Critical scaling in linear response of frictionless granular packings near jamming

TL;DR

This paper investigates the linear response of frictionless granular packings near jamming, revealing diverging length scales, non-self-averaging behavior, and the influence of floppy modes on elastic properties.

Contribution

It provides a detailed analysis of the local and global linear response near jamming, highlighting the role of floppy modes and scaling behavior in elastic constants.

Findings

Response to local forcing is non-self-averaging and fluctuates over a diverging length scale.

Response to global forcing becomes increasingly non-affine near jamming.

Local response governs the anomalous scaling of elastic constants and contact number.

Abstract

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly non-affine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.