Jamming in Perspective

TL;DR

This paper emphasizes the critical role of the contact network's structure in jammed systems, demonstrating how networks with specific properties can be constructed without compressive packing, and exploring their transformation into disk packs.

Contribution

It introduces a novel network construction method based on Delaunay triangulation and edge removal to achieve jammed states without compressive packing, applicable in any dimension.

Findings

Networks with one contact above isostaticity have finite bulk modulus.

The construction method is demonstrated in 2D and can be extended to higher dimensions.

Networks can be transformed into disk packings while maintaining jammed properties.

Abstract

Jamming occurs when objects like grains are packed tightly together (e.g. grain silos). It is highly cooperative and can lead to phenomena like earthquakes, traffic jams, etc. In this Letter we point out the paramount importance of the underlying contact network for jammed systems; the network must have one contact in excess of isostaticity and a finite bulk modulus. Isostatic means that the number of degrees of freedom are exactly balanced by the number of constraints. This defines a large class of networks that can be constructed without the necessity of packing particles together compressively (either in the lab or computationally). One such construction, which we explore here, involves setting up the Delaunay triangulation of a Poisson disk sampling and then removing edges to maximize the bulk modulus until the isostatic plus one point is reached. This construction works in any dimensions and here we give results in 2D where we also show how such networks can be transformed into a disk pack.