A new universality for random sequential deposition of needles

Abstract:

Percolation and jamming phenomena are investigated for random sequential deposition of rectangular needles on d=2 square lattices. Associated thresholds P_c ^perc and P_c ^jam are determined for various needle sizes. Their ratios P_c ^perc /P_c ^jam are found to be a constant $0.62 \pm 0.01$ for all sizes. In addition the ratio of jamming thresholds for respectively square blocks and needles is also found to be a constant $0.79 \pm 0.01$. 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.