Symmetry

29 pages, 8366 KiB

Open AccessEditor’s ChoiceArticle

Elastic Origin of the Unsymmetrical Thermal Hysteresis in Spin Crossover Materials: Evidence of Symmetry Breaking

by Mamadou Ndiaye, Nour El Islam Belmouri, Jorge Linares and Kamel Boukheddaden

Symmetry 2021, 13(5), 828; https://doi.org/10.3390/sym13050828 - 9 May 2021

Cited by 12 | Viewed by 2292

The jungle of experimental behaviors of spin-crossover materials contains a tremendous number of unexpected behaviors, among which, the unsymmetrical hysteresis loops having different shapes on heating and cooling, that we often encounter in literature. Excluding an extra effect of crystallographic phase transitions, we [...] Read more.

The jungle of experimental behaviors of spin-crossover materials contains a tremendous number of unexpected behaviors, among which, the unsymmetrical hysteresis loops having different shapes on heating and cooling, that we often encounter in literature. Excluding an extra effect of crystallographic phase transitions, we study here these phenomena from the point of view of elastic modeling and we demonstrate that a simple model accounting for the bond lengths misfits between the high-spin and low-spin states is sufficient to describe the situation of unsymmetrical hysteresis showing plateaus at the transition only on cooling or on heating branches. The idea behind this effect relates to the existence of a discriminant elastic frustration in the lattice, which expresses only along the high-spin to low-spin transition or in the opposite side. The obtained two-step transitions showed characteristics of self-organization of the spin states under the form of stripes, which we explain as an emergence process of antagonist directional elastic interactions inside the lattice. The analysis of the spin state transformation inside the plateau on cooling in terms of two sublattices demonstrated that the elastic-driven self-organization of the spin states is accompanied with a symmetry breaking. Full article

(This article belongs to the Special Issue Symmetry and Symmetry Breaking: Phase Transitions and Critical Phenomena)

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13 pages, 4906 KiB

Open AccessEditor’s ChoiceArticle

On the Relationship between Generalization and Robustness to Adversarial Examples

by Anibal Pedraza, Oscar Deniz and Gloria Bueno

Symmetry 2021, 13(5), 817; https://doi.org/10.3390/sym13050817 - 7 May 2021

Cited by 8 | Viewed by 2597

Abstract

One of the most intriguing phenomenons related to deep learning is the so-called adversarial examples. These samples are visually equivalent to normal inputs, undetectable for humans, yet they cause the networks to output wrong results. The phenomenon can be framed as a symmetry/asymmetry [...] Read more.

One of the most intriguing phenomenons related to deep learning is the so-called adversarial examples. These samples are visually equivalent to normal inputs, undetectable for humans, yet they cause the networks to output wrong results. The phenomenon can be framed as a symmetry/asymmetry problem, whereby inputs to a neural network with a similar/symmetric appearance to regular images, produce an opposite/asymmetric output. Some researchers are focused on developing methods for generating adversarial examples, while others propose defense methods. In parallel, there is a growing interest in characterizing the phenomenon, which is also the focus of this paper. From some well known datasets of common images, like CIFAR-10 and STL-10, a neural network architecture is first trained in a normal regime, where training and validation performances increase, reaching generalization. Additionally, the same architectures and datasets are trained in an overfitting regime, where there is a growing disparity in training and validation performances. The behaviour of these two regimes against adversarial examples is then compared. From the results, we observe greater robustness to adversarial examples in the overfitting regime. We explain this simultaneous loss of generalization and gain in robustness to adversarial examples as another manifestation of the well-known fitting-generalization trade-off. Full article

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32 pages, 2412 KiB

Open AccessEditor’s ChoiceArticle

Copulaesque Versions of the Skew-Normal and Skew-Student Distributions

by Christopher Adcock

Symmetry 2021, 13(5), 815; https://doi.org/10.3390/sym13050815 - 6 May 2021

Cited by 4 | Viewed by 2084

Abstract

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned [...] Read more.

A recent paper presents an extension of the skew-normal distribution which is a copula. Under this model, the standardized marginal distributions are standard normal. The copula itself depends on the familiar skewing construction based on the normal distribution function. This paper is concerned with two topics. First, the paper presents a number of extensions of the skew-normal copula. Notably these include a case in which the standardized marginal distributions are Student’s t, with different degrees of freedom allowed for each margin. In this case the skewing function need not be the distribution function for Student’s t, but can depend on certain of the special functions. Secondly, several multivariate versions of the skew-normal copula model are presented. The paper contains several illustrative examples. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Multivariate Statistics and Data Science)

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44 pages, 4717 KiB

Open AccessEditor’s ChoiceArticle

Extending the Model-Based Controller Design to Higher-Order Plant Models and Measurement Noise

by Mikulas Huba and Damir Vrancic

Symmetry 2021, 13(5), 798; https://doi.org/10.3390/sym13050798 - 4 May 2021

Cited by 15 | Viewed by 2829

Abstract

The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial [...] Read more.

The article extends a model-based controller design to higher-order systems, focusing on the speed and shapes of the closed loop responses, including the noise attenuation. It shows that, to obtain simple but reliable results, it is necessary to pay attention to the initial process identification and modelling and also to modify the target closed-loop transfer functions, which must remain causal. To attenuate high initial control signal peaks, appropriate pre-filters are introduced. In order to work with as few parameters as possible, all higher-order transfer functions (process models, target closed loops, pre-filters and noise-attenuation filters) are selected in the form of binomial filters with multiple time constants. Consequently, the so-called “half-rule”, used to reduce too complex process transfer functions, has been modified accordingly. Because derived controllers can lead to different transient dynamics depending on the context of use, the article recalls the need to introduce dynamic classes of control to clarify the mission of individual types of controllers. Consequently, also the performance evaluation using the total variation (TV) criterion had to be refined. Indeed, in its original version, TV is not suitable to distinguish between reasonable and excessive control effort due to improper tuning and noise. The modified TVs allow evaluating higher order systems with multiple changes in direction of their control signal increase without contributing to the excessive control increments. The advantages of the proposed modifications, compared to the traditional approaches, are made clear through simulation examples. Full article

(This article belongs to the Special Issue PID Control and Symmetry)

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19 pages, 5042 KiB

Open AccessEditor’s ChoiceArticle

Nanofluids Characterization for Spray Cooling Applications

by Miguel Sanches, Guido Marseglia, Ana P. C. Ribeiro, António L. N. Moreira and Ana S. Moita

Symmetry 2021, 13(5), 788; https://doi.org/10.3390/sym13050788 - 2 May 2021

Cited by 17 | Viewed by 2472

Abstract

In this paper the mathematical and physical correlation between fundamental thermophysical properties of materials, with their structure, for nanofluid thermal performance in spray cooling applications is presented. The present work aims at clarifying the nanofluid characteristics, especially the geometry of their nanoparticles, leading [...] Read more.

