Abstract
The linear double-diffusivity (D-D) model of Aifantis, comprising two coupled
Fick-type partial differential equations and a mass exchange term connecting the
diffusivities, is a paradigm in modeling mass transport in inhomogeneous media,
e.g. fissures or fractures. Uncoupling of these equations led to a higher order Partial Differential Equation (PDE) that reproduced the non-classical transport terms, analyzed independently through Barenblatt’s pseudoparabolic equation and the Cahn-Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction-diffusion (R-D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models.
Fick-type partial differential equations and a mass exchange term connecting the
diffusivities, is a paradigm in modeling mass transport in inhomogeneous media,
e.g. fissures or fractures. Uncoupling of these equations led to a higher order Partial Differential Equation (PDE) that reproduced the non-classical transport terms, analyzed independently through Barenblatt’s pseudoparabolic equation and the Cahn-Hilliard spinodal decomposition equation. In the present article, we study transport in a nonlinearly coupled D-D model and determine the regime-switching of the associated diffusive processes using a revised formulation of the celebrated Lux method that combines forward Fourier transform with a Laplace transform followed by an Inverse Fourier transform of the governing reaction-diffusion (R-D) equations. This new formulation has key application possibilities in a wide range of non-equilibrium biological and financial systems by approximating closed-form analytical solutions of nonlinear models.
| Original language | English |
|---|---|
| Article number | 024701 |
| Journal | Journal of Applied Physics |
| Volume | 135 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 10 Jan 2024 |
Bibliographical note
Copyright © 2024 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.The following article appeared in Amit K. Chattopadhyay, Elias C. Aifantis; Applications of regime-switching in the nonlinear double-diffusivity (D-D) model. J. Appl. Phys. 14 January 2024; 135 (2): 024701 and may be found at https://doi.org/10.1063/5.0188904