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BML model on non-orientable surfaces

Author

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  • Cámpora, Daniel
  • de la Torre, Jaime
  • García Vázquez, Juan Carlos
  • Caparrini, Fernando Sancho

Abstract

Two-dimensional Biham–Middleton–Levine traffic model on a N×N square lattice embedded on a Klein bottle and a projective plane is investigated by computer simulations. The behavior of the model with these boundary conditions is compared with the model under toroidal boundary conditions. Our numerical results show that the phase diagram depends strongly on the underlying topology. We also investigate the influence of the ratio between the number of red and blue particles has over the speed of the system and conclude that the projective plane case differs considerably from the other cases reviewed here.

Suggested Citation

  • Cámpora, Daniel & de la Torre, Jaime & García Vázquez, Juan Carlos & Caparrini, Fernando Sancho, 2010. "BML model on non-orientable surfaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3290-3298.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3290-3298
    DOI: 10.1016/j.physa.2010.03.037
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    References listed on IDEAS

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    1. Linesch, Nicholas J. & D’Souza, Raissa M., 2008. "Periodic states, local effects and coexistence in the BML traffic jam model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6170-6176.
    2. Huang, Ding-wei & Huang, Wei-neng, 2006. "Biham–Middleton–Levine model with four-directional traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 747-755.
    3. Chau, H.F. & Wan, K.Y. & Yan, K.K., 1998. "An improved upper bound for the critical car density of the two-dimensional Biham–Middleton–Levine traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 117-121.
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