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Anomalous Diffusion on Percolating Clusters
Abstract
The mean square distance reached after $t$ random-walk steps on a percolating cluster is shown to behave as ${t}^{\frac{2}{(2+\ensuremath{\theta})}}$ (instead of $t$) for short times (for which the cluster is seen to be self-similar). The exponent $\ensuremath{\theta}$ is related to that describing the dc conductivity near percolation. Averaging over all clusters yields the ac conductivity and dielectric constant near percolation in the high-frequency limit, when the polarization of the medium is unimportant.
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Citations
Cited by
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162
Physics of inhomogeneous inorganic materials
Nan, C.-W. (1993) · Progress in Materials Science · doi:10.1016/0079-6425(93)90004-5 · Cited by 1,050
Fundamental questions relating to ion conduction in disordered solids
Dyre, J. C., Maass, P., Roling, B., & Sidebottom, D. L. (2009) · Reports on Progress in Physics · doi:10.1088/0034-4885/72/4/046501 · Cited by 432
Self-diffusion of a molecule in porous Vycor glass
Dozier, W. D., Drake, J. M., & Klafter, J. (1986) · Physical Review Letters · doi:10.1103/physrevlett.56.197 · Cited by 166
Metadata
- Authors
- Gefen, Y., Aharony, A., & Alexander, S.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1983-01-03
- Volume
- 50
- Issue
- 1
- Pages
- 77-80
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2029093109
- Cited by
- 1,029
- References
- 0
- FWCI
- 49.12
- Type
- journal article
- Language
- en
- Open access
- closed
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- Gefen, Y., Aharony, A., & Alexander, S. (1983). Anomalous Diffusion on Percolating Clusters. Physical Review Letters. https://doi.org/10.1103/physrevlett.50.77
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