An infinite set of integral formulae for polar, nematic, and higher order structures at the interface of motility-induced phase separation

Motility-induced phase separation (MIPS) is a purely non-equilibrium phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and higher order structures at the interfacial region, whose underlying physics remains poorly understood. Starting with a model of MIPS in which all many-body interactions are captured by an effective speed function and an effective pressure function that depend solely on the local particle density, I derive analytically an infinite set of integral formulae for the ordering structures at the interface. I then demonstrate that half of these IF are in fact exact for generic active Brownian particle systems. Finally, I test these integral formulae by applying them to numerical data from direct particle dynamics simulation and find that they remain valid to a great extent.

Automated summary

Motility-induced phase separation (MIPS) is a non-equilibrium phenomenon where self-propelled particles separate into different phases without attractive interactions. It is characterized by the emergence of polar, nematic, and higher order structures at the interface, which are poorly understood. By using a model that captures all many-body interactions through effective speed and pressure functions dependent on local particle density, the study derives an infinite set of integral formulas for the ordering structures at the interface. It is shown that half of these formulas are exact for generic active Brownian particle systems and validated through numerical simulations.