Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling

Details Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling Inhomogeneous sandpile model: Crossover from multifractal scaling to finite size scaling

2005-10-12

arxiv.org/abs/cond-mat/0510326v2

Physical Review E 73, 066125 (2006)

Physics

Condensed Matter

Statistical Mechanics

17 pages, 6 figures

Scientific paper

10.1103/PhysRevE.73.066125

We study an inhomogeneous sandpile model in which two different toppling rules are defined. For any site only one rule is applied corresponding to either the Bak, Tang and Wiesenfeld model {[}P.Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. \textbf{59}, 381 (1987){]} or the Manna two-state sandpile model {[}S. S. Manna, J. Phys. A \textbf{24}, L363 (1991){]}. A parameter $c$ is introduced which describes a density of sites which are randomly deployed and where the stochastic Manna rules are applied. The results show that the avalanche area exponent $\tau_{a}$, avalanche size exponent $\tau_{s}$, and capacity fractal dimension $D_{s}$ depend on the density $c$. A crossover from multifractal scaling of the Bak, Tang, and Wiesenfeld model ($c=0$) to finite size scaling was found. The critical density $c$ is found to be in the interval $0

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