Granular chain between asymmetric boundaries and the quasiequilibrium state

Some 30 years have passed since we learned that any velocity perturbation develops into a propagating solitary wave in a granular chain, and over a decade has passed since we learned that these solitary waves break and reform upon collision, leaving behind small secondary solitary waves. The production of the latter eventually precipitates the quasiequilibrium state characterized by large energy fluctuations in dissipation-free granular systems. Here we present dynamical simulations on the effects of soft boundaries on solitary wave interaction in granular chains held between fixed walls. We show that at short time scales, a gradient in the distribution of kinetic energy between the boundaries is indeed sustained. At long times, however, such a gradient gets obliterated and there is no measurable difference between the average kinetic energies of the particles adjacent to walls. Our findings suggest that (i) the quasiequilibrium state can effectively erase small gradients of the average kinetic energies of the particles adjacent to walls in a system, (ii) Boltzmann distribution of grain speeds is realized in the system of interest, and (iii) time and space averages yield the same result, thus suggesting that the system is ergodic.