Symmetry

10 pages, 460 KiB

Open AccessArticle

Bending of Light by Magnetars within Generalized Born–Infeld Electrodynamics: Insights from the Gauss–Bonnet Theorem

by Nurzada Beissen, Tursynbek Yernazarov, Manas Khassanov, Saken Toktarbay, Aliya Taukenova and Amankhan Talkhat

Symmetry 2024, 16(1), 132; https://doi.org/10.3390/sym16010132 - 22 Jan 2024

Viewed by 834

Abstract

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian [...] Read more.

We compute the weak bending angle of light within generalised Born–Infeld electrodynamics as it passes through the equatorial plane of a magnetic dipole. We start by considering the refractive index associated with the dipole within generalised Born–Infeld electrodynamics. Then, we calculate the Gaussian optical curvature based on these refractive indices. Using the Gauss–Bonnet theorem, we derive a formula to quantify the deflection angle in the presence of a strong magnetic field from a dipole. Our results align with results obtained through traditional geometric optics techniques, underscoring the importance of the Gauss–Bonnet theorem as a versatile tool for solving intricate problems in modern theoretical research. We apply our theoretical deflection angle formula to estimate the light bending in magnetars listed in the McGill catalogue, providing insights into the behaviour of light in environments with strong magnetic fields. Full article

(This article belongs to the Special Issue Exploring Symmetry and Asymmetry in Astrophysics, Astronomy, and Space Science: Paving the Way for a Multiplanetary Future for Humanity)

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14 pages, 11844 KiB

Open AccessArticle

Force and Pressure Dependent Asymmetric Workspace Research of a Collaborative Robot and Human

by Josef Ponikelský, Milan Chalupa, Vít Černohlávek and Jan Štěrba

Symmetry 2024, 16(1), 131; https://doi.org/10.3390/sym16010131 - 22 Jan 2024

Viewed by 755

Abstract

This article discusses creating a methodology for the asymmetric measuring of values and processes of collision forces and pressures of the collaborative robot dependent on time. Furthermore, it verifies the usefulness of this methodology in practice by successfully performing the experimental measurement and [...] Read more.

This article discusses creating a methodology for the asymmetric measuring of values and processes of collision forces and pressures of the collaborative robot dependent on time. Furthermore, it verifies the usefulness of this methodology in practice by successfully performing the experimental measurement and verifying the possibility of using these results by analysing and stating the collaboration level for a robot of the given type. According to the suggested methodology, the measurement results are a specific output based on real measured data, which can be easily rated and can quickly determine the collaborative level of any robot. Measurements were aimed at determining the values of pressure and force with which the robot acts at certain speeds related to distance from the base. Due to the controlled symmetrical impact of the robot on the measuring device, the transfer of energy from the robot to the human body was guaranteed. In theoretical terms, this article primarily provides the assembly of the theoretical foundation of the collaborative environment between humans and robots, and a comprehensive overview of the possibilities of using the technical specification ISO/TS 15066:2016 when deploying a robot in collaboration with humans in a collaborative environment. This new information is highly valuable for both manufacturers and users of collaborative robots. The presented article analyses the possibilities of measuring collaboration and safety elements in cooperation with a robot. The most significant practical benefit is the presentation of a methodology for measuring robot collaboration and verifying its functionality by conducting experimental measurements of robot collaboration according to this methodology. The measurement was performed on a robot made by Universal Robots, model UR10. The measurement coordinates were stationed in a way to create a spatial measurement model. Boundary coordinates of the spatial model were as follows: [450; 200], [450; 500], [850; 200], and [850; 500]. Collisions were measured at 8 different speeds for each coordinate (20 mms⁻¹, 50 mms⁻¹, 100 mms⁻¹, 200 mms⁻¹, 250 mms⁻¹, 300 mms⁻¹, 350 mms⁻¹, and 400 mms⁻¹) to enable the observation of changes in accordance with speed. The measured values indicate a significant fact: the closer the collision is to the robot’s base, the higher the collision forces. An important aspect is that the measured values were only for speeds up to 400 mms⁻¹, which is a very low value for industrial use to meet the desired cycle time. It can be stated with absolute certainty that speed has the greatest impact on collision force values. The speed of the collaborative robot arm can therefore be considered a limiting factor for use in industrial applications with a requirement of a short cycle time. Focusing on the results of the measured values, it can be stated that a new finding is the correct design of robotic movements in relation to possible contact with humans is crucial. The result of the measurement according to the proposed methodology is a specific output of realistically measured data, which can be easily evaluated and the level of collaboration of any robot can be quickly determined. The measured data will also serve as a basis for further processing and preparation of new simulation software. It will be possible to use the intended software for detecting and predetermining the safe asymmetric movements of the collaborative robot already at the stage of production preparations, unlike the method of measuring force and pressure on robots which can be used until the time of implementation into production. In the future, this software may also allow users of collaborative robots to easily and quickly evaluate the robots specified. Full article

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15 pages, 1167 KiB

Open AccessArticle

An Overview of the Searches for the Violation of the Charge-Parity Symmetry in the Leptonic Sector

by Vyacheslav Galymov

Symmetry 2024, 16(1), 130; https://doi.org/10.3390/sym16010130 - 22 Jan 2024

Viewed by 669

Abstract

The existence of a violation of the Charge-Parity (CP) symmetry in the laws of physics is one of the cornerstone conditions for the generation of a matter–antimatter imbalance necessary to the creation of a matter-dominated universe. The first experimental evidence of the fact [...] Read more.

