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Anomalous Fundamental Diagrams in Traffic on Ant Trails

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Book cover Traffic and Granular Flow ’03

Summary

Many insects like ants communicate chemically via chemotaxis. This allows them to build large trail systems which in many respects are similar to human-build highway networks. Using a stochastic cellular automaton model we discuss the basic properties of the traffic flow on existing trails. Surprisingly it is found that in certain regimes the average speed of the ants can vary non-monotonically with their density. This is in sharp contrast to highway traffic. The observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density. We also discuss the effect of counterflow on the trails.

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References

  1. D. Chowdhury, L. Santen, and A. Schadschneider. Statistical physics of vehicular traffic and some related systems. Phys. Rep., 329:199, 2000.

    Article  Google Scholar 

  2. A. Schadschneider. Traffic flow: a statistical physics point of view. Physica A, 313:153, 2002.

    Article  MATH  Google Scholar 

  3. D. Helbing. Traffic and related self-driven many-particle systems. Rev. Mod. Phys., 73:1067, 2001.

    Article  Google Scholar 

  4. T. Nagatani. The physics of traffic jams. Rep. Prog. Phys., 65:1331, 2002.

    Article  Google Scholar 

  5. J.K. Parrish and L. Edelstein-Keshet. Complexity, pattern, and evolutionary trade-offs in animal aggregation. Science, 284:99, 1999.

    Article  Google Scholar 

  6. Y. Tu. Phases and phase transitions in flocking systems. Physica A, 281:30, 2000.

    Article  Google Scholar 

  7. E.M. Rauch, M.M. Millonas, and D.R. Chialvo. Pattern formation and functionality in swarm models. Phys. Lett. A, 207:185, 1995.

    Article  MATH  Google Scholar 

  8. E. Ben-Jacob. From snowflake formation to growth of bacterial colonies. part ii. cooperative formation of complex colonial patterns. Contemp. Phys., 38:205, 1997.

    Article  Google Scholar 

  9. N.R. Franks. Evolution of mass transit systems in ants: a tale of two societies. In I.P. Woiwod, D.R. Reynolds, and C.D. Thomas, editors, Insect Movement: Mechanisms and Consequences. CAB International, 2001.

    Google Scholar 

  10. E.O. Wilson. The insect societies. Belknap, Cambridge, USA, 1971.

    Google Scholar 

  11. B. Hölldobler and E.O. Wilson. The ants. Belknap, Cambridge, USA, 1990.

    Google Scholar 

  12. S. Camazine, J.L. Deneubourg, N. R. Franks, J. Sneyd, G. Theraulaz, and E. Bonabeau. Self-organization in Biological Systems. Princeton University Press, 2001.

    Google Scholar 

  13. A.S. Mikhailov and V. Calenbuhr. From Cells to Societies. Springer, 2002.

    Google Scholar 

  14. F. Schweitzer. Brownian Agents and Active Particles. Springer Series in Synergetics, 2003.

    Google Scholar 

  15. I.D. Couzin and N.R. Franks. Self-organized lane formation and optimized traffic flow in army ants. Proc. Roy. Soc. London B, 270:139, 2003.

    Article  Google Scholar 

  16. B.S. Kerner. Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories. Netw. Spatial Econ., 1:35, 2001.

    Article  Google Scholar 

  17. C. Burstedde, K. Klauck, A. Schadschneider, and J. Zittartz. Simulation of pedestrian dynamics using a 2-dimensional cellular automaton. Physica A, 295:507, 2001.

    Article  MATH  Google Scholar 

  18. A. Kirchner, K. Nishinari, and A. Schadschneider. Friction effects and clogging in a cellular automaton model for pedestrian dynamics. Phys. Rev. E, 67:056122, 2003.

    Article  Google Scholar 

  19. D. Chowdhury, V. Guttal, K. Nishinari, and A. Schadschneider. A cellular-automata model of flow in ant-trails: Non-monotonic variation of speed with density. J. Phys. A: Math. Gen., 35:L573, 2002.

