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 $a$.

9 pages, latex, 4 eps figures included

Cited by in corpus (29)

• Percolation and jamming in random sequential adsorption of linear segments on square lattice
• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• Random sequential adsorption of partially oriented linear $k$-mers on square lattice
• Percolation of the aligned dimers on a square lattice
• Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice
• Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice
• Jamming and percolation in random sequential adsorption of straight rigid rods on a two-dimensional triangular lattice
• Dimer percolation and jamming on simple cubic lattice
• Jammed systems of oriented needles always percolate on square lattices
• On the fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media
• Jamming and percolation in generalized models of random sequential adsorption of linear $k$-mers on a square lattice
• Monte Carlo Simulation of Evaporation Driven Self-Assembly in Suspension of Colloidal Rods
• Electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice
• Diffusion-driven self-assembly of rod-like particles: Monte Carlo simulation on a square lattice
• Jamming and percolation of $k^3$-mers on simple cubic lattices
• Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice
• Jamming and percolation properties of random sequential adsorption with relaxation
• Random sequential adsorption on Euclidean, fractal and random lattices
• Jamming and percolation of $k^2$-mers on simple cubic lattices
• Percolation phase transition by removal of $k^2$-mers from fully occupied lattices
• Jamming and percolation of parallel squares in single-cluster growth model
• Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line
• Interplay between thermal percolation and jamming upon dimer adsorption on binary alloys
• Barrier properties of k-mer packings
• Model of correlated sequential adsorption of colloidal particles
• Effect of shape anisotropy on percolation of aligned and overlapping objects on lattices
• Exponential and power law distribution of mass clusters in a (magnetic-like) deposition model of elongated grains in 2D piles
• Jammed systems of oriented dimers always percolate on hypercubic lattices
• Characterization of domain formation during random sequential adsorption of stiff linear $k$-mers onto a square lattice