The BTW mechanism on a self-similar image of a square: A path to unexpected exponents

Alexander Shapoval and M.G. Shnirman

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 1, 15-20

Abstract: We define the BTW mechanism on a two-dimensional heterogeneous self-similar lattice. Our model exhibits the power distribution of avalanches with the exponent τ=2−2/ν, where ν is the similarity exponent of the lattice. The inequality τ<1, for the first time detected in this paper inside a broad class of sand-piles, is ensured by random loading uniformly distributed over the lattice.

Keywords: Self-organized criticality; Similarity exponent; Heterogeneous sand-pile; Scaling (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:1:p:15-20

DOI: 10.1016/j.physa.2011.08.020

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