  We consider a lattice model of active matter with exclusion and derive its
hydrodynamic description exactly. The hydrodynamic limit leads to an
integro-differential equation for the density of particles with a given
orientation. Volume exclusion results in nonlinear mobility dependent on
spatial density. Such models of active matter can support motility-induced
phase separation, which occurs despite the absence of attractive interactions.
We study the onset of phase separation with linear stability analysis and
numerical simulations.
