Stability of jammed packings I: the rigidity length scale

TL;DR

This paper introduces a new derivation of the rigidity length scale l* in jammed packings, linking it to the onset of rigidity, and provides the first direct numerical measurement of this scale.

Contribution

It offers an alternative, phenomenological derivation of the length scale l* based on rigidity onset, enhancing understanding of jamming phenomena.

Findings

Derived l* from rigidity onset

Provided the first numerical measurement of l*

Linked length scale to physical rigidity transition

Abstract

In 2005, Wyart et al. (Europhys. Lett., 72 (2005) 486) showed that the low frequency vibrational properties of jammed amorphous sphere packings can be understood in terms of a length scale, called l*, that diverges as the system becomes marginally unstable. Despite the tremendous success of this theory, it has been difficult to connect the counting argument that defines l* to other length scales that diverge near the jamming transition. We present an alternate derivation of l* based on the onset of rigidity. This phenomenological approach reveals the physical mechanism underlying the length scale and is relevant to a range of systems for which the original argument breaks down. It also allows us to present the first direct numerical measurement of l*.