Phase segregation in interacting particle systems

Systems of (possibly non-Brownian) interacting particles can exhibit separation into distinct phase regions of differing density.  We explore a multi-species model of interacting particles, where sufficiently large cross-repulsion leads to instability and ultimately formation of domains dominated by one species.   The interface problem between domains is studied, and a multiscale analysis is used to understand the evolution of phase domain boundaries in the limit of small interaction length. This motivates a conjecture on $\Gamma$-convergence of the underlying system energy. Illustrations of coarsening phenomenon and the role of long-range attraction are discussed. Time permitting, motility-induced phase separation is discussed in the context of active-matter systems for self-propelled Brownian particles, along with open problems. For both phase-segregation scenarios, comparisons to the classical picture of phase separation in binary mixtures
will be made.