Although the concept of random close packing with an almost universal packing fraction of approximately 0.64 for hard spheres was introduced more than half a century ago, there are still ongoing debates. The main difficulty in searching the densest packing is that states with packing fractions beyond the glass transition at approximately 0.58 are inherently non-equilibrium systems, where the dy...

In this paper, the effects of two different Particle Size Distributions (PSD) on packingbehavior of ideal rigid spherical nanoparticles using a novel packing model based on parallelalgorithms have been reported. A mersenne twister algorithm was used to generate pseudorandomnumbers for the particles initial coordinates. Also, for this purpose a nanosized tetragonal confinedcontainer with a squar...

The packing fraction of geometric random packings of discretely sized particles is addressed in the present paper. In an earlier paper [Brouwers, Phys. Rev. E 74, 031309 (2006); Brouwers, Phys. Rev. E 74, 069901(E) (2006)], analytical solutions were presented for the packing fraction of polydisperse geometric packings for discretely sized particles with infinitely large size ratio and the packi...

Tetrahedra are special among the platonic solids. They are the simplest polyhedra and the ones most unlike spheres. Surprisingly, much of our knowledge about the packing properties of tetrahedra is very recent: the past year has witnessed a sudden proliferation of novel, and often surprising, findings. Using Monte Carlo simulations, Haji-Akbari et al.[1] found that, upon compression, systems of...

In the random k-uniform hypergraph Hk(n, p) on a vertex set V of size n, each subset of size k of V independently belongs to it with probability p. Motivated by a theorem of Erdős and Rényi [6] regarding when a random graph G(n, p) = H2(n, p) has a perfect matching, Schmidt and Shamir [14] essentially conjectured the following. Conjecture Let k|n for fixed k ≥ 3, and the expected degree d(n, p)...

We study fine properties of Lévy trees that are random compact metric spaces introduced by Le Gall and Le Jan in 1998 as the genealogy of continuous state branching processes. Lévy trees are the scaling limits of Galton-Watson trees and they generalize Aldous’s continuum random tree which corresponds to the Brownian case. In this paper we prove that Lévy trees have always an exact packing measu...

We obtain a non-implication result in the Medvedev degrees by studying sequences that are close to Martin-Löf random in asymptotic Hamming distance. Our result is that the class of stochastically bi-immune sets is not Medvedev reducible to the class of sets having complex packing dimension 1.

A random packing of hard particles represents a fundamental model for granular matter. Despite its importance, analytical modeling of random packings remains difficult due to the existence of strong correlations which preclude the development of a simple theory. Here, we take inspiration from liquid theories for the n-particle angular correlation function to develop a formalism of random packin...

We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination numbers between the species and (ii) the dependence of the coordination numbers with the concentration of species; quantities that are calculated analytically....

Phys. Rev. E. 68, 011306 (2003)] claim that a special point J of a "jamming phase diagram" (in density, temperature, stress space) is related to random close packing of hard spheres and that it represents, for their suggested definitions of jammed and random, the recently introduced maximally random jammed state. We point out several difficulties with their definitions and question some of thei...