  Motility-induced phase separation, MIPS, is arguably the most well-studied
collective phenomenon occurring in active matter without alignment interactions
(scalar active matter). Its basic origin is simple: since self-propelled
particles accumulate where they move slowly, having a propulsion speed that
decreases steeply enough with density, due to collisions or chemical
interactions, leads to a feedback loop that induces the formation of a dense
phase. In these notes, I will discuss some of the main theoretical and
computational efforts that have been made over the last decade in understanding
the basic structural and dynamical properties of MIPS phase coexistence in
microscopic active particle models.
