Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Wolfram, S.: Theory and Applications of Cellular Automata. World Scientific, Singapore (1986)
Chopard, B., Droz, M.: Cellular Automata Modelling of Physical Systems. Cambridge University Press, Cambridge (1998)
Chowdhury, D., Santen, L., Schadschneider, A.: Statistical physics of vehicular traffic and some related systems. Phys. Rep. 329, 199–329 (2000)
Chowdhury, D., Nishinari, K., Schadschneider, A.: Self-organized patterns and traffic flow in colonies of organisms:from bacteria and social insects to vertebrates. Phase Transitions 77, 601–624 (2004)
Chowdhury, D., Guttal, V., Nishinari, K., Schadschneider, A.: A cellular-automata model of flow in ant trails: non-monotonic variation of speed with density. J. Phys. A: Math. Gen. 35, L573–L577 (2002)
Burd, M., Archer, D., Aranwela, N., Stradling, D.J.: Traffic dynamics of the leaf cutting ant. American Natur. 159, 283–293 (2002)
Evans, M.R., Blythe, R.A.: Nonequilibrium dynamics in low-dimensional systems. Physica A 313, 110–152 (2002)
Nishinari, K., Chowdhury, D., Schadschneider, A.: Cluster formation and anomalous fundamental diagaram in an ant trail model. Phys. Rev. E 67, 036120 (2003)
Spitzer, F.: Interaction of markov processes. Advances in Math. 5, 246–290 (1970)
Evans, M.R.: Phase transitions in one-dimensional nonequilibrium systems. Braz. J. Phys. 30, 42–57 (2000)
Camazine, S., Deneubourg, J.L., Franks, N.R., Sneyd, J., Theraulaz, G., Bonabeau, E.: Self-organization in Biological Systems. Princeton University Press, Prinston (2001)
Mikhailov, A.S., Calenbuhr, V.: From Cells to Societies. Springer, Berlin (2002)
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)
Nishinari, K., Takahashi, D.: Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton. J. Phys. A: Math. Gen. 31, 5439–5450 (1998)
Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2, 2221–2229 (1992)
Evans, M.R.: Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics. J. Phys. A: Math. Gen. 30, 5669–5685 (1997)
O’Loan, O.J., Evans, M.R., Cates, M.E.: Jamming Transition in a Homogeneous One-Dimensional System: the Bus Route Model. Phys. Rev. E 58, 1404–1418 (1998); see also Europhys. Lett. 42, 137–142 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nishinari, K., Schadschneider, A., Chowdhury, D. (2004). Traffic of Ants on a Trail: A Stochastic Modelling and Zero Range Process. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_20
Download citation
DOI: https://doi.org/10.1007/978-3-540-30479-1_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23596-5
Online ISBN: 978-3-540-30479-1
eBook Packages: Springer Book Archive