2,890 research outputs found
Some recent theoretical results on amorphous packings of hard spheres
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.Comment: 7 pages, 6 figures; proceedings of the X International Workshop on
Disordered Systems, Molveno (TN), Italy, March 200
The ideal glass transition of Hard Spheres
We use the replica method to study the ideal glass transition of a liquid of
identical Hard Spheres. We obtain estimates of the configurational entropy in
the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62,
and of the random close packing density, in the range 0.64--0.67, depending on
the approximation we use for the equation of state of the liquid. We also
compute the pair correlation function in the glassy states (i.e., dense
amorphous packings) and we find that the mean coordination number at random
close packing is equal to 6. All these results compare well with numerical
simulations and with other existing theories.Comment: 13 pages, 8 figure
- …