Symmetry

30 pages, 11885 KiB

Open AccessArticle

The Effect of Multiple Additional Sampling with Multi-Fidelity, Multi-Objective Efficient Global Optimization Applied to an Airfoil Design

by Tharathep Phiboon, Auraluck Pichitkul, Suradet Tantrairatn, Sujin Bureerat, Masahiro Kanazaki and Atthaphon Ariyarit

Symmetry 2024, 16(8), 1094; https://doi.org/10.3390/sym16081094 - 22 Aug 2024

Viewed by 742

Abstract

The multiple additional sampling point method has become popular for use in Efficient Global Optimization (EGO) to obtain aerodynamically shaped designs in recent years. It is a challenging task to study the influence of adding multi-sampling points, especially when multi-objective and multi-fidelity requirements [...] Read more.

The multiple additional sampling point method has become popular for use in Efficient Global Optimization (EGO) to obtain aerodynamically shaped designs in recent years. It is a challenging task to study the influence of adding multi-sampling points, especially when multi-objective and multi-fidelity requirements are applied in the EGO process, because its factors have not been revealed yet in the research. In this study, the addition of two (multi-) sampling points (2-MAs) and four (multi-) sampling points (4-MAs) in each iteration are used to study the proposed techniques and compare them against results obtained from a single additional sampling point (1-SA); this is the approach that is conventionally used for updating the hybrid surrogate model. The multi-fidelity multi-objective method is included in EGO. The performance of the system, the computational convergence rate, and the model accuracy of the hybrid surrogate are the main elements for comparison. Each technique is verified by mathematical test functions and is applied to the airfoil design. Class Shape Function Transformation is used to create the airfoil shapes. The design objectives are to minimize drag and to maximize lift at designated conditions for a Reynolds number of one million. Computational Fluid Dynamics is used for ensuring high fidelity, whereas the panel method is employed when ensuring low fidelity. The Kriging method and the Radial Basis Function were utilized to construct high-fidelity and low-fidelity functions, respectively. The Genetic Algorithm was employed to maximize the Expected Hypervolume Improvement. Similar results were observed from the proposed techniques with a slight reduction in drag and a significant rise in lift compared to the initial design. Among the different techniques, the 4-MAs were found to converge at the greatest rate, with the best accuracy. Moreover, all multiple additional sampling point techniques are shown to improve the model accuracy of the hybrid surrogate and increase the diversity of the data compared to the single additional point technique. Hence, the addition of four sampling points can enhance the overall performance of multi-fidelity, multi-objective EGO and can be utilized in highly sophisticated aerodynamic design problems. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

13 pages, 3303 KiB

Open AccessArticle

Multistability, Chaos, and Synchronization in Novel Symmetric Difference Equation

by Othman Abdullah Almatroud, Ma’mon Abu Hammad, Amer Dababneh, Louiza Diabi, Adel Ouannas, Amina Aicha Khennaoui and Saleh Alshammari

Symmetry 2024, 16(8), 1093; https://doi.org/10.3390/sym16081093 - 22 Aug 2024

Viewed by 424

Abstract

This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of [...] Read more.

This paper presents a new third-order symmetric difference equation transformed into a 3D discrete symmetric map. The nonlinear dynamics and symmetry of the proposed map are analyzed with two initial conditions for exploring the sensitivity of the map and highlighting the influence of the map parameters on its behaviors, thus comparing the findings. Moreover, the stability of the zero fixed point and symmetry are examined by theoretical analysis, and it is proved that the map generates diverse nonlinear traits comprising multistability, chaos, and hyperchaos, which is confirmed by phase attractors in 2D and 3D space, Lyapunov exponents (

L E_{s}

) analysis and bifurcation diagrams; also, 0-1 test and sample entropy (SampEn) are used to confirm the existence and measure the complexity of chaos. In addition, a nonlinear controller is introduced to stabilize the symmetry map and synchronize a duo of unified symmetry maps. Finally, numerical results are provided to illustrate the findings. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos II)

► Show Figures

Figure 1

12 pages, 283 KiB

Open AccessArticle

Extending Ramsey Numbers for Connected Graphs of Size 3

by Emma Jent, Sawyer Osborn and Ping Zhang

Symmetry 2024, 16(8), 1092; https://doi.org/10.3390/sym16081092 - 22 Aug 2024

Viewed by 567

Abstract

It is well known that the famous Ramsey number

R (K_{3}, K_{3}) = 6

. That is, the minimum positive integer n for which every red-blue coloring of the edges of the complete graph

K_{n}

results in [...] Read more.

It is well known that the famous Ramsey number

R (K_{3}, K_{3}) = 6

. That is, the minimum positive integer n for which every red-blue coloring of the edges of the complete graph

K_{n}

results in a monochromatic triangle

K_{3}

is 6. It is also known that every red-blue coloring of

K_{6}

results in at least two monochromatic triangles, which need not be vertex-disjoint or edge-disjoint. This fact led to an extension of Ramsey numbers. For a graph F and a positive integer t, the vertex-disjoint Ramsey number

V R_{t} (F)

is the minimum positive integer n such that every red-blue coloring of the edges of the complete graph

K_{n}

of order n results in t pairwise vertex-disjoint monochromatic copies of subgraphs isomorphic to F, while the edge-disjoint Ramsey number

E R_{t} (F)

is the corresponding number for edge-disjoint subgraphs. Since

V R_{1} (F)

and

E R_{1} (F)

are the well-known Ramsey numbers of F, these new Ramsey concepts generalize the Ramsey numbers and provide a new perspective for this classical topic in graph theory. These numbers have been investigated for the two connected graphs

K_{3}

and the path

P_{3}

of order 3. Here, we study these numbers for the remaining connected graphs, namely, the path

P_{4}

and the star

K_{1, 3}

of size 3. We show that

V R_{t} (P_{4}) = 4 t + 1

for every positive integer t and

V R_{t} (K_{1, 3}) = 4 t

for every integer

t \geq 2

. For

t \leq 4

, the numbers

E R_{t} (K_{1, 3})

and

E R_{t} (P_{4})

are determined. These numbers provide information towards the goal of determining how the numbers

V R_{t} (F)

and

E R_{t} (F)

increase as t increases for each graph

F \in {K_{1, 3}, P_{4}}

. Full article

(This article belongs to the Special Issue Symmetry in Graph Algorithms and Graph Theory III)

► Show Figures

Figure 1

20 pages, 631 KiB

Open AccessArticle

Enhanced Double Inertial Forward–Backward Splitting Algorithm for Variational Inclusion Problems: Applications in Mathematical Integrated Skill Prediction

by Nipa Jun-On and Watcharaporn Cholamjiak

Symmetry 2024, 16(8), 1091; https://doi.org/10.3390/sym16081091 - 22 Aug 2024

Viewed by 798

Abstract

This paper introduces a new algorithm that combines the forward–backward splitting algorithms with a double inertial technique, utilizing the previous three iterations. The weak convergence theorem is established under certain mild conditions in a Hilbert space, including a relaxed inertial method in real [...] Read more.

