Traffic of Ants on a Trail: A Stochastic Modelling and Zero Range Process

  • Katsuhiro Nishinari
  • Andreas Schadschneider
  • Debashish Chowdhury
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3305)


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.


Cellular Automaton Average Speed Thermodynamic Limit Order Phase Transition Open Boundary Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Katsuhiro Nishinari
    • 1
  • Andreas Schadschneider
    • 2
  • Debashish Chowdhury
    • 3
  1. 1.Department of Applied Mathematics and InformaticsRyukoku UniversityShigaJapan
  2. 2.Institut für Theoretische PhysikUniversität zu KölnKölnGermany
  3. 3.Department of PhysicsIndian Institute of TechnologyKanpurIndia

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