The European Physical Journal B

, Volume 68, Issue 4, pp 549–555 | Cite as

Mapping the train model for earthquakes onto the stochastic sandpile model

  • C. V. Chianca
  • J. S. Sá Martins
  • P. M.C. de Oliveira
Statistical and Nonlinear Physics


We perform a computational study of a variant of the “train” model for earthquakes [Phys. Rev. A 46, 6288 (1992)], where we assume a static friction that is a stochastic function of position rather than being velocity dependent. The model consists of an array of blocks coupled by springs, with the forces between neighbouring blocks balanced by static friction. We calculate the probability, P(s), of the occurrence of avalanches with a size s or greater, finding that our results are consistent with the phenomenology and also with previous models which exhibit a power law over a wide range. We show that the train model may be mapped onto a stochastic sandpile model and study a variant of the latter for non-spherical grains. We show that, in this case, the model has critical behaviour only for grains with large aspect ratio, as was already shown in experiments with real ricepiles. We also demonstrate a way to introduce randomness in a physically motivated manner into the model.


89.75.-k Complex systems 64.60.av Cracks, sandpiles, avalanches, and earthquakes 05.65.+b Self-organized systems 91.30.Px Earthquakes 


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • C. V. Chianca
    • 1
  • J. S. Sá Martins
    • 1
  • P. M.C. de Oliveira
    • 1
  1. 1.Instituto de Física, Universidade Federal Fluminense, and National Institute of Science and Technology for Complex SystemsNiterói-RJBrazil

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