This paper introduces a new algorithm that combines the forward–backward splitting algorithms with a double inertial technique, utilizing the previous three iterations. The weak convergence theorem is established under certain mild conditions in a Hilbert space, including a relaxed inertial method in real numbers. An example of infinite dimension space is given with numerical results to support our proposed algorithm. The algorithm is applied to an asymmetrical educational dataset of students from 109 schools, utilizing asymmetric inputs as nine attributes to predict the output as students’ mathematical integrated skills. The algorithm’s performance is compared with other algorithms in the literature to demonstrate its effectiveness. The proposed algorithm demonstrates comparable precision, recall, accuracy, and F1 score but performs a relatively lower number of iterations. The contributions of each performance aspect to the mathematical integration skill of students are discussed to improve students’ mathematical learning. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)

► Show Figures

Figure 1

18 pages, 340 KiB

Open AccessArticle

The p-Frobenius Number for the Triple of the Generalized Star Numbers

by Ruze Yin, Jiaxin Mu and Takao Komatsu

Symmetry 2024, 16(8), 1090; https://doi.org/10.3390/sym16081090 - 22 Aug 2024

Viewed by 600

Abstract

In this paper, we give closed-form expressions of the p-Frobenius number for the triple of the generalized star numbers

a n (n - 1) + 1

for an integer

a \geq 4

. When

a = 6

, it is [...] Read more.

In this paper, we give closed-form expressions of the p-Frobenius number for the triple of the generalized star numbers

a n (n - 1) + 1

for an integer

a \geq 4

. When

a = 6

, it is reduced to the famous star number. For the set of given positive integers

{a_{1}, a_{2}, \dots, a_{k}}

, the p-Frobenius number is the largest integer N whose number of non-negative integer representations

N = a_{1} x_{1} + a_{2} x_{2} + \dots + a_{k} x_{k}

is at most p. When

p = 0

, the 0-Frobenius number is the classical Frobenius number, which is the central topic of the famous linear Diophantine problem of Frobenius. Full article

(This article belongs to the Special Issue Symmetry in Combinatorial Structures)

► Show Figures

Figure 1

16 pages, 9639 KiB

Open AccessArticle

Hierarchical Hypervapotron Structure Integrated with Microchannels for Advancement of Thermohydraulic Performance

by Xin Meng, Kai Cheng, Qi Zhao and Xuemei Chen

Symmetry 2024, 16(8), 1089; https://doi.org/10.3390/sym16081089 - 22 Aug 2024

Viewed by 393

Abstract

The hypervapotron structure was considered to be a feasible configuration to meet the high heat-dissipating requirement of divertors in nuclear fusion devices. In this work, symmetric CuCrZr-based transverse microchannels (TMHC) and longitudinal microchannels (LMHC) with an integrated hypervapotron channel were proposed and manufactured, [...] Read more.

The hypervapotron structure was considered to be a feasible configuration to meet the high heat-dissipating requirement of divertors in nuclear fusion devices. In this work, symmetric CuCrZr-based transverse microchannels (TMHC) and longitudinal microchannels (LMHC) with an integrated hypervapotron channel were proposed and manufactured, and subcooled flow boiling experiments were conducted using deionized water at an inlet temperature of 20 °C with a traditional flat-type hypervapotron channel (FHC) for comparison. The LMHC and TMHC obtained lower wall temperatures than the FHC for all conditions, and the TMHC yielded the lowest temperatures. The heat transfer coefficients of the LMHC and TMHC outperformed the FHC due to the enlarged heat transfer area, and the TMHC had the greatest heat transfer coefficient (maximumly increased by 132% compared to the FHC) because the transverse-arranged microchannels were conductive, promoting the convection and liquid replenishment ability by introducing branch flow between fins; however, the microchannels of the LMHC were insensible to flow velocities due to the block effect of longitudinal microchannels. The LMHC obtained the largest pressure drop, and the pressure drop for the FHC and TMHC were comparable since the transverse-placed microchannels had little effect on frictional pressure loss. The TMHC attained the greatest comprehensive thermohydraulic performance which might bring significant insight to the structural design of hypervapotron devices. Full article

(This article belongs to the Special Issue Feature Papers in Section "Engineering and Materials" 2024)

► Show Figures

Figure 1

13 pages, 267 KiB

Open AccessArticle

New Fixed Point Theorems for Generalized Meir–Keeler Type Nonlinear Mappings with Applications to Fixed Point Theory

by Shin-Yi Huang and Wei-Shih Du

Symmetry 2024, 16(8), 1088; https://doi.org/10.3390/sym16081088 - 22 Aug 2024

Viewed by 675

Abstract

In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is [...] Read more.

In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is provided to illustrate and support our main results. Full article

(This article belongs to the Special Issue Fixed Point Theory and Its Applications Dedicated to the Memory of Professor William Arthur Kirk)

10 pages, 804 KiB

Open AccessArticle

Sex-Based Differences in Pressure Pain Thresholds of Myofascial Trigger Points in Cervical and Cranial Muscles in Tension-Type Headache: A Cross-Sectional Study

by Sofía Monti-Ballano, María Orosia Lucha-López, César Hidalgo-García, Loreto Ferrández-Laliena, Lucía Vicente-Pina, Rocío Sánchez-Rodríguez, Héctor José Tricás-Vidal and José Miguel Tricás-Moreno

Symmetry 2024, 16(8), 1087; https://doi.org/10.3390/sym16081087 - 21 Aug 2024

Viewed by 508

Abstract

Background: Tension-type headache (TTH) is the most prevalent primary headache. Pressure pain thresholds (PPTs) reflect the pressure pain sensitivity of the tissues. Women with TTH have showed greater pressure hypersensitivity in some muscles compared to men. The aim of this study was to [...] Read more.

