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Cited by 1,031Theoretical and Computational PhysicsStochastic processes and statistical mechanicsComplex Network Analysis Techniques

Percolation and conductivity: A computer study. I

Pike, G. E., Seager, C. H.·1974·Physical Review B
DOI 10.1103/physrevb.10.1421
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Abstract

In this paper and its sequel we consider the relation between various conductivity problems and their associated percolation models. The emphasis of this paper is on the methods of solving percolation problems. Toward that end we define the percolation problem and propose a classification for several types of models. This classification scheme is useful for regular and random lattices and shows the connection between bond and site percolation models. With the aid of a large computer we have used Monte Carlo techniques to solve many random-lattice percolation models in two and three dimensions. These models illustrate the effects of hard-core interactions between sites, of deterministic and probabilistic bonding parameters, and of changing the functional form of the bonding criterion. The random-lattice solutions are used to examine the critical volume fraction concept and the critical number of bonds per site (${B}_{c}$) concept. These concepts have been previously proposed as methods of obtaining solutions to percolation problems. We find that, subject to several conditions, these concepts may be used for approximate solutions.

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Crossref · 10.1103/physrevb.10.1421

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  • According to percolation theory, nanowires, nanotubes, or nanofibers are more effective in forming conductive pathways compared to nanoparticles.

    “According to the percolation theory, [10,11] nanowires, nanotubes, or nanofibers are more effective in forming conductive pathways compared to nanoparticles.”

    From Nanomaterial-Enabled Wearable Sensors for Healthcare (2018) · cites this paper as [10]

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Authors
Pike, G. E., & Seager, C. H.
Affiliations
Sandia National Laboratories (US)
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
1974-08-15
Volume
10
Issue
4
Pages
1421-1434
ISSN
0556-2805 (ISSN-L)
DOI
10.1103/physrevb.10.1421
OpenAlex
W2043490978
Cited by
1,031
References
24
Citations by year
2026: 14 · 2025: 17 · 2024: 15 · 2023: 14 · 2022: 11 · 2021: 20 · 2020: 18 · 2019: 29 · 2018: 26 · 2017: 29 · 2016: 39 · 2015: 41 · 2014: 23 · 2013: 39 · 2012: 38
FWCI
9.24
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. B, Solid state (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
  • Physical Sciences › Mathematics › Mathematical Physics › Stochastic processes and statistical mechanics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
Keywords
percolation, electrical conductivity, random lattices, bond percolation, site percolation, critical volume fraction, hard-core interactions, Monte Carlo simulation, two-dimensional percolation, three-dimensional percolation

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