    Article  MATH  Google Scholar 

  20. K. Nishinari, D. Chowdhury, and A. Schadschneider. Cluster formation and anomalous fundamental diagram in an ant trail model. Phys. Rev. E, 67:036120, 2003.

    Article  Google Scholar 

  21. A. John, A. Schadschneider, D. Chowdhury, and K. Nishinari. Collective effects in traffic on bi-directional ant-trails. J. Theor. Biol., 231:279, 2004.

    Article  Google Scholar 

  22. D. Helbing, F. Schweitzer, J. Keltsch, and P. Molnar. Active walker model for the formation of human and animal trail systems. Phys. Rev. E, 56:2527, 1997.

    Article  Google Scholar 

  23. B. Derrida. An exactly soluble non-equilibrium system: The asymmetric simple exclusion process. Phys. Rep., 301:65, 1998.

    Article  Google Scholar 

  24. K. Nagel and M. Schreckenberg. A cellular automaton model for freeway traffic. J. Phys. I, 2:2221, 1992.

    Article  Google Scholar 

  25. M. Schreckenberg, A. Schadschneider, K. Nagel, and N. Ito. Discrete stochastic models for traffic flow. Phys. Rev. E, 51:2939, 1995.

    Article  Google Scholar 

  26. O.J. O’Loan, M.R. Evans, and M.E. Cates. Jamming transition in a homo-geneous one-dimensional system: the bus route model. Phys. Rev. E, 58:1404, 1998.

    Article  Google Scholar 

  27. O.J. O’Loan, M.R. Evans, and M.E. Cates. Spontaneous jamming in one-dimensional systems. Europhys. Lett., 42:137, 1998.

    Article  Google Scholar 

  28. D. Chowdhury and R.C. Desai. Steady-states and kinetics of ordering in busroute models: Connection with the Nagel-Schreckenberg model. Eur. Phys. J. B, 15:375, 2000.

    Article  Google Scholar 

  29. R. Beckers, J.L. Deneubourg, and S. Goss. Trails and u-turns in the selection of a path by the ant lasius niger. J. Theor. Biol., 159:397, 1992.

    Article  Google Scholar 

  30. S.A. Janowski and J.L. Lebowitz. Finite-size effects and shock fluctuations in the asymmetric simple-exclusion process. Phys. Rev. A, 45:618, 1992.

    Article  Google Scholar 

  31. S.A. Janowski and J.L. Lebowitz. Exact results for the asymmetric simple exclusion process with a blockage. J. Stat. Phys., 77:35, 1994.

    Article  Google Scholar 

  32. G. Tripathy and M. Barma. Steady state and dynamics of driven diffusive systems with quenched disorder. Phys. Rev. Lett., 78:3039, 1997.

    Article  Google Scholar 

  33. J.R.B. Lighton, G.A. Bartholomew, and D.H. Feener. Energetics of locomotion and load carriage and a model of the energy cost of foraging in the leaf-cutting ant atta colombica. Physiol. Zoology, 60:524, 1987.

    Google Scholar 

  34. C.P.E. Zollikofer. Stepping patterns in ants. J. Experimental Biology, 192:95, 1994.

    Google Scholar 

  35. J. A. Weier, D.H. Feener, and J.R.B. Lighton. Inter-individual variation in energy cost of running and loading in the seed-harvester ant pogonomyrmex maricopa. J. Insect Physiology, 41:321, 1995.

    Article  Google Scholar 

  36. M. Burd, D. Archer, N. Aranwela, and D. J. Stradling. Traffic dynamics of the leaf-cutting ant, atta cephalotes. American Natur., 159:283, 2002.

    Article  Google Scholar 

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Schadschneider, A., Chowdhury, D., John, A., Nishinari, K. (2005). Anomalous Fundamental Diagrams in Traffic on Ant Trails. In: Hoogendoorn, S.P., Luding, S., Bovy, P.H.L., Schreckenberg, M., Wolf, D.E. (eds) Traffic and Granular Flow ’03. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28091-X_34

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