Continuous Time Random Walks in periodic systems: fluid limit and fractional differential equations on the circle

Journal Article · Mon Jan 01 00:00:00 EST 2007 · Journal of Physics A-Mathematical and Theoretical

DOI:https://doi.org/10.1088/1751-8113/40/45/002· OSTI ID:932106

Calvo, Ivan ^[1]; Carreras, Benjamin A ^[2]; Sanchez, Raul ^[2]; van Milligen, B. Ph. ^[3]

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1. CIEMAT, Madrid
2. ORNL
3. Asociacion EURATOM-CIEMAT

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out the fluid limit equation, formulated in terms of the periodic version of the fractional Riemann-Liouville operators, for which we provide explicit expressions. Finally, we compute the propagator in some simple cases. The analysis presented herein should be relevant when investigating anomalous transport phenomena in systems with periodic dimensions.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 932106
• Journal Information: Journal of Physics A-Mathematical and Theoretical, Vol. 40, Issue 11
• Country of Publication: United States
• Language: English

Related Subjects

continuous-time random walks
fractional transport
anomalous transport
fluid limits