The existence of a violation of the Charge-Parity (CP) symmetry in the laws of physics is one of the cornerstone conditions for the generation of a matter–antimatter imbalance necessary to the creation of a matter-dominated universe. The first experimental evidence of the fact that this symmetry is broken in nature was obtained in 1964 in the observations of the decays of neutral kaon mesons. The magnitude of CP violation in the quark sector was measured with an increasing precision exploring also decays of other mesons. However, CP violation in the quark sector alone is not sufficient to explain the formation of matter-dominated universe, and additional sources are required. One such potential source is the lepton sector, where the CP violation could be observed by studying neutrino oscillations with neutrino beams generated by particle accelerators. This article reviews the present efforts in this direction. The results obtained in the ongoing experiments, T2K in Japan and NOvA in USA, are discussed. Additionally, the search for leptonic CP violation is one of the key goals in the programs of future experiments, DUNE in USA and Hyper-Kamiokande in Japan. These experiments and their prospects for its discovery are also presented. Full article

(This article belongs to the Special Issue Experimental Tests of Fundamental Symmetries in Particle Physics)

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14 pages, 720 KiB

Open AccessArticle

Explicit Formulas for the Deformation of Chiral Porous Circular Beams in Gradient Thermoelasticity

by Simona De Cicco

Symmetry 2024, 16(1), 129; https://doi.org/10.3390/sym16010129 - 22 Jan 2024

Viewed by 701

Abstract

Chirality and porosity are characteristic properties of nanostructured materials. Their effects on the mechanical behaviour of structural elements, such as shells, plates and beams, cannot be disregarded. In this paper, we study the thermoelastic deformation of a chiral porous circular beam loaded with [...] Read more.

Chirality and porosity are characteristic properties of nanostructured materials. Their effects on the mechanical behaviour of structural elements, such as shells, plates and beams, cannot be disregarded. In this paper, we study the thermoelastic deformation of a chiral porous circular beam loaded with an axial force and torque. The beam is also under the action of a constant temperature field. The analytical solution is obtained using the results established in a paper recently published by the Author within the context of the strain gradient theory proposed by Papanicopolous. In the constitutive equations, the chirality is introduced by a material constant parameter and the porosity is described by means of a scalar function. Displacements, microdilatation function, and stress and strain fields are expressed in explicit form and in terms of engineering constants. Explicit formulas of the stiffness of chiral porous circular beams are presented and the effects of right and left chirality are discussed. Full article

(This article belongs to the Section Engineering and Materials)

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31 pages, 1750 KiB

Open AccessArticle

A Comprehensive Literature Review on Artificial Dataset Generation for Repositioning Challenges in Shared Electric Automated and Connected Mobility

by Antoine Kazadi Kayisu, Witesyavwirwa Vianney Kambale, Taha Benarbia, Pitshou Ntambu Bokoro and Kyandoghere Kyamakya

Symmetry 2024, 16(1), 128; https://doi.org/10.3390/sym16010128 - 21 Jan 2024

Viewed by 1522

Abstract

In the near future, the incorporation of shared electric automated and connected mobility (SEACM) technologies will significantly transform the landscape of transportation into a sustainable and efficient mobility ecosystem. However, these technological advances raise complex scientific challenges. Problems related to safety, energy efficiency, [...] Read more.

In the near future, the incorporation of shared electric automated and connected mobility (SEACM) technologies will significantly transform the landscape of transportation into a sustainable and efficient mobility ecosystem. However, these technological advances raise complex scientific challenges. Problems related to safety, energy efficiency, and route optimization in dynamic urban environments are major issues to be resolved. In addition, the unavailability of realistic and various data of such systems makes their deployment, design, and performance evaluation very challenging. As a result, to avoid the constraints of real data collection, using generated artificial datasets is crucial for simulation to test and validate algorithms and models under various scenarios. These artificial datasets are used for the training of ML (Machine Learning) models, allowing researchers and operators to evaluate performance and predict system behavior under various conditions. To generate artificial datasets, numerous elements such as user behavior, vehicle dynamics, charging infrastructure, and environmental conditions must be considered. In all these elements, symmetry is a core concern; in some cases, asymmetry is more realistic; however, in others, reaching/maintaining as much symmetry as possible is a core requirement. This review paper provides a comprehensive literature survey of the most relevant techniques generating synthetic datasets in the literature, with a particular focus on the shared electric automated and connected mobility context. Furthermore, this paper also investigates central issues of these complex and dynamic systems regarding how artificial datasets could be used in the training of ML models to address the repositioning problem. Hereby, symmetry is undoubtedly a crucial consideration for ML models. In the case of datasets, it is imperative that they accurately emulate the symmetry or asymmetry observed in real-world scenarios to be effectively represented by the generated datasets. Then, this paper investigates the current challenges and limitations of synthetic datasets, such as the reliability of simulations to the real world, and the validation of generative models. Additionally, it explores how ML-based algorithms can be used to optimize vehicle routing, charging infrastructure usage, demand forecasting, and other important operational elements. In conclusion, this paper outlines a series of interesting new research avenues concerning the generation of artificial data for SEACM systems. Full article

(This article belongs to the Special Issue Simulation and Modelling in Natural Sciences, Biomedicine and Engineering III)

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17 pages, 6547 KiB

Open AccessArticle

Virtual Coordinate System Based on a Circulant Topology for Routing in Networks-On-Chip

by Andrei M. Sukhov, Aleksandr Y. Romanov and Maksim P. Selin

Symmetry 2024, 16(1), 127; https://doi.org/10.3390/sym16010127 - 21 Jan 2024

Viewed by 856

Abstract

In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest [...] Read more.

