Driving Sandpiles to Criticality and Beyond
Author(s)Fey, Anne; Levine, Lionel; Wilson, David B.
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Physical Review Letters
American Physical Society
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
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