Traffic of Ants on a Trail: A Stochastic Modelling and Zero Range Process
Recently we have proposed a stochastic cellular automaton model of ants on a trail and investigated its unusual flow-density relation by using a mean field theory and computer simulations. In this paper, we study the model in detail by utilizing the analogy with the zero range process, which is known as one of the exactly solvable stochastic 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 flow-density diagram exhibits a second order phase transition at the critial density only in a limiting case.
KeywordsCellular Automaton Average Speed Thermodynamic Limit Order Phase Transition Open Boundary Condition
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- 8.Nishinari, K., Chowdhury, D., Schadschneider, A.: Cluster formation and anomalous fundamental diagaram in an ant trail model. Phys. Rev. E 67, 036120 (2003)Google Scholar
- 11.Camazine, S., Deneubourg, J.L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-organization in Biological Systems. Princeton University Press, Prinston (2001)Google Scholar
- 13.Kunwar, A., John, A., Nishinari, K., Schadschneider, A., Chowdhury, D.: Collective traffic-like movement of ants on a trail – dynamical phases and phase transitions (submitted for publication)Google Scholar