A simple diffusion model showing anomalous scaling

Journal Article · Fri Aug 15 00:00:00 EDT 2008 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.2969429· OSTI ID:21120505

Rowlands, G ^[1]; Sprott, J C ^[2]

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1. Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2. Department of Physics, University of Wisconsin, Madison, Wisconsin 53706 (United States)

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.

• OSTI ID: 21120505
• Journal Information: Physics of Plasmas, Vol. 15, Issue 8; Other Information: DOI: 10.1063/1.2969429; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
CONVECTION
DIFFUSION
MAPS
SPACE