Anomalous transport in cellular flows: The role of initial conditions and aging

Patrick Pöschke, Igor M. Sokolov, Alexander A. Nepomnyashchy, and Michael A. Zaks
Phys. Rev. E 94, 032128 – Published 23 September 2016

Abstract

We consider the diffusion-advection problem in two simple cellular flow models (often invoked as examples of subdiffusive tracer motion) and concentrate on the intermediate time range, in which the tracer motion indeed may show subdiffusion. We perform extensive numerical simulations of the systems under different initial conditions and show that the pure intermediate-time subdiffusion regime is only evident when the particles start at the border between different cells, i.e., at the separatrix, and is less pronounced or absent for other initial conditions. The motion moreover shows quite peculiar aging properties, which are also mirrored in the behavior of the time-averaged mean squared displacement for single trajectories. This kind of behavior is due to the complex motion of tracers trapped inside the cell and is absent in classical models based on continuous-time random walks with no dynamics in the trapped state.

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  • Received 12 July 2016

DOI:https://doi.org/10.1103/PhysRevE.94.032128

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Patrick Pöschke* and Igor M. Sokolov

  • Institute of Physics, Humboldt University of Berlin, D-12489 Berlin, Germany

Alexander A. Nepomnyashchy

  • Department of Mathematics, Technion—Israel Institute of Technology, Haifa 32000, Israel

Michael A. Zaks

  • Institute of Physics and Astronomy, University of Potsdam, D-14469 Potsdam, Germany

  • *poeschke@physik.hu-berlin.de

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Issue

Vol. 94, Iss. 3 — September 2016

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