Driving sandpiles to criticality and beyond.
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.
Fey
Anne
A
Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands.
Levine
Lionel
L
Wilson
David B
DB