Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved intersectoral mapping of techniques. Material mechanics has benefited hugely from such interpolations from mathematical physics where dislocation patterning of plastically 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.
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Mass Transport in Confined Micro Geometry in Reciprocating Paddle Plating Cell by Numerical Simulation and Neural Network Analysis
The mass transport in confined geometry in a paddle plating cell is studied using numerical simulation with an attempt to extrapolate an explicit correlation to understand the transport physics and to predict the electrodeposition rate of metal microstructures. A moving boundary in conjunction with mapped mesh is used to allow the reciprocating movement of the flow. A correlation is obtained based on a generalized additive model using multivariant linear regression. Neural networks are also used to analyze the efficacy of such correlation and to determine the descriptor characterizing the error in prediction. A two-step convectional mass transport process, one in the bulk electrolyte outside the patterns and the other inside the micro-trenches, is demonstrated to better describe the overall transport physics and improve the correlation.
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- Award ID(s):
- 1941820
- PAR ID:
- 10595965
- Publisher / Repository:
- The Electrochemical Society
- Date Published:
- Journal Name:
- Journal of The Electrochemical Society
- Volume:
- 171
- Issue:
- 9
- ISSN:
- 0013-4651
- Page Range / eLocation ID:
- 092507
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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