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Symmetry, Volume 16, Issue 2 (February 2024) – 122 articles

Cover Story (view full-size image): There is compelling evidence that the early universe underwent a quasi-de-Sitter expansion. Using the framework of the causal theory of relativistic hydrodynamics, we have studied quasi-de-Sitter inflation assisted by bulk viscosity and non-equilibrium effects, which may have been present in the early universe. The crucial outcomes are as follows: (a) the quasi-de-Sitter universe emerges as a natural consequence without adding any scalar field; (b) the equation of state becomes a time-dependent function. The figure shows the behavior of the equation of state and its departure from the exact de-Sitter universe where the timescale characterizing the departure is intricately related to the magnitude of the bulk viscosity, as shown here for two different values of the bulk viscosity. View this paper
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17 pages, 804 KiB  
Article
Performance Analysis and Simulation of IRS-Aided Wireless Networks Communication
by Osman Dikmen
Symmetry 2024, 16(2), 254; https://doi.org/10.3390/sym16020254 - 19 Feb 2024
Viewed by 700
Abstract
This paper introduces the novel IRS-based Optimal Relay Selection (ORS-IRS) method, aimed at analyzing the performance of wireless communication systems with an emphasis on symmetry. The ORS-IRS approach presents an innovative communication algorithm that seamlessly integrates Intelligent Reflecting Surfaces (IRS) with relay selection [...] Read more.
This paper introduces the novel IRS-based Optimal Relay Selection (ORS-IRS) method, aimed at analyzing the performance of wireless communication systems with an emphasis on symmetry. The ORS-IRS approach presents an innovative communication algorithm that seamlessly integrates Intelligent Reflecting Surfaces (IRS) with relay selection techniques. Through adaptive adjustments of reflection coefficients, IRS elements efficiently manipulate incoming signals, fostering symmetry in signal strength enhancement and latency reduction for improved signal delivery to the intended destination. This symmetrical optimization in channel capacity and transmission power ensures reliable data transmission with low latency, achieved through the seamless integration of IRS and relay selection techniques. In contrast, the Cell-Free Massive MIMO (CF-M-MIMO), with its decentralized architecture, excels in serving a larger user base and attaining remarkable capacity gains, showcasing a different dimension of symmetry. The Decode-and-Forward (DF) relaying approach demonstrates its potential in enhancing signal reliability across extended distances, contributing to the overall symmetry of the comparative analysis. This comprehensive evaluation provides valuable insights into selecting appropriate transmission strategies, particularly for applications that demand high capacity and reliability in the design of modern wireless communication systems with a symmetrical focus. Full article
(This article belongs to the Special Issue New Advances in New-Generation Communication and Symmetry)
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18 pages, 857 KiB  
Article
Nonlinear Dynamics of a New Class of Micro-Electromechanical Oscillators—Open Problems
by Nikolay Kyurkchiev, Tsvetelin Zaevski, Anton Iliev, Vesselin Kyurkchiev and Asen Rahnev
Symmetry 2024, 16(2), 253; https://doi.org/10.3390/sym16020253 - 19 Feb 2024
Cited by 1 | Viewed by 567
Abstract
In this paper, we propose a new class of micro-electromechanical oscillators. Some investigations based on Melnikov’s approach are applied for identifying some chaotic possibilities. We demonstrate also some specialized modules for investigating the dynamics of these oscillators. This will be included as an [...] Read more.
In this paper, we propose a new class of micro-electromechanical oscillators. Some investigations based on Melnikov’s approach are applied for identifying some chaotic possibilities. We demonstrate also some specialized modules for investigating the dynamics of these oscillators. This will be included as an integral part of a planned much more general Web-based application for scientific computing. It turns out that the theoretical apparatus for studying the circuit implementation (design, fabricating, etc.) of the considered differential model for large parameter values is extremely complex and requires a serious investigation. This is the reason to offer this model to the attention of specialists working in this scientific direction. Some open problems related to the use of existing computer algebraic systems for the study of this class of oscillators for large values of n,m and N are also posed. In general, the entire article is subordinated to this frank conversation with the readers with the sole purpose being the professional upgrading of the specialized modules provided for this purpose in subsequent licensed versions of CAS. Full article
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25 pages, 897 KiB  
Article
Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation
by Mariusz Ciesielski
Symmetry 2024, 16(2), 252; https://doi.org/10.3390/sym16020252 - 18 Feb 2024
Viewed by 713
Abstract
Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, [...] Read more.
Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented. Full article
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21 pages, 895 KiB  
Review
Analysis of B(s)0μ+μ Decays at the Large Hadron Collider
by Kai-Feng Chen, Titus Mombächer and Umberto De Sanctis
Symmetry 2024, 16(2), 251; https://doi.org/10.3390/sym16020251 - 18 Feb 2024
Viewed by 595
Abstract
This article reviews the most recent measurements of B(s)0μ+μ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of [...] Read more.
This article reviews the most recent measurements of B(s)0μ+μ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of the Bs0μ+μ decay by the ATLAS, CMS, and LHCb collaborations, as well as the search for B0μ+μ decays, are summarized with a focus on the experimental challenges. Furthermore, prospects are given for these measurements and new observables that become accessible with the foreseen amounts of data by the end of the LHC. Full article
(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)
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12 pages, 492 KiB  
Article
Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States
by Jerzy Dajka
Symmetry 2024, 16(2), 250; https://doi.org/10.3390/sym16020250 - 18 Feb 2024
Viewed by 567
Abstract
A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson [...] Read more.
