Szczegóły publikacji
Opis bibliograficzny
Site percolation thresholds on triangular lattice with complex neighborhoods / Krzysztof MALARZ // Chaos : an Interdisciplinary Journal of Nonlinear Science ; ISSN 1054-1500. — 2020 — vol. 30, s. 123123-1-123123-6. — Bibliogr. s. 123123-6, Abstr. — Publikacja dostępna online od: 2020-12-09. - Publikacja dostępna w Internecie http://aip.scitation.org/doi/pdf/10.1063/5.0022336
Autor
Dane bibliometryczne
| ID BaDAP | 131538 |
|---|---|
| Data dodania do BaDAP | 2020-12-16 |
| DOI | 10.1063/5.0022336 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Chaos |
Abstract
We determine thresholds pc for random site percolation on a triangular lattice for neighborhoods containing nearest (NN), next-nearest (2NN), next-next-nearest (3NN), next-next-next-nearest (4NN), and next-next-next-next-nearest (5NN) neighbors, and their combinations forming regular hexagons (3NN+2NN+NN, 5NN+4NN+NN, 5NN+4NN+3NN+2NN, and 5NN+4NN+3NN+2NN+NN). We use a fast Monte Carlo algorithm, by Newman and Ziff [Phys. Rev. E 64, 016706 (2001)], for obtaining the dependence of the largest cluster size on occupation probability. The method is combined with a method, by Bastas et al. [Phys. Rev. E 90, 062101 (2014)], for estimating thresholds from low statistics data. The estimated values of percolation thresholds are pc(4NN)=0.192410(43), pc(3NN+2NN)=0.232008(38), pc(5NN+4NN)=0.140286(5), pc(3NN+2NN+NN)=0.215484(19), pc(5NN+4NN+NN)=0.131792(58), pc(5NN+4NN+3NN+2NN)=0.117579(41), and pc(5NN+4NN+3NN+2NN+NN)=0.115847(21). The method is tested on the standard case of site percolation on the triangular lattice, where pc(NN)=pc(2NN)=pc(3NN)=pc(5NN)=12 is recovered with five digits accuracy pc(NN)=0.500029(46) by averaging over one thousand lattice realizations only. The percolation theory—introduced in the middle 50s of twentieth century—was recently applied in various fields of science ranging from agriculture via studies of polymer composites, materials science, oil and gas exploration, quantifying urban areas to transportation networks. In most cases only sites in the 1st coordination zone are included to site's neighborhood. There are some exceptions, however, where people consider neighborhoods consisting of several coordination zones, i.e. next-nearest neighbors, next-next-nearest neighbors, etc. on hypercubic, cubic or square lattices. Much less is known on percolation threshold values for complex neighborhoods on other low-dimensional lattices. In this paper we try to fill this gap by estimating values of the percolation thresholds for several complex neighborhoods on triangular lattice. To that end we use a fast algorithm for percolation by Newman and Ziff and a low sampling technique by Bastas et al. We determine percolation thresholds for random site percolation with several neighborhoods containing the nearest neighbors, the next-nearest neighbors, the next-next-nearest neighbors, the next-next-next-nearest neighbors and the next-next-next-next-nearest neighbors. Percolation thresholds for lattices with complex neighborhoods have been very recently successfully applied for many problems on square and cubic lattices. We believe that the results presented in this paper can also be applied to practical problems. The percolation threshold values obtained in this work may also be helpful in searching for universal formulas for percolation thresholds in the spirit of some recent attempts.