In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique for calculating optimal network configurations is described. Dense states of the network when all neighborhoods of the central node are filled with nodes and the network has the smallest diameter are defined. It is shown that with an equal number of nodes, the diameter of the circulant is two times smaller than the diameter of the 2D mesh. This is due to the large number of symmetries for the circulant, which leave the set of nodes unchanged. A comparison of communication stability in both topologies in the conditions of failure of network nodes is made, the network behavior under load and failures is modeled, and the advantages of the circulant topology are presented. Full article

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

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14 pages, 284 KiB

Open AccessArticle

Solvable Two-Dimensional Dirac Equation with Matrix Potential: Graphene in External Electromagnetic Field

by Mikhail V. Ioffe and David N. Nishnianidze

Symmetry 2024, 16(1), 126; https://doi.org/10.3390/sym16010126 - 21 Jan 2024

Viewed by 802

Abstract

It is known that the excitations in graphene-like materials in external electromagnetic field are described by solutions of a massless two-dimensional Dirac equation which includes both Hermitian off-diagonal matrix and scalar potentials. Up to now, such two-component wave functions were calculated for different [...] Read more.

It is known that the excitations in graphene-like materials in external electromagnetic field are described by solutions of a massless two-dimensional Dirac equation which includes both Hermitian off-diagonal matrix and scalar potentials. Up to now, such two-component wave functions were calculated for different forms of external potentials, though as a rule depending on only one spatial variable. Here, we shall find analytically the solutions for a wide class of combinations of matrix and scalar external potentials which physically correspond to applied mutually orthogonal magnetic and longitudinal electrostatic fields, both depending really on two spatial variables. The main tool for this progress is provided by supersymmetrical (SUSY) intertwining relations, specifically, by their most general—asymmetrical—form proposed recently by the authors. This SUSY-like method is applied in two steps, similar to the second order factorizable (reducible) SUSY transformations in ordinary quantum mechanics. Full article

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

16 pages, 672 KiB

Open AccessFeature PaperArticle

Detecting Phase Transitions through Non-Equilibrium Work Fluctuations

by Matteo Colangeli, Antonio Di Francesco and Lamberto Rondoni

Symmetry 2024, 16(1), 125; https://doi.org/10.3390/sym16010125 - 20 Jan 2024

Viewed by 806

Abstract

We show how averages of exponential functions of path-dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation—the restriction of the observations to a subset of state space with prescribed probability—is introduced to [...] Read more.

We show how averages of exponential functions of path-dependent quantities, such as those of Work Fluctuation Theorems, detect phase transitions in deterministic and stochastic systems. State space truncation—the restriction of the observations to a subset of state space with prescribed probability—is introduced to obtain that result. Two stochastic processes undergoing first-order phase transitions are analyzed both analytically and numerically: a variant of the Ehrenfest urn model and the 2D Ising model subject to a magnetic field. In the presence of phase transitions, we prove that even minimal state space truncation makes averages of exponentials of path-dependent variables sensibly deviate from full state space values. Specifically, in the case of discontinuous phase transitions, this approach is strikingly effective in locating the transition value of the control parameter. As this approach works even with variables different from those of fluctuation theorems, it provides a new recipe to identify order parameters in the study of non-equilibrium phase transitions, profiting from the often incomplete statistics that are available. Full article

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

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14 pages, 4396 KiB

Open AccessArticle

Oligomeric Symmetry of Purine Nucleoside Phosphorylases

by Boris Gomaz and Zoran Štefanić

Symmetry 2024, 16(1), 124; https://doi.org/10.3390/sym16010124 - 19 Jan 2024

Viewed by 806

Abstract

Many enzymes are composed of several identical subunits, which are arranged in a regular fashion and usually comply with some definite symmetry. This symmetry may be approximate or exact and may or may not coincide with the symmetry of crystallographic packing. Purine nucleoside [...] Read more.

Many enzymes are composed of several identical subunits, which are arranged in a regular fashion and usually comply with some definite symmetry. This symmetry may be approximate or exact and may or may not coincide with the symmetry of crystallographic packing. Purine nucleoside phosphorylases (PNP) are a class of oligomeric enzymes that show an interesting interplay between their internal symmetry and the symmetry of their crystal packings. There are two main classes of this enzyme: trimeric PNPs, or “low-molecular-mass” proteins, which are found mostly in eukaryotic organisms, and hexameric PNPs, or “high-molecular-mass” proteins, which are found mostly in prokaryotic organisms. Interestingly, these two enzyme classes share only 20–30% sequence identity, but the overall fold of the single monomer is similar, yet this monomeric building block results in a different quaternary structure. To investigate this interplay of symmetry in this class of enzymes, a comprehensive database of all PNPs is constructed, containing their local symmetries and interface information. Full article

(This article belongs to the Special Issue Symmetry and Its Application in the Structural and Biochemical Characterization of Enzymes and Protein Complexes)

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21 pages, 437 KiB

Open AccessArticle

Optimizing Connectivity and Coverage for Millimeter-Wave-Based Networks

by Pablo Adasme, Ali Dehghan Firoozabadi and Sergio Cordero

Symmetry 2024, 16(1), 123; https://doi.org/10.3390/sym16010123 - 19 Jan 2024

Viewed by 706

Abstract

In this article, the problem of achieving the minimum backbone connectivity cost while simultaneously maximizing user coverage for 5G millimeter-wave (mmWave)-based networks is considered. Let

G = (N, E)

be an input graph instance with a set of nodes N [...] Read more.

