Time-integral iteration method for two-dimensional anomalous transport

J. E. Maggs and G. J. Morales
Phys. Rev. E 106, 045201 – Published 4 October 2022

Abstract

A methodology is developed to describe time-dependent phenomena associated with nonlocal transport in complex, two-dimensional geometries. It is an extension of the ‘‘iterative method” introduced previously to solve steady-state transport problems [Maggs and Morales, Phys. Rev. E 99, 013307 (2019)], and it is based on the ‘‘jumping particle” concepts associated with the continuous-time random walk (CTRW) model. The method presented explicitly evaluates the time integral contained in the CTRW master equation. A modified version of the Mittag-Leffler function is used for the waiting-time probability distributions to incorporate memory effects. Calculations of the propagation of ‘‘anomalous transport waves” in various systems, with and without memory, illustrate the technique.

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  • Received 24 July 2022
  • Accepted 12 September 2022

DOI:https://doi.org/10.1103/PhysRevE.106.045201

©2022 American Physical Society

Physics Subject Headings (PhySH)

Plasma Physics

Authors & Affiliations

J. E. Maggs and G. J. Morales

  • Department of Physics and Astronomy, University of California, Los Angeles, California 90025, USA

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Vol. 106, Iss. 4 — October 2022

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