What is it about?
The original linear Double-Diffusivity (D-D) model by Aifantis is a paradigm for understanding mass transport in inhomogeneous media. The present article offers the first closed-form solution of the nonlinear D-D model that was previously thought impossible. This was realised through a unique marriage of the forward Fourier Transform with the Laplace Transform to arrive at an integral formulation that has wide-ranging applications in biology, finance, and material science.
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Why is it important?
Our findings show that nonlinear problems involving multiple diffusing species or phenomena, that do not admit of exact analytical solution, can now be formulated to solve cross-disciplinary modelling problems. We verify this by applying a model of material mechanics to solve an infection kinetics problem involving COVID-19 data.
Perspectives
This is a prime example of successful interdisciplinary cohabitation between Mathematics and Mechanical Engineering. It had been a pleasure to collaborate with the illustrious Prof Aifantis.
Amit Chattopadhyay
Aston University
Read the Original
This page is a summary of: Applications of regime-switching in the nonlinear double-diffusivity (D-D) model, Journal of Applied Physics, January 2024, American Institute of Physics,
DOI: 10.1063/5.0188904.
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