Multiple pattern formation in quorum sensing of density enhanced motility

Abstract

Using Langevin dynamics simulations, I investigate nonequilibrium systems of particles following a density-enhanced motility (DEM) rule: particles are passive below a critical local density and active above it. This mechanism represents an inverse of the conventional quorum-sensing rule. I explore specifically quorums much larger than particle size and at two levels of activity. Above critical values of the density, quorum size, and activity, the system undergoes phase separation into low- and high-energy regions. The passive particles organize into distinct spatial patterns, including holes, stripes, and labyrinthine structures, while the active particles form a gas. I characterize the resulting steady states and identify the qualitative mechanisms governing the selection of different morphological regimes. I further discuss the relevance of these results to biological systems governed by analogous quorum-sensing mechanisms and to biological systems exhibiting related forms of spatial organization. Finally, I present directions for future investigation.