Background: Tension-type headache (TTH) is the most prevalent primary headache. Pressure pain thresholds (PPTs) reflect the pressure pain sensitivity of the tissues. Women with TTH have showed greater pressure hypersensitivity in some muscles compared to men. The aim of this study was to compare the PPTs from myofascial trigger points in cervical and cranial muscles which might contribute to headaches between men and women with TTH. Methods: An observational and correlation cross-sectional study was performed. PPTs were evaluated bilaterally and compared between men and women in the following muscles: upper trapezius, splenius capitis and cervicis, semispinalis, rectus capitis posterior major, obliquus capitis superior and inferior, occipitofrontalis posterior and anterior, temporalis, masseter, clavicular and sternal head of sternocleidomastoid, zygomaticus major, and levator scapulae. The mean PPT was calculated as well. Results: Significant differences showing lower PPTs in women compared to men were found in the mean PPT (p = 0.000) and in all the points except in the left clavicular head of the sternocleidomastoid (p = 0.093) and in the left masseter (p = 0.069). Conclusions: Lower PPTs from myofascial trigger points in cervical and cranial muscles, which might contribute to headaches, were observed in women compared to men with TTH. The mean PPT was also lower in women than in men, suggesting the need for gender-specific approaches in the treatment of TTH. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Life Sciences: Feature Papers 2024)

► Show Figures

Figure 1

27 pages, 1550 KiB

Open AccessArticle

An Integrated Bayesian Best–Worst Method and Consensus-Based Intuitionistic Fuzzy Evaluation Based on Distance from Average Solution Approach for Evaluating Alternative Aircraft Models from a Sustainability Perspective

by Ergun Arı and Mehtap Dursun

Symmetry 2024, 16(8), 1086; https://doi.org/10.3390/sym16081086 - 21 Aug 2024

Viewed by 676

Abstract

Sustainability in transportation is vital for lessening environmental effects and ensuring the long-term viability of the transportation industry. The aviation sector, a significant player in sustainable transport, has encountered obstacles in reducing its ecological footprint, especially in aircraft design and operation. Symmetry and [...] Read more.

Sustainability in transportation is vital for lessening environmental effects and ensuring the long-term viability of the transportation industry. The aviation sector, a significant player in sustainable transport, has encountered obstacles in reducing its ecological footprint, especially in aircraft design and operation. Symmetry and asymmetry exist widely in the aviation sector, as in other industrial applications. Multicriteria decision making (MCDM) is an important research topic that is widely applied to practical decision-making problems and is considered a complex tool with which to balance the symmetry between goals and conflicting criteria. This research assesses different airplane models in order to pinpoint the most environmentally friendly options using the Bayesian best–worst (BWM) method for evaluating criteria and the consensus-based intuitionistic fuzzy evaluation based on distance from average solution (IF EDAS) method for assessing alternatives. The Bayesian BWM approach facilitates group decision making on criteria evaluation and systematically evaluates factors like fuel efficiency, emissions, and noise levels, offering a holistic view of each airplane model’s sustainability performance. Conversely, consensus-based IF EDAS allows for the ranking of alternatives based on their distance to the average solution for a sustainable airplane model while concurrently considering multiple criteria, guiding decisionmakers to a consensus and eliminating the asymmetry between opinions before the final decision. This study reveals that technical features are the critical criteria for airplanes and significantly influence alternative rankings. The findings indicate that the chosen decision criteria greatly impact the selection of the most sustainable airplane model as part of a sustainable transportation system, potentially altering ranking orders. Full article

(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)

► Show Figures

Figure 1

31 pages, 12862 KiB

Open AccessArticle

Investigation of Analytical Soliton Solutions to the Non-Linear Klein–Gordon Model Using Efficient Techniques

by Miguel Vivas-Cortez, Maham Nageen, Muhammad Abbas and Moataz Alosaimi

Symmetry 2024, 16(8), 1085; https://doi.org/10.3390/sym16081085 - 21 Aug 2024

Viewed by 668

Abstract

Nonlinear distinct models have wide applications in various fields of science and engineering. The present research uses the mapping and generalized Riccati equation mapping methods to address the exact solutions for the nonlinear Klein–Gordon equation. First, the travelling wave transform is used to [...] Read more.

Nonlinear distinct models have wide applications in various fields of science and engineering. The present research uses the mapping and generalized Riccati equation mapping methods to address the exact solutions for the nonlinear Klein–Gordon equation. First, the travelling wave transform is used to create an ordinary differential equation form for the nonlinear partial differential equation. This work presents the construction of novel trigonometric, hyperbolic and Jacobi elliptic functions to the nonlinear Klein–Gordon equation using the mapping and generalized Riccati equation mapping methods. In the fields of fluid motion, plasma science, and classical physics the nonlinear Klein–Gordon equation is frequently used to identify of a wide range of interesting physical occurrences. It is considered that the obtained results have not been established in prior study via these methods. To fully evaluate the wave character of the solutions, a number of typical wave profiles are presented, including bell-shaped wave, anti-bell shaped wave, W-shaped wave, continuous periodic wave, while kink wave, smooth kink wave, anti-peakon wave, V-shaped wave and flat wave solitons. Several 2D, 3D and contour plots are produced by taking precise values of parameters in order to improve the physical description of solutions. It is noteworthy that the suggested techniques for solving nonlinear partial differential equations are capable, reliable, and captivating analytical instruments. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Partial Differential Equations and Rogue Waves)

► Show Figures

Figure 1

19 pages, 1692 KiB

Open AccessArticle

An Efficient Cross-Modal Privacy-Preserving Image–Text Retrieval Scheme

by Kejun Zhang, Shaofei Xu, Yutuo Song, Yuwei Xu, Pengcheng Li, Xiang Yang, Bing Zou and Wenbin Wang

Symmetry 2024, 16(8), 1084; https://doi.org/10.3390/sym16081084 - 21 Aug 2024

Viewed by 758

Abstract

Preserving the privacy of the ever-increasing multimedia data on the cloud while providing accurate and fast retrieval services has become a hot topic in information security. However, existing relevant schemes still have significant room for improvement in accuracy and speed. Therefore, this paper [...] Read more.

