The Solitary Wave Collision Problem in Granular Alignments

Any impulse travels as a solitary wave in an alignment of spherical elastic grains where the system grains are barely in contact. These solitary waves are about 7 grain diameters wide. Their speeds depend upon the maximum displacement amplitudes associated with these waves. We focus on the dynamical problem associated with the collision of two identical and opposite propagating solitary waves. Interface and grain center collisions reveal markedly different dynamics. Solitary wave collisions lead to the destruction of the original waves and the subsequent creation of new smaller waves along with ``baby" or secondary solitary waves. In the absence of dissipation, these granular systems point towards the existence of a generalized equilibrium phase that involves Maxwellian distribution of velocities with no depedence on initial conditions but one that violates the equipartition theorem.