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

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.

8 pages, 6 figures

References in corpus (7)

• Statistical Physics of Vehicular Traffic and Some Related Systems
• Phase Transitions in one-dimensional nonequilibrium systems
• Jamming transition in a homogeneous one-dimensional system: the Bus Route Model
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• Cluster formation and anomalous fundamental diagram in an ant trail model
• Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model
• Nonequilibrium Dynamics in Low Dimensional Systems

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• Particle Ordering in Zero Range Process : Exact spatial correlations of the corresponding exclusion models
• Counter Chemotactic Flow in Quasi-One-Dimensional Path
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