomo Dimarco, Thi Bich Ngoc Mac, Nan Wang. Macroscopic models of collective motion with repulsion. Communications in Mathematical Sciences, 2015, 13, pp.1615-1638. ⟨hal-00980873⟩