Comment on "Explicit Analytical Solution for Random Close Packing in d=2 and d=3", Physical Review Letters {\bf 128}, 028002 (2022)

TL;DR

This paper critiques a proposed analytical method for calculating the densest random packing fractions in 2D and 3D, showing it overestimates in 2D and is based on flawed assumptions and unsupported simulations.

Contribution

It identifies errors in a recent analytical approach to random packing densities and clarifies the method's limitations and inaccuracies.

Findings

The method overestimates packing density in 2D.

The method's assumptions are violated in the analysis.

The supporting simulation evidence is unfounded.

Abstract

The method, proposed in \cite{Za22} to derive the densest packing fraction of random disc and sphere packings, is shown to yield in two dimensions too high a value that (i) violates the very assumption underlying the method and (ii) corresponds to a high degree of structural order. The claim that the obtained value is supported by a specific simulation is shown to be unfounded. One source of the error is pointed out.