Heterogeneity-induced lane and band formation in self-driven particle systems

TL;DR

This paper explores how different types of heterogeneity in self-driven particle systems lead to the formation of lanes and bands, revealing mechanisms and transitions between disordered and ordered collective motion.

Contribution

It identifies two heterogeneity mechanisms causing segregation: static heterogeneity induces longitudinal lanes, while dynamic heterogeneity causes transverse bands, across different models and parameters.

Findings

Heterogeneity triggers segregation in particle motion.

Longitudinal lanes emerge from static heterogeneity.

Transverse bands arise from dynamic heterogeneity.

Abstract

The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and nonuniform patterns. In this article, we investigate the effects of different types of heterogeneity in a two-species self-driven particle system. We show that heterogeneity can generically initiate segregation in the motion and identify two heterogeneity mechanisms. Longitudinal lanes parallel to the direction of motion emerge when the heterogeneity statically lies in the agent characteristics (quenched disorder). While transverse bands orthogonal to the motion direction arise from dynamic heterogeneity in the interactions (annealed disorder). In both cases, non-linear transitions occur as the heterogeneity increases, from disorder to ordered states with lane or band patterns. These generic features are observed for a first and a second order motion model and different characteristic parameters related to particle speed and size. Simulation results show that the collective dynamics occur in relatively short time intervals, persist stationary, and are partly robust against random perturbations.