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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (30 April 2023) | Viewed by 16082

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Prof. Dr. Dmitry Sergeevich Kulyabov

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1. Department of Applied Probability and Informatics, Peoples' Friendship University of Russia (RUDN University), Moscow 117198, Russia
2. Joint Institute for Nuclear Research, 6 Joliot-Curie st, Dubna, Moscow 141980, Russia
Interests: special relativity; optics; differential geometry; general relativity; electrodynamics; mathematical modeling
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Prof. Dr. Leonid Sevastianov

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1. Department of Applied Probability and Informatics, Peoples' Friendship University of Russia (RUDN University), Moscow 117198, Russia
2. Joint Institute for Nuclear Research, 6 Joliot-Curie st, Dubna, Moscow 141980, Russia
Interests: mathematical modeling; computational physics; waveguide and integrated optics
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Dr. Anna Vladislavovna Korolkova

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Department of Applied Probability and Informatics, Peoples' Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya st, Moscow 117198, Russia
Interests: mathematical modeling; control systems

Special Issue Information

Dear Colleagues,

Mathematical modeling is a powerful scientific method. Application of mathematical models is the main method of physics. In modern research, the method of mathematical modeling is used not only in physics, but also in other areas of science. The classical approach to mathematical modeling is to describe the models themselves in the language of mathematics and study them using various numerical methods.

However, the language of mathematics is only one of the languages for describing models. Additionally, numerical methods are just one of many approaches, although they are the most popular. To describe the same phenomenon, you can use not one model, but a whole ensemble of models. Additionally, you can explore the resulting models in different ways, for example, using a combination of analytical and numerical research methods. We call this approach--where different implementations of models and ensembles of models are applied--the multi-model approach.

This Special Issue focuses on the application of the mathematical modeling method to various fields of science, especially applied science. We would also like to emphasize the multi-model approach, where we describe the same phenomenon using different models (and model approaches) and study it using different methods, including combined ones. We invite you to contribute and present your topical research papers.

Prof. Dr. Dmitry Sergeevich Kulyabov
Prof. Dr. Leonid Sevastianov
Dr. Anna Vladislavovna Korolkova
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
simulation
multi-model approach
computational methods
symbolic computation
analytical–numerical methods

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Published Papers (9 papers)

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Research

23 pages, 15939 KiB

Open AccessArticle

Bubble Sliding Characteristics and Dynamics of R134a during Subcooled Boiling Flow in a Narrow Gap

by Bo Yu, Jinfeng Wang, Jing Xie, Bingjun Wang, Fei Wang and Meng Deng

Mathematics 2023, 11(9), 2197; https://doi.org/10.3390/math11092197 - 6 May 2023

Cited by 1 | Viewed by 1801

Abstract

The numerical method was used to study bubble sliding characteristics and dynamics of R134a during subcooled flow boiling in a narrow gap. In the numerical method, the volume of fraction (VOF) model, level set method, Lee phase change model and the SST k − ω turbulent model were adopted for the construction of the subcooled flow boiling model. In order to explore bubble sliding dynamics during subcooled flow boiling, the bubble sliding model was introduced. The bubble velocity, bubble departure diameter, sliding distance and bubble sliding dynamics were investigated at 0.2 to 5 m/s inlet velocities. The simulation results showed that the bubble velocity at the flow direction was the most important contribution to bubble velocity. Additionally, the bubble velocity of 12 bubbles mostly oscillated with time during the sliding process at 0.2 to 0.6 m/s inlet velocities, while the bubble velocity increased during the sliding process due to the bubble having had a certain inertia at 2 to 5 m/s inlet velocities. It was also found that the average bubble velocity in flow direction accounted for about 80% of the mainstream velocities at 0.2 to 5 m/s. In the investigation of bubble sliding distance and departure diameter, it was concluded that the ratio of the maximum sliding distance to the minimum sliding distance was close to two at inlet velocities of 0.3 to 5 m/s. Moreover, with increasing inlet velocity, the average sliding distance increased significantly. The average bubble departure diameter obviously increased from 0.2 to 0.5 m/s inlet velocity and greatly reduced after 0.6 m/s. Finally, the investigations of the bubble sliding dynamics showed that the surface tension dominated the bubble sliding process at 0.2 to 0.6 m/s inlet velocities. However, the drag force dominated the bubble sliding process at 2 to 5 m/s inlet velocities. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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18 pages, 5772 KiB

Open AccessArticle

A Novel Kinematics Model of Flip-Flow Screen Panel: Inclined Catenary Model

by Jingfeng Fan, Zhanshu He, Yifei Zhang and Mingli Wang

Mathematics 2023, 11(9), 2028; https://doi.org/10.3390/math11092028 - 25 Apr 2023

Cited by 3 | Viewed by 1112

Abstract

A flip-flow screen can effectively screen viscous particles, and its kinematic characteristics determine its screening performance. Since previous kinematic models have errors, a novel kinematics model of the flip-flow screen panel, namely the inclined catenary model, is developed. It is verified by comparing theoretical motion trajectory with experimental motion trajectory. Then, the kinematic characteristics, i.e., displacement, velocity and acceleration, obtained using four kinematic models, are compared. Finally, the effects of rotation speed n, eccentricity e, incline angle α and tensional amount Δl on displacement, velocity and acceleration of the midpoint are investigated. The results show that displacement, velocity and acceleration of each point in the screen panel can be calculated by using the inclined catenary model, and the inclined catenary model possesses higher prediction accuracy than the three previous kinematic models. Moreover, with the increase in n, the absolute value of velocity and acceleration increases, and the maximum absolute value of displacement remains unchanged. With the increase in e, the absolute value of displacement, velocity and acceleration increases. With the increase in α, the absolute value of transverse components of displacement, velocity and acceleration increases slowly and the absolute value of longitudinal components of displacement, velocity and acceleration decreases slightly. With the increase in Δl, the absolute value of displacement, velocity and acceleration increases. Therefore, the inclined catenary model can provide good guidance for selecting reasonable screening parameters. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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20 pages, 5487 KiB

Open AccessArticle

A Dam Deformation Residual Correction Method for High Arch Dams Using Phase Space Reconstruction and an Optimized Long Short-Term Memory Network

by Yantao Zhu, Mingxia Xie, Kang Zhang and Zhipeng Li

Mathematics 2023, 11(9), 2010; https://doi.org/10.3390/math11092010 - 24 Apr 2023

Cited by 22 | Viewed by 2026

Abstract

Dam safety is an important basic part of national water network security. Building a dam deformation prediction model based on monitoring data is crucial to ensure dam safety. However, traditional statistical regression methods have shortcomings, such as a weak nonlinear fitting ability when constructing dam deformation monitoring and prediction models. The residual part of the statistical regression results usually contains parts that cannot be effectively explained by the linear regression method, that is usually highly variable and noisy. In this study, the phase space reconstruction method is used to smooth the residual term of the statistical regression model to eliminate noise interference. On this basis, an improved long short-term memory (LSTM) neural network is used to learn the nonlinearity contained in the residual term of the linear regression. Considering the impact of parameter selection on model performance, the gray wolf optimization (GWO) algorithm is used to determine the optimal parameters of the model for better performance. A high arch dam is used as a case study, with multiple measuring points used as research objects. The experimental results show that the phase space reconstruction can effectively smooth the high-frequency components in the residual term and remove noise interference. In addition, the GWO algorithm can effectively determine the hyperparameters of the LSTM network, thereby constructing a residual prediction model with high prediction accuracy. The combination of statistical models and deep learning prediction methods can effectively improve the model prediction performance while preserving the model interpretability and transparency. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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29 pages, 12246 KiB

