Critical fluctuations of elastic moduli in jammed solids

TL;DR

This paper studies fluctuations in the shear modulus of jammed solids near the jamming transition, revealing a potential-independent critical scaling law consistent across dimensions, with implications for elastic heterogeneity and sound scattering.

Contribution

It uncovers a potential-independent critical exponent for shear modulus fluctuations in jammed packings, confirmed in 2D, advancing understanding of jamming criticality.

Findings

Fluctuations obey a potential-independent critical exponent.

Scaling law holds in both 2D and 3D packings.

Results support heterogeneous-elasticity theory predictions.

Abstract

We investigate sample-to-sample fluctuations of the shear modulus in ensembles of particle packings near the jamming transition. Unlike the average modulus, which exhibits distinct scaling behaviours depending on the interparticle potential, the fluctuations obey a critical exponent that is independent of the potential. Furthermore, this scaling behaviour has been confirmed in two-dimensional packings, indicating that it holds regardless of spatial dimension. Using this scaling law, we discuss the relationship predicted by heterogeneous-elasticity theory between elastic-modulus fluctuations and the Rayleigh scattering of sound waves across different pressures. Our numerical results provide a useful foundation for developing a unified theoretical description of the jamming critical phenomenon.