Related papers: Glass transition and random close packing above th…
Although the concept of random close packing with an almost universal packing fraction of ~ 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…
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…
Based on results from the physics and mathematics literature which suggest a series of clearly defined conjectures, we formulate three simple scenarios for the fate of hard sphere crystallization in high dimension: (A) crystallization is…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
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…
We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear…
We show that in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in…
The most efficient way to pack equally sized spheres isotropically in 3D is known as the random close packed state, which provides a starting point for many approximations in physics and engineering. However, the particle size distribution…
In a recent paper (cond-mat/0506445) we derived an expression for the replicated free energy of a liquid of hard spheres based on the HNC free energy functional. An approximate equation of state for the glass and an estimate of the random…
We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not…
Glass transition is accompanied by a rapid growth of the structural relaxation time and a concomitant decrease of configurational entropy. It remains unclear whether the transition has a thermodynamic origin, and whether the dynamic arrest…
We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate…
Glassy soft matter is often continuously polydisperse, in which the sizes or various properties of the constituent particles are distributed continuously. However, most of the microscopic theories of the glass transition focus on the…
We examine the dynamics of hard spheres and discs at high packing fractions in two and three dimensions, modeling the simplest systems exhibiting a glass transition. As it is well known, cooperativity and dynamic heterogeneity arise as…
Previous studies have suggested a conundrum in the relaxation dynamics of polydisperse supercooled liquids. It has been shown that in two dimensions, the relative relaxation times of particles of different sizes become more similar as the…
There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a…
It has been shown recently that predictions from Mode-Coupling Theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one…
Packing spheres efficiently in large dimension $d$ is a particularly difficult optimization problem. In this paper we add an isotropic interaction potential to the pure hard-core repulsion, and show that one can tune it in order to maximize…
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…
We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits…