Depinning as a coagulation process

Abstract

We consider a one-dimensional sandpile model which mimics an elastic string of particles driven through a strongly pinning periodic environment with phase disorder. The evolution towards depinning occurs by the triggering of avalanches in regions of activity which are at first isolated but later grow and merge. For large system sizes the dynamically critical behavior is dominated by the coagulation of these active regions. Our analysis of the evolution and numerical simulations show that the observed sizes of active regions is well-described by a Smoluchowski coagulation equation, allowing us to predict correlation lengths and avalanche sizes.

5 pages, 2 figures. This version adds new citations to a recent article, the source code used for the numerics, and an animated version of Figure 2

References in corpus (6)

• Statistical Models of Fracture
• Stochastic equation of fragmentation and branching processes related to avalanches
• Gelation for Marcus-Lushnikov process
• Equivalence of the train model of earthquake and boundary driven Edwards-Wilkinson interface
• Subthreshold behavior and avalanches in an exactly solvable Charge Density Wave system
• Exact results for a toy model exhibiting dynamic criticality