Universality of jamming of non-spherical particles

TL;DR

This paper develops a universal theory for hypostatic jamming in non-spherical particles, revealing shared critical behavior, and confirms predictions through analytical models and numerical simulations.

Contribution

It introduces a general framework for hypostatic jamming, maps ellipsoids to breathing particles, and analytically predicts universal critical exponents.

Findings

Hypostatic packings belong to a universal jamming class.

Critical exponents for contact number and vibrational states are identical across systems.

Force and gap distributions lack power-law behavior in hypostatic jamming.

Abstract

Amorphous packings of non-spherical particles such as ellipsoids and spherocylinders are known to be hypostatic: the number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of `breathing' particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic, and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.