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

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 inv...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Slutskii, M G, L Yu Barash, Yu Yu Tarasevich
Format: Article
Language:English
Subjects:
Adsorption
Boundary conditions
Clusters
Computer simulation
Jamming
Mathematical models
Percolation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.06800