Some recent theoretical results on amorphous packings of hard spheres

Details Some recent theoretical results on amorphous packings of hard spheres Some recent theoretical results on amorphous packings of hard spheres

2006-04-27

arxiv.org/abs/cond-mat/0604622v2

Phil. Mag. 87, 485-495 (2007)

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 6 figures; proceedings of the X International Workshop on Disordered Systems, Molveno (TN), Italy, March 2006

Scientific paper

10.1080/14786430600838304

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 numerical simulations in d=3 and somehow also in d=2. The asymptotic predictions for d->oo are within the rigorous bounds. The theory can be extended to binary mixtures and to hard core potentials with an attractive tail or square well.

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