  Motility-induced phase separation is a purely non-equilibrium phenomenon in
which self-propelled particles aggregate without any attractive interactions.
One surprising feature of MIPS is the emergence of polar-nematic order at the
interfacial region, whose underlying physics remains poorly understood. Here, I
will show analytically and numerically that the many-body physics leading to
the interfacial ordering behavior can be captured by an effective speed model.
In this model, each particle's speed depends on the system's density a short
distance ahead of its direction of motion.
