Coarsening dynamics in the Vicsek model of active matter

We study the flocking model introduced by Vicsek in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as L_{\rho}(t) \sim t^{\theta_\rho}(with \theta_\rho \simeq 0.25, while the velocity length scale grows much faster, viz. L_{v}(t) \sim t^{\theta_v}(with \theta_v \simeq 0.83. The...