Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces

TL;DR

This paper analyzes the continuum limit of agent motion driven by competing forces, revealing bifurcations, phase transitions, and scaling laws for vacuum bubble formation, with effects of noise and topological changes.

Contribution

It introduces a detailed bifurcation analysis and scaling laws for vacuum bubbles in collective motion with competing attractive and repulsive forces.

Findings

Destabilization of uniform solutions at critical parameters.

Vertical bifurcating branch indicating a reversible phase transition.

Scaling laws for vacuum bubble sizes near bifurcation.

Abstract

We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find destabilization of a trivial branch of uniformly distributed solutions and analyze bifurcating solutions. Curiously, the bifurcating branch is vertical, leading to a reversible, non-hysteretic phase transition. Near the bifurcation point, we demonstrate scaling laws for the size of vacuum regions, which can form fissures or bubbles. We also study the effect of small noise and the eventual topological transition from vacuum bubbles to isolated particle clusters.