Relaxations and rheology near jamming

TL;DR

This paper investigates the viscoelastic properties of soft sphere packings near jamming, revealing a diverging density of relaxational modes that influence the complex shear modulus, with results confirmed numerically.

Contribution

It introduces a detailed analysis of relaxational modes near jamming and derives the frequency and distance dependence of the shear modulus from the relaxational density of states.

Findings

Anomalous excess of slowly relaxing modes near jamming

Diverging relaxational density of states at jamming

Derived $G^*$ dependence on frequency and jamming proximity

Abstract

We determine the form of the complex shear modulus $G^*$ in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of $G^*$ on frequency and distance to the jamming transition, which is confirmed by numerics.