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arXiv · 1706.02550

Jammed systems of oriented needles always percolate on square lattices

Grzegorz Kondrat·Zbigniew Koza·Piotr Brzeski
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Abstract

Random sequential adsorption (RSA) is a standard method of modeling adsorption of large molecules at the liquid-solid interface. Several studies have recently conjectured that in the RSA of rectangular needles, or $k$-mers, on a square lattice the percolation is impossible if the needles are sufficiently long ($k$ of order of several thousand). We refute these claims and present a strict proof that in any jammed configuration of nonoverlapping, fixed-length, horizontal or vertical needles on a square lattice, all clusters are percolating clusters.

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Grzegorz Kondrat, Zbigniew Koza, Piotr Brzeski. 2017-06-08. Jammed systems of oriented needles always percolate on square lattices. https://doi.org/10.1103/physreve.96.022154

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