https://doi.org/10.1007/s100510051047
A new universality for random sequential deposition of needles
1
GRASP, Institut de Physique B5, Université de Liège, 4000 Liège, Belgium
2
Laboratoire des Milieux Désordonnés et Hétérogènes, Tour 13, Case 86, 4 place Jussieu, 75252
Paris Cedex 05, France
3
2 rue Kockelberg, 9252 Diekirch, Luxembourg
Received:
27
January
2000
Revised:
2
February
2000
Published online: 15 April 2000
Percolation and jamming phenomena are investigated for random sequential
deposition of rectangular needles on d=2 square lattices. Associated
thresholds 
and 
are determined for various needle
sizes. Their ratios 
are found to be a constant
for all sizes. In addition the ratio of jamming thresholds
for respectively square blocks and needles is also found to be a constant
. These constants exhibit some universal connexion in the
geometry of jamming and percolation for both anisotropic shapes (needles
versus square lattices) and isotropic shapes (square blocks on square
lattices). A universal empirical law is proposed for all three thresholds
as a function of a.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.60.Ak – Renormalization-group, fractal, and percolation studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
