Mathematical and Computational Applications

13 pages, 436 KiB

Open AccessArticle

Structural Stability of Pseudo-Parabolic Equations for Basic Data

by Yanping Wang and Yuanfei Li

Math. Comput. Appl. 2024, 29(6), 105; https://doi.org/10.3390/mca29060105 - 15 Nov 2024

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an [...] Read more.

This article investigates the spatial decay properties and continuous dependence on the basic geometric structure. Assuming that the total potential energy is bounded and the homogeneous Dirichlet condition is satisfied on the side of the solution within the cylindrical domain, we establish an auxiliary function related to the solution. By extending the data at the finite end forward, we can establish the continuous dependence on the perturbation of base data. Full article

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22 pages, 56577 KiB

Open AccessArticle

Resolving Contrast and Detail Trade-Offs in Image Processing with Multi-Objective Optimization

by Daniel Molina-Pérez and Alam Gabriel Rojas-López

Math. Comput. Appl. 2024, 29(6), 104; https://doi.org/10.3390/mca29060104 - 11 Nov 2024

Abstract

This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp [...] Read more.

This article addresses the complex challenge of simultaneously enhancing contrast and detail in an image, where improving one property often compromises the other. This trade-off is tackled using a multi-objective optimization approach. Specifically, the proposal’s model integrates the sigmoid transformation function and unsharp masking highboost filtering with the NSGA-II algorithm. Additionally, a posterior preference articulation is introduced to select three key solutions from the Pareto front: the maximum contrast solution, the maximum detail solution, and the knee point solution. The proposed technique is evaluated on a range of image types, including medical and natural scenes. The final solutions demonstrated significant superiority in terms of contrast and detail compared to the original images. The three selected solutions, although all are optimal, captured distinct characteristics within the images, offering different solutions according to field preferences. This highlights the method’s effectiveness across different types and enhancement requirements and emphasizes the importance of the proposed preferences in different contexts. Full article

(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2024)

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16 pages, 504 KiB

Open AccessArticle

An Experimental Comparison of Self-Adaptive Differential Evolution Algorithms to Induce Oblique Decision Trees

by Rafael Rivera-López, Efrén Mezura-Montes, Juana Canul-Reich and Marco-Antonio Cruz-Chávez

Math. Comput. Appl. 2024, 29(6), 103; https://doi.org/10.3390/mca29060103 - 9 Nov 2024

Abstract

This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as [...] Read more.

This study addresses the challenge of generating accurate and compact oblique decision trees using self-adaptive differential evolution algorithms. Although traditional decision tree induction methods create explainable models, they often fail to achieve optimal classification accuracy. To overcome these limitations, other strategies, such as those based on evolutionary computation, have been proposed in the literature. In particular, we evaluate the use of self-adaptive differential evolution variants to evolve a population of oblique decision trees encoded as real-valued vectors. Our proposal includes (1) an alternative initialization strategy that reduces redundant nodes and (2) a fitness function that penalizes excessive leaf nodes, promoting smaller and more accurate decision trees. We perform a comparative performance analysis of these differential evolution variants, showing that while they exhibit similar statistical behavior, the Single-Objective real-parameter optimization (jSO) method produces the most accurate oblique decision trees and is second best in compactness. The findings highlight the potential of self-adaptive differential evolution algorithms to improve the effectiveness of oblique decision trees in machine learning applications. Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2024)

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21 pages, 3240 KiB

Open AccessArticle

A Mathematical Lens on the Zoonotic Transmission of Lassa Virus Infections Leading to Disabilities in Severe Cases

by Yasir Ramzan, Hanadi Alzubadi, Aziz Ullah Awan, Kamel Guedri, Mohammed Alharthi and Bandar M. Fadhl

Math. Comput. Appl. 2024, 29(6), 102; https://doi.org/10.3390/mca29060102 - 7 Nov 2024

Abstract

This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; [...] Read more.

This study aims to analyze the dynamics of Lassa fever transmission and its impact on the brain and spinal cord then devise and analyze preventive actions. The stability of the infection-free equilibrium point is evaluated; the model’s precision is examined using empirical data; and all parameters are estimated and fitted. Subsequently, the basic reproductive number is determined, and subpopulation trends are observed over time. Sensitivity analysis is conducted to identify critical drivers influencing transmission dynamics. Two-dimensional plots visualize the impact of crucial parameters on the reproductive number. Through a comprehensive literature review and case analysis, an association between Lassa fever and various disabilities is established, including conditions such as encephalitis, hearing loss, ataxia, neuropsychiatric manifestations, meningitis, seizures, and coma. Solutions are devised and analyzed to enhance early detection, treatment, and mitigation of disease. Full article

(This article belongs to the Special Issue New Trends in Biomathematics)

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19 pages, 5947 KiB

Open AccessArticle

Analytical Solutions of PBTK Models for Evaluating the Impact of Surface Diffusion Characteristics on the Leaching Profile of Implant Bioproducts

by Matheos Giakoumi, Konstantinos Kapnisis, Andreas Anayiotos and Pavlos S. Stephanou

Math. Comput. Appl. 2024, 29(6), 101; https://doi.org/10.3390/mca29060101 - 4 Nov 2024

Abstract

Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the [...] Read more.

