Driving Sandpiles to Criticality and Beyond
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Fey-2010-Driving Sandpiles to.pdf
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Author(s)
Fey, Anne
Levine, Lionel
Wilson, David B.
Date Issued
April 2010
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Fey, Anne, Lionel Levine, and David B. Wilson. “Driving Sandpiles to Criticality and Beyond.” Physical Review Letters 104.14 (2010): 145703. © 2010 The American Physical Society
Version
Final published version
Abstract
A popular theory of self-organized criticality relates driven dissipative systems to systems with conservation. This theory predicts that the stationary density of the Abelian sandpile model equals the threshold density of the fixed-energy sandpile. We refute this prediction for a wide variety of underlying graphs, including the square grid. Driven dissipative sandpiles continue to evolve even after reaching criticality. This result casts doubt on the validity of using fixed-energy sandpiles to explore the critical behavior of the Abelian sandpile model at stationarity.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.104.145703
