Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice

Abstract

The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and memory usage has been developed and applied to the model involving large linear $k$-mers on a square lattice with periodic boundary conditions. We have obtained the percolation thresholds and jamming concentrations for lengths of $k$-mers up to $2^{17}$. New large $k$ regime of the percolation threshold behavior has been identified. The structure of the percolating and jamming states has been investigated. The theorem of G.~Kondrat, Z.~Koza, and P.~Brzeski [Phys. Rev. E 96, 022154 (2017)] has been generalized to the case of periodic boundary conditions. We have proved that any cluster at jamming is percolating cluster and that percolation occurs before jamming.

8 pages, 9 figures, 1 table, submitted to Phys. Rev. E

References in corpus (3)

• Percolation of linear $k$-mers on square lattice: from isotropic through partially ordered to completely aligned state
• Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice
• Jammed systems of oriented needles always percolate on square lattices

Cited by in corpus (13)

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• 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
• Two-dimensional systems of elongated particles: From diluted to dense
• Jamming and percolation of dimers in restricted-valence random sequential adsorption
• Bond percolation between $k$ separated points on a square lattice
• Percolation of aligned rigid rods on two-dimensional triangular lattices
• Standard and inverse site percolation of straight rigid rods on triangular lattices: Isotropic and nematic deposition/removal
• Random sequential adsorption of aligned rectangles with two discrete orientations: Finite-size scaling effects
• 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
• Percolation in semicontinuum geometries