A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence. Full article
(This article belongs to the Section Physics)
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19 pages, 2093 KiB  
Article
Program Behavior Dynamic Trust Measurement and Evaluation Based on Data Analysis
by Shuai Wang, Aiqun Hu, Tao Li and Shaofan Lin
Symmetry 2024, 16(2), 249; https://doi.org/10.3390/sym16020249 - 17 Feb 2024
Viewed by 715
Abstract
Industrial control terminals play an important role in industrial control scenarios. Due to the special nature of industrial control networks, industrial control terminal systems are vulnerable to malicious attacks, which can greatly threaten the stability and security of industrial production environments. Traditional security [...] Read more.
Industrial control terminals play an important role in industrial control scenarios. Due to the special nature of industrial control networks, industrial control terminal systems are vulnerable to malicious attacks, which can greatly threaten the stability and security of industrial production environments. Traditional security protection methods for industrial control terminals have coarse detection granularity, and are unable to effectively detect and prevent attacks, lacking real-time responsiveness to attack events. Therefore, this paper proposes a real-time dynamic credibility evaluation mechanism based on program behavior, which integrates the matching and symmetry ideas of credibility evaluation. By conducting a real-time dynamic credibility evaluation of function call sequences and system call sequences during program execution, the credibility of industrial control terminal application program behavior can be judged. To solve the problem that the system calls generated during program execution are unstable and difficult to measure, this paper proposes a partition-based dynamic credibility evaluation method, dividing program behavior during runtime into function call behavior and system call behavior within function intervals. For function call behavior, a sliding window-based function call sequence benchmark library construction method is proposed, which matches and evaluates real-time measurement results based on the benchmark library, thereby achieving symmetry between the benchmark library and the measured data. For system call behavior, a maximum entropy system call model is constructed, which is used to evaluate the credibility of system call sequences. Experiment results demonstrate that our method performs better in both detection success rate and detection speed compared to the existing methods. Full article
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26 pages, 3409 KiB  
Article
AntiPhishStack: LSTM-Based Stacked Generalization Model for Optimized Phishing URL Detection
by Saba Aslam, Hafsa Aslam, Arslan Manzoor, Hui Chen and Abdur Rasool
Symmetry 2024, 16(2), 248; https://doi.org/10.3390/sym16020248 - 17 Feb 2024
Viewed by 761
Abstract
The escalating reliance on revolutionary online web services has introduced heightened security risks, with persistent challenges posed by phishing despite extensive security measures. Traditional phishing systems, reliant on machine learning and manual features, struggle with evolving tactics. Recent advances in deep learning offer [...] Read more.
The escalating reliance on revolutionary online web services has introduced heightened security risks, with persistent challenges posed by phishing despite extensive security measures. Traditional phishing systems, reliant on machine learning and manual features, struggle with evolving tactics. Recent advances in deep learning offer promising avenues for tackling novel phishing challenges and malicious URLs. This paper introduces a two-phase stack generalized model named AntiPhishStack, designed to detect phishing sites. The model leverages the learning of URLs and character-level TF-IDF features symmetrically, enhancing its ability to combat emerging phishing threats. In Phase I, features are trained on a base machine learning classifier, employing K-fold cross-validation for robust mean prediction. Phase II employs a two-layered stacked-based LSTM network with five adaptive optimizers for dynamic compilation, ensuring premier prediction on these features. Additionally, the symmetrical predictions from both phases are optimized and integrated to train a meta-XGBoost classifier, contributing to a final robust prediction. The significance of this work lies in advancing phishing detection with AntiPhishStack, operating without prior phishing-specific feature knowledge. Experimental validation on two benchmark datasets, comprising benign and phishing or malicious URLs, demonstrates the model’s exceptional performance, achieving a notable 96.04% accuracy compared to existing studies. This research adds value to the ongoing discourse on symmetry and asymmetry in information security and provides a forward-thinking solution for enhancing network security in the face of evolving cyber threats. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Information Security and Network Security)
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41 pages, 1882 KiB  
Article
Exploring Semi-Inclusive Two-Nucleon Emission in Neutrino Scattering: A Factorized Approximation Approach
by Victor L. Martinez-Consentino and Jose E. Amaro
Symmetry 2024, 16(2), 247; https://doi.org/10.3390/sym16020247 - 17 Feb 2024
Viewed by 581
Abstract
The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an [...] Read more.
The semi-inclusive cross-section of two-nucleon emission induced by neutrinos and antineutrinos is computed by employing the relativistic mean field model of nuclear matter and the dynamics of meson-exchange currents. Within this model, we explore a factorization approximation based on the product of an integrated two-hole spectral function and a two-nucleon cross-section averaged over hole pairs. We demonstrate that the integrated spectral function of the uncorrelated Fermi gas can be analytically computed, and we derive a simple, fully relativistic formula for this function, showcasing its dependency solely on both missing momentum and missing energy. A prescription for the average momenta of the two holes in the factorized two-nucleon cross-section is provided, assuming that these momenta are perpendicular to the missing momentum in the center-of-mass system. The validity of the factorized approach is assessed by comparing it with the unfactorized calculation. Our investigation includes the study of the semi-inclusive cross-section integrated over the energy of one of the emitted nucleons and the cross-section integrated over the emission angles of the two nucleons and the outgoing muon kinematics. A comparison is made with the pure phase-space model and other models from the literature. The results of this analysis offer valuable insights into the influence of the semi-inclusive hadronic tensor on the cross-section, providing a deeper understanding of the underlying nuclear processes. Full article
(This article belongs to the Section Physics)
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11 pages, 292 KiB  
Article
A General Approach to Sylvester-Polynomial-Conjugate Matrix Equations
by Ryszard Mazurek
Symmetry 2024, 16(2), 246; https://doi.org/10.3390/sym16020246 - 17 Feb 2024
Viewed by 682
Abstract
Sylvester-polynomial-conjugate matrix equations unify many well-known versions and generalizations of the Sylvester matrix equation AXXB=C which have a wide range of applications. In this paper, we present a general approach to Sylvester-polynomial-conjugate matrix equations via groupoids, vector [...] Read more.
