Abstract:
We consider a class of models describing alignment for
self-propelled particles, where a particleâ€™s orientation continuously
relaxes to the mean orientation of its neighbors . The rate of this
relaxation is a given function of the norm of the local average momentum
of the neighbors, and the orientation is subject to angular diffusion.
The case where the rate is constant corresponds to a model of Degond &
Motsch, and the case where this function is linear has been studied in
detail with Degond and Liu. In this last case there is a phenomenon of
phase transition. I will present here the different types of phase
transitions that one can observe when the rate of relaxation is an
arbitrary function, focusing on the spatial homogeneous case.
This is a joint work with Pierre Degond and Jian-Guo Liu. |