Preserving the privacy of the ever-increasing multimedia data on the cloud while providing accurate and fast retrieval services has become a hot topic in information security. However, existing relevant schemes still have significant room for improvement in accuracy and speed. Therefore, this paper proposes a privacy-preserving image–text retrieval scheme called PITR. To enhance model performance with minimal parameter training, we freeze all parameters of a multimodal pre-trained model and incorporate trainable modules along with either a general adapter or a specialized adapter, which are used to enhance the model’s ability to perform zero-shot image classification and cross-modal retrieval in general or specialized datasets, respectively. To preserve the privacy of outsourced data on the cloud and the privacy of the user’s retrieval process, we employ asymmetric scalar-product-preserving encryption technology suitable for inner product calculation, and we employ distributed index storage technology and construct a two-level security model. We construct a hierarchical index structure to speed up query matching among massive high-dimensional index vectors. Experimental results demonstrate that our scheme can provide users with secure, accurate, fast cross-modal retrieval service while preserving data privacy. Full article

(This article belongs to the Section Computer)

► Show Figures

Figure 1

19 pages, 527 KiB

Open AccessArticle

Collaborative Service Network Design for Multiple Logistics Carriers Considering Demand Uncertainty

by Qihuan Zhang, Min Huang and Huihui Wang

Symmetry 2024, 16(8), 1083; https://doi.org/10.3390/sym16081083 - 21 Aug 2024

Viewed by 652

Abstract

Collaborative designing of service networks using multiple logistics carriers can bring advantages in both economic and environmental terms, and these carriers have symmetry in their service areas. To enable such a collaborative service network and the corresponding benefits, this study proposes a problem [...] Read more.

Collaborative designing of service networks using multiple logistics carriers can bring advantages in both economic and environmental terms, and these carriers have symmetry in their service areas. To enable such a collaborative service network and the corresponding benefits, this study proposes a problem of collaborative service network design (CSND) considering demand uncertainty. This problem is formulated as a two-stage robust optimization model using a budget uncertainty set to handle the uncertain demand. A column-and-constraint generation algorithm is developed to accurately solve the robust model. Numerical experiments show that the proposed algorithm outperforms the Benders decomposition algorithm in terms of solving efficiency and quality. Through comparative experiments, this research validates the advantages of collaborative designing and the robustness of model solutions. In addition, three allocation mechanisms are tested to investigate the importance of allocation in CSND. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

17 pages, 5693 KiB

Open AccessArticle

Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads

by Liyong Gao, Lei Jiang, Xingzheng Wang, Sheng Gao, Hongxu Cui, Jun Liu and Hekuan Zhou

Symmetry 2024, 16(8), 1082; https://doi.org/10.3390/sym16081082 - 21 Aug 2024

Viewed by 387

Abstract

In recent years, square hollow section (SHS) joints with concrete-filled square hollow section (CFSHS) chords have increasingly been used in truss bridges where the fatigue life reliability is a critical issue. In this paper, a finite element analysis was performed to investigate the [...] Read more.

In recent years, square hollow section (SHS) joints with concrete-filled square hollow section (CFSHS) chords have increasingly been used in truss bridges where the fatigue life reliability is a critical issue. In this paper, a finite element analysis was performed to investigate the SCFs in SHS-CFSHS T-joints under in-plane bending in the brace, axial force in the chord and in-plane bending in the chord. The finite element models were developed and validated with experimental results. Then a parametric study was conducted with a reasonable range of three key non-dimensional parameters, i.e., β (width ratio between brace and chord), 2γ (width–to–wall thickness ratio of the chord) and τ (wall thickness ratio between brace and chord). Consequently, the stress concentration factor formulae for the fatigue design of SHS-CFSHS T-joints were proposed through multiple regression analysis. For in-plane bending in the brace, the maximum stress concentration factors were found at lines B and C for thick-walled chords (2γ = 25.0), while the stress concentration factors at all the lines need to be checked for thin-walled chords (2γ < 16.0). Under axial force in the chord and in-plane bending in the chord, only stress concentration factors at lines C and D needed to be considered. A comparison of stress concentration factors between SHS-SHS and SHS-CFSHS joints showed reductions of 10~26% and 14~31% in stress concentration factors in SHS-CFSHS joints under axial force in the brace and in-plane bending in the brace, respectively. In addition, it showed a general increase in stress concentration factors in SHS-CFSHS joints under axial force and in-plane bending in the chord. This reduction is attributed to the reduction in chord face deformation benefiting from the in-filled concrete. Meanwhile, the stress concentration factors caused by loads in the chord are much lower than those caused by loads in the brace. This work complements earlier studies on SHS-CFSHS T-joints under axial force. Full article

(This article belongs to the Section Engineering and Materials)

► Show Figures

Figure 1

39 pages, 537 KiB

Open AccessArticle

Precise Wigner–Weyl Calculus for the Honeycomb Lattice

by Raphael Chobanyan and Mikhail A. Zubkov

Symmetry 2024, 16(8), 1081; https://doi.org/10.3390/sym16081081 - 20 Aug 2024

Viewed by 266

Abstract

In this paper, we propose a precise Wigner–Weyl calculus for the models defined on the honeycomb lattice. We construct two symbols of operators: the

B

symbol, which is similar to the one introduced by F. Buot, and the W (or, Weyl) symbol. The [...] Read more.

