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Symmetry
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Mathematical Modeling and Computational Methods in Science and Engineering IV
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Mathematical Modeling and Computational Methods in Science and Engineering IV

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 March 2023) | Viewed by 8829

Special Issue Editor

Prof. Dr. Juan Luis García Guirao

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dynamical systems; celestial mechanics; Hamiltonian systems; low-dimensional dynamics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, computational mathematics, science, and engineering have turned into rapidly growing multidisciplinary areas with connections to business, economics, engineering, mathematics, and computer science through academia as well as industry to understand and solve complex problems. Applied Mathematics is currently playing an important role in scientific research. The success of mathematical modeling depends on the parallel development of efficient computational methods as well as more sophisticated mathematical models. To develop novel computational methods, an interdisciplinary approach is needed that involves a variety of methods, including aspects such as stochastics, statistics, numeric, and scientific computing. Please note that all submitted papers must be within the general scope of the Symmetry journal.

The topics of research areas covered for this Special Issue are:

  • Mathematical (biology, chemistry, economics, engineering, and physics);
  • Neural networks;
  • Optimal control problems;
  • Probability and statistics;
  • Scientific computing;
  • Soft computing;
  • System dynamics;
  • System engineering;
  • Artificial intelligence;
  • Automation;
  • Big data analytics;
  • Chaos theory, control, and robotics;
  • Circuits and networks;
  • Complexity theory;
  • Computational mechanics;
  • Information theory;
  • Symmetry.

All papers submitted to the Special Issue will be thoroughly reviewed by at least two or three independent experts. We hope that this Special Issue will bring some changes and some new useful tools and applications in different fields, and that it will enrich the scientific community for the researchers in the concerned fields.

Prof. Dr. Juan Luis García Guirao
Guest Editor

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. Symmetry is an international peer-reviewed open access monthly 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 2400 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.

Published Papers (5 papers)

