Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature of that diversity is the necessity to classify individual jammed configurations according to whether they are locally, collectively, or strictly jammed. Each of these categories contains a multitude of jammed configurations spanning a wide...

Predicting the densest random disc packing fraction is an unsolved paradigm problem relevant to a number of disciplines and technologies. One difficulty is that it is ill-defined without setting a criterion for the disorder. Another is that the density depends on the packing protocol and the multitude of possible protocol parameters has so far hindered a general solution. A new approach is proposed here. After formulating a well-posed form of the general protocol-independent ...

Unraveling the complexities of random packing in three dimensions has long puzzled physicists. While both experiments and simulations consistently show a maximum density of 64 percent for tightly packed random spheres, we still lack an unambiguous and universally accepted definition of random packing. This paper introduces an innovative standpoint, depicting random packing as spheres closest to a quenched Poisson field of random points. We furnish an efficacious algorithm to ...

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point process in d-dimensional Euclidean space for any d, which are special cases of determinantal processes. In particular, we obtain the n-particle correlation functions for any n, which completely specify the point processes. We also demonstra...

Random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time {\it saturation} limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extra...

It is shown that the numerical data in cond-mat/0608362 are in very good agreement with the predictions of cond-mat/0601573.

We present a theoretical prediction on random close packing factor \phi_RCP^b of binary granular packings based on the hard-sphere fluid theory. An unexplored regime is unravelled, where the packing fraction \phi_RCP^b is smaller than that of the mono-sized one \phi_RCP^m, i.e., the so-called loose jamming state. This is against our common perception that binary packings should always reach a denser packing than mono-sized packings at the jamming state. Numerical evidence fur...

A simple dynamical model, Biased Random Organization, BRO, appears to produce configurations known as Random Close Packing (RCP) as BRO's densest critical point in dimension $d=3$. We conjecture that BRO likewise produces RCP in any dimension; if so, then RCP does not exist in $d=1-2$ (where BRO dynamics lead to crystalline order). In $d=3-5$, BRO produces isostatic configurations and previously estimated RCP volume fractions 0.64, 0.46, and 0.30, respectively. For all invest...

Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time or saturation limit for the first six space dimensions ($1 \le d \le 6$). Specifically, we determine the saturation density, pair correlation function, cumulative coordination number and the structure factor in each =of these dimensions. We find that for $2 \le...

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of...