Sandpiles on the Sierpinski gasket

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 ${\tau }_w$ 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.

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

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