Sylvester-polynomial-conjugate matrix equations unify many well-known versions and generalizations of the Sylvester matrix equation AXXB=C which have a wide range of applications. In this paper, we present a general approach to Sylvester-polynomial-conjugate matrix equations via groupoids, vector spaces, and matrices over skew polynomial rings. The obtained results are applied to Sylvester-polynomial-conjugate matrix equations over complex numbers and quaternions. The main role in our approach is played by skew polynomial rings, which are well-known tools in algebra to provide examples of asymmetry between left-sided and right-sided versions of many ring objects. Full article
(This article belongs to the Section Mathematics)
18 pages, 26151 KiB  
Article
Chemically Modified Electrodes Based on 4-((5-Isopropyl-3,8-dimethylazulen-1-yl)methylene)-2-phenyloxazol-5(4H)-one
by Alina-Giorgiana Brotea, Ovidiu-Teodor Matica, Cornelia Musina (Borsaru), Andreea Madalina Pandele, Roxana Trusca and Eleonora-Mihaela Ungureanu
Symmetry 2024, 16(2), 245; https://doi.org/10.3390/sym16020245 - 16 Feb 2024
Viewed by 597
Abstract
Novel chemically modified electrodes (CMEs) based on azulene were prepared by electrooxidation of guaiazulene derivative 4-((5-isopropyl-3,8-dimethylazulen-1-yl)methylene)-2-phenyloxazol-5(4H)-one (G). G is based on guaiazulene non-alternating aromatic hydrocarbon exhibiting a less symmetrical structure compared to naphthalene skeletal derivative. Therefore, it can be used as [...] Read more.
Novel chemically modified electrodes (CMEs) based on azulene were prepared by electrooxidation of guaiazulene derivative 4-((5-isopropyl-3,8-dimethylazulen-1-yl)methylene)-2-phenyloxazol-5(4H)-one (G). G is based on guaiazulene non-alternating aromatic hydrocarbon exhibiting a less symmetrical structure compared to naphthalene skeletal derivative. Therefore, it can be used as a building block for the preparation of novel materials. To evaluate the chemical structure and surface images, the CMEs based on G (G-CMEs) were characterized by ferrocene redox probe, X-ray photon spectroscopy (XPS), and scanning electron microscopy (SEM). They were also tested for the analysis of synthetic samples of heavy metal (HM) ions. The influence of preparation conditions (electric charge and potential) on the properties of these CMEs was examined. This paper highlights the importance of electropolymerization conditions on electrodeposited film surfaces, especially on their analytical properties vs. Cd(II), Pb(II), Cu(II), and Hg(II) investigated ions. This study is relevant for further design and development of advanced materials based on azulenyl-phenyloxazolone for the HM analysis in water. A linear dependence of the peak currents for Pb(II) ion on the concentration in test aqueous solutions was obtained between 10−7 M and 5·10−5 M. The detection limits of 5·10−6 M; 10−7 M; 5·10−6 M; and 10−5 M were estimated for Cd(II), Pb(II), Cu(II), and Hg(II), respectively, for G-CMEs. Full article
(This article belongs to the Section Engineering and Materials)
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16 pages, 3992 KiB  
Article
Investigation into Detection Efficiency Deviations in Aviation Soot and Calibration Particles Based on Condensation Particle Counting
by Liang Chen, Quan Zhou, Guangze Li, Liuyong Chang, Longfei Chen and Yuanhao Li
Symmetry 2024, 16(2), 244; https://doi.org/10.3390/sym16020244 - 16 Feb 2024
Viewed by 556
Abstract
Aviation soot constitutes a significant threat to human well-being, underscoring the critical importance of accurate measurements. The condensation particle counter (CPC) is the primary instrument for quantifying aviation soot, with detection efficiency being a crucial parameter. The properties of small particles and the [...] Read more.
Aviation soot constitutes a significant threat to human well-being, underscoring the critical importance of accurate measurements. The condensation particle counter (CPC) is the primary instrument for quantifying aviation soot, with detection efficiency being a crucial parameter. The properties of small particles and the symmetry of their growth pathways are closely related to the detection efficiency of the CPC. In laboratory environments, sodium chloride is conventionally utilized to calibrate the CPC’s detection efficiency. However, aviation soot exhibits distinctive morphological characteristics compared to the calibration particles, leading to detection efficiencies obtained from calibration particles that may not be applicable to aviation soot. To address this issue, a quantitative study was performed to explore the detection efficiency deviations between aviation soot and calibration particles. The experiment initially utilized a differential mobility analyzer to size select the two types of polydisperse particles into monodisperse particles. Subsequently, measurements of the separated particles were performed using the TSI Corporation’s aerosol electrometer and a rigorously validated CPC (BH-CPC). These allowed for determining the detection efficiency deviation in the BH-CPC for the two types of particles at different particle sizes. Furthermore, the influence of the operating temperature of the BH-CPC on this detection efficiency deviation was investigated. The experimental results indicate a significant detection efficiency deviation between aviation soot and sodium chloride. In the range of 10–40 nm, the absolute detection efficiency deviation can reach a maximum of 0.15, and the relative deviation can reach a maximum of 0.75. And this detection efficiency deviation can be reduced by establishing a relevant relationship between the detection efficiency of the operating temperature and the calibration temperature. Compared to the saturated segment calibration temperature of 50 °C, the aviation soot detection efficiency is closer to the sodium chloride detection efficiency at the calibration temperature of 50 °C when the saturated segment operates at a temperature of 45 °C. These studies provide crucial theoretical guidance for enhancing the precision of aviation soot emission detection and establish a foundation for future research in monitoring and controlling soot emissions within the aviation sector. Full article
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12 pages, 958 KiB  
Article
On the Network Index of MAS with Layered Lattice-like Structures of Multiple Vertex-Related Parameters
by Da Huang, Jibin Yang, Zhiyong Yu and Cheng Hu
Symmetry 2024, 16(2), 243; https://doi.org/10.3390/sym16020243 - 16 Feb 2024
Viewed by 506
Abstract
In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic [...] Read more.
