Jamming and pattern formation in models of segregation.

We investigate the Schelling model of social segregation, formulated as an intrinsically nonequilibrium system, in which the agents occupy districts (or patches) rather than sites on a grid. We show that this allows the equations governing the dynamical behavior of the model to be derived. Analysis of these equations reveals a jamming transition in the regime of low-vacancy density, and inclusion of a spatial dimension in the model leads to a pattern forming instability. Both of these phenomena exhibit unusual characteristics which may be studied through our approach.