Self-organized criticality: sandpiles, singularities, and scaling.
- 18 July 1995
- journal article
- research article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 92 (15) , 6712-6719
- https://doi.org/10.1073/pnas.92.15.6712
Abstract
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.Keywords
This publication has 26 references indexed in Scilit:
- Avalanches and the renormalization group for pinned charge-density wavesPhysical Review B, 1994
- Fluctuations in self-organizing systemsPhysical Review E, 1993
- On self-organized criticality in nonconserving systemsPhysical Review E, 1993
- Self-organizing systems at finite driving ratesPhysical Review E, 1993
- Avalanches, hydrodynamics, and discharge events in models of sandpilesPhysical Review A, 1992
- Asymptotic uniqueness of the sliding state for charge-density wavesPhysical Review Letters, 1992
- Self-organized criticality in sandpiles: Nature of the critical phenomenonPhysical Review A, 1990
- Exactly solved model of self-organized critical phenomenaPhysical Review Letters, 1989
- Critical Exponents and Scaling Relations for Self-Organized Critical PhenomenaPhysical Review Letters, 1988
- Overdamped Frenkel-Kontorova model with randomness as a dynamical system: Mode locking and derivation of discrete mapsPhysical Review A, 1987