A simple diffusion model showing anomalous scaling
Abstract
A number of iterated maps and one flow, which show chaotic behavior, have been studied numerically and their time evolution expressed in terms of higher-order moments M{sub m}(t). All the cases show anomalous behavior with M{sub m}(t){approx}t{sup g(m)}, with g(m){ne}{alpha}m. A simple analytic treatment is given based on an effective diffusion that is dependent on both space and time. This leads to a form for g(m)/m=a-b/m, which is in good agreement with numerical results. This behavior is attributed to the presence of convective motion superimposed on the background diffusion, and hence this behavior is expected in a wide variety of maps and flows.
- Authors:
-
- Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
- Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)
- Publication Date:
- OSTI Identifier:
- 21120505
- Resource Type:
- Journal Article
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 15; Journal Issue: 8; Other Information: DOI: 10.1063/1.2969429; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; CONVECTION; DIFFUSION; MAPS; SPACE
Citation Formats
Rowlands, G, and Sprott, J C. A simple diffusion model showing anomalous scaling. United States: N. p., 2008.
Web. doi:10.1063/1.2969429.
Rowlands, G, & Sprott, J C. A simple diffusion model showing anomalous scaling. United States. https://doi.org/10.1063/1.2969429
Rowlands, G, and Sprott, J C. 2008.
"A simple diffusion model showing anomalous scaling". United States. https://doi.org/10.1063/1.2969429.
@article{osti_21120505,
title = {A simple diffusion model showing anomalous scaling},
author = {Rowlands, G and Sprott, J C},
abstractNote = {A number of iterated maps and one flow, which show chaotic behavior, have been studied numerically and their time evolution expressed in terms of higher-order moments M{sub m}(t). All the cases show anomalous behavior with M{sub m}(t){approx}t{sup g(m)}, with g(m){ne}{alpha}m. A simple analytic treatment is given based on an effective diffusion that is dependent on both space and time. This leads to a form for g(m)/m=a-b/m, which is in good agreement with numerical results. This behavior is attributed to the presence of convective motion superimposed on the background diffusion, and hence this behavior is expected in a wide variety of maps and flows.},
doi = {10.1063/1.2969429},
url = {https://www.osti.gov/biblio/21120505},
journal = {Physics of Plasmas},
issn = {1070-664X},
number = 8,
volume = 15,
place = {United States},
year = {Fri Aug 15 00:00:00 EDT 2008},
month = {Fri Aug 15 00:00:00 EDT 2008}
}
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