Chaotic behavior in a model for grain dynamics

A simple model is presented for the motion of a grain down a rough inclined surface. Considering that the surface has a periodic profile and adopting a simple collision law, we arrive at a model in which the dynamics is described by a three-dimensional map. As the surface inclination increases, this map exhibits a transition from a regime of bounded velocity to accelerated motion. In the region of bounded velocity, the original 3D map can be reduced to an effective one-dimensional map that shows several dynamical features (stable fixed points, periodic orbits, and chaotic behavior). A bifurcation diagram for the 1D map is presented.