In this article, a robust index named first-order network coherence (FONC) for the multi-agent systems (MASs) with layered lattice-like structure is studied via the angle of the graph spectra theory. The union operation of graphs is utilized to construct two pairs of non-isomorphic layered lattice-like structures, and the expression of the index is acquired by the approach of Laplacian spectra, then the corresponding asymptotic results are obtained. It is found that when the cardinality of the node sets of coronary substructures with better connectedness tends to infinity, the FONC of the whole network will have the same asymptotic behavior with the central lattice-like structure in the considered classic graph frameworks. The indices of the networks were simulated to illustrate the the asymptotic results, as described in the last section. Full article
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17 pages, 16216 KiB  
Article
Non-Standard Finite Difference and Vieta-Lucas Orthogonal Polynomials for the Multi-Space Fractional-Order Coupled Korteweg-de Vries Equation
by Khaled M. Saad and Rekha Srivastava
Symmetry 2024, 16(2), 242; https://doi.org/10.3390/sym16020242 - 16 Feb 2024
Viewed by 560
Abstract
This paper focuses on examining numerical solutions for fractional-order models within the context of the coupled multi-space Korteweg-de Vries problem (CMSKDV). Different types of kernels, including Liouville-Caputo fractional derivative, as well as Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, are utilized in the examination. For [...] Read more.
This paper focuses on examining numerical solutions for fractional-order models within the context of the coupled multi-space Korteweg-de Vries problem (CMSKDV). Different types of kernels, including Liouville-Caputo fractional derivative, as well as Caputo-Fabrizio and Atangana-Baleanu fractional derivatives, are utilized in the examination. For this purpose, the nonstandard finite difference method and spectral collocation method with the properties of the Shifted Vieta-Lucas orthogonal polynomials are employed for converting these models into a system of algebraic equations. The Newton-Raphson technique is then applied to solve these algebraic equations. Since there is no exact solution for non-integer order, we use the absolute two-step error to verify the accuracy of the proposed numerical results. Full article
(This article belongs to the Special Issue Theory and Applications of Special Functions II)
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29 pages, 4391 KiB  
Article
Comprehensive Sensitivity Analysis Framework for Transfer Learning Performance Assessment for Time Series Forecasting: Basic Concepts and Selected Case Studies
by Witesyavwirwa Vianney Kambale, Mohamed Salem, Taha Benarbia, Fadi Al Machot and Kyandoghere Kyamakya
Symmetry 2024, 16(2), 241; https://doi.org/10.3390/sym16020241 - 16 Feb 2024
Viewed by 652
Abstract
Recently, transfer learning has gained popularity in the machine learning community. Transfer Learning (TL) has emerged as a promising paradigm that leverages knowledge learned from one or more related domains to improve prediction accuracy in a target domain with limited data. However, for [...] Read more.
Recently, transfer learning has gained popularity in the machine learning community. Transfer Learning (TL) has emerged as a promising paradigm that leverages knowledge learned from one or more related domains to improve prediction accuracy in a target domain with limited data. However, for time series forecasting (TSF) applications, transfer learning is relatively new. This paper addresses the need for empirical studies as identified in recent reviews advocating the need for practical guidelines for Transfer Learning approaches and method designs for time series forecasting. The main contribution of this paper is the suggestion of a comprehensive framework for Transfer Learning Sensitivity Analysis (SA) for time series forecasting. We achieve this by identifying various parameters seen from various angles of transfer learning applied to time series, aiming to uncover factors and insights that influence the performance of transfer learning in time series forecasting. Undoubtedly, symmetry appears to be a core aspect in the consideration of these factors and insights. A further contribution is the introduction of four TL performance metrics encompassed in our framework. These TL performance metrics provide insight into the extent of the transferability between the source and the target domains. Analyzing whether the benefits of transferred knowledge are equally or unequally accessible and applicable across different domains or tasks speaks to the requirement of symmetry or asymmetry in transfer learning. Moreover, these TL performance metrics inform on the possibility of the occurrence of negative transfers and also provide insight into the possible vulnerability of the network to catastrophic forgetting. Finally, we discuss a sensitivity analysis of an Ensemble TL technique use case (with Multilayer Perceptron models) as a proof of concept to validate the suggested framework. While the results from the experiments offer empirical insights into various parameters that impact the transfer learning gain, they also raise the question of network dimensioning requirements when designing, specifically, a neural network for transfer learning. Full article
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25 pages, 5729 KiB  
Article
Enhancing Urban Intersection Efficiency: Visible Light Communication and Learning-Based Control for Traffic Signal Optimization and Vehicle Management
by Manuel Augusto Vieira, Gonçalo Galvão, Manuela Vieira, Paula Louro, Mário Vestias and Pedro Vieira
Symmetry 2024, 16(2), 240; https://doi.org/10.3390/sym16020240 - 16 Feb 2024
Viewed by 739
Abstract
This paper introduces a novel approach, Visible Light Communication (VLC), to optimize urban intersections by integrating VLC localization services with learning-based traffic signal control. The system enhances communication between connected vehicles and infrastructure using headlights, streetlights, and traffic signals to transmit information. Through [...] Read more.
