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Percolation processes: I. Crystals and mazes
Abstract
The paper studies, in a general way, how the random properties of a ‘medium’ influence the percolation of a ‘fluid’ through it. The treatment diifers from conventional diffusion theory, in which it is the random properties of the fluid that matter. Fluid and medium bear general interpretations: for example, solute diffusing through solvent, electrons migrating over an atomic lattice, molecules penetrating a porous solid, disease infecting a community, etc.
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Citations
Cited by
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Kirkpatrick, S. (1973) · Reviews of Modern Physics · doi:10.1103/revmodphys.45.574 · Cited by 5,260
Stochastic geometry and random graphs for the analysis and design of wireless networks
Haenggi, M., Andrews, J. G., Baccelli, F., Dousse, O., & Franceschetti, M. (2009) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2009.090902 · Cited by 1,719
Belitz, D., & Kirkpatrick, T. R. (1994) · Reviews of Modern Physics · doi:10.1103/revmodphys.66.261 · Cited by 991
Metadata
- Authors
- Broadbent, S. R., & Hammersley, J. M.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1957-07
- Volume
- 53
- Issue
- 3
- Pages
- 629-641
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W1610677200
- Cited by
- 2,032
- References
- 0
- FWCI
- 3.39
- Type
- journal article
- Language
- en
- Open access
- closed
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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Percolation processes: I. Crystals and mazes. https://app.cochat.ai/papers/10.1017/s0305004100032680
- The paper
- Broadbent, S. R., & Hammersley, J. M. (1957). Percolation processes: I. Crystals and mazes. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100032680
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
