Continuous time random walks in periodic systems: fluid limit and fractional differential equations on the circle

Calvo, Iván; Carreras, Benjamín A.; Sánchez, Raúl; Van Milligen, Boudewijn Ph.

Continuous time random walks in periodic systems: fluid limit and fractional differential equations on the circle

Author(s): Calvo, Iván; Carreras, Benjamín A.; Sánchez, Raúl; Van Milligen, Boudewijn Ph.

Publisher: Institute of Physics

Issued date: 2007-11-09

Citation: J. Phys. A: Math. Theor. 40, 13511 (2009)
Journal of Physics A: Mathematical and Theoretical, 2009, vol. 40, n. 45, id 13511

ISSN: 1751-8113

DOI: 10.1088/1751-8113/40/45/002

Sponsor: Research sponsored by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2004-04319. Part of this research was sponsored by the Laboratory Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy under contract number DE-AC05-00OR22725.

Review: PeerReviewed

Publisher version: http://dx.doi.org/10.1088/1751-8113/40/45/002

Keywords: [PACS] Random walks and Levy flights , [PACS] Stochastic processes , [PACS] Classical transport , [PACS] Stochastic analysis methods (Fokker-Planck, Langevin, etc.)

URI: http://hdl.handle.net/10016/8898

Rights: © Institute of Physics

Abstract:

In this paper, 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 Lévy flights are allowed. Then, we work out the fluid limit equation [+]