Critical and non-critical jamming of frictional grains

TL;DR

This study investigates the vibrational properties of frictional granular media near the jamming transition, revealing how pressure and friction influence vibrational spectra, contact number, and elastic moduli, with distinctions between critical and non-critical jamming.

Contribution

It provides a detailed analysis of vibrational states and soft modes in frictional grains, highlighting the role of contact number excess and friction in the jamming transition.

Findings

Vibrational density of states shows a crossover at frequency omega^*

Omega^* is proportional to the excess contact number Delta z

Elastic moduli ratio depends on the distance from isostaticity

Abstract

We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient mu. The density of vibrational states exhibits a crossover from a plateau at frequencies omega \gtrsim omega^*(p,mu) to a linear growth for omega \lesssim omega^*(p,mu). We show that omega^* is proportional to Delta z, the excess number of contacts per grains relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have Delta z -> 0, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity.