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Dynamics, Granular flow, Combinatorial dynamics, Avalanches -- Mathematical models


We discuss a toy model to study the dynamics of individual particles in avalanches. The model describes a particle launched from an inclined infinite staircase. The particle is not allowed to bounce when it collides with the staircase. During the collision, the particle loses some energy, and after that slides on to the end of the step it landed on. The process then repeats itself. The dynamics of this no-bounce model can essentially be completely understood. Partial versions of some results were stated and argued in previous work. Here we give a full description together with all the proofs. We also briefly mention a second model where the no-bounce restriction is lifted and briefly describe the main features of that more complicated model.


This is the author’s version of a work that was accepted for publication in Dynamical Systems: An International Journal. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.

A definitive version was subsequently published in Dynamical Systems: An International Journal and can be found online at:



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