In this paper the mathematical and physical correlation between fundamental thermophysical properties of materials, with their structure, for nanofluid thermal performance in spray cooling applications is presented. The present work aims at clarifying the nanofluid characteristics, especially the geometry of their nanoparticles, leading to heat transfer enhancement at low particle concentration. The base fluid considered is distilled water with the surfactant cetyltrimethylammonium bromide (CTAB). Alumina and silver are used as nanoparticles. A systematic analysis addresses the effect of nanoparticles concentration and shape in spray hydrodynamics and heat transfer. Spray dynamics is mainly characterized using phase Doppler interferometry. Then, an extensive processing procedure is performed to thermal and spacetime symmetry images obtained with a high-speed thermographic camera to analyze the spray impact on a heated, smooth stainless-steel foil. There is some effect on the nanoparticles’ shape, which is nevertheless minor when compared to the effect of the nanoparticles concentration and to the change in the fluid properties caused by the addition of the surfactant. Hence, increasing the nanoparticles concentration results in lower surface temperatures and high removed heat fluxes. In terms of the effect of the resulting thermophysical properties, increasing the nanofluids concentration resulted in the increase in the thermal conductivity and dynamic viscosity of the nanofluids, which in turn led to a decrease in the heat transfer coefficients. On the other hand, nanofluids specific heat capacity is increased which correlates positively with the spray cooling capacity. The analysis of the parameters that determine the structure, evolution, physics and both spatial and temporal symmetry of the spray is interesting and fundamental to shed light to the fact that only knowledge based in experimental data can guarantee a correct setting of the model numbers. Full article

(This article belongs to the Special Issue Materials Science: Synthesis, Structure, Properties)

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15 pages, 3042 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Cooperation/Competition between Halogen Bonds and Hydrogen Bonds in Complexes of 2,6-Diaminopyridines and X-CY₃ (X = Cl, Br; Y = H, F)

by Barbara Bankiewicz and Marcin Palusiak

Symmetry 2021, 13(5), 766; https://doi.org/10.3390/sym13050766 - 28 Apr 2021

Cited by 6 | Viewed by 2480

Abstract

The DFT calculations have been performed on a series of two-element complexes formed by substituted 2,6-diaminopyridine (R−PDA) and pyridine (R−Pyr) with X−CY₃ molecules (where X = Cl, Br and Y = H, F). The primary aim of this study was to examine [...] Read more.

The DFT calculations have been performed on a series of two-element complexes formed by substituted 2,6-diaminopyridine (R−PDA) and pyridine (R−Pyr) with X−CY₃ molecules (where X = Cl, Br and Y = H, F). The primary aim of this study was to examine the intermolecular hydrogen and halogen bonds in the condition of their mutual coexistence. Symmetry/antisymmetry of the interrelation between three individual interactions is addressed. It appears that halogen bonds play the main role in the stabilization of the structures of the selected systems. However, the occurrence of one or two hydrogen bonds was associated with the favourable geometry of the complexes. Moreover, the impact of different substituent groups attached in the para position to the aromatic ring of the 2,6-diaminopyridine and pyridine on the character of the intermolecular hydrogen and halogen bonds was examined. The results indicate that the presence of electron-donating substituents strengthens the bonds. In turn, the presence of electron-withdrawing substituents reduces the strength of halogen bonds. Additionally, when hydrogen and halogen bonds lose their leading role in the complex formation, the nonspecific electrostatic interactions between dipole moments take their place. Analysis was based on geometric, energetic, and topological parameters of the studied systems. Full article

(This article belongs to the Special Issue Exploring Inter- and Intramolecular Interactions as Building Blocks of Larger Systems)

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Graphical abstract

14 pages, 261 KiB

Open AccessEditor’s ChoiceArticle

General Fractional Integrals and Derivatives of Arbitrary Order

by Yuri Luchko

Symmetry 2021, 13(5), 755; https://doi.org/10.3390/sym13050755 - 27 Apr 2021

Cited by 58 | Viewed by 3468

Abstract

In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy [...] Read more.

In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced. Whereas the kernels of the general fractional derivatives of arbitrary order possess integrable singularities at the point zero, the kernels of the general fractional integrals can—depending on their order—be both singular and continuous at the origin. For the general fractional integrals and derivatives of arbitrary order with the kernels introduced in this paper, two fundamental theorems of fractional calculus are formulated and proved. Full article

(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus)

21 pages, 3817 KiB

Open AccessEditor’s ChoiceArticle

Fingerprint Classification Based on Deep Learning Approaches: Experimental Findings and Comparisons

by Carmelo Militello, Leonardo Rundo, Salvatore Vitabile and Vincenzo Conti

Symmetry 2021, 13(5), 750; https://doi.org/10.3390/sym13050750 - 26 Apr 2021

Cited by 31 | Viewed by 8517

Abstract

Biometric classification plays a key role in fingerprint characterization, especially in the identification process. In fact, reducing the number of comparisons in biometric recognition systems is essential when dealing with large-scale databases. The classification of fingerprints aims to achieve this target by splitting [...] Read more.