This paper introduces a novel approach, Visible Light Communication (VLC), to optimize urban intersections by integrating VLC localization services with learning-based traffic signal control. The system enhances communication between connected vehicles and infrastructure using headlights, streetlights, and traffic signals to transmit information. Through Vehicle-to-Vehicle (V2V) and Infrastructure-to-Vehicle (I2V) interactions, joint data transmission and collection occur via mobile optical receivers. The goal is to reduce waiting times for pedestrians and vehicles, enhancing overall traffic safety by employing flexible and adaptive measures accommodating diverse traffic movements. VLC cooperative mechanisms, transmission range, relative pose concepts, and queue/request/response interactions help balance traffic flow and improve road network performance. Evaluation in the SUMO urban mobility simulator demonstrates advantages, reducing waiting and travel times for both vehicles and pedestrians. The system employs a reinforcement learning scheme for effective traffic signal scheduling, utilizing VLC-ready vehicles to communicate positions, destinations, and routes. Agents at intersections calculate optimal strategies, communicating to optimize overall traffic flow. The proposed decentralized and scalable approach, especially suitable for multi-intersection scenarios, showcases the feasibility of applying reinforcement learning in real-world traffic scenarios. Full article
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10 pages, 1511 KiB  
Article
On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions
by Qasim Ali Shakir and Waggas Galib Atshan
Symmetry 2024, 16(2), 239; https://doi.org/10.3390/sym16020239 - 16 Feb 2024
Viewed by 513
Abstract
This study presents a subclass S(β) of bi-univalent functions within the open unit disk region D. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (3(1) [...] Read more.
This study presents a subclass S(β) of bi-univalent functions within the open unit disk region D. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (3(1)). In this study, new constraints for the estimates of the third Hankel determinant for the class S(β) are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as S(β) and impose constraints on the coefficients an. Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses. Full article
(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)
22 pages, 5668 KiB  
Article
Nonlinear Dynamic Analysis of a Curved Sandwich Beam with a Time-Dependent Viscoelastic Core Using the Generalized Differential Quadrature Method (GDQM)
by Mehmet Mert Serveren, Ozgur Demir and Aytac Arikoglu
Symmetry 2024, 16(2), 238; https://doi.org/10.3390/sym16020238 - 15 Feb 2024
Viewed by 549
Abstract
This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order [...] Read more.
This paper focuses on the geometrically nonlinear dynamic analyses of a three-layered curved sandwich beam with isotropic face layers and a time-dependent viscoelastic core. The boundary conditions and equations of motion governing the forced vibration are derived by using Hamilton’s principle. The first-order shear deformation theory is used to obtain kinematic relations. The spatial discretization of the equations is achieved using the generalized differential quadrature method (GDQM), and the Newmark-Beta algorithm is used to solve the time variation of the equations. The Newton–Raphson method is used to transform nonlinear equations into linear equations. The validation of the proposed model and the GDQM solution’s reliability are provided via comparison with the results that already exist in the literature and finite element method (FEM) analyses using ANSYS. Then, a series of parametric studies are carried out for a curved sandwich beam with aluminum face layers and a time-dependent viscoelastic core. The resonance and cancellation phenomena for the nonlinear moving-load problem of curved sandwich beams with a time-dependent viscoelastic core are performed using the GDQM for the first time, to the best of the authors’ knowledge. Full article
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25 pages, 8504 KiB  
Review
Analysis of Mixing Efficiency in a Stirred Reactor Using Computational Fluid Dynamics
by Adan Ramírez-López
Symmetry 2024, 16(2), 237; https://doi.org/10.3390/sym16020237 - 15 Feb 2024
Viewed by 635
Abstract
Lead recycling is very important for reducing environmental pollution risks and damages. Liquid lead is recovered from exhaust batteries inside stirred batch reactors; the process requires melting to be cleaned. Nevertheless, it is necessary to establish parameters for evaluating mixing to improve the [...] Read more.
Lead recycling is very important for reducing environmental pollution risks and damages. Liquid lead is recovered from exhaust batteries inside stirred batch reactors; the process requires melting to be cleaned. Nevertheless, it is necessary to establish parameters for evaluating mixing to improve the efficiency of the industrial practices. Computational fluid dynamics (CFD) has become a powerful tool to analyze industrial processes for reducing operating costs, avoiding potential damages, and improving the equipment’s performance. Thus, the present work is focused on simulating the fluid hydrodynamics inside a lead-stirred reactor monitoring the distribution of an injected tracer in order to find the best injection point. Then, different injected points are placed on a control plane for evaluation; these are evaluated one by one by monitoring the tracer concentration at a group of points inside the batch. The analyzed reactor is a symmetrical, vertical batch reactor with two geometrical sections: one cylindrical body and a semi-spherical bottom. Here, one impeller with four flat blades in a shaft is used for lead stirring. The tracer concentration on the monitoring points is measured and averaged for evaluating the efficiency inside the tank reactor. Hydrodynamics theory and a comparison between the concentration profiles and distribution of tracer curves are used to demonstrate both methods’ similarities. Then, the invariability of the tracer concentration on the monitoring points is adopted as the main parameter to evaluate the mixing, and the best injection point is found as a function of the shortest mixing time. Additionally, the influence of the impeller rotation speed is analyzed as an additional control parameter to improve industrial practices. Full article
(This article belongs to the Special Issue Symmetry in Fluid Dynamics)
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13 pages, 3745 KiB  
Article
Cosmic Ray Anisotropy and Spectra as Probes for Nearby Sources
by Aifeng Li, Wei Liu and Yiqing Guo
Symmetry 2024, 16(2), 236; https://doi.org/10.3390/sym16020236 - 15 Feb 2024
Viewed by 568
Abstract
Cosmic ray (CR) spectra and anisotropy are closely related to the distribution of CR sources, making them valuable probes for studying nearby sources. There are 12 nearby sources located within 1 kpc of the solar system, and which ones are the optimal candidates? [...] Read more.
