Random Sequential Addition of Hard Spheres in High Euclidean Dimensions

We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via simulation in d=2, 3, and 4. We show how a broad class of such models exhibit distributions of sphere radii with a universal exponent. We construct a scaling theory that relates the fractal structure of these models to the decay of their pore...

We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in $d=3$ dimensions, and thus obtain an estimate of the random close packing (RCP) volume fraction, $\phi_{\textrm{RCP}}$, as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributi...

A recent letter titled "Explicit Analytical Solution for Random Close Packing in d=2 and d=3" published in Physical Review Letters proposes a first-principle computation of the random close packing (RCP) density in spatial dimensions d=2 and d=3. This problem has a long history of such proposals, but none capture the full picture. This paper, in particular, once generalized to all d fails to describe the known behavior of jammed systems in d>4, thus suggesting that the low-di...

We have formulated the problem of generating periodic dense paritcle packings as an optimization problem called the Adaptive Shrinking Cell (ASC) formulation [S. Torquato and Y. Jiao, Phys. Rev. E {\bf 80}, 041104 (2009)]. Because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in $d$-dimensional Euclidean space $\mathbb{R}^d$, it is most suitable and natural to solve the corresponding ASC optimizat...

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 ...

The aim of this paper is to review and discuss qualitatively some results on the properties of amorphous packings of hard spheres that were recently obtained by means of the replica method. The theory gives predictions for the equation of state of the glass, the complexity of the metastable states, the scaling of the pressure close to jamming, the coordination of the packing and the pair correlation function in any space dimension d. The predictions compare very well with num...

In this short commentary we provide our comment on the article "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$" and its subsequent Erratum that are recently published in Physical Review Letters. In that Letter, the author presented an explicit analytical derivation of the volume fractions $\phi_{\rm RCP}$ for random close packings (RCP) in both $d=2$ and $d=3$. Here we first briefly show the key parts of the derivation in Ref.~\cite{Za22}, and then p...

In previous work [Phys. Rev. X 5, 021020 (2015)], it was shown that stealthy hyperuniform systems can be regarded as hard spheres in Fourier-space in the sense that the the structure factor is exactly zero in a spherical region around the origin in analogy with the pair-correlation function of real-space hard spheres. In this work, we exploit this correspondence to confirm that the densest Fourier-space hard-sphere system is that of a Bravais lattice. This is in contrast to r...

The structural properties of dense random packings of identical hard spheres (HS) are investigated. The bond order parameter method is used to obtain detailed information on the local structural properties of the system for different packing fractions $\phi$, in the range between $\phi=0.53$ and $\phi=0.72$. A new order parameter, based on the cumulative properties of spheres distribution over the rotational invariant $w_6$, is proposed to characterize crystallization of rand...

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectur...