A geometric-Structure Theory for maximally Random Jammed Packings

TL;DR

This paper develops a geometric-structure theory to accurately predict the packing density of maximally random jammed packings for a broad class of two-dimensional particles, including shapes between circles and squares.

Contribution

It introduces a novel geometric-structure approach that provides the first highly accurate formula for MRJ densities of binary convex superdisks.

Findings

Accurate formula for MRJ densities of binary convex superdisks

Applicable to a wide range of particle shapes between circles and squares

Advances understanding of disordered, mechanically rigid packings

Abstract

Maximally random jammed (MRJ) particle packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid. The prediction of the MRJ packing density phi, among other packing properties of frictionless particles, still poses many theoretical challenges, even for congruent spheres or disks. Using the geometric-structure approach, we derive for the first time a highly accurate formula for MRJ densities for a very wide class of twodimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares.