Self-organization in two-dimensional swarms

TL;DR

This paper systematically explores self-organized states in a 2D model of self-propelled particles, identifying various collective motions and phase transitions, including analogies to gas-liquid transitions and external driving effects.

Contribution

It provides a comprehensive phase diagram of collective behaviors and transitions in a deterministic 2D particle model, including novel insights into external driving effects.

Findings

Identified disordered, ring, and droplet states.

Discovered discontinuous phase transitions between different collective states.

Found analogy with gas-liquid phase transition in finite clusters.

Abstract

We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered swarms, rings, and droplets. We construct a "phase diagram," which summarizes our results as it delineates phase transitions ?all discontinuous? between disordered swarms and vortical flocks on one hand and bound vortical flocks and expanding formations on the other. One of the transition lines is found to have a close analogy with the temperature-driven gas-liquid transition, in finite clusters with the same interparticle potential. Furthermore, we report on a type of flocking which takes place in the presence of a uniform external driver. Altogether, our results set a rather firm stage for experimental refinement and/or falsification of this class of models.