In this article, the problem of achieving the minimum backbone connectivity cost while simultaneously maximizing user coverage for 5G millimeter-wave (mmWave)-based networks is considered. Let

G = (N, E)

be an input graph instance with a set of nodes N (base stations) and a set of edges E. It is assumed that G represents a wireless backbone network. Let M represent a set of users to be covered by G. Note that mmWave technology has been considered in the literature as an important candidate solution for 5G networks due to its low latency. However, there remain some problems to be addressed before using this technology. A serious one is that millimeter waves cannot cover large transmission distances. In this article, the proposed methodology consists of formulating mixed-integer programming models to deal with the problem from a management point of view. Our models allow the determination of which of the nodes of G should be active and connected while simultaneously maximizing the total number of covered users. The models are solved with the CPLEX solver using its branch and cut and automatic Benders decomposition algorithms. For this purpose, symmetric complete and sparse graphs are considered. Using the symmetry concept, it is considered that the distances between base stations and users and between base stations themselves are symmetrical. Finally, an efficient local search meta-heuristic is proposed that allows for finding near-optimal solutions. Our numerical experiments indicate that the problem is hard to solve optimally. Thus, instances with up to 40 nodes and 500 users have been solved to optimality so far. In particular, it is observed that one of the models presents slightly better performance in terms of CPU time. Finally, the heuristic approach allows us to obtain tight solutions with less computational effort when dealing with even larger instances of the problem. Full article

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15 pages, 13929 KiB

Open AccessArticle

Effects of KoBo-Processing and Subsequent Annealing Treatment on Grain Boundary Network and Texture Development in Laser Powder Bed Fusion (LPBF) AlSi10Mg Alloy

by Przemysław Snopiński

Symmetry 2024, 16(1), 122; https://doi.org/10.3390/sym16010122 - 19 Jan 2024

Cited by 2 | Viewed by 722

Abstract

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties [...] Read more.

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties that differ from bulk crystalline domains. Their effects on material properties, including mechanical strength, corrosion resistance, and electrical conductivity, make grain boundaries a focus of intense scientific investigation. In this study, the microstructural transformation of an AlSi10Mg alloy subjected to KoBo extrusion and subsequent annealing is investigated. A notable discovery is the effectiveness of a strain-annealing method for grain boundary engineering (GBE) of the LPBF AlSi10Mg alloy. In particular, this study shows a significant increase in the population of coincidence site lattice boundaries (CSL), which embody the symmetry of the crystal lattice structure. These boundaries, which are characterised by a high degree of symmetry, contribute to their special properties compared to random grain boundaries. The experimental results emphasise the crucial role of strain-induced boundary migration (SIBM) in the development of a brass texture in the microstructure of the alloy after annealing. In addition, the presented results demonstrate the feasibility of applying GBE to materials with high stacking fault energy (SFE), which opens up new possibilities for optimizing their properties. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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11 pages, 290 KiB

Open AccessArticle

Variations in the Tensorial Trapezoid Type Inequalities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces

by Vuk Stojiljković, Nikola Mirkov and Stojan Radenović

Symmetry 2024, 16(1), 121; https://doi.org/10.3390/sym16010121 - 19 Jan 2024

Cited by 1 | Viewed by 715

Abstract

In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint [...] Read more.

In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint operators in Hilbert spaces have several tensorial norm inequalities discovered in this study. The convexity features of the mapping f lead to the variation in several inequalities of the trapezoid type. Full article

(This article belongs to the Special Issue Symmetry in Fractional Calculus: Advances and Applications)

22 pages, 367 KiB

Open AccessArticle

Memory-Accelerating Methods for One-Step Iterative Schemes with Lie Symmetry Method Solving Nonlinear Boundary-Value Problem

by Chein-Shan Liu, Chih-Wen Chang and Chung-Lun Kuo

Symmetry 2024, 16(1), 120; https://doi.org/10.3390/sym16010120 - 19 Jan 2024

Cited by 2 | Viewed by 1095

Abstract

In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values

f^{'} (r)

,

f^{″} (r)

, and

f^{‴} (r)

of a nonlinear equation [...] Read more.

In this paper, some one-step iterative schemes with memory-accelerating methods are proposed to update three critical values

f^{'} (r)

,

f^{″} (r)

, and

f^{‴} (r)

of a nonlinear equation

f (x) = 0

with r being its simple root. We can achieve high values of the efficiency index (E.I.) over the bound

2^{2 / 3} = 1.587

with three function evaluations and over the bound

2^{1 / 2} = 1.414

with two function evaluations. The third-degree Newton interpolatory polynomial is derived to update these critical values per iteration. We introduce relaxation factors into the D

\overset{ˇ}{z}

uni

\overset{´}{c}

method and its variant, which are updated to render fourth-order convergence by the memory-accelerating technique. We developed six types optimal one-step iterative schemes with the memory-accelerating method, rendering a fourth-order convergence or even more, whose original ones are a second-order convergence without memory and without using specific optimal values of the parameters. We evaluated the performance of these one-step iterative schemes by the computed order of convergence (COC) and the E.I. with numerical tests. A Lie symmetry method to solve a second-order nonlinear boundary-value problem with high efficiency and high accuracy was developed. Full article

15 pages, 221 KiB

Open AccessArticle

Fixed Point and Convergence Results for Contractive-Type Self-Mappings of Metric Spaces with Graphs

by Alexander J. Zaslavski

Symmetry 2024, 16(1), 119; https://doi.org/10.3390/sym16010119 - 18 Jan 2024

Viewed by 679

Abstract

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of [...] Read more.

