Vortex with four-fold defect lines in a simple model of self-propelled particles

TL;DR

This paper investigates vortex formation with four-fold symmetry in a simple self-propelled particle model, revealing six phases influenced by noise, repulsion, and alignment, supported by simulations, theory, and experiments.

Contribution

It introduces a minimal model showing complex phase behavior and detailed vortex symmetry analysis, including derivation of hydrodynamic equations and comparison with Quincke rotor experiments.

Findings

Six distinct phases identified, including vortex with four-fold symmetry.

Exponential defect lines observed at vortex boundaries.

Hydrodynamic equations agree well with simulations and experiments.

Abstract

We studied formation of vortex with four-fold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observed five other phases in the system: homogeneous gaseous phase, band structures, moving clumps, moving clusters and vibrating rings. All six phases emerge from controlling strength of noise and contribution of repulsion and alignment interactions. We studied shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. Finally, we derived hydro-dynamical equations for our model and compared them with the results of both computer simulations and Quincke rotors. A good agreement between the three is observed.