Branched flows in active random walks and the formation of ant trail patterns

Abstract

Branched flow governs the transition from ballistic to diffusive motion of waves and conservative particle flows in spatially correlated random or complex environments. It occurs in many physical systems from micrometer to interstellar scales. In living matter systems, however, this transport regime is usually suppressed by dissipation and noise. In this article, we demonstrate that, nonetheless, noisy active random walks, characterizing many living systems such as foraging animals and chemotactic bacteria, can show a regime of branched flow. To this end we model the dynamics of trail-forming ants, and we use it to derive a scaling theory of branched flows in active random walks in random bias fields in the presence of noise. We also show how trail patterns, formed by the interaction of ants by depositing pheromones along their trajectories, can be understood as a consequence of branched flow.