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Full-Text Articles in Non-linear Dynamics
A Single Particle Impact Model For Motion In Avalanches, J. J. P. Veerman, Dacian Daescu, M. J. Romero-Vallés, P. J. Torres
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 …
A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman
A Solvable Model For Gravity Driven Granular Dynamics, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
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 …