Percolation thresholds on elongated lattices

S. J. Marrink; Mark A. Knackstedt

doi:10.1088/0305-4470/32/44/101

Percolation thresholds on elongated lattices

S. J. Marrink^*, Mark A. Knackstedt

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of L^d-1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically.

Original language	English
Pages (from-to)	L461-L466
Journal	Journal of Physics A: Mathematical and General
Volume	32
Issue number	44
DOIs	https://doi.org/10.1088/0305-4470/32/44/101
Publication status	Published - 5 Nov 1999

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10.1088/0305-4470/32/44/101

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title = "Percolation thresholds on elongated lattices",

abstract = "We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of Ld-1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically.",

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AU - Knackstedt, Mark A.

PY - 1999/11/5

Y1 - 1999/11/5

N2 - We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of Ld-1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically.

AB - We investigate the percolation thresholds of both random and invasion percolation in two and three dimensions on elongated lattices; lattices with a geometry of Ld-1 × nL in d dimensions, where n denotes the aspect ratio of the lattice. Scaling laws for the threshold and spanning cluster density for random percolation are derived and simulation confirms the behaviour. A direct relationship between thresholds obtained for random percolation and invasion percolation is given and verified numerically.

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U2 - 10.1088/0305-4470/32/44/101

DO - 10.1088/0305-4470/32/44/101

M3 - Article

SN - 0305-4470

VL - 32

SP - L461-L466

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 44

ER -

Percolation thresholds on elongated lattices

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