Physical Sciences and Mathematics Commons^™

A Single Particle Impact Model For Motion In Avalanches, J. J. P. Veerman, Dacian Daescu, M. J. Romero-Vallés, P. J. Torres

Mathematics and Statistics Faculty Publications and Presentations

We describe the global behavior of the dynamics of a particle bouncing down an inclined staircase. For small inclinations all orbits eventually stop (independent of the initial condition). For large enough inclinations all orbits end up accelerating indefinitely (also independent of the initial conditions). There is an interval of inclinations of positive length between these two. In that interval the behavior of an orbit depends on its initial condition. In addition to stopping and accelerating orbits, there are also orbits with speeds bounded away from both zero and infinity. A second hallmark of the dynamics is that the orbits going …