Interacting particles in an activity landscape

We study interacting active Brownian particles (ABPs) with a space-dependent swim velocity via simulation and theory. find that, although an equation of state exists, mechanical equilibrium does not apply to ABPs in activity landscapes. The pressure difference originates the flux polar order gradient across interface between regions different activity. In contrast motility-induced phase separation homogeneous velocity, critical point exist for active-passive patch system, which continuously splits into dense dilute increasing However, if global density is so high that all can be packed onto inactive patch, then MIPS-like behavior restored balanced again.