Journal Description
Mathematical and Computational Applications
Mathematical and Computational Applications
is an international, peer-reviewed, open access journal on applications of mathematical and/or computational techniques, published bimonthly online by MDPI. The South African Association for Theoretical and Applied Mechanics (SAAM) is affiliated with the journal Mathematical and Computational Applications and its members receive discounts on the article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, ESCI (Web of Science), Inspec, and other databases.
- Journal Rank: JCR - Q2 (Mathematics, Interdisciplinary Applications)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 28.8 days after submission; acceptance to publication is undertaken in 2.9 days (median values for papers published in this journal in the first half of 2024).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Testimonials: See what our editors and authors say about MCA.
Impact Factor:
1.9 (2023);
5-Year Impact Factor:
1.6 (2023)
Latest Articles
Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines
Math. Comput. Appl. 2024, 29(6), 100; https://doi.org/10.3390/mca29060100 (registering DOI) - 2 Nov 2024
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Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and
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Anomalous diffusion of particles has been described by the time-fractional reaction–diffusion equation. A hybrid formulation of numerical technique is proposed to solve the time-fractional-order reaction–diffusion (FRD) equation numerically. The technique comprises the semi-discretization of the time variable using an L1 finite-difference scheme and space discretization using the quintic Hermite spline collocation method. The hybrid technique reduces the problem to an iterative scheme of an algebraic system of equations. The stability analysis of the proposed numerical scheme and the optimal error bounds for the approximate solution are also studied. A comparative study of the obtained results and an error analysis of approximation show the efficiency, accuracy, and effectiveness of the technique.
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Open AccessEditorial
Feature Paper Collection of Mathematical and Computational Applications—2023
by
Gianluigi Rozza, Oliver Schütze and Nicholas Fantuzzi
Math. Comput. Appl. 2024, 29(6), 99; https://doi.org/10.3390/mca29060099 (registering DOI) - 1 Nov 2024
Abstract
This Special Issue comprises the second collection of papers submitted by both the Editorial Board Members (EBMs) of the journal Mathematical and Computational Applications (MCA) and the outstanding scholars working in the core research fields of MCA [...]
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(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2023)
Open AccessArticle
Using Artificial Neural Network Analysis to Study Jeffrey Nanofluid Flow in Cone–Disk Systems
by
Nasser Nammas Albaqami
Math. Comput. Appl. 2024, 29(6), 98; https://doi.org/10.3390/mca29060098 (registering DOI) - 31 Oct 2024
Abstract
Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is
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Artificial intelligence (AI) is employed in fluid flow models to enhance the simulation’s accuracy, to more effectively optimize the fluid flow models, and to realize reliable fluid flow systems with improved performance. Jeffery fluid flow through the interstice of a cone-and-disk system is considered in this study. The mathematical description of this flow involves converting a partial differential system into a nonlinear ordinary differential system and solving it using a neurocomputational technique. The fluid streaming through the disk–cone gap is investigated under four contrasting frameworks, i.e., (i) passive cone and spinning disk, (ii) spinning cone and passive disk, (iii) cone and disk rotating in the same direction, and (iv) cone and disk rotating in opposite directions. Employing the recently developed technique of artificial neural networks (ANNs) can be effective for handling and optimizing fluid flow exploits. The proposed approach integrates training, testing and analysis, and authentication based on a locus dataset to address various aspects of fluid problems. The mean square error, regression plots, curve-fitting graphs, and error histograms are used to evaluate the performance of the least mean square neural network algorithm (LMS-NNA). The results show that these equations are consistently aligned, and agreement is, on average, in the order of 10−8. While the resting parameters were kept static, the transverse velocity distribution, in all four cases, exhibited an incremental decreasing behavior in the estimates of magnetic and Jeffery fluid factors. Furthermore, the results obtained were compared with those in the literature, and the close agreement confirms our results. To train the model, 80% of the data were used for LMS-NNA, with 10% used for testing and the remaining 10% for validation. The quantitative and qualitative outputs obtained from the neural network strategy and parameter variation were thoroughly examined and discussed.
