Driving Sandpiles to Criticality and Beyond

Anne Fey, Lionel Levine, David B. Wilson
2010 Physical Review Letters  
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
more » ... energy sandpiles to explore the critical behavior of the abelian sandpile model at stationarity.
doi:10.1103/physrevlett.104.145703 pmid:20481946 fatcat:ku3f6uvat5a3jhcuehk4g3wdrm