Collective motion of binary self-propelled particle mixtures

TL;DR

This paper explores how binary mixtures of self-propelled particles exhibit collective motion, analyzing the effects of different alignment interactions on the onset and nature of flocking behavior through simulations and theoretical models.

Contribution

It introduces a comprehensive analysis of collective motion in binary particle mixtures with various alignment rules, combining simulations and continuum theories to reveal new behaviors.

Findings

Interaction reduces the threshold density for collective motion.

Perpendicular alignment leads to competition between polar and nematic order.

Different alignment rules produce various spatial density profiles.

Abstract

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations, linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both, spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripe-like flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripe-like flocks. The most interesting behavior is found for the case of preferred perpendicular alignment between different species. There, a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species.