Sandpiles on the Sierpinski gasket

Details Sandpiles on the Sierpinski gasket Sandpiles on the Sierpinski gasket

1997-12-16

arxiv.org/abs/cond-mat/9712183v1

Physics

Condensed Matter

Statistical Mechanics

11 pages (Latex), 7 figures, submitted to Physica A

Scientific paper

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 $\tau_w$ which describes the distribution of wave sizes: $\tau_w = \ln{(9/5)}/\ln{3}$. 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 $\tau$ that determines the distribution of avalanche sizes: $\tau=1+\tau_w = \ln{(27/5)}/\ln{3}$. Our predictions are in good agreement with the numerical results.

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