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 particles speed depends on the systems density a short distance ahead of its direction of motion.
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