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

TL;DR

This paper demonstrates that noisy active random walks, such as those of foraging ants, can exhibit branched flow patterns in complex environments, providing a new understanding of trail formation through a scaling theory.

Contribution

It introduces a scaling theory for branched flows in active random walks and explains ant trail patterns as a consequence of this phenomenon.

Findings

Active random walks can show branched flow despite noise and dissipation.

Trail patterns result from branched flow dynamics in pheromone-based interactions.

Theoretical framework links trail formation to physical flow phenomena.

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 like foraging animals, and chemotactic bacteria, can show a regime of branched flow. To this aim we model the dynamics of trail forming ants and 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.