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs. Full article

(This article belongs to the Section Mathematics)

15 pages, 2747 KiB

Open AccessArticle

An Accurate Prediction Method of Human Assembly Motion for Human–Robot Collaboration

by Yangzheng Zhou, Liang Luo and Pengzhong Li

Symmetry 2024, 16(1), 118; https://doi.org/10.3390/sym16010118 - 18 Jan 2024

Viewed by 752

Abstract

In the process of human–robot collaborative assembly, robots need to recognize and predict human behaviors accurately, and then perform autonomous control and work route planning in real-time. To support the judgment of human intervention behaviors and meet the need of real-time human–robot collaboration, [...] Read more.

In the process of human–robot collaborative assembly, robots need to recognize and predict human behaviors accurately, and then perform autonomous control and work route planning in real-time. To support the judgment of human intervention behaviors and meet the need of real-time human–robot collaboration, the Fast Spatial–Temporal Transformer Network (FST-Trans), an accurate prediction method of human assembly actions, is proposed. We tried to maximize the symmetry between the prediction results and the actual action while meeting the real-time requirement. With concise and efficient structural design, FST-Trans can learn about the spatial–temporal interactions of human joints during assembly in the same latent space and capture more complex motion dynamics. Considering the inconsistent assembly rates of different individuals, the network is forced to learn more motion variations by introducing velocity–acceleration loss, realizing accurate prediction of assembly actions. An assembly dataset was collected and constructed for detailed comparative experiments and ablation studies, and the experimental results demonstrate the effectiveness of the proposed method. Full article

(This article belongs to the Section Computer)

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49 pages, 491 KiB

Open AccessReview

FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity

by Boris Latosh

Symmetry 2024, 16(1), 117; https://doi.org/10.3390/sym16010117 - 18 Jan 2024

Viewed by 674

Abstract

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study [...] Read more.

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and

S U (N)

Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development. Full article

(This article belongs to the Section Physics)

11 pages, 1801 KiB

Open AccessArticle

Synthesis of 2,6-Diaminotriptycene Conjugates with Chiral Auxiliaries: Towards the Scalable Resolution of Crucial Triptycene Intermediates

by Giovanni Preda, Emanuele Casali, Alessio Porta and Dario Pasini

Symmetry 2024, 16(1), 116; https://doi.org/10.3390/sym16010116 - 18 Jan 2024

Cited by 1 | Viewed by 735

Abstract

Triptycenes are tridimensional molecular scaffolds with interesting properties for applications in materials science: molecular rigidity and preorganization, tailorable chromophores, and, with an appropriate substitution pattern, chirality. The separation of the two enantiomers of chiral triptycenes has been the subject of increasing interest in [...] Read more.

Triptycenes are tridimensional molecular scaffolds with interesting properties for applications in materials science: molecular rigidity and preorganization, tailorable chromophores, and, with an appropriate substitution pattern, chirality. The separation of the two enantiomers of chiral triptycenes has been the subject of increasing interest in recent years, with limited success. Here, we report the synthesis and characterization of a series of new organic compounds, in which a chiral triptycene scaffold, derivatized in the 2 and 6 positions with amino groups, has been functionalized with different enantiopure chiral auxiliaries, forming diastereoisomeric couples. The properties of such compounds, in terms of the optimization of their chromatographic separation, are elucidated with the aid of computational calculations of preferred conformations and molecular polarities. Full article

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

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23 pages, 381 KiB

Open AccessArticle

Noether Symmetry Analysis of the Klein–Gordon and Wave Equations in Bianchi I Spacetime

by Ugur Camci

Symmetry 2024, 16(1), 115; https://doi.org/10.3390/sym16010115 - 18 Jan 2024

Cited by 1 | Viewed by 1052

Abstract

We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A [...] Read more.

We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A detailed Noether symmetry analysis of the Klein–Gordon and the wave equations for Bianchi I spacetime is presented, and the corresponding conservation laws are derived. Full article

(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)

17 pages, 3859 KiB

Open AccessArticle

Modeling of Particle Size Distribution in the Presence of Flocculant

by Elmira Fedorova, Elena Pupysheva and Vladimir Morgunov

Symmetry 2024, 16(1), 114; https://doi.org/10.3390/sym16010114 - 18 Jan 2024

Viewed by 835

Abstract

This study presents a mathematical description of the solid fraction aggregation process in the presence of a flocculant and its result. The basis is a population balance equation. The model is realized in Python language. Verification was carried out using red mud from [...] Read more.

