Experimental Confirmation of Hyperuniformity of torque fluctuations in Frictional Matter

TL;DR

This paper provides the first experimental evidence that torque fluctuations in frictional granular materials are hyperuniform, confirming a recent theoretical prediction about stress auto-correlation decay in such systems.

Contribution

It experimentally verifies the hyperuniformity of torque fluctuations in frictional matter, supporting theoretical models of stress auto-correlation behavior.

Findings

Torque fluctuations are hyperuniform in frictional granular packings.

Variance of torque fluctuations scales as R^{d-1} in d-dimensional space.

Supports the theoretical prediction of stress auto-correlation decay as elastic Green's function.

Abstract

A recent purely theoretical prediction stated that in frictional granular packings, mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. Moreover, and unexpectedly, the torque fluctuations were predicted to be hyperuniform, a condition for the stress auto-correlation to decay as the elastic Green's function. In this Letter we present first experimental evidence for the hyperuniformity of the stress fluctuations. We propose that quite generally the variance of torque fluctuations in a d-dimensional ball of radius R will increase exactly like $R^{d-1}$, satisfying the definition of hyperuniformity.