Cosmic ray (CR) spectra and anisotropy are closely related to the distribution of CR sources, making them valuable probes for studying nearby sources. There are 12 nearby sources located within 1 kpc of the solar system, and which ones are the optimal candidates? In this work, we have selected the Geminga, Monogem, Vela, Loop I, and Cygnus SNR sources as the focus of our research, aiming to identify the optimal candidate by investigating their contribution to the energy spectra and anisotropy using the Spatially Dependent Propagation (SDP) model. Additionally, the anisotropic diffusion effect of the local regular magnetic field (LRMF) on CR particles is also considered in the SDP model. Our previous work only provided 1D anisotropy along the right ascension; this current work will further present 2D anisotropy maps along the right ascension and declination. When the injection power of different nearby sources is roughly equal, the results show that the Geminga, Momogem, and Loop I SNR sources contribute significantly to the nuclear energy spectra. Under the isotropic diffusion without considering the LRMF, the 2D anisotropy maps indicate that the phase points to the nearby source below 100 TeV. We further adjust the injection power of the Monogem SNR source in accordance with the spin-down energy of the Geminga and Monogem pulsars, and find that the contribution of the corrected Monogem SNR can be disregarded. Because the Loop I SNR source is located in the direction of the Galactic Center (GC), it cannot contribute to the excess of CRs in the anti-GC direction. Under anisotorpic diffusion with the consideration of the LRMF, the 2D anisotropy maps show that only the Geminga SNR can match the anisotropy measurement, while the other sources cannot. Finally, we conclude that the Geminga SNR source is the optimal nearby source. Full article
(This article belongs to the Section Physics)
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15 pages, 2341 KiB  
Article
Bertrand Offsets of Slant Ruled Surfaces in Euclidean 3-Space
by Areej A. Almoneef and Rashad A. Abdel-Baky
Symmetry 2024, 16(2), 235; https://doi.org/10.3390/sym16020235 - 15 Feb 2024
Viewed by 542
Abstract
In this paper, we investigate and specify the Bertrand offsets of slant ruled and developable surfaces in Euclidean 3-space E3. This is accomplished by utilizing the symmetry of slant curves. As a consequence of this, we present the parameterization of the [...] Read more.
In this paper, we investigate and specify the Bertrand offsets of slant ruled and developable surfaces in Euclidean 3-space E3. This is accomplished by utilizing the symmetry of slant curves. As a consequence of this, we present the parameterization of the Bertrand offsets for any slant ruled and developable surfaces. In addition to this, we investigate the monarchies of these ruled surfaces and assign them their own unique classification. Also, we illustrate some examples of slant ruled surfaces. Full article
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23 pages, 12778 KiB  
Article
Research on Mechanical Properties of Rock Mass with Tiny Cracks under FTCs Conditions
by Yin-Ge Zhu, Yue Wu, An-Qi Li and Shuai Zhang
Symmetry 2024, 16(2), 234; https://doi.org/10.3390/sym16020234 - 14 Feb 2024
Viewed by 602
Abstract
After the repeated freezing and dissolution of fractured rock masses in cold regions, the liquid present in the pores undergoes a water–ice phase transition, resulting in frost heave forces and damage to the internal structure of the rock mass. This causes the rock [...] Read more.
After the repeated freezing and dissolution of fractured rock masses in cold regions, the liquid present in the pores undergoes a water–ice phase transition, resulting in frost heave forces and damage to the internal structure of the rock mass. This causes the rock masses to continuously develop new cracks, which further expand and connect, leading to rock mass failure and ultimately reducing the overall stability of the rock mass in engineering projects. In this study, uniaxial compression tests, direct shear tests, and Brazilian splitting tests were conducted on rock after freeze–thaw cycles (FTCs), and the changes in the physical and mechanical properties of the rock under freeze–thaw conditions were obtained (this study used raw rock from an engineering project and processed it into symmetrical jointed rock samples). The roughness of the shear fracture surfaces was analyzed through 3D cross-sectional scanning experiments. Using statistical damage theory, the mechanism of freeze–thaw damage was analyzed, and a constitutive model for freeze–thaw rock damage was established. The research results can provide a theoretical basis and support for engineering safety and stability in cold regions. Full article
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18 pages, 931 KiB  
Article
Comparison of Selected Numerical Methods for Solving Integro-Differential Equations with the Cauchy Kernel
by Rafał Brociek and Mariusz Pleszczyński
Symmetry 2024, 16(2), 233; https://doi.org/10.3390/sym16020233 - 14 Feb 2024
Cited by 1 | Viewed by 564
Abstract
The integro-differential equation with the Cauchy kernel is used in many different technical problems, such as in circuit analysis or gas infrared radiation studies. Therefore, it is important to be able to solve this type of equation, even in an approximate way. This [...] Read more.
The integro-differential equation with the Cauchy kernel is used in many different technical problems, such as in circuit analysis or gas infrared radiation studies. Therefore, it is important to be able to solve this type of equation, even in an approximate way. This article compares two approaches for solving this type of equation. One of the considered methods is based on the application of the differential Taylor series, while the second approach uses selected heuristic algorithms inspired by the behavior of animals. Due to the problem domain, which is symmetric, and taking into account the form of the function appearing in this equation, we can use this symmetry in some cases. The paper also presents numerical examples illustrating how each method works and comparing the discussed approaches. Full article
(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models, Part II)
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17 pages, 14619 KiB  
Article
Shaking Table Tests on the Seismic Response of Symmetrically Integrated Underground Stations
by Shi Ming, Lianjin Tao and Zhigang Wang
Symmetry 2024, 16(2), 232; https://doi.org/10.3390/sym16020232 - 14 Feb 2024
Viewed by 489
Abstract
This paper focuses on the seismic response of symmetrical underground subway stations to seismic waves with varying frequencies and peak ground accelerations (PGAs), essential in light of growing urban underground transit systems. A 1/40 scale station model was subjected to seismic simulations using [...] Read more.