In this paper, we propose a precise Wigner–Weyl calculus for the models defined on the honeycomb lattice. We construct two symbols of operators: the

B

symbol, which is similar to the one introduced by F. Buot, and the W (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner-transformed Green function. This expression may be used for the description of the systems with artificial honeycomb lattice, when magnetic flux through the lattice cell is of the order of elementary quantum of magnetic flux. It is worth mentioning that, in the present paper, we do not consider the effect of interactions. Full article

(This article belongs to the Special Issue Symmetry and Quantum Orders)

► Show Figures

Figure 1

34 pages, 4306 KiB

Open AccessArticle

Post-Earthquake Emergency Logistics Location-Routing Optimization Considering Vehicle Three-Dimensional Loading Constraints

by Xujin Pu and Xu Zhao

Symmetry 2024, 16(8), 1080; https://doi.org/10.3390/sym16081080 - 20 Aug 2024

Viewed by 512

Abstract

An efficient humanitarian emergency logistics network is vital in responding to earthquake disasters. However, the asymmetric information inherent in the location and distribution stages can complicate the humanitarian emergency logistics network designing process, resulting in an asymmetric optimization problem. This paper addresses a [...] Read more.

An efficient humanitarian emergency logistics network is vital in responding to earthquake disasters. However, the asymmetric information inherent in the location and distribution stages can complicate the humanitarian emergency logistics network designing process, resulting in an asymmetric optimization problem. This paper addresses a multi-objective humanitarian emergency logistics network design problem during the earthquake response phase. The objective is to reduce societal expenses (e.g., logistical and deprivation costs) and mitigate risk to the logistics network by identifying ideal sites for distribution hubs, optimal emergency material distribution strategies, and precise material loading plans. The proposed model takes into account various constraint types, such as 3D loading limitations for relief materials, interruptions in distribution hubs, distribution centers’ capacity, transport vehicles’ capacity, and specific time windows for demand points. First, a multi-objective mixed-integer programming model is established to solve the problem. Uncertainty is modeled using a scenario-based probability approach. Second, a multi-objective genetic algorithm based on adaptive large neighborhood search (MOGA-ALNS) is designed to further optimize the solutions obtained from the evolutionary process using an adaptive large neighborhood search algorithm. Furthermore, the MOGA-ALNS integrates a simulated annealing process in the neighborhood search stage to inhibit the algorithm from reaching local optimums. Ultimately, the MOGA-ALNS is compared to three additional multi-objective optimization algorithms. The comprehensive analysis and discussion conducted unequivocally validate the competitiveness and efficacy of the proposed approach. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Operations Research)

► Show Figures

Figure 1

41 pages, 10279 KiB

Open AccessReview

Block Copolymer-Based Symmetric Membranes for Direct Methanol Fuel Cells

by Maria Giovanna Buonomenna and Joonwon Bae

Symmetry 2024, 16(8), 1079; https://doi.org/10.3390/sym16081079 - 20 Aug 2024

Viewed by 901

Abstract

Like batteries, fuel cells provide an inherently clean source of energy with no adverse environmental impact during operation. The utilization of methanol as a fuel is advantageous: it has an energy density of about 6 kWh/kg, which is, much higher than that of [...] Read more.

Like batteries, fuel cells provide an inherently clean source of energy with no adverse environmental impact during operation. The utilization of methanol as a fuel is advantageous: it has an energy density of about 6 kWh/kg, which is, much higher than that of other commercialized batteries. This review is focused on the core of a DMFC, i.e., the symmetric membrane, in particular on the block copolymers used for its preparation as an alternative to well-known Nafion. The synthesis of block copolymer ionomers based on different building block types, with special emphasis on the critical issue of methanol permeability and proton/methanol selectivity, as well as the effect of block length and crosslinking are described and discussed. Full article

(This article belongs to the Collection Feature Papers in Chemistry)

► Show Figures

Figure 1

19 pages, 2422 KiB

Open AccessArticle

Few-Body Precursors of Topological Frustration

by Federico Raffaele De Filippi, Antonio Francesco Mello, Daniel Sacco Shaikh, Maura Sassetti, Niccolò Traverso Ziani and Michele Grossi

Symmetry 2024, 16(8), 1078; https://doi.org/10.3390/sym16081078 - 20 Aug 2024

Viewed by 592

Abstract

Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are [...] Read more.

Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

15 pages, 269 KiB

Open AccessArticle

Quantum Stability of Hamiltonian Evolution on a Finsler Manifold

by Gil Elgressy and Lawrence Horwitz

Symmetry 2024, 16(8), 1077; https://doi.org/10.3390/sym16081077 - 20 Aug 2024

Viewed by 507

Abstract

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us, in the geometrization of quantum mechanical evolution in a Finsler geometry. We find results with dynamical equations governing the evolution of the trajectories defined by [...] Read more.

This paper is a study of a generalization of the quantum Riemannian Hamiltonian evolution, previously analyzed by us, in the geometrization of quantum mechanical evolution in a Finsler geometry. We find results with dynamical equations governing the evolution of the trajectories defined by the expectation values of the position. The analysis appears to provide an underlying geometry described by a geodesic equation, with a connection form with a second term which is an essentially quantum effect. These dynamical equations provide a new geometric approach to the quantum evolution where we suggest a definition for “local instability” in the quantum theory. Full article

(This article belongs to the Special Issue Symmetry in Hamiltonian Dynamical Systems)

19 pages, 9691 KiB

Open AccessArticle

UAV Tracking via Saliency-Aware and Spatial–Temporal Regularization Correlation Filter Learning

by Liqiang Liu, Tiantian Feng, Yanfang Fu, Lingling Yang, Dongmei Cai and Zijian Cao

Symmetry 2024, 16(8), 1076; https://doi.org/10.3390/sym16081076 - 20 Aug 2024

Viewed by 602

Abstract

Due to their great balance between excellent performance and high efficiency, discriminative correlation filter (DCF) tracking methods for unmanned aerial vehicles (UAVs) have gained much attention. Due to these correlations being capable of being efficiently computed in a Fourier domain by discrete Fourier [...] Read more.

