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

Area of Science:

• Physics
• Complex Systems
• Statistical Mechanics

Background:

• Self-propelled particles (SPPs) exhibit rich emergent behaviors.
• Confined SPPs can form complex patterns and collective motion.
• Understanding phase transitions in active matter is crucial.

Purpose of the Study:

• Investigate vortex formation in a minimal SPP model.
• Characterize different emergent regimes beyond the vortex.
• Develop a theoretical framework for vortex dynamics.

Main Methods:

• Computer simulations of SPPs in a squared box.
• Theoretical analysis using hydrodynamical equations.
• Experimental validation with Quincke rotors.

Main Results:

• Observed six distinct regimes: vortex, gas, bands, clumps, clusters, and rings.
• Identified fourfold symmetry in the vortex pattern with exponential defect lines.
• Demonstrated the necessity of alignment and repulsion for vortex formation.

Conclusions:

• Noise and inter-particle interactions control emergent SPP behavior.
• A hydrodynamical model accurately describes the vortex phase.
• The findings show good agreement across simulations, theory, and experiments.