Testing mean-field theory for jamming of non-spherical particles: Contact number, gap distribution, and vibrational density of states

TL;DR

This study numerically investigates the jamming transition of nearly spherical particles in two dimensions, confirming that mean-field theory accurately describes physical quantities like contact number and vibrational states.

Contribution

The paper introduces an analytical gap function for non-spherical particles and demonstrates the validity of mean-field theory for shapes close to disks.

Findings

Physical quantities follow power-law behaviors near the jamming point.

The power-law behaviors are shape-independent and consistent with mean-field theory.

Mean-field theory applies broadly to nearly spherical particles with Fourier-series shapes.

Abstract

We perform numerical simulations of the jamming transition of non-spherical particles in two dimensions. In particular, we systematically investigate how the physical quantities at the jamming transition point behave when the shapes of the particle deviate slightly from the perfect disks. For efficient numerical simulation, we first derive an analytical expression of the gap function, using the perturbation theory around the reference disks. Starting from disks, we observe the effects of the deformation of the shapes of particles by the $n$-th order term of the Fourier series $\sin(n\theta)$. We show that the several physical quantities, such as the number of contacts, gap distribution, and characteristic frequencies of the vibrational density of states, show the power-law behaviors with respect to the linear deviation from the reference disks. The power-law behaviors do not depend on $n$ and are fully consistent with the mean-field theory of the jamming of non-spherical particles. This result suggests that the mean-field theory holds very generally for nearly spherical particles whose shape can be expressed by the Fourier series.