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Theoretical Results for Sandpile Models of SOC with Multiple Topplings

Maya Paczuski·Kevin E. Bassler
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Abstract

We study a directed stochastic sandpile model of Self-Organized Criticality, which exhibits recurrent, multiple topplings, putting it in a separate universality class from the exactly solved model of Dhar and Ramaswamy. We show that in the steady-state all stable states are equally likely. Then we explicitly derive a discrete dynamical equation for avalanches on the lattice. By coarse-graining we arrive at a continuous Langevin equation for the propagation of avalanches and calculate all the critical exponents characterizing them. The avalanche equation is similar to the Edwards-Wilkinson equation, but with a noise amplitude that is a threshold function of the local avalanche activity, or interface height, leading to a stable absorbing state when the avalanche dies. It represents a new type of absorbing state phase transition.

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BibTeXRIS

Maya Paczuski, Kevin E. Bassler. 2000-08-11. Theoretical Results for Sandpile Models of SOC with Multiple Topplings. https://doi.org/10.1103/physreve.62.5347

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