Time-integral iteration method for two-dimensional anomalous transport.
basic_science · Level V
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- Record sourced from PubMed, PMID 36397469.
- Also identified by DOI 10.1103/PhysRevE.106.045201.
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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)10.1103/PhysRevE.99.013307], 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.