This paper focuses on the seismic response of symmetrical underground subway stations to seismic waves with varying frequencies and peak ground accelerations (PGAs), essential in light of growing urban underground transit systems. A 1/40 scale station model was subjected to seismic simulations using waves from the Wenchuan and Tangshan earthquakes and an artificial wave spanning 0.1 g to 0.5 g PGAs. Shaking table tests revealed that seismic impacts divide at PGA = 0.3 g; high-frequency waves affect structures more below this threshold, while low-frequency waves have more impact above it. The columns on the third basement level responded more to seismic activity, particularly at their base. The study recommends prioritizing the seismic design of these columns during station construction, especially in earthquake-prone zones. Understanding the dynamic effects of different frequencies and amplitudes is crucial for selecting and reinforcing materials and structural designs to enhance seismic resistance. Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Structural Dynamics)
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14 pages, 4499 KiB  
Article
Symmetries in Collisions as Explored through the Harmonic Oscillator
by Martin Freer and Miriam Davies
Symmetry 2024, 16(2), 231; https://doi.org/10.3390/sym16020231 - 14 Feb 2024
Viewed by 650
Abstract
The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. [...] Read more.
The present study explores the symmetries associated with the cluster structure of light nuclei and draws the connection between solutions of the Schrödinger equation for the harmonic oscillator and the quasi-crystalline arrangements of α-particles, which gives rise to a series of collective behaviors. The double-center harmonic oscillator is used to formulate the collisions of two nuclei described by harmonic oscillator solutions and traces out the evolution of the cluster structure in the dynamics of the collision process and demonstrates that the symmetries are preserved in this process. The connection between this study and stellar nucleosynthesis is described. Full article
(This article belongs to the Special Issue Role of Symmetries in Nuclear Physics)
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10 pages, 247 KiB  
Article
Wave Surface Symmetry and Petrov Types in General Relativity
by Graham Hall
Symmetry 2024, 16(2), 230; https://doi.org/10.3390/sym16020230 - 14 Feb 2024
Viewed by 499
Abstract
This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M,g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other [...] Read more.
This paper presents a brief study of (2-dimensional, spacelike) wave surfaces to a null direction l on a space-time (M,g) and studies how certain imposed symmetries on the set of such wave surfaces can be used to describe other geometrical features of l and (M,g). It is mainly a review of known material but contains some novelties. For example, the brief discussion of the nature of wave surfaces (when viewed geometrically as wave fronts to a null ray direction) in Wave Surfaces Section is new in the sense that although it appeared in the author’s work by the present author, it has not, to the best of his knowledge, appeared in this form anywhere else. Further, the work on conical symmetry and plane waves are, to the best of the author’s knowledge, original with him from earlier papers and are reviewed here while the work on complete wave surface (sectional curvature-) symmetry is believed to be entirely new. Geometrical use of the sectional curvature function is employed in many places. The consequences of the various symmetry conditions imposed on the collection of all wave surfaces to a null direction spanned by a null vector l are described in terms of l spanning a principal null direction of the Weyl tensor (if non-zero) at the point concerned (in the sense of Petrov and Bel). Full article
(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)
14 pages, 5347 KiB  
Article
Structure and Thermodynamics of Li+Arn Clusters beyond the Second Solvation Shell
by Jorge M. C. Marques and Frederico V. Prudente
Symmetry 2024, 16(2), 229; https://doi.org/10.3390/sym16020229 - 14 Feb 2024
Viewed by 549
Abstract
Small Li+Arn clusters are employed in this work as model systems to study microsolvation. Although first and second solvation shells are expected to be the most relevant ones for this type of atomic solvents, it is also interesting to explore [...] Read more.
Small Li+Arn clusters are employed in this work as model systems to study microsolvation. Although first and second solvation shells are expected to be the most relevant ones for this type of atomic solvents, it is also interesting to explore larger clusters in order to identify the influence of external atoms on structural and thermodynamic properties. In this work, we perform a global geometry optimization for Li+Arn clusters (with n = 41–100) and parallel tempering Monte Carlo (PTMC) simulations for some selected sizes. The results show that global minimum structures of large clusters always have 6 argon atoms in the first solvation shell while maintaining the number of 14 or 16 argon atoms in the second one. By contrast, third and fourth solvation shells vary significantly the number of argon atoms with the cluster size, and other shells can hardly be assigned due to the reduced influence of Li+ on the external argon atoms for large clusters. In turn, PTMC calculations show that the melting of the most external solvation shells of large microsolvation clusters occurs at T50K, which is independent of cluster size. Structural transitions can be observed between quasi-degenerated structures at low temperatures. Moreover, the present results highlight the fluxional character of the external solvation shells of these large Li+Arn clusters, which may be seen as typical “snowball” structures. Full article
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15 pages, 20617 KiB  
Article
Automatic Control of Virtual Cameras for Capturing and Sharing User Focus and Interaction in Collaborative Virtual Reality
by Junhyeok Lee, Dongkeun Lee, Seowon Han, Hyun K. Kim and Kang Hoon Lee
Symmetry 2024, 16(2), 228; https://doi.org/10.3390/sym16020228 - 13 Feb 2024
Viewed by 584
Abstract
As VR technology advances and network speeds rise, social VR platforms are gaining traction. These platforms enable multiple users to socialize and collaborate within a shared virtual environment using avatars. Virtual reality, with its ability to augment visual information, offers distinct advantages for [...] Read more.
