Symmetry

35 pages, 5686 KiB

Open AccessEditor’s ChoiceArticle

An Innovative Design Approach for Resonant DC/AC Converters, Based on Symmetry in Their Operating Modes

by Nikolay Hinov

Symmetry 2023, 15(10), 1864; https://doi.org/10.3390/sym15101864 - 4 Oct 2023

Cited by 4 | Viewed by 1684

The manuscript presents an innovative approach for the engineering design of resonant DC/AC converters used as sources of high-frequency electricity for a variety of needs: industrial and domestic applications, wireless power transmission, high-performance lighting, and more. The methodology is based on the generalized [...] Read more.

The manuscript presents an innovative approach for the engineering design of resonant DC/AC converters used as sources of high-frequency electricity for a variety of needs: industrial and domestic applications, wireless power transmission, high-performance lighting, and more. The methodology is based on the generalized consideration of electromagnetic processes in a series resonant RLC circuit fed by a square-wave voltage source. Due to the symmetry in the form of the current in the AC circuit of the DC/AC converter, it is possible to generalize all their possible operating modes. This was realized by applying the quasi-boundary method to the analysis of resonant DC/AC converters with and without reverse diodes operating in soft and hard switching modes. On this basis, the transfer functions of the devices, which give the relationship between their output and input voltages, are defined and analytically determined. Additionally considered are cases of resonant DC/AC converters with complex output circuits, which are applied to match the load needs and the capabilities of the power electronic device. In this sense, the basic dependencies for designing the main types of resonant DC/AC converters using series and parallel load compensation are given. The effectiveness of the proposed methods is demonstrated through several examples, and their verification and validation is achieved with simulations and prototypes. The proposed innovative design approach is applicable not only in power electronics education, but also in the design and prototyping of a whole class of power electronic devices. The unification of design methodologies formalizes and algorithmizes the design process, which is an important step for its automation and for applying various optimization procedures to achieve certain goals. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Power Electronics)

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15 pages, 481 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Accretion/Ejection Phenomena and Emission-Line Profile (A)symmetries in Type-1 Active Galactic Nuclei

by Paola Marziani

Symmetry 2023, 15(10), 1859; https://doi.org/10.3390/sym15101859 - 3 Oct 2023

Cited by 6 | Viewed by 2595

Abstract

The distinct behaviors of blue- and redshifted broad emission-line shifts, emitted by ionic species with varying ionization potentials in active galactic nuclei (AGN), can be elucidated by considering the balance between radiation and gravitational forces along the quasar main sequence. Blueshifts are attributed [...] Read more.

The distinct behaviors of blue- and redshifted broad emission-line shifts, emitted by ionic species with varying ionization potentials in active galactic nuclei (AGN), can be elucidated by considering the balance between radiation and gravitational forces along the quasar main sequence. Blueshifts are attributed to outflowing motions of the line-emitting gas toward the observer, and they are most pronounced in AGN with high Eddington ratios (Population A) and high luminosities. Conversely, redshifts in the broad-line wings are observed in Balmer emission lines of sources radiating at low Eddington ratios (Population B), though the origin of these redshifts remains a subject of ongoing debate. A correlation linking the redward asymmetry as measured by the centroid shift of the H

β

line profile to the black hole mass lends support to the notion that these shifts arise from gravitational and transverse redshift effects, particularly for black hole masses

M_{BH} ≳ 10^{8.7}

M

_{⊙}

. Full article

(This article belongs to the Special Issue Observational and Theoretical Strategies to Inquire about the Physics and Symmetries of Standard and Exotic Compact Objects)

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20 pages, 727 KiB

Open AccessEditor’s ChoiceArticle

A New Bivariate Family Based on Archimedean Copulas: Simulation, Regression Model and Application

by Gabriela M. Rodrigues, Edwin M. M. Ortega, Roberto Vila and Gauss M. Cordeiro

Symmetry 2023, 15(9), 1778; https://doi.org/10.3390/sym15091778 - 18 Sep 2023

Cited by 3 | Viewed by 2177

Abstract

We use the Clayton and Frank copulas and the exponentiated odd log-logistic family to define a new flexible bivariate model to fit bimodal and asymmetry data. The copulas allow different distributions for the response variable, thus making analysis more suitable. We present some [...] Read more.

We use the Clayton and Frank copulas and the exponentiated odd log-logistic family to define a new flexible bivariate model to fit bimodal and asymmetry data. The copulas allow different distributions for the response variable, thus making analysis more suitable. We present some structural properties of the new model and describe a simulation study to show the consistency of the estimators. We construct a bivariate regression model based on the new family to fit oak lettuce plant data for different concentrations of silicon dioxide and organosilicon compounds. We check the response variables fresh weight and plant height together in order to verify the existing correlation between them. These variables exhibit a bimodal form, and the family used is able to model this behavior. Different marginal distributions are selected, which is an interesting point of the copula methodology. The variables have strong positive dependence, and the experiment is carried out comparing the control treatment with others leading to the following results: (i) the treatment 1-ethoxysilatrane (with concentrations 5 × 10

^{- 4}

mL·L

^{- 1}

and 10

^{- 3}

mL·L

^{- 1}

) is not significant for the response variables; (ii) the treatment amorphous silicon dioxide (with concentrations 50 mg·L

^{- 1}

and 100 mg·L

^{- 1}

) and the same treatment (with concentrations 5 × 10

^{- 3}

mL·L

^{- 1}

and 10

^{- 2}

mL·L

^{- 1}

) are significant and have positive effects on both responses; (iii) the treatment amorphous silicon dioxide (with concentrations 200 mg·L

^{- 1}

and 300 mg·L

^{- 1}

) are significant and have negative effects on the response variables. Overall, the proposed bivariate model is suitable for the current data and can be useful in other applications. Full article

(This article belongs to the Special Issue Skewed (Asymmetrical) Probability Distributions and Applications across Disciplines III)

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10 pages, 329 KiB

Open AccessEditor’s ChoiceArticle

Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

by Reinhard Alkofer

Symmetry 2023, 15(9), 1787; https://doi.org/10.3390/sym15091787 - 18 Sep 2023

Cited by 5 | Viewed by 1565

Abstract

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator [...] Read more.

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of D

χ

SB, the dynamical generation of constituent quark masses, but also makes plausible that D

χ

SB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to D

χ

SB as signalled by its scalar and tensor components but it is also a driver of D

χ

SB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, D

χ

SB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, D

χ

SB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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22 pages, 5890 KiB

Open AccessEditor’s ChoiceArticle

Large-Scale Asymmetry in the Distribution of Galaxy Spin Directions—Analysis and Reproduction

by Lior Shamir

Symmetry 2023, 15(9), 1704; https://doi.org/10.3390/sym15091704 - 6 Sep 2023

Cited by 5 | Viewed by 3628

Abstract

Recent independent observations using several different telescope systems and analysis methods have provided evidence of parity violation between the numbers of galaxies that spin in opposite directions. On the other hand, other studies argue that no parity violation can be identified. This paper [...] Read more.

Recent independent observations using several different telescope systems and analysis methods have provided evidence of parity violation between the numbers of galaxies that spin in opposite directions. On the other hand, other studies argue that no parity violation can be identified. This paper provides detailed analysis, statistical inference, and reproduction of previous reports that show no preferred spin direction. Code and data used for the reproduction are publicly available. The results show that the data used in all of these studies agree with the observation of a preferred direction as observed from Earth. In some of these studies, the datasets were too small, or the statistical analysis was incomplete. In other papers, the results were impacted by experimental design decisions that led directly to showing nonpreferred direction. In some of these cases, these decisions were not stated in the papers but were revealed after further investigation in cases where the reproduction of the work did not match the results reported in the papers. These results show that the data used in all of these previous studies, in fact, agree with the contention that galaxies as observed from Earth have a preferred spin direction, and the distribution of galaxy spin directions as observed from Earth forms a cosmological-scale dipole axis. This study also shows that the reason for the observations is not necessarily an anomaly in the large-scale structure, and can also be related to internal structure of galaxies. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2022)

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20 pages, 7507 KiB

Open AccessEditor’s ChoiceArticle

Numerical Investigation of Cavitation Bubble Jet Dynamics near a Spherical Particle

by Jinsen Hu, Yuhang Liu, Yifan Liu, Jingfei Duan, Xuan Lu, Xiaoxiao Zheng, Jiaxin Yu, Yuning Zhang and Yuning Zhang

Symmetry 2023, 15(9), 1655; https://doi.org/10.3390/sym15091655 - 27 Aug 2023

Cited by 11 | Viewed by 2705

Abstract

Synergistic interaction between cavitation bubbles and particles is critical for the operational performance of hydro turbines. The jet dynamics near the wall have been extensively investigated; however, the jet dynamics near the particles are not clear. In the present paper, the bubble jet [...] Read more.

Synergistic interaction between cavitation bubbles and particles is critical for the operational performance of hydro turbines. The jet dynamics near the wall have been extensively investigated; however, the jet dynamics near the particles are not clear. In the present paper, the bubble jet dynamics near a spherical particle are numerically investigated based on a compressible two-phase flow solver considering the effects of heat transfer and mass transfer between the phases. Furthermore, the effect of the distance between the particle and the initial position of the bubble on the jet characteristics is analyzed in detail. Based on the simulations, three typical cases (i.e., jet during the rebound stage, jet pointing towards the particle, two jets facing each other) of jet behavior are categorized together with the range of dimensionless parameters. As the distance between the particle and the bubble increases, the three cases of jet impacts occur in the rebound stage, in the first period, and in the transition from the first period to the rebound stage, respectively. Full article

(This article belongs to the Section Physics)

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20 pages, 10233 KiB

Open AccessEditor’s ChoiceArticle

Global Multi-Scale Optimization and Prediction Head Attentional Siamese Network for Aerial Tracking

by Qiqi Chen, Jinghong Liu, Xuan Wang, Yujia Zuo and Chenglong Liu

Symmetry 2023, 15(9), 1629; https://doi.org/10.3390/sym15091629 - 24 Aug 2023

Cited by 2 | Viewed by 1355

Abstract

Siamese-based trackers have been widely used in object tracking. However, aerial remote tracking suffers from various challenges such as scale variation, viewpoint change, background clutter and occlusion, while most existing Siamese trackers are limited to single-scale and local features, making it difficult to [...] Read more.

Siamese-based trackers have been widely used in object tracking. However, aerial remote tracking suffers from various challenges such as scale variation, viewpoint change, background clutter and occlusion, while most existing Siamese trackers are limited to single-scale and local features, making it difficult to achieve accurate aerial tracking. We propose the global multi-scale optimization and prediction head attentional Siamese network to solve this problem and improve aerial tracking performance. Firstly, a transformer-based multi-scale and global feature encoder (TMGFE) is proposed to obtain global multi-scale optimization of features. Then, the prediction head attentional module (PHAM) is proposed to add context information to the prediction head by adaptively adjusting the spatial position and channel contribution of the response map. Benefiting from these two components, the proposed tracker solves these challenges of aerial remote sensing tracking to some extent and improves tracking performance. Additionally, we conduct ablation experiments on aerial tracking benchmarks, including UAV123, UAV20L, UAV123@10fps and DTB70, to verify the effectiveness of the proposed network. The comparisons of our tracker with several state-of-the-art (SOTA) trackers are also conducted on four benchmarks to verify its superior performance. It runs at 40.8 fps on the GPU RTX3060ti. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Control Science)

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15 pages, 387 KiB

Open AccessEditor’s ChoiceArticle

The Noether Symmetry Approach: Foundation and Applications: The Case of Scalar-Tensor Gauss–Bonnet Gravity

by Francesco Bajardi, Salvatore Capozziello, Tiziana Di Salvo and Francesca Spinnato

Symmetry 2023, 15(9), 1625; https://doi.org/10.3390/sym15091625 - 23 Aug 2023

Cited by 5 | Viewed by 2639

Abstract

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians [...] Read more.

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator

ξ

, related to the spacetime translations. This approach can be used for several applications. In the second part of the work, we consider a gravity theory, including the coupling between a scalar field

ϕ

and the Gauss–Bonnet topological term

G

. In particular, we study a gravitational action containing the function

F (G, ϕ)

and select viable models by the existence of symmetries. Finally, we evaluate the selected models in a spatially flat cosmological background and use symmetries to find exact solutions. Full article

(This article belongs to the Section Physics)

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22 pages, 8642 KiB

Open AccessEditor’s ChoiceArticle

Multi-Tier 3D Trajectory Planning for Cellular-Connected UAVs in Complex Urban Environments

by Xiling Luo, Tianyi Zhang, Wenxiang Xu, Chao Fang, Tongwei Lu and Jialiu Zhou

Symmetry 2023, 15(9), 1628; https://doi.org/10.3390/sym15091628 - 23 Aug 2023

Cited by 3 | Viewed by 1976

Abstract

Cellular-connected unmanned aerial vehicles (UAVs) present a viable solution to address communication and navigation limitations by leveraging base stations for air–ground communication. However, in complex urban scenarios with stringent communication requirements, achieving asymmetrical control becomes crucial to strike a balance between communication reliability [...] Read more.

Cellular-connected unmanned aerial vehicles (UAVs) present a viable solution to address communication and navigation limitations by leveraging base stations for air–ground communication. However, in complex urban scenarios with stringent communication requirements, achieving asymmetrical control becomes crucial to strike a balance between communication reliability and flight safety. Moreover, existing cellular-connected UAV trajectory planning algorithms often struggle to handle real scenes with sudden and intricate obstacles. To address the aforementioned challenges, this paper presents the multi-tier trajectory planning method (MTTP), which takes into account air–ground communication service assurance and collision avoidance in intricate urban environments. The proposed approach establishes a flight risk model that accounts for both the outage probability of UAV-ground base station (GBS) communication and the complexity of flight environments, and transforms the inherently complex three-dimensional (3D) trajectory optimization problem into a risk distance minimization model. To optimize the flight trajectory, a hierarchical progressive solution approach is proposed, which combines the strengths of the heuristic search algorithm (HSA) and deep reinforcement learning (DRL) algorithm. This innovative fusion of techniques empowers MTTP to efficiently navigate complex scenarios with sudden obstacles and communication challenges. Simulations show that the proposed MTTP method achieves a more superior performance of trajectory planning than the conventional communication-based solution, which yields a substantial reduction in flight distance of at least 8.49% and an impressive 10% increase in the mission success rate. Furthermore, a real-world scenario is chosen from the Yuhang District, Hangzhou (a southern Chinese city), to validate the practical applicability of the MTTP method in highly complex operating scenarios. Full article

(This article belongs to the Section Computer)

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18 pages, 3206 KiB

Open AccessEditor’s ChoiceArticle

Integrated Optimization of Blocking Flowshop Scheduling and Preventive Maintenance Using a Q-Learning-Based Aquila Optimizer

by Zhenpeng Ge and Hongfeng Wang

Symmetry 2023, 15(8), 1600; https://doi.org/10.3390/sym15081600 - 18 Aug 2023

Cited by 5 | Viewed by 1749

Abstract

In recent years, integration of production scheduling and machine maintenance has gained increasing attention in order to improve the stability and efficiency of flowshop manufacturing systems. This paper proposes a Q-learning-based aquila optimizer (QL-AO) for solving the integrated optimization problem of blocking flowshop [...] Read more.

In recent years, integration of production scheduling and machine maintenance has gained increasing attention in order to improve the stability and efficiency of flowshop manufacturing systems. This paper proposes a Q-learning-based aquila optimizer (QL-AO) for solving the integrated optimization problem of blocking flowshop scheduling and preventive maintenance since blocking in the jobs processing requires to be considered in the practice manufacturing environments. In the proposed algorithmic framework, a Q-learning algorithm is designed to adaptively adjust the selection probabilities of four key population update strategies in the classic aquila optimizer. In addition, five local search methods are employed to refine the quality of the individuals according to their fitness level. A series of numerical experiments are carried out according to two groups of flowshop scheduling benchmark. Experimental results show that QL-AO significantly outperforms six peer algorithms and two state-of-the-art hybrid algorithms based on Q-Learning on the investigated integrated scheduling problem. Additionally, the proposed Q-learning and local search strategies are effective in improving its performance. Full article

(This article belongs to the Special Issue Symmetry in Optimization and Its Applications to Machine Learning)

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18 pages, 427 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

An Iterative Wiener Filter Based on a Fourth-Order Tensor Decomposition

by Jacob Benesty, Constantin Paleologu and Laura-Maria Dogariu

Symmetry 2023, 15(8), 1560; https://doi.org/10.3390/sym15081560 - 9 Aug 2023

Cited by 2 | Viewed by 3072

Abstract

This work focuses on linear system identification problems in the framework of the Wiener filter. Specifically, it addresses the challenging identification of systems characterized by impulse responses of long length, which poses significant difficulties due to the existence of large parameter space. The [...] Read more.

This work focuses on linear system identification problems in the framework of the Wiener filter. Specifically, it addresses the challenging identification of systems characterized by impulse responses of long length, which poses significant difficulties due to the existence of large parameter space. The proposed solution targets a dimensionality reduction of the problem by involving the decomposition of a fourth-order tensor, using low-rank approximations in conjunction with the nearest Kronecker product. In addition, the rank of the tensor is controlled and limited to a known value without involving any approximation technique. The final estimate is obtained based on a combination of four (shorter) optimal filters, which are alternatively iterated. As a result, the designed iterative Wiener filter outperforms the traditional counterpart, being more robust to the accuracy of the statistics’ estimates and/or noisy conditions. In addition, simulations performed in the context of acoustic echo cancellation indicate that the proposed iterative Wiener filter that exploits this fourth-order tensor decomposition achieves better performance as compared to some previously developed solutions based on lower decomposition levels. This study could further lead to the development of computationally efficient tensor-based adaptive filtering algorithms. Full article

(This article belongs to the Section Engineering and Materials)

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22 pages, 997 KiB

Open AccessEditor’s ChoiceArticle

A New Class of Trigonometric B-Spline Curves

by Gudrun Albrecht, Esmeralda Mainar, Juan Manuel Peña and Beatriz Rubio

Symmetry 2023, 15(8), 1551; https://doi.org/10.3390/sym15081551 - 7 Aug 2023

Cited by 2 | Viewed by 2001

Abstract

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and [...] Read more.

