Soliton attenuation and emergent hydrodynamics in fragile matter

TL;DR

This paper investigates how solitary waves attenuate in fragile granular matter near zero pressure, revealing emergent hydrodynamic behavior, granular temperature, and anomalous viscosity, with implications for understanding disordered soft materials.

Contribution

It introduces a novel understanding of wave attenuation and emergent hydrodynamics in fragile granular systems, highlighting the role of disorder and energy injection.

Findings

Infinitesimal strains propagate as attenuated solitary waves.

Particle fluctuations act as a granular temperature, leading to finite pressure.

Identified two attenuation regimes: exponential and power-law decay.

Abstract

Disordered packings of soft grains are fragile mechanical systems that loose rigidity upon lowering the external pressure towards zero. At zero pressure, we find that any infinitesimal strain-impulse propagates initially as a non-linear 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 fluid-like 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.