Clumping in a model of self-propelled particles in one dimension

We introduce a model for a one-dimensional system of self-propelled particles with periodic boundary conditions. The self-propulsion is represented by endowing each particle with a natural velocity drawn from a distribution. Following elastic collisions between particles, each collision partner’s velocity decays to its natural velocity over a specified time scale. Numerical simulations of this model generically show that in the long-term, the particles tend to clump spatially, with a rapidly increasing collision rate. This behavior is reminiscent of inelastic collapse but has a completely different origin. The two-particle system was analyzed for the asymptotic form of particle separation and velocity difference in the limit of large collision number. For the multi-particle system, we study analogous measures of the emergent clumping behavior, and we will discuss the scaling of the time to clump as a function of the only two time-scales available in the model.