Time-integral iteration method for two-dimensional anomalous transport
- 4 October 2022
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 106 (4), 045201
- https://doi.org/10.1103/physreve.106.045201
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.This publication has 27 references indexed in Scilit:
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