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Recent Advances and New Challenges in Coupled Systems and Networks:...
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Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications

A special issue of Mathematical and Computational Applications (ISSN 2297-8747).

Deadline for manuscript submissions: 15 October 2024 | Viewed by 8034

Special Issue Editors

Dr. Sundeep Singh

E-Mail Website
Guest Editor
Faculty of Sustainable Design Engineering, University of Prince Edward Island, 550 University Ave, Charlottetown, PE C1A 4P3, Canada
Interests: thermo-fluids; mathematical modeling & simulations; computational fluid dynamics and heat transfer; biomedical engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Weizhong Dai

E-Mail Website
Guest Editor
College of Engineering and Science, Louisiana Tech University, 201 Mayfield Ave, Ruston, LA 71272, USA
Interests: numerical methods for partial differential equations (higher-order compact finite difference schemes, stability, convergence); artificial neural network method for solving partial differential equations; simulations for micro/nano scale heat transfer; bio-heat transfer

Special Issue Information

Dear Colleagues,

This Special Issue aims at collecting original research articles related to the recent advancement, development and challenges pertaining to the development of current state-of-the-art models focused on mathematical and computational sciences, with their applications to modelling natural, social, and engineering systems. Review articles aligned to the scope of this Special Issue are also welcome.

Topics of interest for submissions to this Special Issue include, but are not limited to:

  1. Coupled systems and networks models
  2. Mathematics in biology and medicine
  3. Mathematical models for nanoscience and nanotechnology
  4. Modelling complex systems in life sciences
  5. Coupled human–environment systems
  6. Infectious disease models
  7. Mathematical models for renewable and alternative sources of energy
  8. Coupled models for environmentally friendly materials and technologies
  9. Machine learning and multiscale modelling
  10. Computational neuroscience

This Special Issue is in honor of Professor Roderick Melnik (https://m3ai.wlu.ca/), who has pioneered many advanced mathematical models and has significantly contributed to this field over the past few decades. This Special Issue is open to all researchers working in the above areas, including but not limited to the contributors of the Special Symposium on Coupled Complex Systems organized at the International AMMCS Conference Series, held in Waterloo, Canada.

Dr. Sundeep Singh
Prof. Dr. Weizhong Dai
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematical and Computational Applications is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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Research

