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Mathematics
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Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition
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Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 4296

Special Issue Editors

Prof. Dr. Juan Francisco Sánchez-Pérez

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Guest Editor
Department of Applied Physics and Naval Technology, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: mathematical modeling; numerical simulation; network simulation method; nondimensionalization; dimensionless groups; engineering; applied physics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Gonzalo García Ros

E-Mail Website
Guest Editor
Department of Civil Engineering Department, Technical University of Cartagena, Paseo Alfonso XIII 52, 30203 Cartagena, Spain
Interests: partial differential equations; mathematical modeling; applied mathematics in civil engineering; statistical treatment of acoustic emissions; nondimensionalization of engineering problems; ground engineeringstatistical treatment of acoustic emissions; nondimensionalization of engineering problems; ground engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Manuel Conesa

E-Mail Website
Guest Editor
Department of Applied Physics and Naval Technology, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dimensional analysis; free convection; ordinary differential equations; network method; electrical simulation; multidisciplinary tools; education in science and engineeringon, multidisciplinary tools, education in science and engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue invites you to present papers that solve problems of interest in the fields of science and engineering through the utilization of various mathematical methodologies.

The main objective of this Special Issue is to solve the proposed mathematical model, which comprises complex systems of coupled or non-differential equations that represent the study problem, through novel methodologies, such as the use of dimensional analysis, nondimensionalization, numerical simulation techniques or optimization techniques, among others.

In addition, this Special Issue integrates teaching methodologies that are used to facilitate the learning of mathematical methods for undergraduate and graduate students in various fields of science and engineering, along with their evaluation.

Finally, the scope of this Special Issue includes, but is not limited to, the following potential topics:

  • Mathematical modeling for science and engineering applications;
  • Numerical analysis;
  • Mathematical and computational engineering;
  • Numerical methods for science and engineering applications;
  • Optimization and control in engineering applications;
  • Dynamical systems;
  • Mathematical physics;
  • Analysis of PDEs;
  • Classical analysis and ODEs;
  • Mathematics in engineering and sciences studies.

Prof. Dr. Juan Francisco Sánchez-Pérez
Prof. Dr. Gonzalo García Ros
Dr. Manuel Conesa
Guest Editors

Manuscript Submission Information

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

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

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • mathematical modeling for science and engineering applications
  • numerical analysis
  • mathematical and computational engineering
  • numerical methods for science and engineering applications
  • optimization and control in engineering applications
  • dynamical systems
  • mathematical physics
  • analysis of PDEs
  • classical analysis and ODEs
  • mathematics in engineering and sciences studies

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Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (4 papers)