Open AccessArticle

Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China

by Chenfei Shao, Erfeng Zhao, Yanxin Xu, Sen Zheng and Shiguang Tian

Mathematics 2023, 11(7), 1753; https://doi.org/10.3390/math11071753 - 6 Apr 2023

Cited by 6 | Viewed by 1599

Abstract

During the operational period, unexpected upstream deformation has been observed in several super-high arch dams located in the alpine and gorge regions. In addition, the phenomenon of the downstream dam deformation monitoring values being apparently smaller than the numerical simulation results appears in some super-high arch dams. This paper focuses on the genetic mechanism of a super-high arch dam’s special deformation characteristics. The finite element method (FEM) was used to analyze the effects of solar radiation, valley contraction, and overhanging on super-high arch dam’s deformation behavior. First, the influences of solar radiation on the temperature field and deformation characteristics of the super-high arch dam under the shading effects of the mountain and the dam body were investigated. Second, the impacts of valley contraction on the deformation characteristics of the super-high arch dam during the storage period were studied. Subsequently, the impact of the overhanging effect on the super-high arch dam’s deformation was explored. Finally, a case study was conducted on the basis of the Jinping I super-high arch dam to evaluate the effectiveness of the proposed analytical method. It is indicated that the dam’s special deformation can be explained reasonably. Above all, in order to accurately analyze and predict the deformation characteristics of super high-arch dams in the alpine and gorge regions of Southwest China, solar radiation, valley contraction, and the dam-overhanging effect need to be considered as influencing factors of dam deformation. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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10 pages, 726 KiB

Open AccessArticle

Numerical Study on the Orthogonality of the Fields Radiated by an Aperture

by Lucas Polo-López, Juan Córcoles, Jorge A. Ruiz-Cruz, José R. Montejo-Garai and Jesús M. Rebollar

Mathematics 2023, 11(5), 1198; https://doi.org/10.3390/math11051198 - 28 Feb 2023

Viewed by 1171

Abstract

This work studies the orthogonality of the fields radiated by the different modes of a radiating aperture. Waveguide modes exhibit an orthogonality property at the aperture cross-section that can be used to simplify calculations. However, it is unclear whether this property can be extended to the radiated fields produced by these same modes in apertures antennas, such as horns or open-ended waveguides. A numerical study has been carried out, analysing how the waveguide orthogonality extends to the radiated modal fields. It is observed that propagating modes and also modes that are well below cutoff follow this same behaviour. However, modes that are close to cutoff exhibit values in between those far from this transition region. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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22 pages, 14902 KiB

Open AccessArticle

Ordinary Kriging Interpolation Method Combined with FEM for Arch Dam Deformation Field Estimation

by Chenfei Shao, Yanxin Xu, Huixiang Chen, Sen Zheng and Xiangnan Qin

Mathematics 2023, 11(5), 1106; https://doi.org/10.3390/math11051106 - 22 Feb 2023

Cited by 7 | Viewed by 2049

Abstract

The deformation characteristic of the arch dam can directly reflect its service performance, which can be analyzed on the basis of the dam deformation field. However, restricted by the limited number of dam monitoring points and the inhomogeneity of materials, an accurate measurement of arch dam deformation field is difficult to estimate by using the existing common methods, such as the spatial interpolation methods and the finite element method (FEM). With the aim of ensuring arch dam structure safety, the ordinary kriging interpolation method, combined with FEM, is proposed for arch dam deformation field estimation, in this study. Given the inversion of the computation parameters of the arch dam, FEM is used to calculate the basic arch dam deformation. Subsequently, the ordinary kriging interpolation method is introduced to estimate the spatial variance deformation at each point of the arch dam. One superhigh arch dam in China is selected as a case study; two additional methods are introduced as comparisons that are based on a numerical experiment and the actual monitoring data. The experimental results show that the proposed method considerably improves the accuracy and computational efficiency of the arch dam deformation field estimation and that it is of great practical importance for characterizing the deformation behavior of arch dams. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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17 pages, 8322 KiB

