Granular chains with soft boundaries: Slowing the transition to quasiequilibrium

We present here a detailed numerical study of the dynamical behavior of "soft" uncompressed grains in a granular chain where the grains interact via the intrinsically nonlinear Hertz force. It is well known that such a chain supports the formation of solitary waves (SWs). Here, however, the system response to the material properties of the grains and boundaries is explored further. In particular, we examine the details of the transition of the system from a SW phase to an equilibrium-like (or quasiequilibrium) phase, and for this reason we ignore the effects of dissipation in this study. We find that the soft walls slow the reflection of SWs at the boundaries of the system, which in turn slows the journey to quasiequilibrium. Moreover, the increased grain-wall compression as the boundaries are softened results in fewer average grain-grain contacts at any given time in the quasiequilibrium phase. These effects lead to increased kinetic energy fluctuations in the short term in softer systems. We conclude with a toy model that exploits the results of soft-wall systems. This toy model supports the formation of breather-like entities and may therefore be useful for localizing energy in desired places in the granular chain.