Biometric classification plays a key role in fingerprint characterization, especially in the identification process. In fact, reducing the number of comparisons in biometric recognition systems is essential when dealing with large-scale databases. The classification of fingerprints aims to achieve this target by splitting fingerprints into different categories. The general approach of fingerprint classification requires pre-processing techniques that are usually computationally expensive. Deep Learning is emerging as the leading field that has been successfully applied to many areas, such as image processing. This work shows the performance of pre-trained Convolutional Neural Networks (CNNs), tested on two fingerprint databases—namely, PolyU and NIST—and comparisons to other results presented in the literature in order to establish the type of classification that allows us to obtain the best performance in terms of precision and model efficiency, among approaches under examination, namely: AlexNet, GoogLeNet, and ResNet. We present the first study that extensively compares the most used CNN architectures by classifying the fingerprints into four, five, and eight classes. From the experimental results, the best performance was obtained in the classification of the PolyU database by all the tested CNN architectures due to the higher quality of its samples. To confirm the reliability of our study and the results obtained, a statistical analysis based on the McNemar test was performed. Full article

(This article belongs to the Section Computer)

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11 pages, 317 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Radiative and Meson Decays of Y(4230) in Flavor SU(3)

by Luciano Maiani, Antonio Davide Polosa and Verónica Riquer

Symmetry 2021, 13(5), 751; https://doi.org/10.3390/sym13050751 - 26 Apr 2021

Cited by 4 | Viewed by 1916

Abstract

The charmonium-like exotic states

Y (4230)

and the less known

Y (4320)

, produced in

e^{+} e^{-}

collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and [...] Read more.

The charmonium-like exotic states

Y (4230)

and the less known

Y (4320)

, produced in

e^{+} e^{-}

collisions, are sources of positive parity exotic hadrons in association with photons or pseudoscalar mesons. We analyze the radiative and pion decay channels in the compact tetraquark scheme, with a method that proves to work equally well in the most studied

D^{*} \to γ / π + D

decays. The decay of the vector Y into a pion and a

Z_{c}

state requires a flip of charge conjugation and isospin that is described appropriately in the formalism used. Rates are found to depend on the fifth power of pion momentum, which would make the final states

π Z_{c} (4020)

strongly suppressed with respect to

π Z_{c} (3900)

. The agreement with BES III data would be improved considering the

π Z_{c} (4020)

events to be fed by the tail of the

Y (4320)

resonance under the

Y (4230)

. These results should renovate the interest in further clarifying the emerging experimental picture in this mass region. Full article

(This article belongs to the Special Issue Search for New Phenomena in Heavy-Quark Physics)

15 pages, 772 KiB

Open AccessEditor’s ChoiceArticle

Algebra of Symmetry Operators for Klein-Gordon-Fock Equation

by Valeriy V. Obukhov

Symmetry 2021, 13(4), 727; https://doi.org/10.3390/sym13040727 - 20 Apr 2021

Cited by 23 | Viewed by 2139

Abstract

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time

V_{4}

a group of motion

G_{3}

acts simply transitively on a non-null subspace of transitivity

V_{3}

. It is [...] Read more.

All external electromagnetic fields in which the Klein-Gordon-Fock equation admits the first-order symmetry operators are found, provided that in the space-time

V_{4}

a group of motion

G_{3}

acts simply transitively on a non-null subspace of transitivity

V_{3}

. It is shown that in the case of a Riemannian space

V_{n}

, in which the group

G_{r}

acts simply transitively, the algebra of symmetry operators of the n-dimensional Klein-Gordon-Fock equation in an external admissible electromagnetic field coincides with the algebra of operators of the group

G_{r}

. Full article

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

10 pages, 269 KiB

Open AccessEditor’s ChoiceArticle

Improved Bounds on Lorentz Symmetry Violation from High-Energy Astrophysical Sources

by Brett Altschul

Symmetry 2021, 13(4), 688; https://doi.org/10.3390/sym13040688 - 15 Apr 2021

Cited by 5 | Viewed by 1676

Abstract

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron [...] Read more.

Observations of the synchrotron and inverse Compton emissions from ultrarelativistic electrons in astrophysical sources can reveal a great deal about the energy–momentum relations of those electrons. They can thus be used to place bounds on the possibility of Lorentz violation in the electron sector. Recent

γ

-ray telescope data allow the Lorentz-violating electron

c^{ν μ}

parameters to be constrained extremely well, so that all bounds are at the level of

7 \times 10^{- 16}

or better. Full article

(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)

18 pages, 340 KiB

Open AccessEditor’s ChoiceArticle

Gravity with Explicit Diffeomorphism Breaking

by Robert Bluhm and Yumu Yang

Symmetry 2021, 13(4), 660; https://doi.org/10.3390/sym13040660 - 12 Apr 2021

Cited by 9 | Viewed by 1979

Abstract

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a [...] Read more.

Modified theories of gravity that explicitly break diffeomorphism invariance have been used for over a decade to explore open issues related to quantum gravity, dark energy, and dark matter. At the same time, the Standard-Model Extension (SME) has been widely used as a phenomenological framework in investigations of spacetime symmetry breaking. Until recently, it was thought that the SME was suitable only for theories with spontaneous spacetime symmetry breaking due to consistency conditions stemming from the Bianchi identities. However, it has recently been shown that, particularly with matter couplings included, the consistency conditions can also be satisfied in theories with explicit breaking. An overview of how this is achieved is presented, and two examples are examined. The first is massive gravity, which includes a nondynamical background tensor. The second is a model based on a low-energy limit of Hořava gravity, where spacetime has a physically preferred foliation. In both cases, bounds on matter–gravity interactions that explicitly break diffeomorphisms are obtained using the SME. Full article

(This article belongs to the Special Issue Space-Time Symmetries and Violations of Lorentz Invariance)

13 pages, 2140 KiB

Open AccessEditor’s ChoiceArticle

The Fluctuating Asymmetry of the Butterfly Wing Pattern Does Not Change along an Industrial Pollution Gradient

by Vitali Zverev and Mikhail V. Kozlov

Symmetry 2021, 13(4), 626; https://doi.org/10.3390/sym13040626 - 9 Apr 2021

Cited by 6 | Viewed by 2867

Abstract

The rapid and selective responses to changes in habitat structure and climate have made butterflies valuable environmental indicators. In this study, we asked whether the decline in butterfly populations near the copper-nickel smelter in Monchegorsk in northwestern Russia is accompanied by phenotypic stress [...] Read more.