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties. Full article

(This article belongs to the Special Issue Computer-Aided Geometric Design and Matrices)

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15 pages, 3759 KiB

Open AccessEditor’s ChoiceArticle

Evaluation of Thermodynamic Parameters for Cu(II) Ions Biosorption on Algae Biomass and Derived Biochars

by Alina Alexandra Ciobanu, Dumitru Bulgariu, Ioana Alexandra Ionescu, Diana Maria Puiu, Gabriela Geanina Vasile and Laura Bulgariu

Symmetry 2023, 15(8), 1500; https://doi.org/10.3390/sym15081500 - 28 Jul 2023

Cited by 14 | Viewed by 1612

Abstract

The removal of metal ions by biosorption on inexpensive materials is still a challenge for environmental engineering research. In this study, marine green algae biomass (Ulva lactuca sp.) and the biochars obtained from this biomass, at 320 °C (BC-320) and 550 °C [...] Read more.

The removal of metal ions by biosorption on inexpensive materials is still a challenge for environmental engineering research. In this study, marine green algae biomass (Ulva lactuca sp.) and the biochars obtained from this biomass, at 320 °C (BC-320) and 550 °C (BC-550), were used as biosorbents for the removal of Cu(II) ions from aqueous solution. In addition to comparing the biosorption capacities, the determination of the thermodynamic parameters allows the choice of the most suitable material for the biosorption processes. The experimental results, obtained for Cu(II) ions biosorption on each biosorbent (algae biomass (AB), BC-320 and BC-550), at three different temperatures (10, 30 and 50 °C) were analyzed using Langmuir and Freundlich isotherm models, while pseudo-first order, pseudo-second order and intra-particle diffusions models were used to model the kinetic data. The biosorption of Cu(II) ions is best described by the Langmuir model and the pseudo-second kinetic model, regardless of the type of biosorbent. Such behavior is characteristic for the retention of metal ions on low-cost materials, and is explained in the literature using the concepts of molecular symmetry. The maximum biosorption capacity (q_max, mg/g) depends on the temperature, but also on the type of biosorbent, and follow the order: BC-320 < AB < BC-550. Using the experimental isotherms, the thermodynamic parameters (ΔG⁰, ΔH⁰ and ΔS⁰) for the biosorption of Cu(II) ions on each biosorbent were calculated. The analysis of the obtained values constitutes the main arguments in choosing BC-550 as the most effective biosorbent for the removal of Cu(II) ions from aqueous media. Full article

(This article belongs to the Special Issue Mathematical Modeling and Evaluation of Thermodynamic Parameters)

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17 pages, 3560 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Spontaneous Symmetry Breaking in Systems Obeying the Dynamics of On–Off Intermittency and Presenting Bimodal Amplitude Distributions

by Stelios M. Potirakis, Pericles Papadopoulos, Niki-Lina Matiadou, Michael P. Hanias, Stavros G. Stavrinides, Georgios Balasis and Yiannis Contoyiannis

Symmetry 2023, 15(7), 1448; https://doi.org/10.3390/sym15071448 - 20 Jul 2023

Cited by 2 | Viewed by 2992

Abstract

In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the “PNA-based symbolic time-series analysis method” (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the [...] Read more.

In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the “PNA-based symbolic time-series analysis method” (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the symbolic dynamics of two symbols produced by the 3D Ising model in its critical state. After this numerical verification of the reliability of PNA-STSM, three examples of how PNA-STSM can be applied to the category of systems that obey the dynamics of the on–off intermittency are presented. Usually, such time series, with on–off intermittency, present bimodal amplitude distributions (i.e., with two lobes). As has recently been found, the phenomenon of on–off intermittency is associated with the spontaneous symmetry breaking (SSB) of the second-order phase transition. Thus, the revelation that a system is close to SSB supports a deeper understanding of its dynamics in terms of criticality, which is quite useful in applications such as the analysis of pre-earthquake fracture-induced electromagnetic emission (also known as fracture-induced electromagnetic radiation) (FEME/FEMR) signals. Beyond the case of on–off intermittency, PNA-STSM can provide credible results for the dynamics of any two-symbol symbolic dynamics, even in cases in which there is an imbalance in the probability of the appearance of the two respective symbols since the two symbols are not considered separately but, instead, simultaneously, considering the information from both branches of the symbolic dynamics. Full article

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

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22 pages, 4668 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Longitudinal–Transverse Vibration of a Functionally Graded Nanobeam Subjected to Mechanical Impact and Electromagnetic Actuation

by Nicolae Herisanu, Bogdan Marinca and Vasile Marinca

Symmetry 2023, 15(7), 1376; https://doi.org/10.3390/sym15071376 - 6 Jul 2023

Cited by 3 | Viewed by 2696

Abstract

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered [...] Read more.

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton’s principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function. Full article

(This article belongs to the Special Issue Theories and Applications for Dynamical Systems, Symmetry Problems and Differential Equations)

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10 pages, 273 KiB

Open AccessEditor’s ChoiceArticle

Quantum Mechanics of the Extended Snyder Model

by Stjepan Meljanac and Salvatore Mignemi

Symmetry 2023, 15(7), 1373; https://doi.org/10.3390/sym15071373 - 6 Jul 2023

Cited by 4 | Viewed by 1301

Abstract

We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by D spatial coordinates and

D (D - 1) / 2

tensorial degrees of [...] Read more.

We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by D spatial coordinates and

D (D - 1) / 2

tensorial degrees of freedom, together with their conjugated momenta. The coordinates obey nontrivial commutation relations and generate a noncommutative geometry, which admits nicer properties than the usual realization of the model, in particular giving rise to an associative star product. The spectrum of the harmonic oscillator is studied through the introduction of creation and annihilation operators. Some physical consequences of the introduction of the additional degrees of freedom are discussed. Full article

(This article belongs to the Special Issue Extreme Regimes of Classical and Quantum Gravity Models. Theory, Observations, and the Role of Symmetries)

15 pages, 2030 KiB

Open AccessEditor’s ChoiceArticle

Oracle-Preserving Latent Flows

by Alexander Roman, Roy T. Forestano, Konstantin T. Matchev, Katia Matcheva and Eyup B. Unlu

Symmetry 2023, 15(7), 1352; https://doi.org/10.3390/sym15071352 - 3 Jul 2023

Cited by 5 | Viewed by 2020

Abstract

A fundamental task in data science is the discovery, description, and identification of any symmetries present in the data. We developed a deep learning methodology for the simultaneous discovery of multiple non-trivial continuous symmetries across an entire labeled dataset. The symmetry transformations and [...] Read more.

A fundamental task in data science is the discovery, description, and identification of any symmetries present in the data. We developed a deep learning methodology for the simultaneous discovery of multiple non-trivial continuous symmetries across an entire labeled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function, ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to invariant transformations with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset, where the oracle is provided by the 10-dimensional vector of logits of a trained classifier. We find classes of symmetries that transform each image from the dataset into new synthetic images while conserving the values of the logits. We illustrate these transformations as lines of equal probability (“flows”) in the reduced latent space. These results show that symmetries in the data can be successfully searched for and identified as interpretable non-trivial transformations in the equivalent latent space. Full article

(This article belongs to the Special Issue Computer Vision, Pattern Recognition, Machine Learning, and Symmetry)

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14 pages, 9517 KiB

Open AccessEditor’s ChoiceArticle

A Family of 1D Chaotic Maps without Equilibria

by Marcin Lawnik, Lazaros Moysis and Christos Volos

Symmetry 2023, 15(7), 1311; https://doi.org/10.3390/sym15071311 - 27 Jun 2023

Cited by 8 | Viewed by 3318

Abstract

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each [...] Read more.

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each piece, the generated maps have no equilibria and can showcase chaotic behavior. This family thus belongs to the category of systems with hidden attractors. Numerous examples of chaotic maps are provided, showcasing fractal-like, symmetrical patterns at the interchange between chaotic and non-chaotic behavior. Moreover, the application of the proposed maps to a pseudorandom bit generator is successfully performed. Full article

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

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76 pages, 2612 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Tetraquarks and Pentaquarks from Quark Model Perspective

by Hongxia Huang, Chengrong Deng, Xuejie Liu, Yue Tan and Jialun Ping

Symmetry 2023, 15(7), 1298; https://doi.org/10.3390/sym15071298 - 22 Jun 2023

Cited by 25 | Viewed by 3461

Abstract

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review [...] Read more.