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Research

18 pages, 3040 KiB  
Article
Bioconvective Flow Characteristics of NEPCM–Water Nanofluid over an Inclined Cylinder in Porous Medium: An Extended Darcy Model Approach
by Bikash Das, Sahin Ahmed and Joaquín Zueco
Mathematics 2024, 12(24), 4012; https://doi.org/10.3390/math12244012 - 20 Dec 2024
Viewed by 836
Abstract
Bioconvection phenomena play a pivotal role in diverse applications, including the synthesis of biological polymers and advancements in renewable energy technologies. This study develops a comprehensive mathematical model to examine the effects of key parameters, such as the Lewis number (Lb), Peclet number [...] Read more.
Bioconvection phenomena play a pivotal role in diverse applications, including the synthesis of biological polymers and advancements in renewable energy technologies. This study develops a comprehensive mathematical model to examine the effects of key parameters, such as the Lewis number (Lb), Peclet number (Pe), volume fraction (φ), and angle of inclination (α), on the flow and heat transfer characteristics of a nanofluid over an inclined cylinder embedded in a non-Darcy porous medium. The investigated nanofluid comprises nano-encapsulated phase-change materials (NEPCMs) dispersed in water, offering enhanced thermal performance. The governing non-linear partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations and solved numerically via the Network Simulation Method (NSM) and an implicit Runge–Kutta method implemented through the bvp4c routine in MATLAB R2021a. Validation against the existing literature confirms the accuracy and reliability of the numerical approach, with strong convergence observed. Quantitative analysis reveals that an increase in the Peclet number reduces the shear stress at the cylinder wall by up to 18% while simultaneously enhancing heat transfer by approximately 12%. Similarly, the angle of inclination (α) significantly boosts heat transmission rates. Additionally, higher Peclet and Lewis numbers, along with greater nanoparticle volume fractions, amplify the density gradient of microorganisms, intensifying the bioconvection process by nearly 15%. These findings underscore the critical interplay between bioconvection and transport phenomena, providing a framework for optimizing bioconvection-driven heat and mass transfer systems. The insights from this investigation hold substantial implications for industrial processes and renewable energy technologies, paving the way for improved efficiency in applications such as thermal energy storage and advanced cooling systems. Full article
(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition)
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25 pages, 4782 KiB  
Article
Improving Ti Thin Film Resistance Deviations in Physical Vapor Deposition Sputtering for Dynamic Random-Access Memory Using Dynamic Taguchi Method, Artificial Neural Network and Genetic Algorithm
by Chia-Ming Lin and Shang-Liang Chen
Mathematics 2024, 12(17), 2688; https://doi.org/10.3390/math12172688 - 29 Aug 2024
Viewed by 802
Abstract
Many dynamic random-access memory (DRAM) manufacturing companies encounter significant resistance value deviations during the PVD sputtering process for manufacturing Ti thin films. These resistance values are influenced by the thickness of the thin films. Current mitigation strategies focus on adjusting film thickness to [...] Read more.
Many dynamic random-access memory (DRAM) manufacturing companies encounter significant resistance value deviations during the PVD sputtering process for manufacturing Ti thin films. These resistance values are influenced by the thickness of the thin films. Current mitigation strategies focus on adjusting film thickness to reduce resistance deviations, but this approach affects product structure profile and performance. Additionally, varying Ti thin film thicknesses across different product structures increase manufacturing complexity. This study aims to minimize resistance value deviations across multiple film thicknesses with minimal resource utilization. To achieve this goal, we propose the TSDTM-ANN-GA framework, which integrates the two-stage dynamic Taguchi method (TSDTM), artificial neural networks (ANN), and genetic algorithms (GA). The proposed framework requires significantly fewer experimental resources than traditional full factorial design and grid search method, making it suitable for resource-constrained and low-power computing environments. Our TSDTM-ANN-GA framework successfully identified an optimal production condition configuration for five different Ti thin film thicknesses: Degas temperature = 245 °C, Ar flow = 55 sccm, DC power = 5911 W, and DC power ramp rate = 4009 W/s. The results indicate that the deviation between the resistance values and their design values for the five Ti thin film thicknesses decreased by 86.8%, 94.1%, 95.9%, 98.2%, and 98.8%, respectively. The proposed method effectively reduced resistance deviations for the five Ti thin film thicknesses and simplified manufacturing management, allowing the required design values to be achieved under the same manufacturing conditions. This framework can efficiently operate on resource-limited and low-power computers, achieving the goal of real-time dynamic production parameter adjustments and enabling DRAM manufacturing companies to improve product quality promptly. Full article
(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition)
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16 pages, 5437 KiB  
Article
A Discrete Resistance Network Based on a Multiresolution Grid for 3D Ground-Return Current Forward Modeling
by Lijun Duan, Xiao Feng, Ruiheng Li, Tianyang Li, Yi Di and Tian Hao
Mathematics 2024, 12(15), 2392; https://doi.org/10.3390/math12152392 - 31 Jul 2024
Viewed by 1212
Abstract
While the high-voltage direct current (HVDC) transmission system is in monopolar operation, it produces thousands of amperes of ground-return currents (GRCs). Accurate computation of the GRCs is essential for assessing safety implications for nearby industrial infrastructure. Current three-dimensional forward models of GRCs are [...] Read more.
While the high-voltage direct current (HVDC) transmission system is in monopolar operation, it produces thousands of amperes of ground-return currents (GRCs). Accurate computation of the GRCs is essential for assessing safety implications for nearby industrial infrastructure. Current three-dimensional forward models of GRCs are typically constructed based on discrete differential equations, and their solving efficiency is constrained by the increased degrees of freedom resulting from the fine discretization grids in high-conductivity conductors and ground points. To address this issue, we present a new resistor network (RN) forward solver based on a multi-resolution grid approach. This solver utilizes an RN to avoid the massive degrees of freedom resulting from fine discretization of high-voltage conductors and enhances grid discretization efficiency near the surface grounding system through multi-resolution grids. We demonstrate, through multiple three-dimensional geoelectrical model cases, that the proposed method reduces the forward modeling misfit to 1% and possesses only 3‰ of the required discrete elements compared to traditional approaches. Furthermore, practical HVDC grid model analyses indicate the successful application of the proposed method for GRC analysis in complex geoelectric conditions. Full article
(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition)
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23 pages, 3780 KiB  
Article
An Efficient Approach for Localizing Sensor Nodes in 2D Wireless Sensor Networks Using Whale Optimization-Based Naked Mole Rat Algorithm
by Goldendeep Kaur, Kiran Jyoti, Samer Shorman, Anas Ratib Alsoud and Rohit Salgotra
Mathematics 2024, 12(15), 2315; https://doi.org/10.3390/math12152315 - 24 Jul 2024
Cited by 1 | Viewed by 806
Abstract
Localization has emerged as an important and critical component of research in Wireless Sensor Networks (WSNs). WSN is a network of numerous sensors distributed across broad areas of the world to conduct numerous activities, including sensing the data and transferring it to various [...] Read more.
Localization has emerged as an important and critical component of research in Wireless Sensor Networks (WSNs). WSN is a network of numerous sensors distributed across broad areas of the world to conduct numerous activities, including sensing the data and transferring it to various devices. Most applications, like animal tracking, object monitoring, and innumerable resources put in the interior as well as outdoor locations, need to identify the position of the occurring incident. The primary objective of localization is to identify the locality of sensor nodes installed in a network so that the location of a particular event can be traced. Different optimization approaches are observed in the work for solving the localization challenge in WSN and assigning the apt positions to undiscovered sensor nodes. This research employs the approach of localizing sensor nodes in a 2D platform utilizing an exclusive static anchor node and virtual anchors to detect dynamic target nodes by projecting these six virtual anchors hexagonally at different orientations and then optimizing the estimated target node co-ordinates employing Whale Optimization-based Naked Mole Rat Algorithm (WONMRA). Moreover, the effectiveness of a variety of optimization strategies employed for localization is compared to the WONMRA strategy concerning localization error and the number of nodes being localized, and it has been investigated that the average error in localization is 0.1999 according to WONMRA and is less than all other optimization techniques. Full article
(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications, 2nd Edition)
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