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Diffusion in disordered media
Abstract
Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.
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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
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Song, C., Qu, Z., Blumm, N., & Barabási, A.-L. (2010) · Science · doi:10.1126/science.1177170 · Cited by 3,234
Quantifying brain microstructure with diffusion MRI: Theory and parameter estimation
Novikov, D. S., Fieremans, E., Jespersen, S. N., & Kiselev, V. G. (2019) · NMR in Biomedicine · doi:10.1002/nbm.3998 · Cited by 581
Metadata
- Authors
- Havlin, S., & Ben-Avraham, D.
- Venue
- Advances in Physics
- Publisher
- Informa UK Limited
- Published
- 2002-01
- Volume
- 51
- Issue
- 1
- Pages
- 187-292
- ISSN
- 0001-8732 (ISSN-L)
- 1460-6976
- OpenAlex
- W2100376401
- Cited by
- 902
- References
- 0
- FWCI
- 17.86
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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