According to the classification of the quark model, the hadrons going beyond three-quark baryon and quark-antiquark meson pictures are called exotic hadrons. Many new hadrons have been observed since 2003, some of which exhibit exotic behaviors. There are a lot of excellent review articles on exotic hadrons available so far; the present article tries to focus on the recent experimental and theoretical progress on the exotic states from the perspective of the quark model. Although lattice quantum chromodynamics may give the final answer of the problem, the phenomenological models are still powerful tools to explore the exotic states and to provide insight on the phenomenology of hadrons. The spatial and color structures of multiquark states and the channel coupling calculation are emphasized through reviewing some bound states, molecular and color structure resonances. Finally, the unquench effects of some exotic states are reviewed. With the accumulation of experimental data on multiquark states and inspiration of underlying theory developments, more reasonable phenomenological models incorporating multi-body interactions and high Fock components to unify the description of normal hadrons and exotic hadrons are expectable. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2022)

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17 pages, 1204 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Influence of Magnetic Field and Porous Medium on the Steady State and Flow Resistance of Second Grade Fluids over an Infinite Plate

by Constantin Fetecau and Costică Moroşanu

Symmetry 2023, 15(6), 1269; https://doi.org/10.3390/sym15061269 - 16 Jun 2023

Cited by 3 | Viewed by 1930

Abstract

The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an [...] Read more.

The main purpose of this work is to completely solve two motion problems of some differential type fluids when velocity or shear stress is given on the boundary. In order to do that, isothermal MHD motions of incompressible second grade fluids over an infinite flat plate are analytically investigated when porous effects are taken into consideration. The fluid motion is due to the plate moving in its plane with an arbitrary time-dependent velocity or applying a time-dependent shear stress to the fluid. Closed-form expressions are established both for the dimensionless velocity and shear stress fields and the Darcy’s resistance corresponding to the first motion. The dimensionless shear stress corresponding to the second motion has been immediately obtained using a perfect symmetry between the governing equations of velocity and the non-trivial shear stress. Furthermore, the obtained results provide the first exact general solutions for MHD motions of second grade fluids through porous media. Finally, for illustration, as well as for their use in engineering applications, the starting and/or steady state solutions of some problems with technical relevance are provided, and the validation of the results is graphically proved. The influence of magnetic field and porous medium on the steady state and the flow resistance of fluid are graphically underlined and discussed. It was found that the flow resistance of the fluid declines or increases in the presence of a magnetic field or porous medium, respectively. In addition, the steady state is obtained earlier in the presence of a magnetic field or porous medium. Full article

(This article belongs to the Section Mathematics)

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19 pages, 7215 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Myrtenal and Myrtanal as Auxiliaries in the Synthesis of Some C,P-Stereogenic Hydroxyphosphine Oxides and Hydroxyphosphine-Boranes Possessing up to Four Contiguous Centers of Chirality

by K. Michał Pietrusiewicz, Anna E. Kozioł, Hanna Małuszyńska and Sylwia Sowa

Symmetry 2023, 15(6), 1172; https://doi.org/10.3390/sym15061172 - 30 May 2023

Cited by 1 | Viewed by 2095

Abstract

1,4- and 1,2-additons of secondary phosphine oxides to (1R)-myrtenal and (1S)-myrtanal were evaluated as potential routes to P,C-stereogenic phosphine oxides bearing additional hydroxyl or aldehyde functions. 1,4-Additions of racemic secondary phosphine oxides to (1R)-myrtenal were found to [...] Read more.

1,4- and 1,2-additons of secondary phosphine oxides to (1R)-myrtenal and (1S)-myrtanal were evaluated as potential routes to P,C-stereogenic phosphine oxides bearing additional hydroxyl or aldehyde functions. 1,4-Additions of racemic secondary phosphine oxides to (1R)-myrtenal were found to offer moderate to good stereoselectivity which shows some promise for utility in kinetic resolution processes, especially at lower conversions. In case of 1,2-additions making the process doubly asymmetric by using an enantiomerically pure secondary phosphine oxide as substrate turned out to be practical. The stereochemical course of the addition reactions under study is presented. The P-resolved 1,2-addition products were demonstrated to undergo facile reduction by BH₃ at room temperature leading to the formation of the corresponding α-hydroxyphosphine-boranes with clean inversion of configuration at the P-centre. All P,C-stereogenic phosphine oxides and boranes that were isolated in the form of a single diastereoisomer were assigned their absolute configurations by means of X-ray crystallography and/or 2D NMR spectral techniques. Full article

(This article belongs to the Special Issue Asymmetric Centers in Optically Active Molecules Containing a Heteroatom)

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26 pages, 16642 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Deep Learning Approach to Extracting Nuclear Matter Properties from Neutron Star Observations

by Plamen G. Krastev

Symmetry 2023, 15(5), 1123; https://doi.org/10.3390/sym15051123 - 20 May 2023

Cited by 18 | Viewed by 2897

Abstract

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and [...] Read more.

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave detectors will offer even more detailed neutron-star observations. Employing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feasibility of using deep learning to extract the equation of state directly from observations of neutron stars, and to also obtain related nuclear matter properties such as the slope, curvature, and skewness of nuclear symmetry energy at saturation density. Most importantly, it shows that this deep learning approach is able to reconstruct realistic equations of state and deduce realistic nuclear matter properties. This highlights the potential of artificial neural networks in providing a reliable and efficient means to extract crucial information about the equation of state and related properties of dense neutron-rich matter in the era of multi-messenger astrophysics. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

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19 pages, 2058 KiB

Open AccessEditor’s ChoiceArticle

Privacy-Preserving Medical Data-Sharing System with Symmetric Encryption Based on Blockchain

by Mingqi Hu, Yanli Ren and Cien Chen

Symmetry 2023, 15(5), 1010; https://doi.org/10.3390/sym15051010 - 30 Apr 2023

Cited by 6 | Viewed by 2749

Abstract

Nowadays, data between hospitals are usually not interoperable, which brings great inconvenience to medical data sharing and patients’ medical treatment. In addition, patients do not want their medical data to be leaked during the sharing process. Researchers have employed blockchain to build data-sharing [...] Read more.

Nowadays, data between hospitals are usually not interoperable, which brings great inconvenience to medical data sharing and patients’ medical treatment. In addition, patients do not want their medical data to be leaked during the sharing process. Researchers have employed blockchain to build data-sharing systems to address these issues. However, current systems do not restrict the power of participants, nor do they prevent visitors from sharing the obtained data to unauthorized parties. To address these issues, we propose a private data-sharing system with symmetric encryption for the medical industry that implements power restriction and access control, and prevents the leakage of private data. To be specific, firstly, symmetric encryption algorithm is utilized to encrypt medical data to protect the privacy of data owner. Secondly, our proposed system is built on a new blockchain framework, in which only visitors with permission can access the medical data. Thirdly, we employ chameleon signature to prevent visitors from sharing data with other parties without permission. Finally, we make the power of participants in the system revocable to prevent them from abusing their power. Our proposed system has been proven to be secure through security analysis and can protect the privacy of patients. In addition, the experimental results show that our system has excellent performance in terms of time overhead compared to other systems. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Cryptography and Outsourcing Computation)

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12 pages, 6811 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Building an Equation of State Density Ladder

by Marc Salinas and Jorge Piekarewicz

Symmetry 2023, 15(5), 994; https://doi.org/10.3390/sym15050994 - 27 Apr 2023

Cited by 6 | Viewed by 1850

Abstract

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in [...] Read more.

The confluence of major theoretical, experimental, and observational advances are providing a unique perspective on the equation of state of dense neutron-rich matter—particularly its symmetry energy—and its imprint on the mass-radius relation for neutron stars. In this contribution, we organize these developments in an equation of the state density ladder. Of particular relevance to this discussion are the impact of the various rungs on the equation of state and the identification of possible discrepancies among the various methods. A preliminary analysis identifies possible tension between laboratory measurements and gravitational-wave detections that could indicate the emergence of a phase transition in the stellar core. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

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18 pages, 324 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Expansion-Free Dissipative Fluid Spheres: Analytical Solutions

by Luis Herrera, Alicia Di Prisco and Justo Ospino

Symmetry 2023, 15(3), 754; https://doi.org/10.3390/sym15030754 - 19 Mar 2023

Cited by 15 | Viewed by 1934

Abstract

We search for exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar

Θ

). To accomplish this, we shall impose additional restrictions allowing integration of the field equations. The solutions are analyzed, and possible applications [...] Read more.

We search for exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar

Θ

). To accomplish this, we shall impose additional restrictions allowing integration of the field equations. The solutions are analyzed, and possible applications to astrophysical scenarios as well as alternative approaches to obtaining new solutions are discussed. Full article

(This article belongs to the Special Issue Symmetry in Cosmology and Gravity: Topic and Advance)

30 pages, 3480 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Chiral Restoration of Nucleons in Neutron Star Matter: Studies Based on a Parity Doublet Model

by Takuya Minamikawa, Bikai Gao, Toru Kojo and Masayasu Harada

Symmetry 2023, 15(3), 745; https://doi.org/10.3390/sym15030745 - 17 Mar 2023

Cited by 20 | Viewed by 4257

Abstract

We review the chiral variant and invariant components of nucleon masses and the consequence of their existence on the chiral restoration in extreme conditions, particularly in neutron star matter. We consider a model of linear realization of chiral symmetry with the nucleon parity [...] Read more.