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(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
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Design and Optimization of Microfluidic Vortex Diode
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Krzysztof Tadyszak, Alessandro Jäger, Jiří Pánek and Martin Hrubý
Math. Comput. Appl. 2024, 29(6), 97; https://doi.org/10.3390/mca29060097 (registering DOI) - 30 Oct 2024
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The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS k-ε in COMSOL
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The performed research presents modeling results for designing microfluidic vortex diodes. These devices rectify fluid flow and can be used in many applications on micro and macro scales. The modeling, utilizing computational fluid dynamics (CFD) with the turbulence model RANS k-ε in COMSOL Multiphysics, has led to optimizing diodicity—the reversed-to-forward flow pressure drop ratio. The goal was to find the best flow-rectifying geometry within the 2D vortex-type design by changing the wall geometry, diode shape, and inflow velocities, identifying significant parameters and dependencies. Improving diodicity can be achieved by increasing the radius r1 of the central channel, increasing the entire diode radius r2, decreasing the width w of the rectangular channel, and reducing its length L. Additionally, changing the circular shape of the diode to an elliptical one can improve diodicity. The significance of this research is evident in the potential applications of these devices in microfluidic setups where fixed-geometry unidirectional flow is required, e.g., mixing, filtration, cell separation, and drug delivery, or on industrial scales, e.g., energy harvesting, wastewater treatment, and water sterilization.
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Open AccessArticle
Sliding Mode Fault-Tolerant Control for Nonlinear LPV Systems with Variable Time-Delay
by
Omayma Mansouri, Ali Ben Brahim, Fayçal Ben Hmida and Anis Sellami
Math. Comput. Appl. 2024, 29(6), 96; https://doi.org/10.3390/mca29060096 - 26 Oct 2024
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This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states
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This paper presents a robust sliding mode fault-tolerant control (FTC) strategy for a class of linear parameter variant (LPV) systems with variable time-delays and uncertainties. First fault estimation (FE) is conducted using a robust sliding mode observer, synthesized to simultaneously estimate the states and actuator faults of LPV polytopic delayed systems. Second, a sliding mode FTC is developed, ensuring all states of the closed-loop system converge to the origin. This paper presents an integrated sliding mode FTC strategy to achieve optimal robustness between the observer and controller models. The integrated design approach offers several advantages over traditional separated FTC methods. Our novel approach is based on incorporating adaptive law into the design of the Lyapunov–Krasovskii functional to improve both robustness and performance. This is achieved by combining the concept of sliding mode control (SMC) with the Lyapunov–Krasovskii function under the criteria, which plays a key role in guaranteeing the stability of this class of system. The effectiveness of the proposed method is demonstrated through a diesel engine example, which highlights the validity and benefits of the integrated and separated FTC strategy for uncertain nonlinear systems with time delays and the sliding mode control.
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(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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Bag of Feature-Based Ensemble Subspace KNN Classifier in Muscle Ultrasound Diagnosis of Diabetic Peripheral Neuropathy
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Kadhim K. Al-Barazanchi, Ali H. Al-Timemy and Zahid M. Kadhim
Math. Comput. Appl. 2024, 29(5), 95; https://doi.org/10.3390/mca29050095 - 20 Oct 2024
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Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD)
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Muscle ultrasound quantification is a valuable complementary diagnostic tool for diabetic peripheral neuropathy (DPN), enhancing physicians’ diagnostic capabilities. Quantitative assessment is generally regarded as more reliable and sensitive than visual evaluation, which often necessitates specialized expertise. This work develops a computer-aided diagnostic (CAD) system based on muscle ultrasound that integrates the bag of features (BOF) and an ensemble subspace k-nearest neighbor (KNN) algorithm for DPN detection. The BOF creates a histogram of visual word occurrences to represent the muscle ultrasound images and trains an ensemble classifier through cross-validation, determining optimal parameters to improve classification accuracy for the ensemble diagnosis system. The dataset includes ultrasound images of six muscles from 53 subjects, consisting of 27 control and 26 patient cases. An empirical analysis was conducted for each binary classifier based on muscle type to select the best vocabulary tree properties or K values for BOF. The result indicates that ensemble subspace KNN classification, based on the bag of features, achieved an accuracy of 97.23%. CAD systems can effectively diagnose muscle pathology, thereby addressing limitations and identifying issues in individuals with diabetes. This research underscores muscle ultrasound as a promising diagnostic tool to aid physicians in making accurate diagnoses, streamlining workflow, and uncovering muscle-related complications in DPN patients.
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(This article belongs to the Section Engineering)
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Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization
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Ikram Ullah, Imtiaz Ahmad, Nigar Ali, Ihtisham Ul Haq, Mohammad Idrees, Mohammed Daher Albalwi and Mehmet Yavuz
Math. Comput. Appl. 2024, 29(5), 94; https://doi.org/10.3390/mca29050094 - 12 Oct 2024
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This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public
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This study implements a minded approach to studying Ebola virus disease (EVD) by dividing the infected population into aware and unaware groups and including a hospitalized compartment. This offers a more detailed understanding of illness distribution, potential analyses, and the influence of public knowledge. The findings might improve healthcare budget apportionment, public health policy, and contest Ebola and related infections. In this study, we fully observe the new model that we have constructed. We start by outlining the essential concepts of the model and confirming its mathematical reliability. Next, we calculate the fundamental reproductive number , which is critical for appreciating how the infection spreads and how effective treatments might be. We also study stability analysis, which looks at when the disease may decline or become chronic. Furthermore, we exhibit the occurrence of bifurcation in the EVD Epidemic Model and perform a sensitivity analysis of . The main findings of this study show that for , the disease-free equilibrium, is globally stable, meaning the disease will die out, whereas for , the endemic equilibrium is stable, meaning the disease persists. Additionally, the sensitivity analysis reveals that the most influential parameters in controlling are the transmission rate and the recovery rate, which could guide effective intervention strategies. Finally, we use numerical simulations so that out outcomes are more significant.
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Open AccessArticle
Application of Bispectral Analysis to Assess the Effect of Drought on the Photosynthetic Activity of Lettuce Plants Lactuca sativa L.
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Maxim E. Astashev, Dmitriy E. Burmistrov, Denis V. Yanykin, Andrey A. Grishin, Inna V. Knyazeva, Alexey S. Dorokhov and Sergey V. Gudkov
Math. Comput. Appl. 2024, 29(5), 93; https://doi.org/10.3390/mca29050093 - 11 Oct 2024
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This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of L. sativa plants and analyzing the resulting time series
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This article proposes a new method for determining the pathological state of a plant, based on a combination of the method for measuring the dynamics of photosystem II pigment fluorescence in the leaves of L. sativa plants and analyzing the resulting time series using bispectral analysis based on the wavelet transform. The article theoretically shows a possible mechanism for the appearance of a peak on the map of bispectrum indexes during nonlinear analog conversion of a physiological signal in a biological object. The phenomenon of increasing the degree of nonlinearity in the transmission of an external periodic signal in plant signaling systems has been experimentally demonstrated.
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(This article belongs to the Section Natural Sciences)
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Lie Symmetry Analysis, Closed-Form Solutions, and Conservation Laws for the Camassa–Holm Type Equation
by
Jonathan Lebogang Bodibe and Chaudry Masood Khalique
Math. Comput. Appl. 2024, 29(5), 92; https://doi.org/10.3390/mca29050092 - 10 Oct 2024
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In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim
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In this paper, we study the Camassa–Holm type equation, which has applications in mathematical physics and engineering. Its applications extend across disciplines, contributing to our understanding of complex systems and helping to develop innovative solutions in diverse areas of research. Our main aim is to construct closed-form solutions of the equation using a powerful technique, namely the Lie group analysis method. Firstly, we derive the Lie point symmetries of the equation. Thereafter, the equation is reduced to non-linear ordinary differential equations using symmetry reductions. Furthermore, the solutions of the equation are derived using the extended Jacobi elliptic function technique, the simplest equation method, and the power series method. In conclusion, we construct conservation laws for the equation using Noether’s theorem and the multiplier approach, which plays a crucial role in understanding the behavior of non-linear equations, especially in physics and engineering, and these laws are derived from fundamental principles such as the conservation of mass, energy, momentum, and angular momentum.
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(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
Open AccessArticle
Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation
by
Willy Hereman and Ünal Göktaş
Math. Comput. Appl. 2024, 29(5), 91; https://doi.org/10.3390/mca29050091 - 3 Oct 2024
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In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the
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In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica, but can be adapted for major computer algebra systems.
