Applications of Regime-switching in the Nonlinear Double-Diffusivity (D-D) Model


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.

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Divisions: College of Engineering & Physical Sciences > School of Computer Science and Digital Technologies > Applied Mathematics & Data Science
College of Engineering & Physical Sciences > School of Computer Science and Digital Technologies
College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > Aston Fluids Group
College of Engineering & Physical Sciences > Aston Centre for Artifical Intelligence Research and Application
Funding Information: The authors gratefully acknowledge partial financial support from the H2020-MSCA-RISE-2016 program, Grant No. 734485, entitled “Fracture Across Scales and Materials, Processes and Disciplines (FRAMED).”
Additional Information: 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
Publication ISSN: 1089-7550
Last Modified: 17 May 2024 07:22
Date Deposited: 12 Jan 2024 11:45
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PURE Output Type: Article
Published Date: 2024-01-10
Accepted Date: 2023-12-25
Authors: Chattopadhyay, Amit (ORCID Profile 0000-0001-5499-6008)
Aifantis, Elias



Version: Accepted Version

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