We review the chiral variant and invariant components of nucleon masses and the consequence of their existence on the chiral restoration in extreme conditions, particularly in neutron star matter. We consider a model of linear realization of chiral symmetry with the nucleon parity doublet structure that permits the chiral invariant mass,

m_{0}

, for positive and negative parity nucleons. The nuclear matter is constructed with the parity doublet nucleon model coupled to scalar fields

σ

, vector fields

(ω, ρ)

, and mesons with strangeness through the U(1)

_{A}

anomaly. In models with a large

m_{0}

, the nucleon mass is insensitive to the medium, and the nuclear saturation properties can be reproduced without demanding strong couplings of the nucleons to the scalar fields

σ

and vector fields

ω

. We confront the resulting nuclear equations of state with nuclear constraints and neutron star observations and delineate the chiral invariant mass and effective interactions. To further examine the nuclear equations of state beyond the saturation density, we supplement quark models to set the boundary conditions from the high-density side. The quark models are constrained by the two-solar-mass conditions, and such constraints are transferred to nuclear models through the causality and thermodynamic stability conditions. We also calculate various condensates and the matter composition from nuclear to quark matter in a unified matter by constructing a generating functional that interpolates the nuclear and quark matter with external fields. Two types of chiral restoration are discussed: one due to the positive scalar charges of nucleons and the other triggered by the evolution of the Dirac sea. We found that the U(1)

_{A}

anomaly softens equations of state from low to high density. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

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27 pages, 13869 KiB

Open AccessEditor’s ChoiceArticle

Chaotification of 1D Maps by Multiple Remainder Operator Additions—Application to B-Spline Curve Encryption

by Lazaros Moysis, Marcin Lawnik, Ioannis P. Antoniades, Ioannis Kafetzis, Murilo S. Baptista and Christos Volos

Symmetry 2023, 15(3), 726; https://doi.org/10.3390/sym15030726 - 14 Mar 2023

Cited by 10 | Viewed by 2360

Abstract

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map’s value for the next iteration, so that the most- and least-significant digits are combined. By [...] Read more.

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map’s value for the next iteration, so that the most- and least-significant digits are combined. By appropriate parameter tuning, the resulting map can achieve a higher Lyapunov exponent value, a result that was first proven theoretically and then showcased through numerical simulations for a collection of chaotic maps. As a proposed application of the transformed maps, the encryption of B-spline curves and patches was considered. The symmetric encryption consisted of two steps: a shuffling of the control point coordinates and an additive modulation. A transformed chaotic map was utilised to perform both steps. The resulting ciphertext curves and patches were visually unrecognisable compared to the plaintext ones and performed well on several statistical tests. The proposed work gives an insight into the potential of the remainder operator for chaotification, as well as the chaos-based encryption of curves and computer graphics. Full article

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

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28 pages, 825 KiB

Open AccessEditor’s ChoiceArticle

Near-Miss Symmetric Polyhedral Cages

by Bernard M. A. G. Piette and Árpad Lukács

Symmetry 2023, 15(3), 717; https://doi.org/10.3390/sym15030717 - 13 Mar 2023

Cited by 5 | Viewed by 2770

Abstract

Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons [...] Read more.

Following the experimental discovery of several nearly symmetric protein cages, we define the concept of homogeneous symmetric congruent equivalent near-miss polyhedral cages made out of P-gons. We use group theory to parameterize the possible configurations and we minimize the irregularity of the P-gons numerically to construct all such polyhedral cages for

P = 6

to

P = 20

with deformation of up to 10%. Full article

(This article belongs to the Section Mathematics)

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17 pages, 3212 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation

by Konstantinos Tzirakis, Yiannis Kamarianakis, Nikolaos Kontopodis and Christos V. Ioannou

Symmetry 2023, 15(3), 630; https://doi.org/10.3390/sym15030630 - 2 Mar 2023

Cited by 10 | Viewed by 4152

Abstract

The assumed rheological behavior of blood influences the hemodynamic characteristics of numerical blood flow simulations. Until now, alternative rheological specifications have been utilized, with uncertain implications for the results obtained. This work aims to group sixteen blood rheological models in homogeneous clusters, by [...] Read more.

The assumed rheological behavior of blood influences the hemodynamic characteristics of numerical blood flow simulations. Until now, alternative rheological specifications have been utilized, with uncertain implications for the results obtained. This work aims to group sixteen blood rheological models in homogeneous clusters, by exploiting data generated from numerical simulations on an idealized symmetrical arterial bifurcation. Blood flow is assumed to be pulsatile and is simulated using a commercial finite volume solver. An appropriate mesh convergence study is performed, and all results are collected at three different time instants throughout the cardiac cycle: at peak systole, early diastole, and late diastole. Six hemodynamic variables are computed: the time average wall shear stress, oscillatory shear index, relative residence time, global and local non-Newtonian importance factor, and non-Newtonian effect factor. The resulting data are analyzed using hierarchical agglomerative clustering algorithms, which constitute typical unsupervised classification methods. Interestingly, the rheological models can be partitioned into three homogeneous groups, whereas three specifications appear as outliers which do not belong in any partition. Our findings suggest that models which are defined in a similar manner from a mathematical perspective may behave substantially differently in terms of the data they produce. On the other hand, models characterized by different mathematical formulations may belong to the same statistical group (cluster) and can thus be considered interchangeably. Full article

(This article belongs to the Special Issue Biology and Symmetry/Asymmetry：Feature Papers 2022)

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15 pages, 313 KiB

Open AccessEditor’s ChoiceArticle

The η-Anti-Hermitian Solution to a System of Constrained Matrix Equations over the Generalized Segre Quaternion Algebra

by Bai-Ying Ren, Qing-Wen Wang and Xue-Ying Chen

Symmetry 2023, 15(3), 592; https://doi.org/10.3390/sym15030592 - 24 Feb 2023

Cited by 18 | Viewed by 1987

Abstract

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the

η

-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also [...] Read more.

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence of the

η

-anti-Hermitian solution to a system of constrained matrix equations over the generalized Segre quaternion algebra. We also obtain the expression of the general

η

-anti-Hermitian solution to the system when it is solvable. Finally, we provide a numerical example to verify the main results of this paper. Full article

(This article belongs to the Section Mathematics)

16 pages, 2144 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Intermolecular Interactions in Binary and Ternary Solutions of a Zwitterionic Compound Studied by Solvatochromism

by Dana Ortansa Dorohoi, Dorina Emilia Creanga and Dan Gheorghe Dimitriu

Symmetry 2023, 15(2), 563; https://doi.org/10.3390/sym15020563 - 20 Feb 2023

Cited by 1 | Viewed by 2264

Abstract

The 1-dithiocarboxy-2-ethoxy-1-(isoquinolin-2-yl)-2-oxoethan-1-ylid (iQTCY) zwitterionic molecule has been studied by computational and spectral means in order to establish some of its structural parameters in the ground electronic state as well as the nature and the strength of its universal and specific interactions with different [...] Read more.

The 1-dithiocarboxy-2-ethoxy-1-(isoquinolin-2-yl)-2-oxoethan-1-ylid (iQTCY) zwitterionic molecule has been studied by computational and spectral means in order to establish some of its structural parameters in the ground electronic state as well as the nature and the strength of its universal and specific interactions with different solvents. The prevalence of the orientation–induction interactions in the diluted solutions of iQTCY in aprotic solvents and the additional specific interactions by hydrogen bonds (HB) in the protic solvents were demonstrated. Three theoretical models were comparatively used to estimate the composition of the first solvation shell of the iQTCY molecule in ternary solutions. The difference between the interaction energies in molecular pairs solute–solvent was computed based on the statistical cell model of ternary solutions of iQTCY in mixtures of water–ethanol and water–methanol. Using the electro-optical parameters computed by the quantum-mechanical technique and the results of the solvatochromic study, the excited state dipole moment of iQTCY was estimated within the limit of the variational method applicable to molecules that show only an absorption electronic spectrum. Full article

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

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22 pages, 1233 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Detecting Heavy Neutral SUSY Higgs Bosons Decaying to Sparticles at the High-Luminosity LHC

by Howard Baer, Vernon Barger, Xerxes Tata and Kairui Zhang

Symmetry 2023, 15(2), 548; https://doi.org/10.3390/sym15020548 - 18 Feb 2023

Cited by 6 | Viewed by 2097

Abstract

In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY), which have been suggested to be the most likely version of SUSY to emerge from the string landscape, higgsinos are expected at the few hundred GeV scale, whilst electroweak gauginos inhabit the TeV scale. [...] Read more.

