J. Phys. I France
Volume 7, Numéro 12, December 1997
Page(s) 1677 - 1692
DOI: 10.1051/jp1:1997162
J. Phys. I France 7 (1997) 1677-1692

Packing at Random in Curved Space and Frustration: a Numerical Study

Rémi Jullien1, Jean-François Sadoc2 and Rémy Mosseri3

1  Laboratoire des Verres, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France
2  Laboratoire de Physique des Solides, Université Paris-Sud, Centre d'Orsay, 91405 Orsay Cedex, France
3  Groupe de Physique des Solides, Université Paris VII, Place Jussieu, 75251 Paris Cedex 5, France

(Received 3 July 1997, received in final form 11 August 1997, accepted 18 August 1997)

Random packings of discs on the sphere S 2 and spheres on the (hyper-)sphere S 3 have been built on a computer using an extension of the Jodrey-Tory algorithm. Structural quantities such as the volume fraction, the pair correlation function and some mean characteristics of the Voronoi cells have been calculated for various packings containing up to N=8192 units. While the disc packings on S 2 converge continuously, but very slowly, to the regular triangular lattice, the sphere packings on S 3 converge to the disordered frustrated Bernal's packing, of volume fraction $c\simeq 0.645$, in the ( $N=\infty$) flat space limit. In the S 3 case, the volume fraction exhibits maxima for particular values of N, for which the corresponding packings have a narrower histogram for the number of edges of Voronoi polyhedra faces.

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