Due to their great balance between excellent performance and high efficiency, discriminative correlation filter (DCF) tracking methods for unmanned aerial vehicles (UAVs) have gained much attention. Due to these correlations being capable of being efficiently computed in a Fourier domain by discrete Fourier transform (DFT), the DFT of an image has symmetry in the Fourier domain. However, DCF tracking methods easily generate unwanted boundary effects where the tracking object suffers from challenging situations, such as deformation, fast motion and occlusion. To tackle the above issue, this work proposes a novel saliency-aware and spatial–temporal regularized correlation filter (SSTCF) model for visual object tracking. First, the introduced spatial–temporal regularization helps build a more robust correlation filter (CF) and improve the temporal continuity and consistency of the model to effectively lower boundary effects and enhance tracking performance. In addition, the relevant objective function can be optimized into three closed-form subproblems which can be addressed by using the alternating direction method of multipliers (ADMM) competently. Furthermore, utilizing a saliency detection method to acquire a saliency-aware weight enables the tracker to adjust to variations in appearance and mitigate disturbances from the surroundings environment. Finally, we conducted numerous experiments based on three different benchmarks, and the results showed that our proposed model had better performance and higher efficiency compared to the most advanced trackers. For example, the distance precision (DP) score was 0.883, and the area under the curve (AUC) score was 0.676 on the OTB2015 dataset. Full article

(This article belongs to the Special Issue Symmetry Applied in Computer Vision, Automation, and Robotics)

► Show Figures

Figure 1

17 pages, 47189 KiB

Open AccessArticle

The Properties of Structures with Two Planes of Symmetry

by Sorin Vlase and Calin Itu

Symmetry 2024, 16(8), 1075; https://doi.org/10.3390/sym16081075 - 20 Aug 2024

Viewed by 553

Abstract

In the domain of civil engineering, the structures encountered usually present symmetries of different types. The causes that determine the use of these symmetries are diverse, starting from esthetic motivations but also dictated by practical reasons, such as the reduction in construction time [...] Read more.

In the domain of civil engineering, the structures encountered usually present symmetries of different types. The causes that determine the use of these symmetries are diverse, starting from esthetic motivations but also dictated by practical reasons, such as the reduction in construction time and costs. These geometric symmetries lead to specific properties that, in certain situations, can help to simplify the calculation of these structures. They can be identified both in the static analysis and the deformability of the structure, as well as in the dynamic analysis in the study of vibrations. If these properties are used, it is possible to reduce the analysis time, and the designer can obtain a quick estimate of the behavior of the structure. Starting from these considerations, this work will determine some of the properties specific to the natural vibrations of certain structures with identical parts in their components (structures that present two planes of symmetry) and will demonstrate how these properties can contribute to reducing the time required for dynamic analysis. An example will be used to exemplify the presented methods. This work allows for further developments and makes possible the development of the existing finite element software by adding some modules to identify such situations by analyzing the input data and using the properties described in the newly introduced algorithms. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Structural Dynamics)

► Show Figures

Figure 1

18 pages, 514 KiB

Open AccessArticle

Nonlocal Effects in Asymptotically Safe Gravity

by Sándor Nagy

Symmetry 2024, 16(8), 1074; https://doi.org/10.3390/sym16081074 - 19 Aug 2024

Viewed by 379

Abstract

The asymptotically safe gravity is investigated in the framework of the functional renormalization group method. The low energy region of the model can account for the cosmological behavior, where it is assumed that the nonlocal effects play a crucial role. Using the Wegner–Houghton [...] Read more.

The asymptotically safe gravity is investigated in the framework of the functional renormalization group method. The low energy region of the model can account for the cosmological behavior, where it is assumed that the nonlocal effects play a crucial role. Using the Wegner–Houghton equation it is shown that the dynamically induced bilocal term modifies the infrared scaling of the model. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

15 pages, 270 KiB

Open AccessArticle

Topological Crystals: Independence of Spectral Properties with Respect to Reference Systems

by Koichi Kato and Serge Richard

Symmetry 2024, 16(8), 1073; https://doi.org/10.3390/sym16081073 - 19 Aug 2024

Viewed by 395

Abstract

It is a common postulate that spectral properties of operators describing physical systems are independent of the underlying reference frames. For the Laplace operator on topological crystals, we prove such a statement from a deeper analysis of the behavior of spectral properties with [...] Read more.

It is a common postulate that spectral properties of operators describing physical systems are independent of the underlying reference frames. For the Laplace operator on topological crystals, we prove such a statement from a deeper analysis of the behavior of spectral properties with respect to arbitrary choices. In particular, we investigate the impact of the choice of a unit cell, and of the choice of a family of generators for the transformation group. Full article

(This article belongs to the Section Mathematics)

17 pages, 2577 KiB

Open AccessArticle

Filter Cake Neural-Objective Data Modeling and Image Optimization

by Dennis Delali Kwesi Wayo, Sonny Irawan, Alfrendo Satyanaga, Jong Kim, Mohd Zulkifli Bin Mohamad Noor and Vamegh Rasouli

Symmetry 2024, 16(8), 1072; https://doi.org/10.3390/sym16081072 - 19 Aug 2024

Viewed by 416

Abstract

Designing drilling mud rheology is a complex task, particularly when it comes to preventing filter cakes from obstructing formation pores and making sure they can be easily decomposed using breakers. Incorporating both multiphysics and data-driven numerical simulations into the design of mud rheology [...] Read more.

Designing drilling mud rheology is a complex task, particularly when it comes to preventing filter cakes from obstructing formation pores and making sure they can be easily decomposed using breakers. Incorporating both multiphysics and data-driven numerical simulations into the design of mud rheology experiments creates an additional challenge due to their symmetrical integration. In this computational intelligence study, we introduced numerical validation techniques using 498 available datasets from mud rheology and images from filter cakes. The goal was to symmetrically predict flow, maximize filtration volume, monitor void spaces, and evaluate formation damage occurrences. A neural-objective and image optimization approach to drilling mud rheology automation was employed using an artificial neural network feedforward (ANN-FF) function, a non-ANN-FF function, an image processing tool, and an objective optimization tool. These methods utilized the Google TensorFlow Sequential API-DNN architecture, MATLAB-nftool, the MATLAB-image processing tool, and a single-objective optimization algorithm. However, the analysis emanating from the ANN-FF and non-ANN-FF (with neurons of 10, 12, and 18) indicated that, unlike non-ANN-FF, ANN-FF obtained the highest correlation coefficient of 0.96–0.99. Also, the analysis of SBM and OBM image processing revealed a total void area of 1790 M µm² and 1739 M µm², respectively. Both SBM and OBM exhibited notable porosity and permeability that contributed to the enhancement of the flow index. Nonetheless, this study did reveal that the experimental-informed single objective analysis impeded the filtration volume; hence, it demonstrated potential formation damage. It is, therefore, consistent to note that automating flow predictions from mud rheology and filter cakes present an alternative intelligence method for non-programmers to optimize drilling productive time. Full article

(This article belongs to the Section Computer)

► Show Figures

Figure 1

13 pages, 322 KiB

Open AccessArticle

The Symmetry Group of the Grand Antiprism

by Barry Monson

Symmetry 2024, 16(8), 1071; https://doi.org/10.3390/sym16081071 - 19 Aug 2024

Viewed by 275

Abstract

The grand antiprism

A

is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff’s construction. Its symmetry group

G (A)

has been incorrectly described as

[[10, 2^{+}, 10]]

or even [...] Read more.

