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arXiv · 1810.06800

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

M. G. Slutskii·L. Yu. Barash·Yu. Yu. Tarasevich
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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.

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M. G. Slutskii, L. Yu. Barash, Yu. Yu. Tarasevich. 2018-12-21. Percolation and jamming of random sequential adsorption samples of large linear $k$-mers on a square lattice. https://doi.org/10.1103/physreve.98.062130

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