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Percolation thresholds of 3D all-sided percolation clusters in non-cubic domains

Katunin A.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

63--69

The critical 3D all-sided percolation clusters in aL×L×L and aL×aL×L threedimensional domains with a side length L and an aspect ratio a obtained from continuous percolation problem were analysed in this paper. The simulations of continuous percolation were performed in parallelepiped domains starting from a = 1 and ending at a = 10 using the Monte Carlo algorithm. The resulting percolation thresholds for the simulated domains and percolation clusters as well as variability of number of cells in a domain and in a percolation cluster with variation of a were analysed. The obtained results are useful for evaluation of a content of electrically conducting particles in the dielectric matrix of a composite developed for aircraft lightning strike protection purposes.