The grand antiprism

A

is an outlier among the uniform 4-polytopes, since it is not obtainable from Wythoff’s construction. Its symmetry group

G (A)

has been incorrectly described as

[[10, 2^{+}, 10]]

or even as an ‘ionic diminished Coxeter group’. In fact,

G (A)

is another group of order 400, namely the group

\pm [D_{10} \times D_{10}] \cdot 2

, in the notation of Conway and Smith. We explain all this and so correct a persistent error in the literature. This fresh look at the beautiful geometry of the polytope

A

is also a fine opportunity to introduce the reader to the elegance of Wythoff’s construction and to the less familiar use of quaternions to classify the finite 4-dimensional isometry groups. Full article

(This article belongs to the Special Issue Symmetry in Combinatorial Structures)

► Show Figures

Figure 1

27 pages, 18674 KiB

Open AccessArticle

An Innovative Algorithm Based on Chaotic Maps Amalgamated with Bit-Level Permutations for Robust S-Box Construction and Its Application in Medical Image Privacy

by Mohammad Mazyad Hazzazi, Souad Ahmad Baowidan, Awais Yousaf and Muhammad Adeel

Symmetry 2024, 16(8), 1070; https://doi.org/10.3390/sym16081070 - 19 Aug 2024

Viewed by 666

Abstract

Data security and privacy have become essential due to the increasingly advanced interconnectivity in today’s world, hence the reliance on cryptography. This paper introduces a new algorithm that uses a novel hybrid Tent–May chaotic map to generate pseudo-random numbers, as well as block [...] Read more.

Data security and privacy have become essential due to the increasingly advanced interconnectivity in today’s world, hence the reliance on cryptography. This paper introduces a new algorithm that uses a novel hybrid Tent–May chaotic map to generate pseudo-random numbers, as well as block encryption. We design a robust S-box by combining the Tent and May Maps, which yields a chaotic system with improved cryptographic properties. This S-box is a critical cryptographic primitive that significantly improves encryption security and leverages the strengths of both maps. The encryption process involves two key steps: block-wise substitution and permutation. First, we divide the image into

16 \times 16

blocks, then substitute each pixel with the

8 - b y t e

key and S-box. Next, we convert the encrypted image back into vector form, reorganize it using the permutation vector based on the subgroups of

S_{16}

, and finally return it to its original form. This approach greatly improves block cipher security when used, especially to protect medical images by guaranteeing their confidentiality and noninterference. Performance measures like PSNR, UACI, MSE, NCC, AD, SC, MD, and NAE prove how immune our method is to various cryptographic and statistical attacks, making it more accurate and more secure than the existing techniques. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

24 pages, 9808 KiB

Open AccessArticle

Analysis and Design of an Airborne-Dangled Monopole-Antenna Symmetric Remote-Sensing Radiation Source for Airport Runway Monitoring

by Qianqian Tian, Haifeng Fan, Jingjie Chen and Lei Zhang

Symmetry 2024, 16(8), 1069; https://doi.org/10.3390/sym16081069 - 19 Aug 2024

Viewed by 369

Abstract

Traditional methods for monitoring the foundation settlement of airport runways predominantly employ equipment such as leveling instruments, total stations, layered settlement instruments, magnetic ring settlement instruments, ground-penetrating radar (GPR), and synthetic aperture radar. These methods suffer from low automation levels, are time-consuming, labor-intensive, [...] Read more.

Traditional methods for monitoring the foundation settlement of airport runways predominantly employ equipment such as leveling instruments, total stations, layered settlement instruments, magnetic ring settlement instruments, ground-penetrating radar (GPR), and synthetic aperture radar. These methods suffer from low automation levels, are time-consuming, labor-intensive, and can significantly disrupt airport operations. An alternative electromagnetic detection technique, Controlled Source Audio-Frequency Magnetotellurics (CSAMT), offers deep-depth detection capabilities. However, CSAMT faces significant challenges, particularly in generating high signal-to-noise ratio (SNR) signals in the far-field region (FfR). Traditional CSAMT utilizes grounded horizontal dipoles (GHDs), which radiate symmetric beams. Due to the low directivity of GHDs, only a small fraction of the radiated energy is effectively utilized in FfR observations. Enhancing the SNR in FfR typically requires either reducing the transceiving distance or increasing the transmitting power, both of which introduce substantial complications. This paper proposes an airborne-dangled monopole-antenna symmetric remote-sensing radiation source for airport runway monitoring, which replaces the conventional GHD. The analytical, simulation, and experimental verification results indicate that the energy required by the airborne-dangled symmetric source to generate the same electric field amplitude in the FfR is only one-third of that needed by traditional CSAMT. This results in significant energy savings and reduced emissions, underscoring the advantages of the airborne-dangled monopole-antenna symmetric source in enhancing energy efficiency for CSAMT. The theoretical analysis, simulations, and experimental results consistently verify the validity and efficacy of the proposed airborne-dangled monopole-antenna symmetric remote-sensing radiation source in CSAMT. This innovative approach holds substantial promise for airport runway monitoring, offering a more efficient and less intrusive solution compared to traditional methods. Full article

(This article belongs to the Section Engineering and Materials)

► Show Figures

Figure 1

19 pages, 3999 KiB

Open AccessArticle

A Modified Brain Storm Optimization Algorithm for Solving Scheduling of Double-End Automated Storage and Retrieval Systems

by Liduo Hu, Sai Geng, Wei Zhang, Chenhang Yan, Zhi Hu and Yuhang Cai

Symmetry 2024, 16(8), 1068; https://doi.org/10.3390/sym16081068 - 19 Aug 2024

Viewed by 397

Abstract

As a product of modern development, logistics plays a significant role in economic growth with its advantages of integrated management, unified operations, and speed. With the rapid advancement of technology and economy, traditional manual storage and retrieval methods can no longer meet industry [...] Read more.

