Swarming in bounded domains

The Vicsek model is a prototype for the emergence of collective motion. In free space, it is characterized by a swarm of particles all moving in the same direction. Since this dynamic does not include attraction among particles, the swarm, while aligning in velocity space, has no spatial coherence. Adding specular reflection at the boundaries generates global spatial coherence of the swarms while maintaining its velocity alignment. We investigate numerically how the geometry of the domain influences the Vicsek model using three type of geometry: a channel, a disk and a rectangle. Varying the parameters of the Vicsek model (e.g. noise levels and influence horizons), we discuss the mechanisms that generate spatial coherence and show how they create new dynamical solutions of the swarming motions in these geometries. Several observables are introduced to characterize the simulated patterns (e.g. mass profile, center of mass, connectivity of the swarm).