Anti-aligning interaction induces gyratory flocking of simple self-propelled particles: The impact of translational noise

Abstract

This report considers a set of simple active particles (non-self-rotating particles) interacting due to a purely anti-aligning force. Recently, it has been shown that such anti-aligning interaction may induce a finite wavelength instability. The instability occurs with an oscillatory frequency. Consequently, the system displays pattern formation. The formed patterns consist of propagative dissipative structures (two counterpropagating traveling waves). Here, we explore the impact of including translational noise in the dynamics. The finite wavelength instability persists; however, the oscillatory frequency only persists if the particle’s self-propulsion speed is larger enough than the translational noise intensity. We focus on this case. Near criticality, where fluctuations predominate, it is possible to distinguish propagative patterns. Moving away from criticality, a new pattern emerges via a secondary transition. Namely, a hexagonal structure formed of rotating clusters. These clusters rotate in unison, giving rise to a global gyratory synchrony. This secondary transition is discontinuous. Finally, we discuss the main ingredients that induce this sort of rotatory synchronization, showing that short-range repulsion might produce a similar effect to translational noise.