The rapid and selective responses to changes in habitat structure and climate have made butterflies valuable environmental indicators. In this study, we asked whether the decline in butterfly populations near the copper-nickel smelter in Monchegorsk in northwestern Russia is accompanied by phenotypic stress responses to toxic pollutants, expressed as a decrease in body size and an increase in fluctuating asymmetry. We measured the concentrations of nickel and copper, forewing length, and fluctuating asymmetry in two elements of wing patterns in Boloria euphrosyne, Plebejus idas, and Agriades optilete collected 1–65 km from Monchegorsk. Body metal concentrations increased toward the smelter, confirming the local origin of the collected butterflies. The wings of butterflies from the most polluted sites were 5–8% shorter than those in unpolluted localities, suggesting adverse effects of pollution on butterfly fitness due to larval feeding on contaminated plants. However, fluctuating asymmetry averaged across two hindwing spots did not change systematically with pollution, thereby questioning the use of fluctuating asymmetry as an indicator of habitat quality in butterfly conservation projects. Full article

(This article belongs to the Special Issue Fluctuating Asymmetry and Environmental Stress)

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10 pages, 290 KiB

Open AccessEditor’s ChoiceArticle

Regularity Criteria for the 3D Magneto-Hydrodynamics Equations in Anisotropic Lorentz Spaces

by Maria Alessandra Ragusa and Fan Wu

Symmetry 2021, 13(4), 625; https://doi.org/10.3390/sym13040625 - 8 Apr 2021

Cited by 5 | Viewed by 1959

Abstract

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions

(\partial_{1} u_{1}, \partial_{1} b_{1})

, [...] Read more.

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions

(\partial_{1} u_{1}, \partial_{1} b_{1})

,

(\partial_{2} u_{2}, \partial_{2} b_{2})

and

(\partial_{3} u_{3}, \partial_{3} b_{3})

in anisotropic Lorentz space. Full article

(This article belongs to the Special Issue Applied Mathematics and Fractional Calculus)

13 pages, 516 KiB

Open AccessEditor’s ChoiceArticle

Scalable Codes for Precision Calculations of Properties of Complex Atomic Systems

by Charles Cheung, Marianna Safronova and Sergey Porsev

Symmetry 2021, 13(4), 621; https://doi.org/10.3390/sym13040621 - 8 Apr 2021

Cited by 13 | Viewed by 2568

Abstract

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that [...] Read more.

High precision atomic data are indispensable for studies of fundamental symmetries, tests of fundamental physics postulates, developments of atomic clocks, ultracold atom experiments, astrophysics, plasma science, and many other fields of research. We have developed a new parallel atomic structure code package that enables computations that were not previously possible due to system complexity. This code package also allows much quicker computations to be run with higher accuracy for simple systems. We explored different methods of load-balancing matrix element calculations for many-electron systems, which are very difficult due to the intrinsic nature of the computational methods used to calculate them. Furthermore, dynamic memory allocation and MPI parallelization have been implemented to optimize and accelerate the computations. We have achieved near-perfect linear scalability and efficiency with the number of processors used for calculation, paving the way towards the future where most open-shell systems will finally be able to be treated with good accuracy. We present several examples illustrating new capabilities of the newly developed codes, specifically correlating up to all 60 electrons in the highly charged Ir

^{17 +}

ion and predicting certain properties of Fe

^{16 +}

. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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32 pages, 1571 KiB

Open AccessEditor’s ChoiceArticle

Two-Stage Hybrid Data Classifiers Based on SVM and kNN Algorithms

by Liliya A. Demidova

Symmetry 2021, 13(4), 615; https://doi.org/10.3390/sym13040615 - 7 Apr 2021

Cited by 27 | Viewed by 3975

Abstract

The paper considers a solution to the problem of developing two-stage hybrid SVM-kNN classifiers with the aim to increase the data classification quality by refining the classification decisions near the class boundary defined by the SVM classifier. In the first stage, the SVM [...] Read more.

The paper considers a solution to the problem of developing two-stage hybrid SVM-kNN classifiers with the aim to increase the data classification quality by refining the classification decisions near the class boundary defined by the SVM classifier. In the first stage, the SVM classifier with default parameters values is developed. Here, the training dataset is designed on the basis of the initial dataset. When developing the SVM classifier, a binary SVM algorithm or one-class SVM algorithm is used. Based on the results of the training of the SVM classifier, two variants of the training dataset are formed for the development of the kNN classifier: a variant that uses all objects from the original training dataset located inside the strip dividing the classes, and a variant that uses only those objects from the initial training dataset that are located inside the area containing all misclassified objects from the class dividing strip. In the second stage, the kNN classifier is developed using the new training dataset above-mentioned. The values of the parameters of the kNN classifier are determined during training to maximize the data classification quality. The data classification quality using the two-stage hybrid SVM-kNN classifier was assessed using various indicators on the test dataset. In the case of the improvement of the quality of classification near the class boundary defined by the SVM classifier using the kNN classifier, the two-stage hybrid SVM-kNN classifier is recommended for further use. The experimental results approve the feasibility of using two-stage hybrid SVM-kNN classifiers in the data classification problem. The experimental results obtained with the application of various datasets confirm the feasibility of using two-stage hybrid SVM-kNN classifiers in the data classification problem. Full article

(This article belongs to the Special Issue 2020 Big Data and Artificial Intelligence Conference)

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14 pages, 1076 KiB

Open AccessEditor’s ChoiceArticle

Kinematic Analysis of Lower Limb Joint Asymmetry During Gait in People with Multiple Sclerosis

by Massimiliano Pau, Bruno Leban, Michela Deidda, Federica Putzolu, Micaela Porta, Giancarlo Coghe and Eleonora Cocco

Symmetry 2021, 13(4), 598; https://doi.org/10.3390/sym13040598 - 3 Apr 2021

Cited by 11 | Viewed by 3888

Abstract

The majority of people with Multiple Sclerosis (pwMS), report lower limb motor dysfunctions, which may relevantly affect postural control, gait and a wide range of activities of daily living. While it is quite common to observe a different impact of the disease on [...] Read more.

