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A Huygens principle for diffusion and anomalous diffusion in spatially extended systems
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Gottwald, G. A. and Melbourne, Ian (2013) A Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Proceedings of the National Academy of Sciences of the United States of America, Volume 110 (Number 21). pp. 8411-8416. doi:10.1073/pnas.1217926110 ISSN 0027-8424.
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Official URL: http://dx.doi.org/10.1073/pnas.1217926110
Abstract
We present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behavior (Brownian motion with drift) and weak chaos leads to superdiffusive behavior (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
| Journal or Publication Title: | Proceedings of the National Academy of Sciences of the United States of America | ||||
| Publisher: | National Academy of Sciences | ||||
| ISSN: | 0027-8424 | ||||
| Official Date: | 2013 | ||||
| Dates: |
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| Volume: | Volume 110 | ||||
| Number: | Number 21 | ||||
| Page Range: | pp. 8411-8416 | ||||
| DOI: | 10.1073/pnas.1217926110 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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