Jamming and pattern formation in models of segregation

Abstract

We investigate the Schelling model of social segregation, formulated as an intrinsically non-equilibrium 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 behaviour 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.