Jamming and pattern formation in models of segregation

TL;DR

This paper analyzes a non-equilibrium Schelling segregation model with districts, revealing a jamming transition at low vacancy rates and pattern formation due to spatial effects, providing new insights into segregation dynamics.

Contribution

It derives dynamical equations for the model and uncovers novel phenomena like jamming and pattern formation in a district-based segregation framework.

Findings

Jamming transition occurs at low vacancy density.

Spatial dimension induces pattern forming instability.

Unusual characteristics of these phenomena are identified.

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.