Sandpiles on a Sierpinski gasket

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• 作者：Daerden ; Frank ; Vanderzande ; Carlo
• 关键词：Sandpile model ; Fractals ; 64.60.Ak ; 5.40.+j ; 5.70.Ln
• 刊名：Physica A
• 出版年：1998
• 出版时间：August 1, 1998
• 年：1998
• 卷：256
• 期：3-4
• 页码：533-546
• 全文大小：214 K

文摘

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 τ_w which describes the distribution of wave sizes: τ_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 τ that determines the distribution of avalanche sizes: τ=1+τ_w=ln(27/5)/ln 3. Our predictions are in good agreement with the numerical results.