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Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model

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  • Batac, Rene
  • Longjas, Anthony
  • Monterola, Christopher

Abstract

Sandpile-based models have successfully shed light on key features of nonlinear relaxational processes in nature, particularly the occurrence of fat-tailed magnitude distributions and exponential return times, from simple local stress redistributions. In this work, we extend the existing sandpile paradigm into an inter-sandpile cascade, wherein the avalanches emanating from a uniformly-driven sandpile (first layer) is used to trigger the next (second layer), and so on, in a successive fashion. Statistical characterizations reveal that avalanche size distributions evolve from a power-law p(S)≈S−1.3 for the first layer to gamma distributions p(S)≈Sαexp(−S/S0) for layers far away from the uniformly driven sandpile. The resulting avalanche size statistics is found to be associated with the corresponding waiting time distribution, as explained in an accompanying analytic formulation. Interestingly, both the numerical and analytic models show good agreement with actual inventories of non-uniformly driven events in nature.

Suggested Citation

  • Batac, Rene & Longjas, Anthony & Monterola, Christopher, 2012. "Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 616-624.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:616-624
    DOI: 10.1016/j.physa.2011.08.032
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    1. Drossel, B. & Schwabl, F., 1992. "Self-organized criticality in a forest-fire model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 47-50.
    2. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & W. Kantelhardt, Jan, 2004. "Return intervals of rare events in records with long-term persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 308-314.
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    4. Batac, Rene & Pastor, Marissa & Arciaga, Marko & Bantang, Johnrob & Monterola, Christopher, 2009. "Kinks, logarithmic tails, and super-stability in bi-disperse granular media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3072-3082.
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    Cited by:

    1. Tarun, Anjali B. & Paguirigan, Antonino A. & Batac, Rene C., 2015. "Spatiotemporal recurrences of sandpile avalanches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 293-300.

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