As a product of modern development, logistics plays a significant role in economic growth with its advantages of integrated management, unified operations, and speed. With the rapid advancement of technology and economy, traditional manual storage and retrieval methods can no longer meet industry demands. Achieving efficient storage and retrieval of goods on densely packed, symmetrically shaped logistics shelves has become a critical issue that needs urgent resolution. The brain storm optimization (BSO) algorithm, introduced in 2010, has found extensive applications across various fields. This paper presents a modified BSO algorithm (MBSO) aimed at addressing the scheduling challenges of double-end automated storage and retrieval systems (DE-AS/RSs). Traditional AS/RSs suffer from slow scheduling efficiency and the current heuristic algorithms exhibit low accuracy. To overcome these limitations, we propose a new scheduling strategy for the stacker to select I/O stations in DE-AS/RSs. The MBSO incorporates two key enhancements to the basic BSO algorithm. First, it employs an objective space clustering method in place of the standard k-means clustering to achieve more accurate solutions for AS/RS scheduling problems. Second, it utilizes a mutation operation based on a greedy strategy and an improved crossover operation for updating individuals. Extensive comparisons were made between the well-known heuristic algorithms NIGA and BSO in several specific enterprise warehouse scenarios. The experimental results show that the MBSO has significant accuracy, optimization speed, and robustness in solving scheduling of AS/RSs. Full article

(This article belongs to the Special Issue Advances in Mechanics and Control II)

► Show Figures

Figure 1

28 pages, 6255 KiB

Open AccessArticle

Spatial Predictive Modeling of Liver Fluke Opisthorchis viverrine (OV) Infection under the Mathematical Models in Hexagonal Symmetrical Shapes Using Machine Learning-Based Forest Classification Regression

by Benjamabhorn Pumhirunroj, Patiwat Littidej, Thidarut Boonmars, Atchara Artchayasawat, Narueset Prasertsri, Phusit Khamphilung, Satith Sangpradid, Nutchanat Buasri, Theeraya Uttha and Donald Slack

Symmetry 2024, 16(8), 1067; https://doi.org/10.3390/sym16081067 - 19 Aug 2024

Viewed by 938

Abstract

Infection with liver flukes (Opisthorchis viverrini) is partly due to their ability to thrive in habitats in sub-basin areas, causing the intermediate host to remain in the watershed system throughout the year. Spatial modeling is used to predict water source infections, [...] Read more.

Infection with liver flukes (Opisthorchis viverrini) is partly due to their ability to thrive in habitats in sub-basin areas, causing the intermediate host to remain in the watershed system throughout the year. Spatial modeling is used to predict water source infections, which involves designing appropriate area units with hexagonal grids. This allows for the creation of a set of independent variables, which are then covered using machine learning techniques such as forest-based classification regression methods. The independent variable set was obtained from the local public health agency and used to establish a relationship with a mathematical model. The ordinary least (OLS) model approach was used to screen the variables, and the most consistent set was selected to create a new set of variables using the principal of component analysis (PCA) method. The results showed that the forest classification and regression (FCR) model was able to accurately predict the infection rates, with the PCA factor yielding a reliability value of 0.915. This was followed by values of 0.794, 0.741, and 0.632, respectively. This article provides detailed information on the factors related to water body infection, including the length and density of water flow lines in hexagonal form, and traces the depth of each process. Full article

(This article belongs to the Special Issue Mathematical Modeling of the Infectious Diseases and Their Controls)

► Show Figures

Figure 1

11 pages, 452 KiB

Open AccessArticle

Stable Majorana Zero-Energy Modes in Two-Dimensional Josephson Junctions

by Yuting Huang, Qinyi Wang, Lei Li and Zhenying Wen

Symmetry 2024, 16(8), 1066; https://doi.org/10.3390/sym16081066 - 19 Aug 2024

Viewed by 488

Abstract

In this paper, a modified Josephson junction model is proposed, which splits the two-dimensional electron gas by inserting a middle superconductor strip into a conventional Josephson junction. This modification enhances the superconducting proximity effect, thus avoiding the appearance of a soft gap and [...] Read more.

In this paper, a modified Josephson junction model is proposed, which splits the two-dimensional electron gas by inserting a middle superconductor strip into a conventional Josephson junction. This modification enhances the superconducting proximity effect, thus avoiding the appearance of a soft gap and inducing a stable Majorana zero-energy mode. Through numerical simulation, the impact of the middle superconductor strip with different widths on the energy band structure is studied, and a significant increase in the topological energy gap is found. In addition, the modified system maintains a robust topological gap even at a strong in-plane magnetic field. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

19 pages, 425 KiB

Open AccessArticle

Inverse Boundary Conditions Interface Problems for the Heat Equation with Cylindrical Symmetry

by Miglena N. Koleva and Lubin G. Vulkov

Symmetry 2024, 16(8), 1065; https://doi.org/10.3390/sym16081065 - 18 Aug 2024

Viewed by 564

Abstract

In this paper, we study inverse interface problems with unknown boundary conditions, using point observations for parabolic equations with cylindrical symmetry. In the one-dimensional, two-layer interface problem, the left interval

0 < r < l_{1}

, i.e., the zero degeneracy, causes serious [...] Read more.

In this paper, we study inverse interface problems with unknown boundary conditions, using point observations for parabolic equations with cylindrical symmetry. In the one-dimensional, two-layer interface problem, the left interval

0 < r < l_{1}

, i.e., the zero degeneracy, causes serious solution difficulty. For this, we investigate the well-posedness of the direct (forward) problem. Next, we formulate and solve five inverse boundary condition problems for the interface heat equation with cylindrical symmetry from internal measurements. The finite volume difference method is developed to construct second-order schemes for direct and inverse problems. The correctness of the proposed numerical solution decomposition algorithms for the inverse problems is discussed. Several numerical examples are presented to illustrate the efficiency of the approach. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Theory and Simulation Methods for Backward Problems)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Symmetry, Volume 16, Issue 8 (August 2024) – 157 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI