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Volume 29, April
 
 

Math. Comput. Appl., Volume 29, Issue 3 (June 2024) – 10 articles

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13 pages, 7450 KiB  
Article
Numerical Solution of Natural Convection Problems Using Radial Point Interpolation Meshless (RPIM) Method Combined with Artificial-Compressibility Model
by Pranowo, Albertus Joko Santoso and Agung Tri Wijayanta
Math. Comput. Appl. 2024, 29(3), 39; https://doi.org/10.3390/mca29030039 - 20 May 2024
Viewed by 253
Abstract
A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The [...] Read more.
A numerical method is used to solve the thermal analysis of natural convection in enclosures. This paper proposes the use of an implicit artificial-compressibility model in conjunction with the Radial Point Interpolation Meshless (RPIM) method to mimic laminar natural convective heat transport. The technique couples the pressure with the velocity components using an artificial compressibility model. The RPIM is used to discretize the spatial terms of the governing equation. We solve the semi-algebraic system implicitly in backward Euler pseudo-time. The proposed method solves two test problems—natural convection in the annulus of concentric circular cylinders and trapezoidal cavity. Additionally, the results are validated using experimental and numerical data available in the literature. Excellent agreement was seen between the numerical results acquired with the suggested method and those obtained through the standard techniques found in the literature. Full article
(This article belongs to the Section Engineering)
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15 pages, 3611 KiB  
Article
Detailed Investigation of the Eddy Current and Core Losses in Coaxial Magnetic Gears through a Two-Dimensional Analytical Model
by Nikolina Nikolarea, Panteleimon Tzouganakis, Vasilios Gakos, Christos Papalexis, Antonios Tsolakis and Vasilios Spitas
Math. Comput. Appl. 2024, 29(3), 38; https://doi.org/10.3390/mca29030038 - 18 May 2024
Viewed by 267
Abstract
This work introduces a 2D model that calculates power losses in coaxial magnetic gears (CMGs). The eddy current losses of the magnets are computed analytically, whereas the core losses of the ferromagnetic segments are computed using an analytical–finite element hybrid model. The results [...] Read more.
This work introduces a 2D model that calculates power losses in coaxial magnetic gears (CMGs). The eddy current losses of the magnets are computed analytically, whereas the core losses of the ferromagnetic segments are computed using an analytical–finite element hybrid model. The results were within 1.51% and 3.18% of those obtained from an FEA for the eddy current and core losses in the CMG for an indicative inner rotor speed of 2500 rpm. In addition, the significance of the circumferential magnet segmentation is demonstrated in the CMGs. Furthermore, a parametric investigation of the efficiency of the system for different applied external loads is carried out. Finally, a mesh sensitivity analysis is performed, along with the computation of the average power losses throughout one full period, resulting in an at least 80% reduction in computational costs with a negligible effect on accuracy. The developed model could be a valuable tool for the minimization of power losses in CMGs since it combines high accuracy with a low computational cost. Full article
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27 pages, 1287 KiB  
Article
Exploring Trust Dynamics in Online Social Networks: A Social Network Analysis Perspective
by Stavroula Kridera and Andreas Kanavos
Math. Comput. Appl. 2024, 29(3), 37; https://doi.org/10.3390/mca29030037 - 15 May 2024
Viewed by 633
Abstract
This study explores trust dynamics within online social networks, blending social science theories with advanced machine-learning (ML) techniques. We examine trust’s multifaceted nature—definitions, types, and mechanisms for its establishment and maintenance—and analyze social network structures through graph theory. Employing a diverse array of [...] Read more.
This study explores trust dynamics within online social networks, blending social science theories with advanced machine-learning (ML) techniques. We examine trust’s multifaceted nature—definitions, types, and mechanisms for its establishment and maintenance—and analyze social network structures through graph theory. Employing a diverse array of ML models (e.g., KNN, SVM, Naive Bayes, Gradient Boosting, and Neural Networks), we predict connection strengths on Facebook, focusing on model performance metrics such as accuracy, precision, recall, and F1-score. Our methodology, executed in Python using the Anaconda distribution, unveils insights into trust formation and sustainability on social media, highlighting the potent application of ML in understanding these dynamics. Challenges, including the complexity of modeling social behaviors and ethical data use concerns, are discussed, emphasizing the need for continued innovation. Our findings contribute to the discourse on trust in social networks and suggest future research directions, including the application of our methodologies to other platforms and the study of online trust over time. This work not only advances the academic understanding of digital social interactions but also offers practical implications for developers, policymakers, and online communities. Full article
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13 pages, 660 KiB  
Article
Periodic Solutions in a Simple Delay Differential Equation
by Anatoli Ivanov and Sergiy Shelyag
Math. Comput. Appl. 2024, 29(3), 36; https://doi.org/10.3390/mca29030036 - 12 May 2024
Viewed by 340
Abstract
A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in [...] Read more.
A simple-form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback coefficient. The periodic solutions are built explicitly in the case with piecewise constant nonlinearities involved. The periodic dynamics are shown to persist under small perturbations of the equation, which make it smooth. The theoretical results are verified through extensive numerical simulations. Full article
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16 pages, 3437 KiB  
Article
Clustering of Wind Speed Time Series as a Tool for Wind Farm Diagnosis
by Ana Alexandra Martins, Daniel C. Vaz, Tiago A. N. Silva, Margarida Cardoso and Alda Carvalho
Math. Comput. Appl. 2024, 29(3), 35; https://doi.org/10.3390/mca29030035 - 9 May 2024
Viewed by 507
Abstract
In several industrial fields, environmental and operational data are acquired with numerous purposes, potentially generating a huge quantity of data containing valuable information for management actions. This work proposes a methodology for clustering time series based on the K-medoids algorithm using a convex [...] Read more.
In several industrial fields, environmental and operational data are acquired with numerous purposes, potentially generating a huge quantity of data containing valuable information for management actions. This work proposes a methodology for clustering time series based on the K-medoids algorithm using a convex combination of different time series correlation metrics, the COMB distance. The multidimensional scaling procedure is used to enhance the visualization of the clustering results, and a matrix plot display is proposed as an efficient visualization tool to interpret the COMB distance components. This is a general-purpose methodology that is intended to ease time series interpretation; however, due to the relevance of the field, this study explores the clustering of time series judiciously collected from data of a wind farm located on a complex terrain. Using the COMB distance for wind speed time bands, clustering exposes operational similarities and dissimilarities among neighboring turbines which are influenced by the turbines’ relative positions and terrain features and regarding the direction of oncoming wind. In a significant number of cases, clustering does not coincide with the natural geographic grouping of the turbines. A novel representation of the contributing distances—the COMB distance matrix plot—provides a quick way to compare pairs of time bands (turbines) regarding various features. Full article
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13 pages, 270 KiB  
Article
New Model for Hill’s Problem in the Framework of Continuation Fractional Potential
by Elbaz I. Abouelmagd
Math. Comput. Appl. 2024, 29(3), 34; https://doi.org/10.3390/mca29030034 - 2 May 2024
Viewed by 810
Abstract
In this work, we derived a new type model for spatial Hill’s system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect [...] Read more.
In this work, we derived a new type model for spatial Hill’s system considering the created perturbation by the parameter effect of the continuation fractional potential. The new model is considered a reduced system from the restricted three-body problem under the same effect for describing Hill’s problem. We identified the associated Lagrangian and Hamiltonian functions of the new system, and used them to verify the existence of the new equations of motion. We also proved that the new model has different six valid solutions under different six symmetries transformations as well as the original solution, where the new model is an invariant under these transformations. The several symmetries of Hill’s model can extremely simplify the calculation and analysis of preparatory studies for the dynamical behavior of the system. Finally, we confirm that these symmetries also authorize us to explore the similarities and differences among many classes of paths that otherwise differ from the obtained trajectories by restricted three-body problem. Full article
17 pages, 10189 KiB  
Article
Evaluation of Aortic Valve Pressure Gradients for Increasing Severities of Rheumatic and Calcific Stenosis Using Empirical and Numerical Approaches
by Lindi Grobler, Ryno Laubscher, Johan van der Merwe and Philip G. Herbst
Math. Comput. Appl. 2024, 29(3), 33; https://doi.org/10.3390/mca29030033 - 28 Apr 2024
Viewed by 653
Abstract
The evaluation and accurate diagnosis of the type and severity of aortic stenosis relies on the precision of medical imaging technology and clinical correlations and the expertise of medical professionals. The application of the clinical correlation to different aortic stenosis morphologies and severities [...] Read more.
The evaluation and accurate diagnosis of the type and severity of aortic stenosis relies on the precision of medical imaging technology and clinical correlations and the expertise of medical professionals. The application of the clinical correlation to different aortic stenosis morphologies and severities is investigated. The manner in which numerical techniques can be used to simulate the blood flow through pathological aortic valves was analysed and compared to the ground-truth CFD model. Larger pressure gradients are estimated in all severities of rheumatic aortic valves compared to calcific aortic valves. The zero-dimensional morphology-insensitive model underpredicted the transvalvular pressure gradient with the greatest error. The 1D model underestimated the pressure gradient in rheumatic cases and overestimated the pressure gradient in calcific cases. The pressure gradients estimated by the clinical approach depends on the location of the flow vena contracta and is sensitive to the severity and type of valve lesion. Through the analysis of entropy generation within the flow domain, the dominant parameters and regions driving adverse pressure gradients were identified. It is concluded that sudden expansion is the dominant parameter leading to higher pressure gradients in rheumatic heart valves compared to calcific ones. Full article
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15 pages, 512 KiB  
Article
Recognizable Languages of k-Forcing Automata
by Marzieh Shamsizadeh, Mohammad Mehdi Zahedi, Khadijeh Abolpour and Manuel De la Sen
Math. Comput. Appl. 2024, 29(3), 32; https://doi.org/10.3390/mca29030032 - 25 Apr 2024
Viewed by 458
Abstract
In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and [...] Read more.
In this study, we show that automata theory is also a suitable tool for analyzing a more complex type of the k-forcing process. First, the definition of k-forcing automata is presented according to the definition of k-forcing for graphs. Moreover, we study and discuss the language of k-forcing automata for particular graphs. Also, for some graphs with different k-forcing sets, we study the languages of their k-forcing automata. In addition, for some given recognizable languages, we study the structure of graphs. After that, we show that k-forcing automata arising from isomorph graphs are also isomorph. Also, we present the style of words that can be recognized with k-forcing automata. Moreover, we introduce the structure of graphs the k-forcing automata arising from which recognize some particular languages. To clarify the notions and the results obtained in this study, some examples are submitted as well. Full article
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15 pages, 313 KiB  
Article
A New Generalized Definition of Fractal–Fractional Derivative with Some Applications
by Francisco Martínez and Mohammed K. A. Kaabar
Math. Comput. Appl. 2024, 29(3), 31; https://doi.org/10.3390/mca29030031 - 25 Apr 2024
Viewed by 484
Abstract
In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical [...] Read more.
In this study, a new generalized fractal–fractional (FF) derivative is proposed. By applying this definition to some elementary functions, we show its compatibility with the results of the FF derivative in the Caputo sense with the power law. The main elements of classical differential calculus are introduced in terms of this new derivative. Thus, we establish and demonstrate the basic operations with derivatives, chain rule, mean value theorems with their immediate applications and inverse function’s derivative. We complete the theory of generalized FF calculus by proposing a notion of integration and presenting two important results of integral calculus: the fundamental theorem and Barrow’s rule. Finally, we analytically solve interesting FF ordinary differential equations by applying our proposed definition. Full article
16 pages, 4439 KiB  
Article
Simulation of Temperature Field in Steel Billets during Reheating in Pusher-Type Furnace by Meshless Method
by Qingguo Liu, Umut Hanoglu, Zlatko Rek and Božidar Šarler
Math. Comput. Appl. 2024, 29(3), 30; https://doi.org/10.3390/mca29030030 - 24 Apr 2024
Viewed by 592
Abstract
Using a meshless method, a simulation of steel billets in a pusher-type reheating furnace is carried out for the first time. The simulation represents an affordable way to replace the measurements. The heat transfer from the billets with convection and radiation is considered. [...] Read more.
Using a meshless method, a simulation of steel billets in a pusher-type reheating furnace is carried out for the first time. The simulation represents an affordable way to replace the measurements. The heat transfer from the billets with convection and radiation is considered. Inside each of the billets, the heat diffusion equation is solved on a two-dimensional central slice of the billet. The diffusion equation is solved in a strong form by the Local Radial Basis Function Collocation Method (LRBFCM) with explicit time-stepping. The ray tracing procedure solves the radiation, where the view factors are computed with the Monte Carlo method. The changing number of billets in the furnace at the start and the end of the loading and unloading of the furnace is considered. A sensitivity study on billets’ temperature evolution is performed as a function of a different number of rays used in the Monte Carlo method, different stopping times of the billets in the furnace, and different spacing between the billets. The temperature field simulation is also essential for automatically optimizing the furnace’s productivity, energy consumption, and the billet’s quality. For the first time, the LRBFCM is successfully demonstrated for solving such a complex industrial problem. Full article
(This article belongs to the Special Issue Radial Basis Functions)
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