Soliton attenuation and emergent hydrodynamics in fragile matter

Abstract

Disordered packings of soft grains are fragile mechanical systems that lose rigidity upon lowering the external pressure toward zero. At zero pressure, we find that any infinitesimal strain impulse propagates initially as a nonlinear solitary wave progressively attenuated by disorder. We demonstrate that the particle fluctuations generated by the solitary-wave decay can be viewed as a granular analogue of temperature. Their presence is manifested by two emergent macroscopic properties absent in the unperturbed granular packing: a finite pressure that scales with the injected energy (akin to a granular temperature) and an anomalous viscosity that arises even when the microscopic mechanisms of energy dissipation are negligible. Consistent with the interpretation of this state as a fluidlike thermalized state, the shear modulus remains zero. Further, we follow in detail the attenuation of the initial solitary wave, identifying two distinct regimes-an initial exponential decay, followed by a longer power-law decay-and suggest simple models to explain these two regimes.