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Sandpiles on a Sierpinski gasket

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  • Daerden, Frank
  • Vanderzande, Carlo

Abstract

We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent τw which describes the distribution of wave sizes: τw=ln(9/5)/ln3. Numerically, it is found that the number of waves in an avalanche is proportional to the number of distinct sites toppled in the avalanche. This leads to a conjecture for the exponent τ that determines the distribution of avalanche sizes: τ=1+τw=ln(27/5)/ln3. Our predictions are in good agreement with the numerical results.

Suggested Citation

  • Daerden, Frank & Vanderzande, Carlo, 1998. "Sandpiles on a Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 533-546.
    • Handle: RePEc:eee:phsmap:v:256:y:1998:i:3:p:533-546
    DOI: 10.1016/S0378-4371(98)00210-6
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    Cited by:

    1. Kaiser, Robin & Sava-Huss, Ecaterina, 2024. "Random rotor walks and i.i.d. sandpiles on Sierpiński graphs," Statistics & Probability Letters, Elsevier, vol. 209(C).
    2. M. Ausloos & K. Ivanova & N. Vandewalle, 2001. "Crashes : symptoms, diagnoses and remedies," Papers cond-mat/0104127, arXiv.org, revised Apr 2001.
    3. 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.
    4. Dhar, Deepak, 1999. "The Abelian sandpile and related models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 4-25.

    More about this item

    Keywords

    Sandpile model; Fractals;

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