The majority of people with Multiple Sclerosis (pwMS), report lower limb motor dysfunctions, which may relevantly affect postural control, gait and a wide range of activities of daily living. While it is quite common to observe a different impact of the disease on the two limbs (i.e., one of them is more affected), less clear are the effects of such asymmetry on gait performance. The present retrospective cross-sectional study aimed to characterize the magnitude of interlimb asymmetry in pwMS, particularly as regards the joint kinematics, using parameters derived from angle-angle diagrams. To this end, we analyzed gait patterns of 101 pwMS (55 women, 46 men, mean age 46.3, average Expanded Disability Status Scale (EDSS) score 3.5, range 1–6.5) and 81 unaffected individuals age- and sex-matched who underwent 3D computerized gait analysis carried out using an eight-camera motion capture system. Spatio-temporal parameters and kinematics in the sagittal plane at hip, knee and ankle joints were considered for the analysis. The angular trends of left and right sides were processed to build synchronized angle–angle diagrams (cyclograms) for each joint, and symmetry was assessed by computing several geometrical features such as area, orientation and Trend Symmetry. Based on cyclogram orientation and Trend Symmetry, the results show that pwMS exhibit significantly greater asymmetry in all three joints with respect to unaffected individuals. In particular, orientation values were as follows: 5.1 of pwMS vs. 1.6 of unaffected individuals at hip joint, 7.0 vs. 1.5 at knee and 6.4 vs. 3.0 at ankle (p < 0.001 in all cases), while for Trend Symmetry we obtained at hip 1.7 of pwMS vs. 0.3 of unaffected individuals, 4.2 vs. 0.5 at knee and 8.5 vs. 1.5 at ankle (p < 0.001 in all cases). Moreover, the same parameters were sensitive enough to discriminate individuals of different disability levels. With few exceptions, all the calculated symmetry parameters were found significantly correlated with the main spatio-temporal parameters of gait and the EDSS score. In particular, large correlations were detected between Trend Symmetry and gait speed (with rho values in the range of −0.58 to −0.63 depending on the considered joint, p < 0.001) and between Trend Symmetry and EDSS score (rho = 0.62 to 0.69, p < 0.001). Such results suggest not only that MS is associated with significantly marked interlimb asymmetry during gait but also that such asymmetry worsens as the disease progresses and that it has a relevant impact on gait performances. Full article

(This article belongs to the Special Issue Neuroscience, Neurophysiology and Symmetry)

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12 pages, 2949 KiB

Open AccessEditor’s ChoiceArticle

Electrochemical Comparison on New (Z)-5-(Azulen-1-Ylmethylene)-2-Thioxo-Thiazolidin-4-Ones

by Eleonora-Mihaela Ungureanu, Mariana Popescu (Apostoiu), Georgiana-Luiza Tatu (Arnold), Liviu Birzan, Raluca Isopescu, Gabriela Stanciu and George-Octavian Buica

Symmetry 2021, 13(4), 588; https://doi.org/10.3390/sym13040588 - 2 Apr 2021

Cited by 7 | Viewed by 2016

Abstract

Three (Z)-5-(azulen-1-ylmethylene)-2-thioxo-thiazolidin-4-ones are electrochemically characterized by cyclic voltammetry, differential pulse voltammetry, and rotating disk electrode voltammetry. The electrochemical investigations revealed that the redox potential is influenced by the number and position of the alkyl groups, and the possible oxidation mechanism is proposed. These [...] Read more.

Three (Z)-5-(azulen-1-ylmethylene)-2-thioxo-thiazolidin-4-ones are electrochemically characterized by cyclic voltammetry, differential pulse voltammetry, and rotating disk electrode voltammetry. The electrochemical investigations revealed that the redox potential is influenced by the number and position of the alkyl groups, and the possible oxidation mechanism is proposed. These compounds, after their immobilization on glassy carbon electrodes during oxidative electropolymerization, were examined as complexing ligands for heavy metal ions from aqueous solutions through adsorptive stripping voltammetry. Full article

(This article belongs to the Special Issue Electrochemical Behavior of the Nonbenzenoid Aromatic Hydrocarbon Azulene and Its Derivatives)

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18 pages, 3666 KiB

Open AccessEditor’s ChoiceArticle

High-Capacity Embedding Method Based on Double-Layer Octagon-Shaped Shell Matrix

by Chin-Feng Lee, Jau-Ji Shen, Somya Agrawal and Yen-Hsi Li

Symmetry 2021, 13(4), 583; https://doi.org/10.3390/sym13040583 - 1 Apr 2021

Cited by 7 | Viewed by 1839

Abstract

Data hiding is a technique that embeds a secret message into a cover medium and transfers the hidden information in the secret message to the recipient. In the past, several data hiding methods based on magic matrix have used various geometrical shapes to [...] Read more.

Data hiding is a technique that embeds a secret message into a cover medium and transfers the hidden information in the secret message to the recipient. In the past, several data hiding methods based on magic matrix have used various geometrical shapes to transmit secret data. The embedding capacity achieved in these methods was often limited due to simple geometrical layouts. This paper proposes a data hiding scheme based on a double-layer octagon-shaped shell matrix. Compared to previous octagon-shaped data hiding methods, the proposed method embeds a total of 7 bits in each pixel pair, reaching an embedding capacity of 3.5 bits per pixel (bpp). Experimental results show that the proposed scheme has a higher embedding capacity compared to other irreversible data hiding schemes. Using the proposed method, it is possible to maintain the Peak Signal to Noise Ratio (PSNR) within an acceptable range with the embedding time less than 2 s. Full article

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15 pages, 1262 KiB

Open AccessEditor’s ChoiceArticle

Thermodynamics of Barrow Holographic Dark Energy with Specific Cut-Off

by Gargee Chakraborty, Surajit Chattopadhyay, Ertan Güdekli and Irina Radinschi

Symmetry 2021, 13(4), 562; https://doi.org/10.3390/sym13040562 - 29 Mar 2021

Cited by 38 | Viewed by 4357

Abstract

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking [...] Read more.