In supersymmetry (SUSY) models with low electroweak naturalness (natSUSY), which have been suggested to be the most likely version of SUSY to emerge from the string landscape, higgsinos are expected at the few hundred GeV scale, whilst electroweak gauginos inhabit the TeV scale. For TeV-scale heavy neutral SUSY Higgs bosons H and A, as currently required by LHC searches, the dominant decay modes of

H, A

are gaugino plus higgsino provided these decays are kinematically open. The light higgsinos decay to soft particles, so are largely invisible, whilst the gauginos decay to W, Z or h plus missing transverse energy (

\frac{E}{T}

). Thus, we examine the viability of

H, A \to W + \frac{E}{T}

,

Z + \frac{E}{T}

and

h + \frac{E}{T}

signatures at the high luminosity LHC (HL-LHC) in light of large standard model (SM) backgrounds from (mainly)

t \bar{t}

,

V V

and

V h

production (where

V = W, Z

). We also examine whether these signal channels can be enhanced over backgrounds by requiring the presence of an additional soft lepton from the decays of the light higgsinos. We find significant regions in the vicinity of

m_{A} \sim 1 - 2

TeV of the

m_{A}

vs.

tan β

plane, which can be probed at the high luminosity LHC, using these dominant signatures by HL-LHC at

5 σ

and at the 95% confidence level (CL). Full article

(This article belongs to the Special Issue Supersymmetry with Higgs Bosons Research)

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10 pages, 2168 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Study on the Intersection of Ground Reaction Forces during Overground Walking in Down Syndrome: Effects of the Pathology and Left–Right Asymmetry

by Johanna Vielemeyer, Cristina Sole, Manuela Galli, Matteo Zago, Roy Müller and Claudia Condoluci

Symmetry 2023, 15(2), 544; https://doi.org/10.3390/sym15020544 - 17 Feb 2023

Cited by 4 | Viewed by 5639

Abstract

Motor dysfunctions in patients with Down Syndrome (DS) result in poor locomotion and an altered gait phenotype, characterized by compromised stability management and frequent bilateral asymmetries. Directing ground reaction forces to a point above the center of mass, referred to as the virtual [...] Read more.

Motor dysfunctions in patients with Down Syndrome (DS) result in poor locomotion and an altered gait phenotype, characterized by compromised stability management and frequent bilateral asymmetries. Directing ground reaction forces to a point above the center of mass, referred to as the virtual pivot point (VPP), is one means of maintaining stability during walking. This cross-sectional observational study compared the dynamic gait function of 33 individuals with DS (mean age: 17.7 ± 6.4 years, 13 females) to a group of 36 healthy controls (mean age: 15.5 ± 6.1 years, 15 females), using the concept of the VPP. Results showed that the VPP was located more anteriorly in individuals with DS compared to healthy controls, with no differences in the variability (R²) or symmetry of VPP coordinates. This anterior VPP position is likely due to the larger hip moments observed in patients with DS during the propulsive phase of stance. High R² values in DS suggest that the VPP is strongly related to dynamic stability during walking. Full article

(This article belongs to the Special Issue Biology and Symmetry/Asymmetry：Feature Papers 2022)

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13 pages, 6325 KiB

Open AccessEditor’s ChoiceArticle

Electrochemical Studies of Azulene Modified Electrodes

by Veronica Anăstăsoaie, Ovidiu Teodor Matica, Cecilia Lete, Raluca Isopescu, Vesna Miskovic-Stankovic and Eleonora-Mihaela Ungureanu

Symmetry 2023, 15(2), 514; https://doi.org/10.3390/sym15020514 - 15 Feb 2023

Cited by 1 | Viewed by 2290

Abstract

Previous studies performed on 2-(azulen-1-yldiazenyl)-5-phenyl-1,3,4-thiadiazole (T) showed that T is a ligand with complexing properties towards heavy metals (HMs) in solution and can be attached to electrode surfaces. Films of T were deposited on glassy carbon to obtain chemically modified electrodes [...] Read more.

Previous studies performed on 2-(azulen-1-yldiazenyl)-5-phenyl-1,3,4-thiadiazole (T) showed that T is a ligand with complexing properties towards heavy metals (HMs) in solution and can be attached to electrode surfaces. Films of T were deposited on glassy carbon to obtain chemically modified electrodes (T-CMEs), either through scanning or using controlled potential electrolysis in tetrabutylammonium perchlorate in acetonitrile. They were investigated using cyclic voltammetry (CV), differential pulse voltammetry (DPV), electrochemical impedance spectroscopy (EIS), and spectroelectrochemistry. All methods provided evidence for showing the formation of insulating films, with properties depending on their electropolymerization potential. CV and EIS studies of T-CMEs in tetrabutylammonium perchlorate in acetonitrile as supporting electrolyte, and in the presence of a ferrocene redox probe resulted in a thickness of ~10 µm, an active surface area about 6 times higher than the geometrical one, and conductivity of about 10⁻⁶ S/cm. This characterization performed using voltammetric techniques reveals the symmetry of the reversible anodic and cathodic redox CV peaks for the polymer, while spectroelectrochemistry shows the intensification of the charge transport process through polarons, due to the anodic polarization of the film. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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20 pages, 905 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Collective Excitation in High-Energy Nuclear Collisions—In Memory of Professor Lianshou Liu

by Huan Zhong Huang, Feng Liu, Xiaofeng Luo, Shusu Shi, Fuqiang Wang and Nu Xu

Symmetry 2023, 15(2), 499; https://doi.org/10.3390/sym15020499 - 13 Feb 2023

Cited by 5 | Viewed by 2406

Abstract

We celebrate the legacies of our friend and mentor Professor Lianshou Liu who was one of the pioneers for the phenomenology of multi-particle interactions and initiated the physics of relativistic heavy-ion collisions in China. In this article, we discuss some of the recent [...] Read more.

We celebrate the legacies of our friend and mentor Professor Lianshou Liu who was one of the pioneers for the phenomenology of multi-particle interactions and initiated the physics of relativistic heavy-ion collisions in China. In this article, we discuss some of the recent exciting experimental observations on the collective phenomena including collectivity, chirality, criticality, strangeness production, and thermal equilibrium in high-energy nuclear collisions. Future directions, especially the physics at high baryon density, will be discussed with a focus on the first-order phase boundary and hyperon–nucleon interactions. Full article

(This article belongs to the Special Issue Heavy-Ion Collisions and Multiparticle Production)

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21 pages, 380 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Potentials from the Polynomial Solutions of the Confluent Heun Equation

by Géza Lévai

Symmetry 2023, 15(2), 461; https://doi.org/10.3390/sym15020461 - 9 Feb 2023

Cited by 6 | Viewed by 2957

Abstract

Polynomial solutions of the confluent Heun differential equation (CHE) are derived by identifying conditions under which the infinite power series expansions around the

z = 0

singular point can be terminated. Assuming a specific structure of the expansion coefficients, these conditions lead to [...] Read more.

Polynomial solutions of the confluent Heun differential equation (CHE) are derived by identifying conditions under which the infinite power series expansions around the

z = 0

singular point can be terminated. Assuming a specific structure of the expansion coefficients, these conditions lead to four non-trivial polynomials that can be expressed as special cases of the confluent Heun function

H c (p, β, γ, δ, σ; z)

. One of these recovers the generalized Laguerre polynomials

L_{N}^{(α)}

, and another one the rationally extended

X_{1}

type Laguerre polynomials

{\hat{L}}_{N}^{(α)}

. The two remaining solutions represent previously unknown polynomials that do not form an orthogonal set and exhibit features characteristic of semi-classical orthogonal polynomials. A standard method of generating exactly solvable potentials in the one-dimensional Schrödinger equation is applied to the CHE, and all known potentials with solutions expressed in terms of the generalized Laguerre polynomials within, or outside the Natanzon confluent potential class, are recovered. It is also found that the potentials generated from the two new polynomial systems necessarily depend on the N quantum number. General considerations on the application of the Heun type differential differential equations within the present framework are also discussed. Full article

(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials II)

19 pages, 2126 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Metamaterial with Tunable Positive and Negative Hygrothermal Expansion Inspired by a Four-Fold Symmetrical Islamic Motif

by Teik-Cheng Lim

Symmetry 2023, 15(2), 462; https://doi.org/10.3390/sym15020462 - 9 Feb 2023

Cited by 5 | Viewed by 2164

Abstract

A metamaterial with controllable positive and negative thermal and hygroscopic expansions is investigated herein by inspiration from a range of Islamic geometric patterns. Constructing from eight pairs of pin-jointed Y-elements, each unit cell manifests eight rhombi that are arranged circumferentially, thereby manifesting four [...] Read more.

A metamaterial with controllable positive and negative thermal and hygroscopic expansions is investigated herein by inspiration from a range of Islamic geometric patterns. Constructing from eight pairs of pin-jointed Y-elements, each unit cell manifests eight rhombi that are arranged circumferentially, thereby manifesting four axes of symmetry. By attachment of bimaterial spiral springs of contrasting expansion coefficients to the far arms of the paired Y-elements, a change in the environment’s thermal or hygroscopic condition alters the offset angle of the paired Y-elements such that the unit cell of the metamaterial ranges from the eight-pointed star to the regular octagon. The effective coefficient of thermal expansion (CTE) and the coefficient of moisture expansion (CME) of this metamaterial were developed for small and large changes in environmental fluctuations using infinitesimal and finite models, respectively. Generated data indicates that the sign and magnitude of the effective thermal and hygroscopic expansion coefficients can be controlled by geometrical descriptors of the bimaterial spiral spring—such as its coil number and the ratio of its mean radius to its thickness—as well as the properties of the bimaterial’s layers such as their expansion coefficients, Young’s moduli and, in the case of effective hygroscopic expansion, their relative absorptivity. The obtained results suggest that the proposed metamaterial can be designed to perform as highly sensitive thermal and/or moisture sensors, as well as other functional materials or devices that take advantage of environmental changes as stimuli. Full article

(This article belongs to the Special Issue Materials Science and Symmetry)

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20 pages, 355 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Gravity as a Quantum Field Theory

by Roberto Percacci

Symmetry 2023, 15(2), 449; https://doi.org/10.3390/sym15020449 - 8 Feb 2023

Cited by 7 | Viewed by 4734

Abstract

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a [...] Read more.

