| Operator Lévy motion and multiscaling anomalous diffusion. | |
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MedLine Citation:
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PMID: 11308473 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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The long-term limit motions of individual heavy-tailed (power-law) particle jumps that characterize anomalous diffusion may have different scaling rates in different directions. Operator stable motions [Y(t):t> or =0] are limits of d-dimensional random jumps that are scale-invariant according to c(H)Y(t)=Y(ct), where H is a dxd matrix. The eigenvalues of the matrix have real parts 1/alpha(j), with each positive alpha(j)< or =2. In each of the j principle directions, the random motion has a different Fickian or super-Fickian diffusion (dispersion) rate proportional to t(1/alpha(j)). These motions have a governing equation with a spatial dispersion operator that is a mixture of fractional derivatives of different order in different directions. Subsets of the generalized fractional operator include (i) a fractional Laplacian with a single order alpha and a general directional mixing measure m(straight theta); and (ii) a fractional Laplacian with uniform mixing measure (the Riesz potential). The motivation for the generalized dispersion is the observation that tracers in natural aquifers scale at different (super-Fickian) rates in the directions parallel and perpendicular to mean flow. |
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Authors:
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M M Meerschaert; D A Benson; B Baeumer |
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Publication Detail:
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Type: Journal Article Date: 2001-01-25 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 63 ISSN: 1539-3755 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2001 Feb |
Date Detail:
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Created Date: 2001-04-19 Completed Date: 2004-02-23 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 021112 Citation Subset: - |
Affiliation:
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Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084, USA. mcubed@unr.edu |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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