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 multiparticle system onto the dynamics of bands provides a unified framework to understand the emergence and stability of nonequilibrium patterns in this self-propelled particle system. In this regard, our results constitute a proof of principle in favor of the hypothesis in microbiology that velocity reversal of gliding rod-shaped bacteria regulates the transitions between various self-organized patterns observed during the bacterial life cycle.