Motivated by the work of Saridakis (Phys. Rev. D102, 123525 (2020)), the present study reports the cosmological consequences of Barrow holographic dark energy (HDE) and its thermodynamics. The literature demonstrates that dark energy (DE) may result from electroweak symmetry breaking that triggers a phase transition from early inflation to late-time acceleration. In the present study, we incorporated viscosity in the Barrow HDE. A reconstruction scheme is presented for the parameters associated with Barrow holographic dark energy under the purview of viscous cosmology. The equation of state (EoS) parameter is reconstructed in this scenario and quintessence behaviour is observed. Considering Barrow HDE as a specific case of Nojiri–Odintsov (NO) HDE, we have observed quintom behaviour of the EoS parameter and for some values of n the EoS has been observed to be very close to

- 1

for the current universe. The generalised second law of thermodynamics has come out to be valid in all the scenarios under consideration. Physical viability of considering Barrow HDE as a specific case of NO HDE is demonstrated in this study. Finally, it has been observed that the model under consideration is very close to

Λ

CDM and cannot go beyond it. Full article

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

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18 pages, 5063 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Structure-Property Relationship in Selected Naphtho- and Anthra-Quinone Derivatives on the Basis of Density Functional Theory and Car–Parrinello Molecular Dynamics

by Beata Kizior, Jarosław J. Panek, Bartłomiej M. Szyja and Aneta Jezierska

Symmetry 2021, 13(4), 564; https://doi.org/10.3390/sym13040564 - 29 Mar 2021

Cited by 5 | Viewed by 2548

Abstract

Intra- and inter-molecular interactions were studied in 2,3-dichloro-5,8-dihydroxy-1,4-naphthoquinone and 1,4-dihydroxy-anthraquinone to shed more light on the molecular assembly phenomena. The electronic ground and excited states features of the compounds were investigated to find structure-property dependencies. The theoretical study was carried out on the [...] Read more.

Intra- and inter-molecular interactions were studied in 2,3-dichloro-5,8-dihydroxy-1,4-naphthoquinone and 1,4-dihydroxy-anthraquinone to shed more light on the molecular assembly phenomena. The electronic ground and excited states features of the compounds were investigated to find structure-property dependencies. The theoretical study was carried out on the basis of Density Functional Theory (DFT), its Time-Dependent (TD-DFT) extension, and using Car–Parrinello Molecular Dynamics (CPMD). In order to show how the environmental effects modulate the physico-chemical properties, the simulations were performed in vacuo, with the solvent reaction field (Polarizable Continuum Model (PCM) and water as a solvent) and crystalline phase. The intramolecular hydrogen bonds and the bridged proton dynamics were analyzed in detail. The aromatic rings and electronic structure changes were estimated using the Harmonic Oscillator Model of Aromaticity (HOMA) and Atoms in Molecules (AIM) theory. The Symmetry-Adapted Perturbation Theory (SAPT) was employed for interaction energy decomposition in the studied dimers and trimers. It was found that the presence of a polar solvent decreased the energy barrier for the bridged proton transfer. However, it did not significantly affect the aromaticity and electronic structure. The SAPT results showed that the mutual polarization of the monomers in the dimer was weak and that the dispersion was responsible for most of the intermolecular attraction. The intermolecular hydrogen bonds seem to be much weaker than the intramolecular bridges. The TD-DFT results confirmed that the electronic excitations do not play any significant role in the intramolecular proton transfer. The CPMD results indicated that the protons are very labile in the hydrogen bridges. Short proton transfer and proton-sharing events were observed, and a correlation between them in the twin bridges was noticed, especially for the first investigated compound. Full article

(This article belongs to the Special Issue Exploring Inter- and Intramolecular Interactions as Building Blocks of Larger Systems)

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21 pages, 4208 KiB

Open AccessEditor’s ChoiceReview

Azulene Moiety as Electron Reservoir in Positively Charged Systems; A Short Survey

by Alexandru C. Razus

Symmetry 2021, 13(4), 526; https://doi.org/10.3390/sym13040526 - 24 Mar 2021

Cited by 14 | Viewed by 3892

Abstract

The non-alternant aromatic azulene, an isomer of alternant naphthalene, differs from the latter in peculiar properties. The large polarization of the π-electron system over the seven and five rings gives to azulene electrophile property a pronounced tendency to donate electrons to an acceptor, [...] Read more.

The non-alternant aromatic azulene, an isomer of alternant naphthalene, differs from the latter in peculiar properties. The large polarization of the π-electron system over the seven and five rings gives to azulene electrophile property a pronounced tendency to donate electrons to an acceptor, substituted at azulene 1 position. This paper presents cases in which azulene transfers electrons to a suitable acceptor as methylium ions, positive charged heteroaromatics and examples of neutral molecules that can accept electrons. The proposed product synthesis was outlined and the expected electron transfer was highlighted by analyzing the NMR, UV-Vis spectra and the pK_R⁺ values. Full article

(This article belongs to the Special Issue Electrochemical Behavior of the Nonbenzenoid Aromatic Hydrocarbon Azulene and Its Derivatives)

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6 pages, 304 KiB

Open AccessEditor’s ChoiceArticle

What Is the Size and Shape of a Wave Packet?

by Larry S. Schulman

Symmetry 2021, 13(4), 527; https://doi.org/10.3390/sym13040527 - 24 Mar 2021

Cited by 2 | Viewed by 1775

Abstract

Under pure quantum evolution, for a wave packet that diffuses (like a Gaussian), scattering can cause localization. Other forms of the wave function, spreading more rapidly than a Gaussian, are unlikely to localize. Full article

(This article belongs to the Special Issue Symmetries in Quantum Mechanics and Statistical Physics)

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18 pages, 584 KiB

Open AccessEditor’s ChoiceArticle

Atomic Cascade Computations

by Stephan Fritzsche, Patrick Palmeri and Stefan Schippers

Symmetry 2021, 13(3), 520; https://doi.org/10.3390/sym13030520 - 23 Mar 2021

Cited by 26 | Viewed by 3666

Abstract

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these [...] Read more.