As VR technology advances and network speeds rise, social VR platforms are gaining traction. These platforms enable multiple users to socialize and collaborate within a shared virtual environment using avatars. Virtual reality, with its ability to augment visual information, offers distinct advantages for collaboration over traditional methods. Prior research has shown that merely sharing another person’s viewpoint can significantly boost collaborative efficiency. This paper presents an innovative non-verbal communication technique designed to enhance the sharing of visual information. By employing virtual cameras, our method captures where participants are focusing and what they are interacting with, then displays these data above their avatars. The direction of the virtual camera is automatically controlled by considering the user’s gaze direction, the position of the object the user is interacting with, and the positions of other objects around that object. The automatic adjustment of these virtual cameras and the display of captured images are symmetrically conducted for all participants engaged in the virtual environment. This approach is especially beneficial in collaborative settings, where multiple users work together on a shared structure of multiple objects. We validated the effectiveness of our proposed technique through an experiment with 20 participants tasked with collaboratively building structures using block assembly. Full article
(This article belongs to the Special Issue Symmetry Applied in Computer Vision, Automation, and Robotics)
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19 pages, 4238 KiB  
Article
Symmetry Breaking in the U-Net: Hybrid Deep-Learning Multi-Class Segmentation of HeLa Cells in Reflected Light Microscopy Images
by Ali Ghaznavi, Renata Rychtáriková, Petr Císař, Mohammad Mehdi Ziaei and Dalibor Štys
Symmetry 2024, 16(2), 227; https://doi.org/10.3390/sym16020227 - 13 Feb 2024
Viewed by 678
Abstract
Multi-class segmentation of unlabelled living cells in time-lapse light microscopy images is challenging due to the temporal behaviour and changes in cell life cycles and the complexity of these images. The deep-learning-based methods achieved promising outcomes and remarkable success in single- and multi-class [...] Read more.
Multi-class segmentation of unlabelled living cells in time-lapse light microscopy images is challenging due to the temporal behaviour and changes in cell life cycles and the complexity of these images. The deep-learning-based methods achieved promising outcomes and remarkable success in single- and multi-class medical and microscopy image segmentation. The main objective of this study is to develop a hybrid deep-learning-based categorical segmentation and classification method for living HeLa cells in reflected light microscopy images. A symmetric simple U-Net and three asymmetric hybrid convolution neural networks—VGG19-U-Net, Inception-U-Net, and ResNet34-U-Net—were proposed and mutually compared to find the most suitable architecture for multi-class segmentation of our datasets. The inception module in the Inception-U-Net contained kernels with different sizes within the same layer to extract all feature descriptors. The series of residual blocks with the skip connections in each ResNet34-U-Net’s level alleviated the gradient vanishing problem and improved the generalisation ability. The m-IoU scores of multi-class segmentation for our datasets reached 0.7062, 0.7178, 0.7907, and 0.8067 for the simple U-Net, VGG19-U-Net, Inception-U-Net, and ResNet34-U-Net, respectively. For each class and the mean value across all classes, the most accurate multi-class semantic segmentation was achieved using the ResNet34-U-Net architecture (evaluated as the m-IoU and Dice metrics). Full article
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13 pages, 290 KiB  
Article
Bi-Concave Functions Connected with the Combination of the Binomial Series and the Confluent Hypergeometric Function
by Hari M. Srivastava, Sheza M. El-Deeb, Daniel Breaz, Luminita-Ioana Cotîrlă and Grigore Stefan Sălăgean
Symmetry 2024, 16(2), 226; https://doi.org/10.3390/sym16020226 - 13 Feb 2024
Viewed by 473
Abstract
In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the [...] Read more.
In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients |a2| and |a3| for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper. Full article
(This article belongs to the Section Mathematics)
28 pages, 5465 KiB  
Review
Towards Experimental Confirmation of Quarkonia Melting in Quark–Gluon Plasma: A Review of Recent Measurements of Quarkonia Production in Relativistic Heavy-Ion Collisions
by Kara R. Mattioli
Symmetry 2024, 16(2), 225; https://doi.org/10.3390/sym16020225 - 13 Feb 2024
Viewed by 541
Abstract
The dissociation, or “melting”, of heavy quarkonia states due to color charge screening is a predicted signature of quark–gluon plasma (QGP) formation, with a quarkonium state predicted to dissociate when the temperature of the medium is higher than the binding energy of the [...] Read more.
The dissociation, or “melting”, of heavy quarkonia states due to color charge screening is a predicted signature of quark–gluon plasma (QGP) formation, with a quarkonium state predicted to dissociate when the temperature of the medium is higher than the binding energy of the quarkonium state. A conclusive experimental observation of quarkonium melting coupled with a detailed theoretical understanding of the melting mechanism would enable the use of quarkonia states as temperature probes of the QGP, a long-sought goal in the field of relativistic heavy-ion collisions. However, the interpretation of quarkonia suppression measurements in heavy-ion collisions is complicated by numerous other cold nuclear matter effects that also result in the dissociation of bound quarkonia states. A comprehensive understanding of these cold nuclear matter effects is therefore needed in order to correctly interpret quarkonia production measurements in heavy-ion collisions and to observe the melting of quarkonium states experimentally. In this review, recent measurements of quarkonia production in pA and AA collisions and their state-of-the-art theoretical interpretations will be discussed, as well as the future measurements needed to further the knowledge of cold nuclear matter effects and realize a measurement of quarkonia melting in heavy-ion collisions. Full article
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