Classical gravity is understood as the geometry of spacetime, and it seems very different from the other known interactions. In this review, I will instead stress the analogies: Like strong interactions, the low energy effective field theory of gravity is related to a nonlinearly realized symmetry, and like electroweak interactions, it is a gauge theory in Higgs phase, with a massive connection. I will also discuss the possibility of finding a UV complete quantum field theoretic description of all interactions. Full article

(This article belongs to the Special Issue Advances in Theoretical High Energy Physics - Solving Quantum Field Theory)

33 pages, 11453 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Nonextensive Footprints in Dissipative and Conservative Dynamical Systems

by Antonio Rodríguez, Alessandro Pluchino, Ugur Tirnakli, Andrea Rapisarda and Constantino Tsallis

Symmetry 2023, 15(2), 444; https://doi.org/10.3390/sym15020444 - 7 Feb 2023

Cited by 7 | Viewed by 2145

Abstract

Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate [...] Read more.

Despite its centennial successes in describing physical systems at thermal equilibrium, Boltzmann–Gibbs (BG) statistical mechanics have exhibited, in the last several decades, several flaws in addressing out-of-equilibrium dynamics of many nonlinear complex systems. In such circumstances, it has been shown that an appropriate generalization of the BG theory, known as nonextensive statistical mechanics and based on nonadditive entropies, is able to satisfactorily handle wide classes of anomalous emerging features and violations of standard equilibrium prescriptions, such as ergodicity, mixing, breakdown of the symmetry of homogeneous occupancy of phase space, and related features. In the present study, we review various important results of nonextensive statistical mechanics for dissipative and conservative dynamical systems. In particular, we discuss applications to both discrete-time systems with a few degrees of freedom and continuous-time ones with many degrees of freedom, as well as to asymptotically scale-free networks and systems with diverse dimensionalities and ranges of interactions, of either classical or quantum nature. Full article

(This article belongs to the Special Issue Hamiltonian and Overdamped Complex Systems, Symmetry of Phase-Space Occupancy)

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22 pages, 3802 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Making and Breaking—Insight into the Symmetry of Salen Analogues

by Katarzyna M. Krupka, Sylwia Banach, Michał Pocheć, Jarosław J. Panek and Aneta Jezierska

Symmetry 2023, 15(2), 424; https://doi.org/10.3390/sym15020424 - 5 Feb 2023

Cited by 1 | Viewed by 2761

Abstract

This study focuses on selected members of the general salen-analogues family possessing two O-H⋯N hydrogen bonds, namely three isomers of N,N’-bis(salicylidene)-X-phenylenediamine, denoted as ortho, meta and para. Two of the isomers are not planar in the published crystal [...] Read more.

This study focuses on selected members of the general salen-analogues family possessing two O-H⋯N hydrogen bonds, namely three isomers of N,N’-bis(salicylidene)-X-phenylenediamine, denoted as ortho, meta and para. Two of the isomers are not planar in the published crystal structures. The current study tackles the problem of symmetry and interactions within the molecules, as well as in the crystal lattice. The aromaticity of the phenyl rings is evaluated using the Harmonic Oscillator Model of Aromaticity (HOMA) index. Intra- and inter-molecular non-covalent interactions are studied via Hirshfeld surface analysis, Independent Gradient Model (IGM), Quantum Theory of Atoms in Molecules (QTAIM), Non-Covalent Interaction (NCI) index, Electron Localisation Function (ELF), Core-Valence Bifurcation (CVB) index and Symmetry-Adapted Perturbation Theory (SAPT). Density Functional Theory (DFT) simulations were carried out in vacuo and with solvent reaction field based on Polarisable Continuum Model (IEF-PCM formulation) at the

ω

B97XD/6-311+G(2d,2p) level. Crystal structure analyses were performed for the data reported previously in the literature. The obtained results demonstrate that the three isomers differ greatly in their structural properties (molecular symmetry is broken for the ortho and meta isomers in the solid state) and ability to form intermolecular interactions, while retaining overall similar physico-chemical characteristics, e.g., aromaticity of the phenyl rings. It was found that the presence of the polar solvent does not significantly affect the structure of the studied compounds. An application of the Hirshfeld surface analysis revealed the nature of the non-covalent interactions present in the investigated crystals. The SAPT results showed that the stability of the dimers extracted from the crystals of the Schiff base derivatives arises from electrostatics and dispersion. Full article

(This article belongs to the Special Issue Structural Symmetry and Asymmetry Implications in Development of Recent Pharmacy and Medicine)

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35 pages, 542 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

More Insights into Symmetries in Multisymplectic Field Theories

by Arnoldo Guerra IV and Narciso Román-Roy

Symmetry 2023, 15(2), 390; https://doi.org/10.3390/sym15020390 - 1 Feb 2023

Cited by 7 | Viewed by 1704

Abstract

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, [...] Read more.

This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics and in the geometric formulation of these theories are clarified. Finally, a general discussion is given on the structure of symmetries in the presence of constraints appearing in singular field theories. Symmetries of some typical theories in theoretical physics are analyzed through the construction of the relevant multimomentum maps which are the conserved quantities (by Noether’s theorem) on the (pre)multisymplectic phase spaces. Full article

(This article belongs to the Special Issue Symmetry in Geometric Mechanics and Mathematical Physics)

12 pages, 3207 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Synthesis and Spectroscopic Properties of Selected Acrylic and Methacrylic Derivatives of 2-Mercaptobenzothiazole

by Janina Kabatc-Borcz, Przemysław Czeleń and Agnieszka Skotnicka

Symmetry 2023, 15(2), 370; https://doi.org/10.3390/sym15020370 - 30 Jan 2023

Cited by 1 | Viewed by 1796

Abstract

One of the most basic properties of chemical compounds is structural symmetry or asymmetry. This property can be considered at different levels of structural organization. The physical, chemical, biological, and technological properties of organic compounds depend on their chemical structure and are systematically [...] Read more.

One of the most basic properties of chemical compounds is structural symmetry or asymmetry. This property can be considered at different levels of structural organization. The physical, chemical, biological, and technological properties of organic compounds depend on their chemical structure and are systematically related to it. The presented paper is focused on the synthesis and study of the spectroscopic properties of selected photoinitiators from the acrylate and methacrylate derivatives of 2-(benzothiazolylthio)ethyl. The indicated compounds can find potential application in medicine. The 2-(benzothiazolylthio)ethyl acrylate and methacrylate derivatives were characterized using infrared spectroscopy (IR) and nuclear magnetic resonance (NMR) spectroscopy. Their spectroscopic properties were determined on the basis of UV–Vis spectra. The calculated DFT energies and Frontier Molecular Orbitals calculations of the studied compounds were proved to be consistent with the experimental observations. The results have showed that the introduction of the ethoxy substituent increases the reactivity of the compounds and results in the slight bathochromic shift (~19 nm) of the absorption spectra maxima. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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21 pages, 2060 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

On Analogies in Proton-Transfers for Pyrimidine Bases in the Gas Phase (Apolar Environment)—Cytosine Versus Isocytosine

by Ewa D. Raczyńska

Symmetry 2023, 15(2), 342; https://doi.org/10.3390/sym15020342 - 26 Jan 2023

Cited by 4 | Viewed by 1653

Abstract

Inter- and intra-molecular proton-transfers between functional groups in nucleobases play a principal role in their interactions (pairing) in nucleic acids. Although prototropic rearrangements (intramolecular proton-transfers) for neutral pyrimidine bases are well documented, they have not always been considered for their protonated and deprotonated [...] Read more.

Inter- and intra-molecular proton-transfers between functional groups in nucleobases play a principal role in their interactions (pairing) in nucleic acids. Although prototropic rearrangements (intramolecular proton-transfers) for neutral pyrimidine bases are well documented, they have not always been considered for their protonated and deprotonated forms. The complete isomeric mixtures in acid-base equilibria and in acidity–basicity parameters have not yet been examined. Taking into account the lack of literature and data, research into the question of prototropy for the ionic (protonated and deprotonated) forms has been undertaken in this work. For the purposes of this investigation, two isomeric pyrimidine bases (C—cytosine and iC—isocytosine) were chosen. They exhibit analogous (symmetrical) general acid-base equilibria (intermolecular proton-transfers). Being similar polyfunctional tautomeric systems, C and iC possess two labile protons and five conjugated tautomeric sites. However, positions of exo groups are different. Consequently, structural conversions such as prototropy, rotational, and geometrical isomerism of exo groups (=O/−OH and =NH/−NH₂) and their intramolecular interactions with endo groups (=N−/>NH) possible in neutral C and iC and in their ionic forms lead to some differences in compositions of isomeric mixtures. By application of quantum–chemical methods to the isolated (in vacuo) species, stability of all possible neutral and ionic isomers has been examined and the candidate isomers selected. The complete isomeric mixtures have been considered for the first time for di-deprotonated, mono-deprotonated, mono-protonated, and di-protonated forms. Protonation–deprotonation reactions have been analyzed in the gas phase that models non-polar environment. The gas-phase microscopic (kinetic) and macroscopic (thermodynamic) acidity–basicity parameters have been estimated for each step of acid-base equilibria. When proceeding from di-anion to di-cation in four steps of protonation–deprotonation reaction, the macroscopic proton affinities for C and iC differ by less than 10 kcal mol⁻¹. Their DFT-calculated values are as follows: 451 and 457, 340 and 339, 228 and 224, and 100 and 104 kcal mol⁻¹, respectively. Differences between the microscopic proton affinities for analogous isomers of C and iC seem to be larger for the exo than endo groups. Owing to variations of relative stabilities for neutral and ionic isomers, in some cases they are even larger than 10 kcal mol⁻¹. Full article

(This article belongs to the Special Issue Symmetry in Acid-Base Chemistry II)

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20 pages, 756 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Popcorn Transitions and Approach to Conformality in Homogeneous Holographic Nuclear Matter

by Jesús Cruz Rojas, Tuna Demircik and Matti Järvinen

Symmetry 2023, 15(2), 331; https://doi.org/10.3390/sym15020331 - 25 Jan 2023

Cited by 12 | Viewed by 3314

Abstract

We study cold and dense nuclear matter by using the gauge/gravity duality. To this end, we use the Witten–Sakai–Sugimoto model and the V-QCD models with an approach where the nuclear matter is taken to be spatially homogeneous. We focus on the “popcorn” transitions, [...] Read more.