Atomic cascades are ubiquitous in nature and they have been explored within very different scenarios, from precision measurements to the modeling of astrophysical spectra, and up to the radiation damage in biological matter. However, up to the present, a quantitative analysis of these cascades often failed because of their inherent complexity. Apart from utilizing the rotational symmetry of atoms and a proper distinction of different physical schemes, a hierarchy of useful approaches is therefore needed in order to keep cascade computations feasible. We here suggest a classification of atomic cascades and demonstrate how they can be modeled within the framework of the Jena Atomic Calculator. As an example, we shall compute within a configuration-average approach the stepwise decay cascade of atomic magnesium, following a

1 s

inner-shell ionization, and simulate the corresponding (final) ion distribution. Our classification of physical scenarios (schemes) and the hierarchy of computational approaches are both flexible to further refinements as well as to complex shell structures of the atoms and ions, for which the excitation and decay dynamics need to be modeled in good detail. Full article

(This article belongs to the Special Issue Development of New Methods in Atomic and Molecular Theory)

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38 pages, 2536 KiB

Open AccessEditor’s ChoiceArticle

Projected-Reflected Subgradient-Extragradient Method and Its Real-World Applications

by Aviv Gibali, Olaniyi S. Iyiola, Lanre Akinyemi and Yekini Shehu

Symmetry 2021, 13(3), 489; https://doi.org/10.3390/sym13030489 - 16 Mar 2021

Cited by 8 | Viewed by 2124

Abstract

Our main focus in this work is the classical variational inequality problem with Lipschitz continuous and pseudo-monotone mapping in real Hilbert spaces. An adaptive reflected subgradient-extragradient method is presented along with its weak convergence analysis. The novelty of the proposed method lies in [...] Read more.

Our main focus in this work is the classical variational inequality problem with Lipschitz continuous and pseudo-monotone mapping in real Hilbert spaces. An adaptive reflected subgradient-extragradient method is presented along with its weak convergence analysis. The novelty of the proposed method lies in the fact that only one projection onto the feasible set in each iteration is required, and there is no need to know/approximate the Lipschitz constant of the cost function a priori. To illustrate and emphasize the potential applicability of the new scheme, several numerical experiments and comparisons in tomography reconstruction, Nash–Cournot oligopolistic equilibrium, and more are presented. Full article

(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems)

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27 pages, 2549 KiB

Open AccessEditor’s ChoiceArticle

Tensor-Based Adaptive Filtering Algorithms

by Laura-Maria Dogariu, Cristian-Lucian Stanciu, Camelia Elisei-Iliescu, Constantin Paleologu, Jacob Benesty and Silviu Ciochină

Symmetry 2021, 13(3), 481; https://doi.org/10.3390/sym13030481 - 15 Mar 2021

Cited by 25 | Viewed by 3449

Abstract

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is [...] Read more.

Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and the channels can be grouped in the form of rank-1 tensors. Nevertheless, the approach could be further extended for single-input/single-output system identification scenarios, where the impulse responses (of more general forms) can be modeled as higher-rank tensors. As compared to the conventional adaptive filters, which involve a single (usually long) filter for the estimation of the global impulse response, the tensor-based algorithms achieve faster convergence rate and tracking, while also providing better accuracy of the solution. Simulation results support the theoretical findings and indicate the advantages of the tensor-based algorithms over the conventional ones, in terms of the main performance criteria. Full article

(This article belongs to the Special Issue Advances in Symmetric Tensor Decomposition Methods)

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9 pages, 284 KiB

Open AccessEditor’s ChoiceArticle

Connecting in the Dirac Equation the Clifford Algebra of Lorentz Invariance with the Lie Algebra of SU(N) Gauge Symmetry

by Eckart Marsch and Yasuhito Narita

Symmetry 2021, 13(3), 475; https://doi.org/10.3390/sym13030475 - 14 Mar 2021

Cited by 6 | Viewed by 1805

Abstract

In this paper, we study possible mathematical connections of the Clifford algebra with the

s u (N)

-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal

S U (N)

gauge-symmetry for a [...] Read more.

In this paper, we study possible mathematical connections of the Clifford algebra with the

s u (N)

-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal

S U (N)

gauge-symmetry for a massive spin one-half fermion described by the Dirac equation. The related matrix algebra is worked out in particular for the

S U (2)

symmetry and outlined as well for the color gauge group

S U (3)

. Possible perspectives of this approach to unification of symmetries are briefly discussed. The calculations make extensive use of tensor multiplication of the matrices involved, whereby our focus is on revisiting the Coleman–Mandula theorem. This permits us to construct unified symmetries between Lorentz invariance and gauge symmetry in a direct product sense. Full article

(This article belongs to the Section Physics)

10 pages, 919 KiB

Open AccessEditor’s ChoiceArticle

Theoretical Study of closo-Borate Anions [B_nH_n]²⁻ (n = 5–12): Bonding, Atomic Charges, and Reactivity Analysis

by Ilya N. Klyukin, Yulia S. Vlasova, Alexander S. Novikov, Andrey P. Zhdanov, Konstantin Y. Zhizhin and Nikolay T. Kuznetsov

Symmetry 2021, 13(3), 464; https://doi.org/10.3390/sym13030464 - 12 Mar 2021

Cited by 21 | Viewed by 3321

Abstract

This study has focused on the structure, bonding, and reactivity analysis of closo-borate anions [B_nH_n]²⁻ (n = 5–12). Several descriptors of B–H interactions have been calculated. It has been found that the values of electron density [...] Read more.

