We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents τ=1.51±0.04, α=1.63±0.04, and μ=1.36±0.04. The avalanche size distribution shows power-law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent [Formula Presented]≡τ+iδ, where the real part τ corresponds to the power law and the imaginary part δ is related to the period of the logarithmic oscillations
Sandpile model on the Sierpinski gasket fractal / B. Kutnjak-Urbanc, S. Zapperi, S. Milošević, H. Eugene Stanley. - In: PHYSICAL REVIEW E. - ISSN 1063-651X. - 54:1(1996 Jul 01), pp. 272-277.
Sandpile model on the Sierpinski gasket fractal
S. Zapperi;
1996
Abstract
We investigate the sandpile model on the two-dimensional Sierpinski gasket fractal. We find that the model displays interesting critical behavior, and we analyze the distribution functions of avalanche sizes, lifetimes, and topplings and calculate the associated critical exponents τ=1.51±0.04, α=1.63±0.04, and μ=1.36±0.04. The avalanche size distribution shows power-law behavior modulated by logarithmic oscillations which can be related to the discrete scale invariance of the underlying lattice. Such a distribution can be formally described by introducing a complex scaling exponent [Formula Presented]≡τ+iδ, where the real part τ corresponds to the power law and the imaginary part δ is related to the period of the logarithmic oscillationsFile | Dimensione | Formato | |
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