The jamming transition is a k-core percolation transition

TL;DR

This paper links the jamming transition in granular matter to a k-core percolation transition, showing that rigidity emerges suddenly at specific coordination numbers related to k-core percolation theory.

Contribution

It reveals that the structural origin of jamming is the emergence of k-cores, connecting finite-dimensional jammed packings to mean-field k-core percolation in random networks.

Findings

Jamming transition corresponds to the sudden appearance of k-cores.

k-core variables freeze at the transition point.

Mean-field k-core percolation explains 3-D simulation results.

Abstract

We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the sudden emergence of the 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdos-Renyi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network.