This study presents a mathematical description of the solid fraction aggregation process in the presence of a flocculant and its result. The basis is a population balance equation. The model is realized in Python language. Verification was carried out using red mud from the investigated enterprise; Flomin AL P 99 VHM was used as a flocculant. The mean square deviation for the parameter “mean aggregate diameter” is equal to 19.88 μm. The time required for the model calculation is about 3 min. The time spent on modeling depends on the number of calculation channels. In this study, 40 channels (20 with PSD source data, and 20 with empty values required for the calculation) were used for the calculation. The time spent on the model calculation is much shorter than the inertia via each of the communication channels for the studied symmetric radial type thickener. A user interface is developed, where the input parameters are the initial pulp particle size distribution, viscosity and density of pulp in the thickener, particle surface area, concentration and flow rate of flocculant, concentration of solid particles, inner diameter and height of the feed well, and simulation time. The result of the simulation is particle size distribution in the feed well of the washer and the mean flocculus diameter. Full article

(This article belongs to the Special Issue Advanced Digital, Modeling and Control Applies into Various Processes II)

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12 pages, 412 KiB

Open AccessArticle

General Randić Index of Unicyclic Graphs and Its Applications to Drugs

by Alaa Altassan and Muhammad Imran

Symmetry 2024, 16(1), 113; https://doi.org/10.3390/sym16010113 - 18 Jan 2024

Viewed by 714

Abstract

In this work, we determine the maximum general Randić index (a general symmetric function of vertex degrees) for

η_{0} \leq η < 0

among all n-vertex unicyclic graphs with a fixed maximum degree

Δ

and the maximum and the second maximum [...] Read more.

In this work, we determine the maximum general Randić index (a general symmetric function of vertex degrees) for

η_{0} \leq η < 0

among all n-vertex unicyclic graphs with a fixed maximum degree

Δ

and the maximum and the second maximum general Randić index for

η_{0} \leq η < 0

among all n-vertex unicyclic graphs, where

η_{0} \approx - 0.21

. We establish sharp inequalities and identify the graphs attaining the inequalities. Thereby, extremal graphs are obtained for the general Randić index, and certain open gaps in the theory of extremal unicyclic graphs are filled (some open problems are provided). We use computational software to calculate the Randić index for the chemical trees up to order 7 and use the statistical (linear regression) analysis to discuss the various applications of the Randić index with the physical properties of drugs on the said chemical trees. We show that the Randić index is better correlated with the heat of vaporization for these alkanes. Full article

(This article belongs to the Section Mathematics)

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10 pages, 908 KiB

Open AccessArticle

Photon Acceleration by Superluminal Ionization Fronts

by José Tito Mendonça

Symmetry 2024, 16(1), 112; https://doi.org/10.3390/sym16010112 - 18 Jan 2024

Viewed by 674

Abstract

This paper explores the use of superluminal ionization fronts to accelerate and amplify electromagnetic radiation. These fronts are defined as optical boundaries between two regions of a gas, the neutral region and the plasma region, characterized by two different values of the refractive [...] Read more.

This paper explores the use of superluminal ionization fronts to accelerate and amplify electromagnetic radiation. These fronts are defined as optical boundaries between two regions of a gas, the neutral region and the plasma region, characterized by two different values of the refractive index. For that reason, the front velocity is not necessarily related to the motion of material particles, such as neutral atoms, ions and electrons, which can stay at rest. The fronts can therefore become superluminal without violating causality. In recent years, different experimental configurations, such as the flying focus, showed that it is possible to create superluminal fronts in the laboratory. These fronts can easily be described theoretically in a special reference frame, called the time frame, which is used here. In this frame, superluminal fronts reduce to time refraction, a process that is symmetrical to the well-known optical refraction. It is shown that propagation through such fronts can lead to considerable frequency shifts and energy amplification of probe laser beams. This could eventually be used to develop new sources of tunable radiation. Full article

(This article belongs to the Section Physics)

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19 pages, 6448 KiB

Open AccessArticle

Constraints on Phase Transitions in Neutron Star Matter

by Len Brandes and Wolfram Weise

Symmetry 2024, 16(1), 111; https://doi.org/10.3390/sym16010111 - 18 Jan 2024

Cited by 4 | Viewed by 929

Abstract

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known [...] Read more.

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities

c_{s}^{2} > 0.1

in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range

Δ ρ / ρ < 0.2

(at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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15 pages, 453 KiB

Open AccessArticle

Numerical Analysis of the Transfer Dynamics of Heavy Metals from Soil to Plant and Application to Contamination of Honey

by Atanas Atanasov, Slavi Georgiev and Lubin Vulkov

Symmetry 2024, 16(1), 110; https://doi.org/10.3390/sym16010110 - 18 Jan 2024

Viewed by 679

Abstract

We analyze a mathematical model of the effects of soil contamination by heavy metals, which is expressed as systems of nonlinear ordinary differential equations (ODEs). The model is based on the symmetry dynamics of heavy metals soil–plant interactions. We aim to study this [...] Read more.

We analyze a mathematical model of the effects of soil contamination by heavy metals, which is expressed as systems of nonlinear ordinary differential equations (ODEs). The model is based on the symmetry dynamics of heavy metals soil–plant interactions. We aim to study this symmetric process and its long-term behavior, as well as to discuss the role of two crucial parameters, namely the flux of the hydrogen protons to the soil in rainfall events

W (t)

, and the available water for roots

p (t)

. We study the boundedness and positivity of the solution. Further, a parameter identification analysis of the model is presented. Numerical experiments with synthetic and realistic data of honeybee population are discussed. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)

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16 pages, 1672 KiB

Open AccessArticle

Charged Particles Orbiting Charged Black-Bounce Black Holes

by Sardor Murodov, Kodir Badalov, Javlon Rayimbaev, Bobomurat Ahmedov and Zdeněk Stuchlík

Symmetry 2024, 16(1), 109; https://doi.org/10.3390/sym16010109 - 16 Jan 2024

Cited by 2 | Viewed by 917

Abstract

The detailed and comprehensive analysis of radiation processes in accretion disks consisting of electrically charged particles around black holes may provide powerful information about the spacetime geometry of the central black hole. We investigate the circular orbits of electrically charged particles around an [...] Read more.

