Traffic jams, gliders, and bands in the quest for collective motion

TL;DR

This paper investigates a lattice-based swarming model revealing how local interactions and volume exclusion lead to diverse self-organized patterns like jams, gliders, and bands, with phase transitions depending on density.

Contribution

It introduces a simple lattice model demonstrating rich pattern formation and phase transition behaviors driven by alignment and exclusion effects.

Findings

Particles form disordered aggregates, traffic jams, and migrating gliders.

Elongated high-density bands form at maximum order.

Phase transition nature varies with density, being first-order below percolation and second-order at full occupancy.

Abstract

We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node is empty. Here we show that such effects lead to a surprisingly rich variety of self-organized spatial patterns. As particles exhibit an increasingly higher tendency to align to neighbors, they first self-segregate into disordered particle aggregates. Aggregates turn into traffic jams. Traffic jams evolve toward gliders, triangular high density regions that migrate in a well-defined direction. Maximum order is achieved by the formation of elongated high density regions - bands - that transverse the entire system. Numerical evidence suggests that below the percolation density the phase transition associated to orientational order is of first-order, while at full occupancy it is of second-order. The model highlights the (pattern formation) importance of a coupling between local density, orientation, and local speed.