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Stochastic pathway to anomalous diffusion
Abstract
We present an appraisal of differential-equation models for anomalous diffusion, in which the time evolution of the mean-square displacement is 〈${r}^{2}$(t)〉\ensuremath{\sim}${t}^{\ensuremath{\gamma}}$ with \ensuremath{\gamma}\ensuremath{\ne}1. By comparison, continuous-time random walks lead via generalized master equations to an integro-differential picture. Using L\'evy walks and a kernel which couples time and space, we obtain a generalized picture for anomalous transport, which provides a unified framework both for dispersive (\ensuremath{\gamma}<1) and for enhanced diffusion (\ensuremath{\gamma}>1).
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Citations
Cited by
Metzler, R., Jeon, J.-H., Cherstvy, A. G., & Barkai, E. (2014) · Phys. Chem. Chem. Phys. · doi:10.1039/c4cp03465a · Cited by 1,765
Vermeersch, B., Mohammed, A. M. S., Pernot, G., Koh, Y. R., & Shakouri, A. (2015) · Physical Review B · doi:10.1103/physrevb.91.085203 · Cited by 78
Metadata
- Authors
- Klafter, J., Blumen, A., & Shlesinger, M. F.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1987-04-01
- Volume
- 35
- Issue
- 7
- Pages
- 3081-3085
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2093067381
- Cited by
- 719
- References
- 0
- FWCI
- 9.09
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Stochastic pathway to anomalous diffusion. https://app.cochat.ai/papers/10.1103/physreva.35.3081
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- Klafter, J., Blumen, A., & Shlesinger, M. F. (1987). Stochastic pathway to anomalous diffusion. Physical Review A. https://doi.org/10.1103/physreva.35.3081
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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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