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Proceedings of the National Academy of Sciences, Vol 92, 6712-6719, Copyright © 1995 by National Academy of Sciences

ARTICLE

Self-Organized Criticality: Sandpiles, Singularities, and Scaling

JM Carlson and GH Swindle

We present an overview of the statistical mechanics of self-organized criticality. We focus on the successes and failures of hydrodynamic description of transport, which consists of singular diffusion equations. When this description applies, it can predict the scaling features associated with these systems. We also identify a hard driving regime where singular diffusion hydrodynamics fails due to fluctuations and give an explicit criterion for when this failure occurs.
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