Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions

TL;DR

This paper models ant trail traffic using a stochastic cellular automaton, revealing non-monotonic flow behavior and phase transitions, with insights gained through an analogy to the exactly solvable zero range process.

Contribution

It introduces an alternative analytical approach based on the zero range process to study ant traffic flow and phase transitions, extending previous mean field and simulation analyses.

Findings

Quantitative explanation of non-monotonic speed-density relation

Identification of a continuous phase transition at critical density

Phase diagram analysis under open boundary conditions

Abstract

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.