Open AccessArticle

Structural Modal Parameter Identification Method Based on the Delayed Transfer Rate Function under Periodic Excitations

by Yanxin Xu, Dongjian Zheng, Chenfei Shao, Sen Zheng and Hao Gu

Mathematics 2023, 11(4), 1019; https://doi.org/10.3390/math11041019 - 16 Feb 2023

Cited by 2 | Viewed by 1393

Abstract

The dynamic response transfer rate function (TRF) is increasingly used in the field of structural modal parameter identification because it does not depend on the white noise assumption of the excitation. In this paper, the interference of periodic excitation on structural modal parameter identification using TRF is analyzed theoretically for a class of civil engineering structures with obvious periodic components in excitation, and then an identification method of structural real modal parameters is proposed. First, a delayed TRF is constructed, and the pseudo-frequency response function is further obtained to identify the periodic spurious poles of the whole system. Then, the effective identification of the real modal parameters of the structure is achieved by comparing the system poles identified via conventional TRF. Finally, the feasibility and robustness of the proposed method were verified using a calculation example with four-degrees-of-freedom system. In addition, the modal parameters of a structure under periodic excitation were effectively identified by taking a pumping station as an example, and the results show that the method accurately identified the structural modal parameters when the excitation contained periodic components, which has wider prospects for technical applications. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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24 pages, 1053 KiB

Open AccessArticle

The Optical Path Method for the Problem of Oblique Incidence of a Plane Electromagnetic Wave on a Plane-Parallel Scatterer

by Aleksandr Belov and Zhanna Dombrovskaya

Mathematics 2023, 11(2), 466; https://doi.org/10.3390/math11020466 - 15 Jan 2023

Viewed by 1862

Abstract

A number of actual problems of integrated photonics are reduced to an oblique incidence of radiation on a plane-parallel scatterer. For such problems, an approximate method of integrating the Maxwell equations along the beam propagation direction is proposed. As a result, the original two-dimensional problem is reduced to a one-dimensional one, and recently proposed one-dimensional bicompact schemes are used to solve it. This approach provides a significant reduction of computational costs compared to traditional two-dimensional methods such as finite differences and finite elements. To verify the proposed method, calculations of test and applied problems with known exact reflection spectra are carried out. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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14 pages, 17667 KiB

Open AccessArticle

Multiaxial Strength Criterion Model of Concrete Based on Random Forest

by Xingqiao Chen, Dongjian Zheng, Yongtao Liu, Xin Wu, Haifeng Jiang and Jianchun Qiu

Mathematics 2023, 11(1), 244; https://doi.org/10.3390/math11010244 - 3 Jan 2023

Cited by 3 | Viewed by 1703

Abstract

The concrete strength criterion is the basis of strength analysis and evaluation under a complex stress state. In this paper, a large number of multiaxial strength tests were carried out, and many mathematical expressions of strength criteria were proposed based on the geometric characteristics and the assumption of a convex function. However, the rationality of the assumption of a convex function limits the use of these strength criteria. In particular, misjudgment will occur near the failure curve surface. Therefore, this paper does not assume the shape function of the criterion in advance. By collecting experimental data and using a machine learning method, it proposes a method of hidden function of failure curve surface. Based on 777 groups of experimental data, the random forest (RF), the back propagation neural network (BP) and the radial basis neural network (RBF) models were used to analyze and verify the feasibility and effectiveness of the method. Subsequently, the results were compared with the Ottosen strength criterion, the Guo Wang strength criterion and the Drucker–Prager (DP) strength criterion. The results show that the consistency between the strength criterion model established by the machine learning algorithm (especially random forest) and the experimental data is higher than the convex function multiaxis strength criterion of the preset failure surface shape. Moreover, the physical significance is clearer, the deficiency of the convex function failure surface hypothesis is avoided and the established multiaxial strength criterion of concrete is more universal. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

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