Study Of The Phase Shift Introduced By The Frontal Collision Of Two Solitary Waves In One-Dimensional Granular Chains

Granular matters are ubiquitous in nature and give rich phenomena in physics.Being a typical but special nonlinear system, granular matter exhibits both solid-like and liquid-like characters, and even gas-like under some certain conditions. Coupled with the inherent discrete of the system, solitary waves’ propagation in a one-dimensional granular chain has a wealth of content. And it helps us to know the granular system and particles’ interaction in-depth in the system to study the matter while it can give some guides for the study of a multi-dimensional granular system.Phase shift producing by the frontal collision of two solitary waves in one-dimensional chains is investigated by using computer simulation. Focus on the impact of particles’ discrete on the phase shift of solitary waves after collision. We find for two equal solitary waves colliding in both an even chain and an odd chain,phases of the waves in respect to the non-interacting waves are shifted, the phase shift in the odd chain is slightly larger than that in the even chain. By delaying the time of opposite solitary wave entering granular chain, simulations show that the phase shift is dependent on not only position of head-on solitary wave collisions, but also the location measuring the phase of the wave. As the position of wave collisions moves along the granular chain, the phase shift varies periodically. The period of the phase shift is exactly equal to the time taken by the wave to pass a granule. The phenomenon indicates that energy of solitary wave changes also periodically as the position of solitary collisions is shifted along the granular chain. As the velocity of opposite solitary wave increases, the phase shift increases oscillating when the velocity of wave is larger. The phase shifts of head-on solitary wave collisions both in an odd chain and even chain are analytically obtained and in excellent agreement with numerical results, also coincide with the experimental results of Francisco et. al.