Generating ultradense jammed ellipse packings using biased SWAP

TL;DR

This paper introduces a novel algorithm combining growth methods and biased SWAP Monte Carlo to generate ultradense, disordered ellipse packings with high local nematic order and minimal density fluctuations across various aspect ratios.

Contribution

The study develops a new approach for creating ultradense ellipse packings that are disordered yet highly dense, with detailed analysis of their structural properties across aspect ratios.

Findings

Packings exhibit smaller density fluctuations and greater nematic order than less-dense packings.

Densest packings are disordered with packing fractions close to crystalline values.

Fractionation patterns vary with aspect ratio, showing polycrystalline and nematic domain structures.

Abstract

Using a Lubachevsky-Stillinger-like growth algorithm combined with biased SWAP Monte Carlo and transient degrees of freedom, we generate ultradense disordered jammed ellipse packings. For all aspect ratios $\alpha$, these packings exhibit significantly smaller intermediate-wavelength density fluctuations and greater local nematic order than their less-dense counterparts. The densest packings are disordered despite having packing fractions $\phi_{\rm J}(\alpha)$ that are within less than 0.5% of that of the monodisperse-ellipse crystal [$\phi_{\rm xtal} = \pi/(2\sqrt{3}) \simeq .9069$] over the range $1.25 \lesssim \alpha \lesssim 1.4$ and coordination numbers $Z_{\rm J}(\alpha)$ that are within less than 0.5% of isostaticity [$Z_{\rm iso} = 6$] over the range $1.3 \lesssim \alpha \lesssim 2.0$. Lower-$\alpha$ packings are strongly fractionated and consist of polycrystals of intermediate-size particles, with the largest and smallest particles isolated at the grain boundaries. Higher-$\alpha$ packings are also fractionated, but in a qualitatively-different fashion; they are composed of increasingly-large locally-nematic domains reminiscent of liquid glasses.