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(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
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Modeling of Sedimentation of Particles near Corrugated Surfaces by the Meshless Method of Fundamental Solutions
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Alex Povitsky
Math. Comput. Appl. 2024, 29(5), 90; https://doi.org/10.3390/mca29050090 - 3 Oct 2024
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The velocity and trajectory of particles moving along the corrugated (rough) surface under the action of gravity is obtained by a modified Method of Fundamental Solutions (MFS). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with
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The velocity and trajectory of particles moving along the corrugated (rough) surface under the action of gravity is obtained by a modified Method of Fundamental Solutions (MFS). This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green’s function for Stokeslets. In the present study, the velocity of a moving particle under the action of the gravity force is not known and becomes a part of the MFS solution. This requires an adjustment of the matrix of the MFS linear system to include the unknown particle velocity and incorporate in the MFS the balance of hydrodynamic and gravity forces acting on the particle. The study explores the combination of the regularization of Stokeslets and placement of Stokeslets outside the flow domain to ensure the accuracy and stability of computations for particles moving in proximity to the wall. The MFS results are compared to prior published approximate analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particles, including their deviation from the vertical trajectory, and select the optimal set of computational parameters. The developed MFS methodology is then applied to the sedimentation of a pair of two spherical particles in proximity to the corrugated wall, in which case, the analytical solution is not available. The MFS results show that particles in the pair deviate from the trajectory of a single particle: the particle located below moves farther away from vertical wall, and the particle located above shifts closer to the wall.
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(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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Open AccessArticle
Loss of the Sturm–Liouville Property of Time-Varying Second-Order Differential Equations in the Presence of Delayed Dynamics
by
Manuel De la Sen
Math. Comput. Appl. 2024, 29(5), 89; https://doi.org/10.3390/mca29050089 - 3 Oct 2024
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This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system
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This paper considers a nominal undelayed and time-varying second-order Sturm–Liouville differential equation on a finite time interval which is a nominal version of another perturbed differential equation subject to a delay in its dynamics. The nominal delay-free differential equation is a Sturm–Liouville system in the sense that it is subject to prescribed two-point boundary conditions. However, the perturbed differential system is not a Sturm–Liouville system, in general, due to the presence of delayed dynamics. The main objective of the paper is to investigate the loss of the boundary values of the Sturm–Liouville nominal undelayed system in the presence of the delayed dynamics. Such a delayed dynamics is considered a perturbation of the nominal dynamics related to the Sturm–Liouville system with given two-point boundary values. In particular, this loss of the Sturm–Liouville exact tracking of the prescribed two-point boundary values might happen because the nominal boundary values may become lost by the state trajectory solution in the presence of delays, related to the undelayed case, due to the presence of the delayed dynamics. The worst-case error description of the deviation of the two-point boundary values of the current perturbed differential with respect to those of the nominal Sturm–Liouville system is characterized in terms of error norms related to the nominal system. Under sufficiently small deviations of the parameterization of the perturbed system with respect to the nominal one, such a worst-error characterization makes the current perturbed system an approximate Sturm–Liouville system of the nominal undelayed one.
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(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)
Open AccessArticle
Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization
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Maeva Cybelle Zoleko Zambou, Alain Soup Tewa Kammogne, Martin Siewe Siewe, Ahmad Taher Azar, Saim Ahmed and Ibrahim A. Hameed
Math. Comput. Appl. 2024, 29(5), 88; https://doi.org/10.3390/mca29050088 - 2 Oct 2024
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This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by
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This paper proposes a high-performing, hybrid method for Maximum Power Point Tracking (MPPT) in photovoltaic (PV) systems. The approach is based on an intelligent Nonlinear Discrete Proportional–Integral–Derivative (N-DPID) controller with the Perturb and Observe (P&O) method. The feedback gains derived are optimized by a metaheuristic algorithm called Particle Swarm Optimization (PSO). The proposed methods appear to present adequate solutions to overcome the drawbacks of existing methods despite various weather conditions considered in the analysis, providing a robust solution for dynamic environmental conditions. The results showed better performance and accuracy compared to those encountered in the literature. We also recall that this technique provides a systematic design procedure in the search for the MPPT in photovoltaic (PV) systems that has not yet been documented in the literature to the best of our knowledge.
