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. Here we provide the Python source code used in this project, together with an animation showing the active region size distribution together with the Smoluchowski solution as time varies.
This research is supported by funding from the National Science Foundation, grant ID DMS-1148284
İşeri, Melih, and Kaspar, David C.,
"Code library and video from article 'Depinning as a coagulation process'"
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