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Research

14 pages, 2742 KiB  
Article
Parameter Estimation in the Mathematical Model of Bacterial Colony Patterns in Symmetry Domain
by Rafał Brociek, Agata Wajda, Giacomo Capizzi and Damian Słota
Symmetry 2023, 15(4), 782; https://doi.org/10.3390/sym15040782 - 23 Mar 2023
Viewed by 1047
Abstract
The paper presents a solution to the problem related to the reconstruction of parameters in the mathematical model of bacterial colony patterns in a domain with symmetry. The inverse problem consists of determining the value of the diffusion coefficient of active bacteria. The [...] Read more.
The paper presents a solution to the problem related to the reconstruction of parameters in the mathematical model of bacterial colony patterns in a domain with symmetry. The inverse problem consists of determining the value of the diffusion coefficient of active bacteria. The model describing the distribution of active bacteria in a given region, as well as the concentration of the substrate over time is considered. Such a model consists of a system of partial differential equations with appropriate initial-boundary conditions. The finite element method was used to solve the direct problem. However, the Fibonacci search method was used to minimize the functional description of the error of the approximate solution. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)
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26 pages, 1303 KiB  
Article
Comparing the Min–Max–Median/IQR Approach with the Min–Max Approach, Logistic Regression and XGBoost, Maximising the Youden Index
by Rocío Aznar-Gimeno, Luis M. Esteban, Gerardo Sanz and Rafael del-Hoyo-Alonso
Symmetry 2023, 15(3), 756; https://doi.org/10.3390/sym15030756 - 19 Mar 2023
Cited by 1 | Viewed by 1490
Abstract
Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of [...] Read more.
Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of biomarkers, which is computationally tractable and has been shown to be optimal in certain scenarios. We developed the Min–Max–Median/IQR algorithm under Youden index optimisation which, although more computationally intensive, is still approachable and includes more information. The aim of this work is to compare the performance of these algorithms with well-known Machine Learning algorithms, namely logistic regression and XGBoost, which have proven to be efficient in various fields of applications, particularly in the health sector. This comparison is performed on a wide range of different scenarios of simulated symmetric or asymmetric data, as well as on real clinical diagnosis data sets. The results provide useful information for binary classification problems of better algorithms in terms of performance depending on the scenario. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)
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15 pages, 2314 KiB  
Article
Selection of Relative DEM Time Step for Modelling Fast Fluidized Bed of A-Type FCC Particles
by Guorong Wu, Zhanfei Zuo and Yanggui Li
Symmetry 2023, 15(2), 488; https://doi.org/10.3390/sym15020488 - 13 Feb 2023
Cited by 1 | Viewed by 1005
Abstract
In chemical production processes, the most suitable operation regime for A-Type powders such as typical FCC particles is high-speed fast fluidization owing to their uniquely advantageous properties. Discrete element method (DEM) for modelling fast fluidization with A-Type powders has rarely been reported. How [...] Read more.
In chemical production processes, the most suitable operation regime for A-Type powders such as typical FCC particles is high-speed fast fluidization owing to their uniquely advantageous properties. Discrete element method (DEM) for modelling fast fluidization with A-Type powders has rarely been reported. How to appropriately select the DEM time step and the stiffness coefficient is one of the most critical problems for stable and accurate calculation. This article mainly discusses the effect of the stiffness coefficient and DEM time step on simulations of A-type FCC particles. In order to describe the effect of both parameters and their complex interaction, a dimensionless relative DEM time step is introduced. In total, nine cases with different numbers of relative time steps are adopted for modelling a microfluidized bed of A-Type FCC particles, the regime of which is proved to be fast fluidization. Results show that three bifurcations occur in all the simulations. Only the moderate relative time step possesses the capability of modelling the process of particle collision and thus predicts the right flow regime with asymmetric and heterogeneous typical fast fluidized structures. When the relative time step increases to large rank, simulations predict untrue fluidization regimes with symmetric and homogeneous structures. Moreover, both over-large and over-low relative time steps cause excessive particle overlap and thus a divergence of simulation. The further optimization of moderate relative DEM time step in relation to real particle property is unidentifiable and is thus an outstanding issue. That the range of the moderate relative time step is limited indicates that the common soft-sphere model is poor at modelling fast fluidization of A-Type particles. It is suggested that possible future work should be focused on improving the simulation frame and employing the molecular dynamics model to more appropriately deal with particle contact. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)
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23 pages, 2306 KiB  
Article
Analysis of MHD Falkner–Skan Boundary Layer Flow and Heat Transfer Due to Symmetric Dynamic Wedge: A Numerical Study via the SCA-SQP-ANN Technique
by Kamsing Nonlaopon, Muhammad Fawad Khan, Muhammad Sulaiman, Fahad Sameer Alshammari and Ghaylen Laouini
Symmetry 2022, 14(10), 2180; https://doi.org/10.3390/sym14102180 - 17 Oct 2022
Cited by 3 | Viewed by 1742
Abstract
This article considers Falkner–Skan flow over a dynamic and symmetric wedge under the influence of a magnetic field. The Hall effect on a magnetic field is negligible for small magnetic Reynolds numbers. The magnetic field B(x) is considered over x [...] Read more.
This article considers Falkner–Skan flow over a dynamic and symmetric wedge under the influence of a magnetic field. The Hall effect on a magnetic field is negligible for small magnetic Reynolds numbers. The magnetic field B(x) is considered over x-axis, which is in line with the wedge i.e., parallel, while the flow is transverse over the y-axis. This study has numerous device-centric applications in engineering, such as power generators, cooling reactor and heat exchanger design, and MHD accelerators. The Third and second-ordered ordinary differential equations characterize the system. A novel hybrid computational technique is designed for the surrogate solutions of the Falkner–Skan flow system. The designed technique is based on the sine–cosine optimization algorithm and sequential quadratic programming. Reference solutions are calculated by using the Runge–Kutta numerical technique. Performance matrices evaluate the accuracy and stability of our surrogate solutions, mean-absolute deviation (MAD), root-mean-square error (RMSE), and error in Nash-–Sutcliffe efficiency (ENSE). Furthermore, graphical representations in terms of convergence graphs, mesh graphs, stem graphs, stairs plots, and boxplots are presented to establish the symmetry, reliability, and validity of our solutions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)
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23 pages, 2471 KiB  
Article
A Machine Learning Strategy for the Quantitative Analysis of the Global Warming Impact on Marine Ecosystems
by Hosam Alhakami, Mustafa Kamal, Muhammad Sulaiman, Wajdi Alhakami and Abdullah Baz
Symmetry 2022, 14(10), 2023; https://doi.org/10.3390/sym14102023 - 26 Sep 2022
Cited by 14 | Viewed by 2218
Abstract
It is generally observed that aquatic organisms have symmetric abilities to produce oxygen (O2) and fix carbon dioxide (CO2). A simulation model with time-dependent parameters was recently proposed to better understand the symmetric effects of [...] Read more.
It is generally observed that aquatic organisms have symmetric abilities to produce oxygen (O2) and fix carbon dioxide (CO2). A simulation model with time-dependent parameters was recently proposed to better understand the symmetric effects of accelerated climate change on coastal ecosystems. Changes in environmental elements and marine life are two examples of variables that are expected to change over time symmetrically. The sustainability of each equilibrium point is examined in addition to proving the existence and accuracy of the proposed model. To support the conclusions of this research compared to other studies, numerical simulations of the proposed model and a case study are investigated. This paper proposes an integrated bibliographical analysis of artificial neural networks (ANNs) using the Reverse-Propagation with Levenberg–Marquaradt Scheme (RP-LMS) to evaluate the main properties and applications of ANNs. The results obtained by RP-LMS show how to prevent global warming by improving the management of marine fish resources. The reference dataset for greenhouse gas emissions, environmental temperature, aquatic population, and fisheries population (GAPF) is obtained by varying parameters in the numerical Adam approach for different scenarios. The accuracy of the proposed RP-LMS neural network is demonstrated using mean square error (MSE), regression plots, and best-fit output. According to RP-LMS, the current scenario of rapid global warming will continue unabated over the next 50 years, damaging marine ecosystems, particularly fish stocks. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)
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