Stability of two-dimensional packings of disks built with ballistic deposition

Rémi Jullien; Paul Meakin

doi:doi:10.1051/jp1:1991201

Numéro		J. Phys. I France Volume 1, Numéro 9, September 1991


Page(s)		1263 - 1277
DOI		https://doi.org/10.1051/jp1:1991201

DOI: 10.1051/jp1:1991201
J. Phys. I France 1 (1991) 1263-1277

Stability of two-dimensional packings of disks built with ballistic deposition

Rémi Jullien¹ and Paul Meakin²

¹ Bât. 510, Physique des Solides, Université Paris-Sud, Centre d'Orsay, 91405 Orsay, France
² Central Research and Development Departement, E.I. du Pont de Nemours and Company, Wilmington, DE 19880-0356, U.S.A.

(Received 6 March 1991, accepted in final form 23 April 1991)

Abstract
Two-dimensional packings of identical hard disks of unit diameter are generated using a ballistic model with complete restructuring and starting from a first row made with disks horizontally regularly spaced by $a=2\sin \psi$ , with $\psi$ ranging from $\frac{\pi}{6}$ to $\frac{\pi}{3}$ . The stability with respect to random vertical displacements for the disks in the first row was studied. A transition from a pseudo-regular array without defects to a random structure with defects is observed when the amount of disorder $\delta$ (amplitude of the vertical displacements) passes a critical value $\delta_{\rm c}$ and a phase diagram is measured in the $(\psi,\delta)$ plane which can be understood in terms of simple geometrical arguments. The random structure found for $\delta>\delta_{\rm c}$ does not depend too much on $\psi$ and strongly ressembles to the one obtained when starting from a horizontal basal line: the density of defects decreases as a power law with height and the large-height defect-free structure is characterized by a broad distribution of bond angles.