A cellular-automata model of flow in ant trails: non-monotonic variation of speed with density

Generically, in models of driven interacting particles, the average speed of the particles decreases monotonically with increasing density. We propose a counterexample, motivated by the motion of ants in a trail, where the average speed of the particles varies non-monotonically with their density because of the coupling of their dynamics with another dynamical variable. These results, in principle, can be tested experimentally.

[1]  A. Schadschneider,et al.  Simulation of pedestrian dynamics using a two dimensional cellular automaton , 2001 .

[2]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[3]  A. Schadschneider,et al.  Cellular automation models and traffic flow , 1993, cond-mat/9306017.

[4]  Andreas Schadschneider,et al.  Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics , 2002 .

[5]  D. de Cogan,et al.  Cellular Automata Modelling of Physical Systems, by Bastien Chopard & Michel Droz, Cambridge University Press (Aléa Saclay Collection), 336 pp., ISBN 0‐521‐46168‐5, hardback, £55 , 2000 .

[6]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[7]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[8]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

[9]  Maurice Parmelee,et al.  Insect societies: The ants. , 1921 .

[10]  R. Dickman,et al.  Nonequilibrium Phase Transitions in Lattice Models , 1999 .

[11]  M. Burd,et al.  Traffic Dynamics of the Leaf‐Cutting Ant, Atta cephalotes , 2002, The American Naturalist.

[12]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[13]  E. Wilson.  The Insect Societies , 1974 .

[14]  M. Evans,et al.  Jamming transition in a homogeneous one-dimensional system: The bus route model , 1997, cond-mat/9712243.

[15]  Guy Theraulaz,et al.  Self-Organization in Biological Systems , 2001, Princeton studies in complexity.

[16]  A. Schadschneider.  The Nagel-Schreckenberg model revisited , 1999, cond-mat/9902170.

[17]  D. Chowdhury,et al.  Steady-states and kinetics of ordering in bus-route models: connection with the Nagel-Schreckenberg model , 2000, cond-mat/0003212.

[18]  Bartlett,et al.  Single-photon multiple ionization of argon in the K-edge region. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[19]  David P. Landau,et al.  Phase transitions and critical phenomena , 1989, Computing in Science & Engineering.

[20]  Iain D. Couzin,et al.  Self‐Organization in Biological Systems.Princeton Studies in Complexity. ByScott Camazine,, Jean‐Louis Deneubourg,, Nigel R Franks,, James Sneyd,, Guy Theraulaz, and, Eric Bonabeau; original line drawings by, William Ristineand, Mary Ellen Didion; StarLogo programming by, William Thies. Princeton (N , 2002 .

[21]  Stephen Wolfram,et al.  Cellular Automata And Complexity , 1994 .

[22]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.