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The BTW mechanism on a self-similar image of a square: A path to unexpected exponents

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  • Shapoval, A.B.
  • Shnirman, M.G.

Abstract

We define the BTW mechanism on a two-dimensional heterogeneous self-similar lattice. Our model exhibits the power distribution of avalanches with the exponent τ=2−2/ν, where ν is the similarity exponent of the lattice. The inequality τ<1, for the first time detected in this paper inside a broad class of sand-piles, is ensured by random loading uniformly distributed over the lattice.

Suggested Citation

  • Shapoval, A.B. & Shnirman, M.G., 2012. "The BTW mechanism on a self-similar image of a square: A path to unexpected exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 15-20.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:1:p:15-20
    DOI: 10.1016/j.physa.2011.08.020
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    References listed on IDEAS

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    1. Ivashkevich, E.V. & Priezzhev, V.B., 1998. "Introduction to the sandpile model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 97-116.
    2. Daerden, F. & Priezzhev, V.B. & Vanderzande, C., 2001. "Waves in the sandpile model on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 43-54.
    3. Daerden, Frank & Vanderzande, Carlo, 1998. "Sandpiles on a Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 533-546.
    4. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
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