The restitution coefficient of a particle repeatedly bouncing off a rough surface

We present a geometric model to investigate the characteristics of the restitution coefficient of a particle-wall collisions process in the case of a structured wall surface. Specifically, we examine the case of a sinusoidal modulation of the roughness heights. We show that (i) The restitution coefficient performs fluctuations around the mean value which also is the value of the local restitution coefficient. These fluctuations are caused by the surface roughness and are due to the exchange of the kinetic energy between the motion in the vertical and horizontal degrees of freedom. (ii) Due to the energy exchange, the restitution coefficient may reach values larger than unity. (iii) The impact phase of the collision has a peculiar pattern, which is fractal-like for initial impact velocities less than 0.99 m/s and potentially chaotic for larger velocities.