Chattopadhyay, Amit K. and Kundu, Bidisha and Nath, Sujit Kumar and Aifantis, Elias C. (2022) Transmissibility in Interactive Nanocomposite Diffusion: The Nonlinear Double-Diffusion Model. Frontiers in Applied Mathematics and Statistics, 8. ISSN 2297-4687
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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.
Item Type: | Article |
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Subjects: | Science Repository > Mathematical Science |
Depositing User: | Managing Editor |
Date Deposited: | 16 Feb 2023 06:49 |
Last Modified: | 17 Jul 2024 07:18 |
URI: | http://research.manuscritpub.com/id/eprint/801 |