Diffusion-Reaction Models of Denitrification in Soil Microsites

Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous Cu2+-(β-alanine) electrolyte are presented.

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Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness

Mathematics ◽

10.3390/math9030206 ◽

2021 ◽

Vol 9 (3) ◽

pp. 206

Author(s):

María Consuelo Casabán ◽

Rafael Company ◽

Lucas Jódar

Keyword(s):

Stochastic Process ◽

Finite Difference ◽

Coming Out ◽

Finite Difference Methods ◽

Diffusion Reaction ◽

Finite Difference Schemes ◽

Finite Degree ◽

Mean Square Stability ◽

Reaction Models ◽

Difference Methods

This paper deals with the search for reliable efficient finite difference methods for the numerical solution of random heterogeneous diffusion reaction models with a finite degree of randomness. Efficiency appeals to the computational challenge in the random framework that requires not only the approximating stochastic process solution but also its expectation and variance. After studying positivity and conditional random mean square stability, the computation of the expectation and variance of the approximating stochastic process is not performed directly but through using a set of sampling finite difference schemes coming out by taking realizations of the random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic expressions collapsing the approach is avoided keeping reliability. Results are simulated and a procedure for the numerical computation is given.

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Exponential asymptotics and convection-diffusion-reaction models

Analyzing Multiscale Phenomena Using Singular Perturbation Methods - Proceedings of Symposia in Applied Mathematics ◽

10.1090/psapm/056/1718885 ◽

1999 ◽

pp. 151-184 ◽

Cited By ~ 10

Author(s):

Michael J. Ward

Keyword(s):

Diffusion Reaction ◽

Convection Diffusion ◽

Reaction Models ◽

Exponential Asymptotics

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Diffusion–reaction models of genipin incorporation into fibrin networks

Journal of Materials Chemistry B ◽

10.1039/c4tb02025a ◽

2015 ◽

Vol 3 (22) ◽

pp. 4607-4615 ◽

Cited By ~ 12

Author(s):

Chi Ninh ◽

Aimon Iftikhar ◽

Madeline Cramer ◽

Christopher J. Bettinger

Keyword(s):

Controlled Release ◽

Small Molecule ◽

Diffusion Reaction ◽

Forward Guidance ◽

Naturally Occurring ◽

Fibrin Networks ◽

Reaction Models ◽

Potential Applications

Genipin, a naturally occurring small molecule from gardenia plant, has potential applications as a compound to stabilize clots for many embolization strategies. This work uses a combination of data and predictive frameworks to provide forward guidance in designing controlled release strategies that use genipin for clot stabilization.

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