Exact hydrodynamics and onset of phase separation for an active exclusion process

We consider a lattice model of active matter with exclusion and derive its hydrodynamic description exactly. The macroscopic limit is an integro-differential equation for the particles' density in phase space (positions and orientations) and includes nonlinearities in both the diffusive and advective components. Systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motility-induced phase separation. We explore the onset of such a transition in the parameter space of occupied volume fraction and self-propulsion speed via a linear stability analysis and numerical simulations. At low densities, the stability boundary is consistent with the linear analysis, but for higher densities, the homogeneous state is found to be less stable than the linearised model predicts.Comment: 31 Pages, 8 figure