Effect of Elastic Vibrations on Normal Head on Collisions of Isothermal Spheres

We numerically investigate head on collisions of isothermal visco-elastic spheres. We find that the restitution coefficient oscillates against the impact speed if the solid viscosity inside the sphere is small enough. We confirm that the oscillation arises from the resonance between the duration of contact and the eigen-frequencies of the sphere. This oscillation disappears if there exists the strong solid viscosity in spheres. We also find that a sinusoidal behavior of the restitution coefficient against the initial phase in the eigenmodes for collisions between a thermally activated sphere and a flat wall. As a result, the restitution coefficient can exceed unity if the impact speed of the colliding sphere is nearly equal to or slower than the thermal speed. We have confirmed the existence of the fluctuation theorem for impact processes through our simulation.