We study cold and dense nuclear matter by using the gauge/gravity duality. To this end, we use the Witten–Sakai–Sugimoto model and the V-QCD models with an approach where the nuclear matter is taken to be spatially homogeneous. We focus on the “popcorn” transitions, which are phase transitions in the nuclear matter phases induced by changes in the layer structure of the configuration on the gravity side. We demonstrate that the equation of state for the homogeneous nuclear matter becomes approximately conformal at high densities, and compare our results to other approaches. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

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23 pages, 1063 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Jacobi and Lyapunov Stability Analysis of Circular Geodesics around a Spherically Symmetric Dilaton Black Hole

by Cristina Blaga, Paul Blaga and Tiberiu Harko

Symmetry 2023, 15(2), 329; https://doi.org/10.3390/sym15020329 - 24 Jan 2023

Cited by 8 | Viewed by 2201

Abstract

We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the [...] Read more.

We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potential of the geodesic motion. The Lyapunov stability analysis leads to the same results. Hence, we can conclude that, in the particular case of the geodesic motion on circular orbits in the Gibbons–Maeda–Garfinkle–Horowitz–Strominger, the Lyapunov and the Jacobi stability analysis gives equivalent results. Full article

(This article belongs to the Special Issue BGL 2022: Dedicated to the Creators of the Non-euclidean Geometry: János Bolyai (220th Anniversary) and N.I. Lobachevski (230th Anniversary))

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10 pages, 1961 KiB

Open AccessEditor’s ChoiceArticle

A New Program to Estimate the Parameters of Preston’s Equation, a General Formula for Describing the Egg Shape of Birds

by Peijian Shi, Lin Wang, Brady K. Quinn and Johan Gielis

Symmetry 2023, 15(1), 231; https://doi.org/10.3390/sym15010231 - 13 Jan 2023

Cited by 7 | Viewed by 3018

Abstract

Preston’s equation is a general model describing the egg shape of birds. The parameters of Preston’s equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg’s actual length to two. This method assumes that the straight line through [...] Read more.

Preston’s equation is a general model describing the egg shape of birds. The parameters of Preston’s equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg’s actual length to two. This method assumes that the straight line through the two points on an egg’s profile separated by the maximum distance (i.e., the longest axis of an egg’s profile) is the mid-line. It hypothesizes that the photographed egg’s profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston’s equation considers an angle of deviation for the longest axis of an egg’s profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg’s center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg’s profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston’s equation by automatically searching for the optimal mid-line of an egg’s profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston’s equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg’s profile) and the egg’s maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations. Full article

(This article belongs to the Section Life Sciences)

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12 pages, 698 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nanoscale Bending Dynamics in Mixed-Chain Lipid Membranes

by Elizabeth G. Kelley, Moritz P. K. Frewein, Orsolya Czakkel and Michihiro Nagao

Symmetry 2023, 15(1), 191; https://doi.org/10.3390/sym15010191 - 9 Jan 2023

Cited by 3 | Viewed by 2346

Abstract

Lipids that have two tails of different lengths are found throughout biomembranes in nature, yet the effects of this asymmetry on the membrane properties are not well understood, especially when it comes to the membrane dynamics. Here we study the nanoscale bending fluctuations [...] Read more.

Lipids that have two tails of different lengths are found throughout biomembranes in nature, yet the effects of this asymmetry on the membrane properties are not well understood, especially when it comes to the membrane dynamics. Here we study the nanoscale bending fluctuations in model mixed-chain 14:0–18:0 PC (MSPC) and 18:0–14:0 PC (SMPC) lipid bilayers using neutron spin echo (NSE) spectroscopy. We find that despite the partial interdigitation that is known to persist in the fluid phase of these membranes, the collective fluctuations are enhanced on timescales of tens of nanoseconds, and the chain-asymmetric lipid bilayers are softer than an analogous chain-symmetric lipid bilayer with the same average number of carbons in the acyl tails, di-16:0 PC (DPPC). Quantitative comparison of the NSE results suggests that the enhanced bending fluctuations at the nanosecond timescales are consistent with experimental and computational studies that showed the compressibility moduli of chain-asymmetric lipid membranes are 20% to 40% lower than chain-symmetric lipid membranes. These studies add to growing evidence that the partial interdigitation in mixed-chain lipid membranes is highly dynamic in the fluid phase and impacts membrane dynamic processes from the molecular to mesoscopic length scales without significantly changing the bilayer thickness or area per lipid. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Cellular Membranes)

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34 pages, 2488 KiB

Open AccessFeature PaperEditor’s ChoiceReview

The Proxy-SU(3) Symmetry in Atomic Nuclei

by Dennis Bonatsos, Andriana Martinou, Spyridon Kosmas Peroulis, Theodoros John Mertzimekis and Nikolay Minkov

Symmetry 2023, 15(1), 169; https://doi.org/10.3390/sym15010169 - 6 Jan 2023

Cited by 22 | Viewed by 8642

Abstract

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated [...] Read more.

The microscopic origins and the current predictions of the proxy-SU(3) symmetry model of atomic nuclei were reviewed. Beginning with experimental evidence for the special roles played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced; its validity is demonstrated through Nilsson model calculations and its connection to the spherical shell model. The major role played by the highest weight-irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables

β

and

γ

for even–even nuclei in the explanation of the dominance of prolate over oblate shapes in the ground states of even–even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, and in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined. Full article

(This article belongs to the Special Issue Symmetry in Nuclear Physics: Model Calculations, Advances and Applications)

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18 pages, 2415 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Symmetry In-between the Shapes, Shells, and Clusters of Nuclei

by József Cseh, Gábor Riczu and Judit Darai

Symmetry 2023, 15(1), 115; https://doi.org/10.3390/sym15010115 - 31 Dec 2022

Cited by 7 | Viewed by 3124

Abstract

The multiconfigurational dynamical symmetry (MUSY) connects the shell, collective, and cluster models of atomic nuclei for the case of multi-shell excitations. Therefore, it can give a unified description of various phenomena. The shape isomers are obtained from the investigation of the stability and [...] Read more.

The multiconfigurational dynamical symmetry (MUSY) connects the shell, collective, and cluster models of atomic nuclei for the case of multi-shell excitations. Therefore, it can give a unified description of various phenomena. The shape isomers are obtained from the investigation of the stability and consistency of the symmetry, and selection rules connect them to the possible cluster configurations and the related reaction channels. A simple, dynamically symmetric Hamiltonian turns out to be able to provide a unified description of the gross features of spectra of different regions of excitation energy and deformation. Some predictions of MUSY have been justified by experimental observations. Full article

(This article belongs to the Special Issue Selected Papers from Shapes and Symmetries in Nuclei: From Experiment to Theory (SSNET’21 Conference))

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11 pages, 2622 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Symmetrization of Mechanical Response in Fibrous Metamaterials through Micro-Shear Deformability

by Mario Spagnuolo

Symmetry 2022, 14(12), 2660; https://doi.org/10.3390/sym14122660 - 16 Dec 2022

Cited by 8 | Viewed by 2019

Abstract

The basic concept of this study consists of the investigation of symmetrization of the mechanical response in extension and compression for fibrous metamaterials endowed with a symmetric microstructure relative to the axial direction. It is known that generally, this response is non-symmetric due [...] Read more.

The basic concept of this study consists of the investigation of symmetrization of the mechanical response in extension and compression for fibrous metamaterials endowed with a symmetric microstructure relative to the axial direction. It is known that generally, this response is non-symmetric due to the different deformation mechanisms activated in the two tests. If a further deformation mechanism based on the micro-shearing of connective elements is taken into account, the global mechanical response is observed to be symmetric for given sets of stiffnesses. The studied problem is addressed with the help of numerical simulations. Full article

(This article belongs to the Special Issue Recent Advances in the Study of Symmetry and Continuum Mechanics II)

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