14 pages, 1926 KiB  
Article
Modeling of Chemical Vapor Infiltration for Fiber-Reinforced Silicon Carbide Composites Using Meshless Method of Fundamental Solutions
by Patrick Mahoney and Alex Povitsky
Math. Comput. Appl. 2024, 29(2), 27; https://doi.org/10.3390/mca29020027 - 22 Mar 2024
Viewed by 753
Abstract
In this study, the Method of Fundamental Solutions (MFSs) is adopted to model Chemical Vapor Infiltration (CVI) in a fibrous preform. The preparation of dense fiber-reinforced silicon carbide composites is considered. The reaction flux at the solid surface is equal to the diffusion [...] Read more.
In this study, the Method of Fundamental Solutions (MFSs) is adopted to model Chemical Vapor Infiltration (CVI) in a fibrous preform. The preparation of dense fiber-reinforced silicon carbide composites is considered. The reaction flux at the solid surface is equal to the diffusion flux towards the surface. The Robin or third-type boundary condition is implemented into the MFS. From the fibers’ surface concentrations obtained by MFS, deposition rates are calculated, and the geometry is updated at each time step, modeling the pore filling over time. The MFS solution is verified by comparing the results to a known analytical solution for a simplified geometry of concentric cylinders with a concentration set at the outer cylinder and a reaction at the inner cylinder. MFS solutions are compared to published experimental data. Porosity transients are obtained by a combination of MFSs with surface deposition to show the relation between the initial and final porosities. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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13 pages, 1239 KiB  
Article
Magnesium and Calcium Transport along the Male Rat Kidney: Effect of Diuretics
by Pritha Dutta and Anita T. Layton
Math. Comput. Appl. 2024, 29(1), 13; https://doi.org/10.3390/mca29010013 - 07 Feb 2024
Viewed by 1077
Abstract
Calcium (Ca2+) and magnesium (Mg2+) are essential for cellular function. The kidneys play an important role in maintaining the homeostasis of these cations. Their reabsorption along the nephron is dependent on distinct trans- and paracellular pathways and is coupled [...] Read more.
Calcium (Ca2+) and magnesium (Mg2+) are essential for cellular function. The kidneys play an important role in maintaining the homeostasis of these cations. Their reabsorption along the nephron is dependent on distinct trans- and paracellular pathways and is coupled to the transport of other electrolytes. Notably, sodium (Na+) transport establishes an electrochemical gradient to drive Ca2+ and Mg2+ reabsorption. Consequently, alterations in renal Na+ handling, under pathophysiological conditions or pharmacological manipulations, can have major effects on Ca2+ and Mg2+ transport. One such condition is the administration of diuretics, which are used to treat a large range of clinical conditions, but most commonly for the management of blood pressure and fluid balance. While the pharmacological targets of diuretics typically directly mediate Na+ transport, they also indirectly affect renal Ca2+ and Mg2+ handling through alterations in the electrochemical gradient. To investigate renal Ca2+ and Mg2 handling and how those processes are affected by diuretic treatment, we have developed computational models of electrolyte transport along the nephrons. Model simulations indicate that along the proximal tubule and thick ascending limb, the transport of Ca2+ and Mg2+ occurs in parallel with Na+, but those processes are dissociated along the distal convoluted tubule. We also simulated the effects of acute administration of loop, thiazide, and K-sparing diuretics. The model predicted significantly increased Ca2+ and Mg2+ excretions and significantly decreased Ca2+ and Mg2+ excretions on treatment with loop and K-sparing diuretics, respectively. Treatment with thiazide diuretics significantly decreased Ca2+ excretion, but there was no significant alteration in Mg2+ excretion. The present models can be used to conduct in silico studies on how the kidney adapts to alterations in Ca2+ and Mg2+ homeostasis during various physiological and pathophysiological conditions, such as pregnancy, diabetes, and chronic kidney disease. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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15 pages, 645 KiB  
Article
A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation
by Mengli Yao and Zhifeng Weng
Math. Comput. Appl. 2024, 29(1), 6; https://doi.org/10.3390/mca29010006 - 15 Jan 2024
Viewed by 1208
Abstract
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation [...] Read more.
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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21 pages, 851 KiB  
Article
A Finite Difference Method for Solving the Wave Equation with Fractional Damping
by Manruo Cui, Cui-Cui Ji and Weizhong Dai
Math. Comput. Appl. 2024, 29(1), 2; https://doi.org/10.3390/mca29010002 - 29 Dec 2023
Viewed by 1546
Abstract
In this paper, we develop a finite difference method for solving the wave equation with fractional damping in 1D and 2D cases, where the fractional damping is given based on the Caputo fractional derivative. Firstly, based on the weighted method, we propose a [...] Read more.
In this paper, we develop a finite difference method for solving the wave equation with fractional damping in 1D and 2D cases, where the fractional damping is given based on the Caputo fractional derivative. Firstly, based on the weighted method, we propose a new numerical approximation for the Caputo fractional derivative and apply it for the 1D case to obtain a time-stepping method. We then develop an alternating direction implicit (ADI) scheme for the 2D case. Using the discrete energy method, we prove that the proposed difference schemes are unconditionally stable and convergent in both 1D and 2D cases. Finally, several numerical examples are given to verify the theoretical results. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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21 pages, 4591 KiB  
Article
Continuum and Molecular Modeling of Chemical Vapor Deposition at Nano-Scale Fibrous Substrates
by Himel Barua and Alex Povitsky
Math. Comput. Appl. 2023, 28(6), 112; https://doi.org/10.3390/mca28060112 - 06 Dec 2023
Viewed by 1291
Abstract
Chemical vapor deposition (CVD) is a common industrial process that incorporates a complex combination of fluid flow, chemical reactions, and surface deposition. Understanding CVD processes requires rigorous and costly experimentation involving multiple spatial scales, from meters to nanometers. The numerical modeling of deposition [...] Read more.
Chemical vapor deposition (CVD) is a common industrial process that incorporates a complex combination of fluid flow, chemical reactions, and surface deposition. Understanding CVD processes requires rigorous and costly experimentation involving multiple spatial scales, from meters to nanometers. The numerical modeling of deposition over macro-scale substrates has been conducted in the literature and results show compliance with experimental data. For smaller-scale substrates, where the corresponding Knudsen number is larger than zero, continuum modeling does not provide accurate results, which calls for the implementation of molecular-level modeling techniques. In the current study, the finite-volume method (FVM) and Direct Simulation Monte Carlo (DSMC) method were combined to model the reactor-scale flow with CVD around micro- and nano-scale fibers. CVD at fibers with round cross-sections was modeled in the reactor, where fibers were oriented perpendicularly with respect to the feedstock gas flow. The DSMC method was applied to modeling flow around the matrix of nano-scale circular individual fibers. Results show that for smaller diameters of individual fibers with the same filling ratio, the residence time of gas particles inside the fibrous media reduces, and, consequently, the amount of material surface deposition decreases. The sticking coefficient on the fibers’ surface plays an important role; for instance, increasing the sticking coefficient from 20% to 80% will double the deposition rate. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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8 pages, 763 KiB  
Article
Explicit Integrating Factor Runge–Kutta Method for the Extended Fisher–Kolmogorov Equation
by Yanan Wang and Shuying Zhai
Math. Comput. Appl. 2023, 28(6), 110; https://doi.org/10.3390/mca28060110 - 22 Nov 2023
Viewed by 1254
Abstract
The extended Fisher–Kolmogorov (EFK) equation is an important model for phase transitions and bistable phenomena. This paper presents some fast explicit numerical schemes based on the integrating factor Runge–Kutta method and the Fourier spectral method to solve the EFK equation. The discrete global [...] Read more.
The extended Fisher–Kolmogorov (EFK) equation is an important model for phase transitions and bistable phenomena. This paper presents some fast explicit numerical schemes based on the integrating factor Runge–Kutta method and the Fourier spectral method to solve the EFK equation. The discrete global convergence of these new schemes is analyzed rigorously. Three numerical examples are presented to verify the theoretical analysis and the efficiency of the proposed schemes. Full article
(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
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