Mesoscale pattern formation of self-propelled rods with velocity reversal

Abstract

We study self-propelled particles with velocity reversal interacting by uniaxial (nematic) alignment within a coarse-grained hydrodynamic theory. Combining analytical and numerical continuation techniques, we show that the physics of this active system is essentially controlled by the reversal frequency. In particular, we find that elongated, high-density, ordered patterns, called bands, emerge via subcritical bifurcations from spatially homogeneous states. Our analysis reveals further that the interaction of bands is weakly attractive and, consequently, bands fuse upon collision in analogy with nonequilibrium nucleation processes. Moreover, we demonstrate that a renormalized positive line tension can be assigned to stable bands below a critical reversal rate, beyond which they are transversally unstable. In addition, we discuss the kinetic roughening of bands as well as their nonlinear dynamics close to the threshold of transversal instability. Altogether, the reduction of the multi-particle system onto the dynamics of bands provides a framework to understand the impact of the reversal frequency on the emerging nonequilibrium patterns in self-propelled particle systems. In this regard, our results constitute a proof-of-principle in favor of the hypothesis in microbiology that reversal of gliding rod-shaped bacteria regulates the occurrence of various self-organized pattens observed during life-cycle phases.