Toxicokinetic or pharmacokinetic models, physiologically based or not, offer a unique avenue to understand the transport of toxins or pharmaceuticals in living organisms. The availability of analytical solutions to such models offers the means to engage in a plethora of applications. In the present work, we provide the framework to solve analytically such models using the matrix exponential, and we then apply this method to derive an explicit solution to four-to-five-compartment physiologically based toxicokinetic (PBTK) models considering a single- and an infinite-exponential expression for the amount of mass released from an implantable device. We also offer the conditions that need to be met for analytical solutions to be obtained when the kinetic rates are time-dependent functions. Our analysis compares the computation time between analytical and numerical solutions and characterizes the dependency of the maximum substance mass value and the time it occurs in the various tissue compartments from the material surface diffusion characteristics. Our analytical solutions, which have several advantages over the solutions obtained using numerical solvers, can be incorporated into in silico tools and provide valuable information for human health risk assessment. Full article

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17 pages, 532 KiB

Open AccessArticle

Numerical Study of Multi-Term Time-Fractional Sub-Diffusion Equation Using Hybrid L1 Scheme with Quintic Hermite Splines

by Priyanka Priyanka, Shelly Arora, Saroj Sahani and Sharandeep Singh

Math. Comput. Appl. 2024, 29(6), 100; https://doi.org/10.3390/mca29060100 - 2 Nov 2024

Abstract

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 [...] Read more.

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. Full article

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3 pages, 154 KiB

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 - 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 [...] Full article

(This article belongs to the Collection Feature Papers in Mathematical and Computational Applications 2023)

24 pages, 6455 KiB

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 - 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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

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13 pages, 7092 KiB

Open AccessArticle

Design and Optimization of Microfluidic Vortex Diode

by Krzysztof Tadyszak, Alessandro Jäger, Jiří Pánek and Martin Hrubý

Math. Comput. Appl. 2024, 29(6), 97; https://doi.org/10.3390/mca29060097 - 30 Oct 2024

Abstract

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 [...] Read more.

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. Full article

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30 pages, 858 KiB

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

Abstract

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 [...] Read more.

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

H_{\infty}

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. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

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16 pages, 2663 KiB

Open AccessArticle

Bag of Feature-Based Ensemble Subspace KNN Classifier in Muscle Ultrasound Diagnosis of Diabetic Peripheral Neuropathy

by 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

Abstract

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) [...] Read more.

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. Full article

(This article belongs to the Section Engineering)

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16 pages, 1037 KiB

Open AccessArticle

Mathematical Modeling and Analysis of Ebola Virus Disease Dynamics: Implications for Intervention Strategies and Healthcare Resource Optimization

by 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

Abstract

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 [...] Read more.

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

S E I H R

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

(R_{0})

, 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

(R_{0})

. The main findings of this study show that for

R_{0} < 1

, the disease-free equilibrium, is globally stable, meaning the disease will die out, whereas for

R_{0} > 1

, the endemic equilibrium is stable, meaning the disease persists. Additionally, the sensitivity analysis reveals that the most influential parameters in controlling

R_{0}

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. Full article

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13 pages, 4030 KiB

Open AccessArticle

Application of Bispectral Analysis to Assess the Effect of Drought on the Photosynthetic Activity of Lettuce Plants Lactuca sativa L.

by 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

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Section Natural Sciences)

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17 pages, 293 KiB

Open AccessArticle

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

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

35 pages, 970 KiB

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

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Symmetry Methods for Solving Differential Equations)

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19 pages, 2708 KiB

Open AccessArticle

Modeling of Sedimentation of Particles near Corrugated Surfaces by the Meshless Method of Fundamental Solutions

by Alex Povitsky

Math. Comput. Appl. 2024, 29(5), 90; https://doi.org/10.3390/mca29050090 - 3 Oct 2024

Abstract

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 [...] Read more.

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. 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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18 pages, 328 KiB

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

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Recent Advances and New Challenges in Coupled Systems and Networks: Theory, Modelling, and Applications)

14 pages, 3165 KiB

Open AccessArticle

Optimized Nonlinear PID Control for Maximum Power Point Tracking in PV Systems Using Particle Swarm Optimization

by 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

Cited by 1

Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

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25 pages, 20472 KiB

Open AccessArticle

Meshless Error Recovery Parametric Investigation in Incompressible Elastic Finite Element Analysis

by Essam Althaqafi, Devinder Singh and Mohd Ahmed

Math. Comput. Appl. 2024, 29(5), 87; https://doi.org/10.3390/mca29050087 - 30 Sep 2024

Abstract

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 [...] Read more.

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. Full article

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