The detailed and comprehensive analysis of radiation processes in accretion disks consisting of electrically charged particles around black holes may provide powerful information about the spacetime geometry of the central black hole. We investigate the circular orbits of electrically charged particles around an electrically charged black-bounce Reissner–Nordström (RN) black hole, known as an RN Simpson–Visser (SV) black hole. We also study the profiles of the innermost stable circular orbits (ISCOs), energy, and angular momentum of the particles in their ISCOs, as well as the efficiency of energy release processes in the accretion disk in the Novikov–Thorne model. Finally, we calculate and study the effects of the black-bounce parameter as well as the black-hole charge on the intensity of the radiation of ultrarelativistic charged particles orbiting the charged RN SV black hole along circular orbits and falling into the black hole. It is observed that the black-bounce parameter essentially decreases the ISCO radius, and consequently the energy extraction and intensity of electromagnetic radiation. Full article

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18 pages, 7483 KiB

Open AccessArticle

Further Stability Criteria for Sampled-Data-Based Dynamic Positioning Ships Using Takagi–Sugeno Fuzzy Models

by Minjie Zheng, Yulai Su and Changjian Yan

Symmetry 2024, 16(1), 108; https://doi.org/10.3390/sym16010108 - 16 Jan 2024

Viewed by 659

Abstract

This article discusses the stability problem of sampled-data-based dynamic positioning ships (DPSs) using Takagi–Sugeno (T-S) fuzzy models. Firstly, dynamic equations for sampled-data DPSs are established. Simultaneously combining several symmetric matrices with new integral terms, a novel Lyapunov–Krasovskii function (LKF) is constructed, which allows [...] Read more.

This article discusses the stability problem of sampled-data-based dynamic positioning ships (DPSs) using Takagi–Sugeno (T-S) fuzzy models. Firstly, dynamic equations for sampled-data DPSs are established. Simultaneously combining several symmetric matrices with new integral terms, a novel Lyapunov–Krasovskii function (LKF) is constructed, which allows the information of a sampling pattern to be fully captured. Next, via the constructed LKF, the positive definiteness requirements of a LKF are further relaxed, and the conservatism of the result can be reduced. Consequently, stability criteria are given, and fuzzy sampled-data controllers are designed in terms of linear matrix inequality (LMI). Finally, a simulation example is provided to verify the superiority and applicability of the developed methods. Full article

(This article belongs to the Section Mathematics)

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19 pages, 325 KiB

Open AccessArticle

Asymptotically Stable Solutions of Infinite Systems of Quadratic Hammerstein Integral Equations

by Józef Banaś and Justyna Madej

Symmetry 2024, 16(1), 107; https://doi.org/10.3390/sym16010107 - 16 Jan 2024

Viewed by 658

Abstract

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real [...] Read more.

In this paper, we present a result on the existence of asymptotically stable solutions of infinite systems (IS) of quadratic Hammerstein integral equations (IEs). Our study will be conducted in the Banach space of functions, which are continuous and bounded on the half-real axis with values in the classical Banach sequence space consisting of real bounded sequences. The main tool used in our investigations is the technique associated with the measures of noncompactness (MNCs) and a fixed point theorem of Darbo type. The applicability of our result is illustrated by a suitable example at the end of the paper. Full article

(This article belongs to the Special Issue Nonlinear Differential and Integral Equations and Their Infinite Systems)

18 pages, 8554 KiB

Open AccessArticle

An Efficient Trajectory Planning Approach for Autonomous Ground Vehicles Using Improved Artificial Potential Field

by Xianjian Jin, Zhiwei Li, Nonsly Valerienne Opinat Ikiela, Xiongkui He, Zhaoran Wang, Yinchen Tao and Huaizhen Lv

Symmetry 2024, 16(1), 106; https://doi.org/10.3390/sym16010106 - 15 Jan 2024

Viewed by 844

Abstract

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on [...] Read more.

In this paper, the concept of symmetry is utilized in the promising trajectory planning design of autonomous ground vehicles—that is, the construction and the solution of improved artificial potential field-based trajectory planning approach are symmetrical. Despite existing artificial potential fields (APF) achievements on trajectory planning in autonomous ground vehicles (AGV), applying the traditional approach to dynamic traffic scenarios is inappropriate without considering vehicle dynamics environment and road regulations. This paper introduces a highly efficient approach for planning trajectories using improved artificial potential fields (IAPF) to handle dynamic road participants and address the issue of local minima in artificial potential fields. To begin with, potential fields are created with data obtained from other sensors. By incorporating rotational factors, the potential field will spin when the obstacle executes a maneuver; then, a safety distance model is also developed to limit the range of influence in order to minimize the computational burden. Furthermore, during the planning process, virtual forces using the gradient descent method are generated to direct the vehicle’s movement. During each timestep, the vehicle will assess whether it is likely to encounter a local minimum in the future. Once a local minimum is discovered, the method will create multiple temporary objectives to guide the vehicle toward the global minimum. Consequently, a trajectory that is both collision-free and feasible is planned. Traffic scenarios are carried out to validate the effectiveness of the proposed approach. The simulation results demonstrate that the improved artificial potential field approach is capable of generating a secure trajectory with both comfort and stability. Full article

