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Updated: Jun 12, 2026
06:55
Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
Published on: August 5, 2016
Driving sandpiles to criticality and beyond
Anne Fey1, Lionel Levine, David B Wilson
1Delft Institute of Applied Mathematics, Delft University of Technology, The Netherlands.
Physical Review Letters
|May 21, 2010
Summary
We challenge the popular theory linking driven dissipative systems to conserved systems. Our findings show that the stationary density of Abelian sandpiles differs from fixed-energy sandpiles, questioning current models of self-organized criticality.
Area of Science:
- Complex Systems
- Statistical Physics
- Dynamical Systems
Background:
- Self-organized criticality (SOC) theory commonly relates driven dissipative systems to systems with conservation laws.
- A key prediction of SOC is that the stationary density in the Abelian sandpile model matches the threshold density in fixed-energy sandpiles.
- This prediction is foundational for understanding critical phenomena in various complex systems.
Purpose of the Study:
- To rigorously test the widely accepted prediction relating stationary density in driven dissipative Abelian sandpiles to fixed-energy sandpiles.
- To investigate the validity of using fixed-energy sandpile models to represent the critical behavior of driven dissipative systems at stationarity.
Main Methods:
- Simulations of the Abelian sandpile model on diverse underlying graphs, including the standard square grid.
- Analysis of system dynamics to determine stationary density and compare it with threshold density.
- Focus on driven dissipative systems and their evolution post-criticality.
Main Results:
- The study refutes the prediction for a broad range of graphs, notably including the square grid.
- Driven dissipative sandpiles exhibit continuous evolution even after reaching a critical state.
- The stationary density was found to differ significantly from the threshold density in fixed-energy models.
Conclusions:
- The established link between driven dissipative systems and conserved systems, based on density predictions, is invalidated.
- Fixed-energy sandpile models are insufficient for accurately exploring the stationary critical behavior of Abelian sandpile models.
- Further research is needed to develop more accurate theoretical frameworks for driven dissipative critical systems.
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