Chattopadhyay, AK, Kundu, B, Nath, SK orcid.org/0000-0001-8922-1341 et al. (1 more author) (2022) Transmissibility in Interactive Nanocomposite Diffusion: The Nonlinear Double-Diffusion Model. Frontiers in Applied Mathematics and Statistics, 8. 852040. ISSN 2297-4687
Abstract
Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical physics where dislocation patterning of platstically deformed metals and mass transport in nanocomposite materials with high diffusivity paths such as dislocation and grain boundaries, have been traditionally analyzed using the paradigmatic Walgraef-Aifantis (W-A) double-diffusivity (D-D) model. A long standing challenge in these studies has been the inherent nonlinear correlation between the diffusivity paths, making it extremely difficult to analyze their interdependence. Here, we present a novel method of approximating a closed form solution of the ensemble averaged density profiles and correlation statistics of coupled dynamical systems, drawing from a technique used in mathematical biology to calculate a quantity called the basic reproduction number R0, which is the average number of secondary infections generated from every infected. We show that the R0 formulation can be used to calculate the correlation between diffusivity paths, agreeing closely with the exact numerical solution of the D-D model. The method can be generically implemented to analyze other reaction-diffusion models.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 Chattopadhyay, Kundu, Nath and Aifantis. This is an open access article under the terms of the Creative Commons Attribution 4.0 International License (CC BY 4.0) (https://creativecommons.org/licenses/by/4.0/) |
Keywords: | double diffusion, reproduction number, autocorrelation, spatiotemporal correlation, Fick’s diffusion |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Biological Sciences (Leeds) > School of Biology (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 05 Sep 2022 14:33 |
Last Modified: | 05 Sep 2022 14:33 |
Status: | Published |
Publisher: | Frontiers Media |
Identification Number: | 10.3389/fams.2022.852040 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:189014 |