(This article belongs to the Special Issue Emerging Applications of Machine Learning in Smart Systems Symmetry)

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13 pages, 5884 KiB

Open AccessArticle

A New Symmetry-Enhanced Simulation Approach Considering Poromechanical Effects and Its Application in the Hydraulic Fracturing of a Carbonate Reservoir

by Chuanrui Wang, Yao Yue, Zhongkai Huang, Yue Tong, Wei Zhang and Shiying Ye

Symmetry 2024, 16(1), 105; https://doi.org/10.3390/sym16010105 - 15 Jan 2024

Viewed by 684

Abstract

The exploration of fractured-vuggy carbonate reservoirs usually involves hydraulic fracturing to maximize recovery. At present, effectively communicating natural discontinuities is a technical challenge. In this article, we investigated the origin and propagation of cracks in fractured-vuggy reservoirs using discrete element hydraulic fracturing simulations [...] Read more.

The exploration of fractured-vuggy carbonate reservoirs usually involves hydraulic fracturing to maximize recovery. At present, effectively communicating natural discontinuities is a technical challenge. In this article, we investigated the origin and propagation of cracks in fractured-vuggy reservoirs using discrete element hydraulic fracturing simulations that included poromechanical effects. A particular focus on the microscopic force-displacement symmetry of adjacent pore pressures is introduced. Our results demonstrate that the poromechanical effect significantly increases the strength of overpressurized reservoir formations. Moreover, the effect of injected fluid viscosity on the hydraulic fracturing effectiveness was studied through two simulation tests. The outcomes highlight the critical influence of fluid viscosity on the propagation of micro-cracks in overpressure fractured-vuggy reservoirs. Full article

(This article belongs to the Special Issue Physically Data-Driven Research on Symmetry/Asymmetry in Underground Engineering Construction and Maintenance)

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11 pages, 1400 KiB

Open AccessArticle

Selectivity in Catalytic Asymmetric Formal [3 + 3] Annulation of 2-Enoyl-pyridine N-Oxide with Benzyl Methyl Ketone

by Zuzanna Wrzeszcz, Jakub A. Warachim and Renata Siedlecka

Symmetry 2024, 16(1), 104; https://doi.org/10.3390/sym16010104 - 15 Jan 2024

Viewed by 729

Abstract

The asymmetric formal [3 + 3] annulation process of (E)-2-(3-phenylacryloyl)pyridine N-oxide with benzyl methyl ketone was investigated. The possibility of a stereoselective outcome was checked using salts of natural amino acids, as well as chiral bifunctional derivatives containing amino groups [...] Read more.

The asymmetric formal [3 + 3] annulation process of (E)-2-(3-phenylacryloyl)pyridine N-oxide with benzyl methyl ketone was investigated. The possibility of a stereoselective outcome was checked using salts of natural amino acids, as well as chiral bifunctional derivatives containing amino groups and thiourea or squaramide fragments as organocatalysts. Different types of organocatalysts applied led to opposite enantiomers of 2-(3-oxo-4,5-diphenyl-cyclohex-1-en-yl)pyridine 1-oxide (up to 60% ee). Spectroscopic analysis of the isolated product and analysis of the reaction course was carried out, taking into account the obtained regio- and stereoselectivity. In order to verify the postulated results, calculations of the energy of the intermediate reaction products and the final product using the Kohn–Sham Density Functional Theory (KS-DFT) were made. Full article

(This article belongs to the Special Issue Novel Approaches for Asymmetric Synthesis)

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15 pages, 4938 KiB

Open AccessArticle

Structure of Current Sheets Formed in 2D Magnetic Configurations with X-Type Null Lines in the Presence of the Hall Currents and Inverse Currents

by Anna G. Frank and Sergey A. Savinov

Symmetry 2024, 16(1), 103; https://doi.org/10.3390/sym16010103 - 15 Jan 2024

Cited by 1 | Viewed by 727

Abstract

We present experimental results on the formation and evolution of current sheets in two-dimensional magnetic configurations with an X-type null line. Typical features of both the initial magnetic field and the current sheet are their symmetry properties. The experiments were carried out using [...] Read more.

We present experimental results on the formation and evolution of current sheets in two-dimensional magnetic configurations with an X-type null line. Typical features of both the initial magnetic field and the current sheet are their symmetry properties. The experiments were carried out using the CS-3D setup. The formation of a current sheet occurs just after the magneto-sonic wave converges at the null line; then, both the electric current and plasma become compressed in a planar 2D sheet, which accumulates an excess of magnetic energy. The excitation of the Hall currents, which build up the out-of-plane magnetic fields inside the 2D current sheet, brings about the modification of the sheet structure. As a result, the magnetic fields and plasma currents become 3D. The dynamic plasma processes give rise to additional current sheet deformations, which are caused by the excitation of inverse currents at the side edges of the sheet. As a consequence, the out-of-plane magnetic fields are reversed, and strong Ampère’s forces of the opposite directions come into play. These forces slow down the previously accelerated high-speed plasma flows so that the flows become limited in time and space. Full article

(This article belongs to the Special Issue Symmetry in Physics of Plasma Technologies II)

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