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(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)
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Meshless Error Recovery Parametric Investigation in Incompressible Elastic Finite Element Analysis
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Essam Althaqafi, Devinder Singh and Mohd Ahmed
Math. Comput. Appl. 2024, 29(5), 87; https://doi.org/10.3390/mca29050087 - 30 Sep 2024
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The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and
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The meshless displacement error-recovery parametric investigation in finite element method-based incompressible elastic analysis is presented in this study. It investigates key parameters such as interpolation schemes, patch configurations, dilation indexes, weight functions, and meshing patterns. The study evaluates error recovery effectiveness (local and global), convergence rates, and adaptive mesh improvement for triangular/quadrilateral discretization schemes. It uses meshless moving least squares (MLS) interpolation with rectangular and circular support regions and solves benchmark plate and cylinder problems. It is observed that a circular influence region, a cubic spline weight function, and regular mesh patterns yield a better performance of than an MLS-based error recovery method. The study also concludes that lower dilation index values with rectangular influence regions are preferable for regular meshes, while higher dilation index values with radial influence regions are suitable for preferable meshes to enhance MLS error recovery.
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Open AccessArticle
Periodic and Axial Perturbations of Chaotic Solitons in the Realm of Complex Structured Quintic Swift-Hohenberg Equation
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Naveed Iqbal, Wael W. Mohammed, Mohammad Alqudah, Amjad E. Hamza and Shah Hussain
Math. Comput. Appl. 2024, 29(5), 86; https://doi.org/10.3390/mca29050086 - 30 Sep 2024
Abstract
This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems
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This research work employs a powerful analytical method known as the Riccati Modified Extended Simple Equation Method (RMESEM) to investigate and analyse chaotic soliton solutions of the (1 + 1)-dimensional Complex Quintic Swift–Hohenberg Equation (CQSHE). This model serves to describe complex dissipative systems that produce patterns. We have found that there exist numerous chaotic soliton solutions with periodic and axial perturbations to the intended CQSHE, provided that the coefficients are constrained by certain conditions. Furthermore, by applying a sophisticated transformation, the provided transformative approach RMESEM transforms CQSHE into a set of Nonlinear Ordinary Differential Equations (NODEs). The resulting set of NODEs is then transformed into an algebraic system of equations by incorporating the extended Riccati NODE to assume a series form solution. The soliton solutions to this system of equations can be found as periodic, hyperbolic, exponential, rational-hyperbolic, and rational families of functions. A variety of 3D and contour visuals are also provided to graphically illustrate the axially and periodically perturbed dynamics of these chaotic soliton solutions and the formation of fractals. Our findings are noteworthy because they shed light on the chaotic nature of the framework we are examining, enabling us to better understand the dynamics that underlie it.
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(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)
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Latent Space Perspicacity and Interpretation Enhancement (LS-PIE) Framework
by
Jesse Stevens, Daniel N. Wilke and Isaac I. Setshedi
Math. Comput. Appl. 2024, 29(5), 85; https://doi.org/10.3390/mca29050085 - 25 Sep 2024
Abstract
Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or unordered. These data are then projected onto the latent directions to obtain their
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Linear latent variable models such as principal component analysis (PCA), independent component analysis (ICA), canonical correlation analysis (CCA), and factor analysis (FA) identify latent directions (or loadings) either ordered or unordered. These data are then projected onto the latent directions to obtain their projected representations (or scores). For example, PCA solvers usually rank principal directions by explaining the most variance to the least variance. In contrast, ICA solvers usually return independent directions unordered and often with single sources spread across multiple directions as multiple sub-sources, severely diminishing their usability and interpretability. This paper proposes a general framework to enhance latent space representations to improve the interpretability of linear latent spaces. Although the concepts in this paper are programming language agnostic, the framework is written in Python. This framework simplifies the process of clustering and ranking of latent vectors to enhance latent information per latent vector and the interpretation of latent vectors. Several innovative enhancements are incorporated, including latent ranking (LR), latent scaling (LS), latent clustering (LC), and latent condensing (LCON). LR ranks latent directions according to a specified scalar metric. LS scales latent directions according to a specified metric. LC automatically clusters latent directions into a specified number of clusters. Lastly, LCON automatically determines the appropriate number of clusters to condense the latent directions for a given metric to enable optimal latent discovery. Additional functionality of the framework includes single-channel and multi-channel data sources and data pre-processing strategies such as Hankelisation to seamlessly expand the applicability of linear latent variable models (LLVMs) to a wider variety of data. The effectiveness of LR, LS, LC, and LCON is shown in two foundational problems crafted with two applied latent variable models, namely, PCA and ICA.
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(This article belongs to the Special Issue Current Problems and Advances in Computational and Applied Mechanics (AfriComp6))
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Open AccessArticle
Computational Modeling of Sodium-Ion-Channel-Based Glucose Sensing Biophysics to Study Cardiac Pacemaker Action Potential
by
Chitaranjan Mahapatra, Kirubanandan Shanmugam and Maher Ali Rusho
Math. Comput. Appl. 2024, 29(5), 84; https://doi.org/10.3390/mca29050084 - 21 Sep 2024
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Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate
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Elevated blood glucose levels, known as hyperglycemia, play a significant role in sudden cardiac arrest, often resulting in sudden cardiac death, particularly among those with diabetes. Understanding the internal mechanisms has been a challenge for healthcare professionals, leading many research groups to investigate the relationship between blood glucose levels and cardiac electrical activity. Our hypothesis suggests that glucose-sensing biophysics mechanisms in cardiac tissue could clarify this connection. To explore this, we adapted a single-compartment computational model of the human pacemaker action potential. We incorporated glucose-sensing mechanisms with voltage-gated sodium ion channels using ordinary differential equations. Parameters for the model were based on existing experimental studies to mimic the impact of glucose levels on pacemaker action potential firing. Simulations using voltage clamp and current clamp techniques showed that elevated glucose levels decreased sodium ion channel currents, leading to a reduction in the pacemaker action potential frequency. In summary, our mathematical model provides a cellular-level understanding of how high glucose levels can lead to bradycardia and sudden cardiac death.
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Open AccessArticle
Design and Implementation of a Discrete-PDC Controller for Stabilization of an Inverted Pendulum on a Self-Balancing Car Using a Convex Approach
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Yasmani González-Cárdenas, Francisco-Ronay López-Estrada, Víctor Estrada-Manzo, Joaquin Dominguez-Zenteno and Manuel López-Pérez
Math. Comput. Appl. 2024, 29(5), 83; https://doi.org/10.3390/mca29050083 - 18 Sep 2024
Abstract
This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique
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This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers the nonlinearities associated with the nonholonomic constraint. The design of a discrete parallel distributed compensation controller is achieved through an alternative method due to the presence of uncontrollable points that avoid finding a solution for the entire polytope. Finally, simulations and experimental results using a prototype illustrate the effectiveness of the proposal.
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(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)
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Open AccessEditorial
Significance of Mathematical Modeling and Control in Real-World Problems: New Developments and Applications
by
Mehmet Yavuz and Ioannis Dassios
Math. Comput. Appl. 2024, 29(5), 82; https://doi.org/10.3390/mca29050082 - 18 Sep 2024
Abstract
Mathematical modeling and system control are employed in many research problems, ranging from physical and chemical processes to biomathematics and life sciences [...]
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(This article belongs to the Special Issue Significance of Mathematical Modelling and Control in Real-World Problems: New Developments and Applications)
Open AccessArticle
A Corruption Impunity Model Considering Anticorruption Policies
by
Sandra E. Delgadillo-Alemán, Roberto A. Kú-Carrillo and Alejandra Torres-Nájera
Math. Comput. Appl. 2024, 29(5), 81; https://doi.org/10.3390/mca29050081 - 14 Sep 2024
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Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later
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Corruption is a global problem that affects the fair distribution of wealth of every country to different degrees and represents a problem to be solved to prevent the diversion and waste of resources. Among the different efforts to first measure it and later reduce it by proposing strategies, there exist a variety of indices, such as the corruption perception index, and other related issues, such as the global impunity index, the laxness of anticorruption policies, etc., which are computed for different countries worldwide. Based on these indices, we propose a model for corruption using a system of ordinary differential equations, considering anticorruption policies. Those three factors were identified after analyzing the phenomenon and available data, particularly for Mexico. Also, we fit it to the reported data of this country and perform simulations expecting to predict the short term, and performed a sensitivity analysis. The model is capable of reproducing the observed oscillatory behavior of the phenomenon. The model fit can still be improved by including the data for the anticorruption policies, which were only studied for different scenarios. Moreover, the model is susceptible to application in other countries, as long as data are available, and then provides a computational tool to predict and visualize the effect of appropriate public policies to fight corruption.
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