Geometric order parameters derived from the Voronoi tessellation show signatures of the jamming transition

TL;DR

This paper introduces geometric order parameters based on Voronoi tessellations to identify and analyze the jamming transition in frictionless sphere packings, providing a purely geometric perspective on the phenomenon.

Contribution

It presents novel geometric order parameters and correlation functions derived from Voronoi tessellations that effectively characterize the jamming transition.

Findings

Order parameters show clear signatures of jamming transition.

Scaling exponents associated with the transition are identified.

Geometric correlation functions reveal transition signatures.

Abstract

A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponents. Furthermore, we define a real space geometric correlation function which also displays a signature of jamming. Taken together, these results demonstrate the validity and usefulness of a purely geometric approach to jamming.