Amorphous packings of hard spheres in large space dimension

ar X iv : c on d - m at / 0 60 15 73 v 1 2 5 Ja n 20 06 Amorphous packings of hard spheres in large space dimension

In a recent paper 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 close packing density were obtained in d = 3. Here we show that the HNC approximation is not needed: the same expression can be obtained from the full diagrammatic expansion of ...

Mean field theory of the glass transition and jamming of hard spheres

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 o...

Mean field theory of hard sphere glasses and jamming

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 o...

Some recent theoretical results on amorphous packings of hard spheres

Self-similar space-filling packings in three dimensions

We develop an algorithm to construct new self-similar space-filling packings of spheres. Each topologically different configuration is characterized by its own fractal dimension. We also find the first bicromatic packing known up to now.