AUTHOR=Chattopadhyay Amit K. , Kundu Bidisha , Nath Sujit Kumar , Aifantis Elias C. 

TITLE=Transmissibility in Interactive Nanocomposite Diffusion: The Nonlinear Double-Diffusion Model

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 8 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.852040

DOI=10.3389/fams.2022.852040

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 [1, 2, 3] 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 [4, 5, 6, 7, 8, 9]. 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 R_0, which is the average number of secondary infections generated from every infected. We show that the R_0 formulation can be used to calculate the correlation between diffusivity paths, agreeing closely with the exact numerical solution of the D-D model.