New algorithm to test percolation conditions within the Newman–Ziff algorithm

I. V. Tronin ()
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I. V. Tronin: Molecular Physics Department, National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409, Russian Federation

International Journal of Modern Physics C (IJMPC), 2014, vol. 25, issue 11, 1-11

Abstract: A new algorithm to test percolation conditions for the solution of percolation problems on a lattice and continuum percolation for spaces of an arbitrary dimension has been proposed within the Newman–Ziff algorithm. The algorithm is based on the use of bitwise operators and does not reduce the efficiency of the operation of the Newman–Ziff algorithm as a whole. This algorithm makes it possible to verify the existence of both clusters touching boundaries at an arbitrary point and single-loop clusters continuously connecting the opposite boundaries in a percolating system with periodic boundary conditions. The existence of a cluster touching the boundaries of the system at an arbitrary point for each direction, the formation of a one-loop cluster, and the formation of a cluster with an arbitrary number of loops on a torus can be identified in one calculation by combining the proposed algorithm with the known approaches for the identification of the existence of a percolation cluster. The operation time of the proposed algorithm is linear in the number of objects in the system.

Keywords: Percolation theory; numerical algorithms; continuum percolation; lattice percolation; 02.70.-c; 05.10.Ln; 05.70.Jk (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0129183114500648

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