This study has focused on the structure, bonding, and reactivity analysis of closo-borate anions [B_nH_n]²⁻ (n = 5–12). Several descriptors of B–H interactions have been calculated. It has been found that the values of electron density and total energy at bond critical point are the most useful descriptors for investigation of B–H interactions. Using results from the descriptor analysis, one may conclude that orbital interactions in [B_nH_n]²⁻ increase with increasing the boron cluster size. Several approaches to estimate atomic charges have been applied. Boron atoms in apical positions have more negative values of atomic charges as compared with atoms from equatorial positions. The mean values of boron and hydrogen atomic charges tend to be more positive with the increasing of boron cluster size. Global and local reactivity descriptors using conceptual density functional theory (DFT) theory have been calculated. Based on this theory, the closo-borate anions [B_nH_n]²⁻ (n = 5–9) can be considered strong and moderate electrophiles, while the closo-borate anions [B_nH_n]²⁻ (n = 10–12) can be considered marginal electrophiles. Fukui functions for electrophilic attack have been calculated. Fukui functions correlate well with atomic charges of the closo-borate anions. Boron atoms in apical positions have the most positive values of Fukui functions. Full article

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

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14 pages, 1749 KiB

Open AccessEditor’s ChoiceArticle

Two Faces of Water in the Formation and Stabilization of Multicomponent Crystals of Zwitterionic Drug-Like Compounds

by Artem O. Surov, Nikita A. Vasilev, Andrei V. Churakov, Olga D. Parashchuk, Sergei V. Artobolevskii, Oleg A. Alatortsev, Denis E. Makhrov and Mikhail V. Vener

Symmetry 2021, 13(3), 425; https://doi.org/10.3390/sym13030425 - 6 Mar 2021

Cited by 14 | Viewed by 3544

Abstract

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of [...] Read more.

Two new hydrated multicomponent crystals of zwitterionic 2-aminonicotinic acid with maleic and fumaric acids have been obtained and thoroughly characterized by a variety of experimental (X-ray analysis and terahertz Raman spectroscopy) and theoretical periodic density functional theory calculations, followed by Bader analysis of the crystalline electron density) techniques. It has been found that the Raman-active band in the region of 300 cm⁻¹ is due to the vibrations of the intramolecular O-H...O bond in the maleate anion. The energy/enthalpy of the intermolecular hydrogen bonds was estimated by several empirical approaches. An analysis of the interaction networks reflects the structure-directing role of the water molecule in the examined multicomponent crystals. A general scheme has been proposed to explain the proton transfer between the components during the formation of multicomponent crystals in water. Water molecules were found to play the key role in this process, forming a “water wire” between the COOH group of the dicarboxylic acid and the COO^– group of the zwitterion and the rendering crystal lattice of the considered multicomponent crystals. Full article

(This article belongs to the Special Issue Quantum Chemistry)

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56 pages, 725 KiB

Open AccessEditor’s ChoiceArticle

Lorentz Symmetry Group, Retardation and Energy Transformations in a Relativistic Engine

by Shailendra Rajput, Asher Yahalom and Hong Qin

Symmetry 2021, 13(3), 420; https://doi.org/10.3390/sym13030420 - 5 Mar 2021

Cited by 12 | Viewed by 1945

Abstract

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot [...] Read more.

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in

\frac{1}{c}

and no lower order relativistic engine effect on the energy exists. Full article

(This article belongs to the Special Issue Symmetry and Geometry in Physics)

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50 pages, 639 KiB

Open AccessEditor’s ChoiceArticle

Power Law Duality in Classical and Quantum Mechanics

by Akira Inomata and Georg Junker

Symmetry 2021, 13(3), 409; https://doi.org/10.3390/sym13030409 - 3 Mar 2021

Cited by 5 | Viewed by 2724

Abstract

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is [...] Read more.

The Newton–Hooke duality and its generalization to arbitrary power laws in classical, semiclassical and quantum mechanics are discussed. We pursue a view that the power-law duality is a symmetry of the action under a set of duality operations. The power dual symmetry is defined by invariance and reciprocity of the action in the form of Hamilton’s characteristic function. We find that the power-law duality is basically a classical notion and breaks down at the level of angular quantization. We propose an ad hoc procedure to preserve the dual symmetry in quantum mechanics. The energy-coupling exchange maps required as part of the duality operations that take one system to another lead to an energy formula that relates the new energy to the old energy. The transformation property of the Green function satisfying the radial Schrödinger equation yields a formula that relates the new Green function to the old one. The energy spectrum of the linear motion in a fractional power potential is semiclassically evaluated. We find a way to show the Coulomb–Hooke duality in the supersymmetric semiclassical action. We also study the confinement potential problem with the help of the dual structure of a two-term power potential. Full article

(This article belongs to the Special Issue Symmetries in Quantum Mechanics and Statistical Physics)

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26 pages, 1194 KiB

Open AccessEditor’s ChoiceReview

Siberian Snakes, Figure-8 and Spin Transparency Techniques for High Precision Experiments with Polarized Hadron Beams in Colliders

by Yaroslav S. Derbenev, Yury N. Filatov, Anatoliy M. Kondratenko, Mikhail A. Kondratenko and Vasiliy S. Morozov

Symmetry 2021, 13(3), 398; https://doi.org/10.3390/sym13030398 - 28 Feb 2021

Cited by 9 | Viewed by 2549

Abstract

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the [...] Read more.

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the recently elicited advantageous possibility to conduct high precision experiments in a regime of the spin transparency (ST) when the design global spin tune is close to zero. In this regime, the polarization control is realized by use of spin navigators (SN), which are compact special insertions of magnets dedicated to a high flexibility spin manipulation including frequent spin flips. Full article

(This article belongs to the Special Issue Advances in Spin Physics)

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19 pages, 20807 KiB

Open AccessEditor’s ChoiceArticle

A Novel Plaintext-Related Color Image Encryption Scheme Based on Cellular Neural Network and Chen’s Chaotic System

by Renxiu Zhang, Longfei Yu, Donghua Jiang, Wei Ding, Jian Song, Kuncheng He and Qun Ding

Symmetry 2021, 13(3), 393; https://doi.org/10.3390/sym13030393 - 28 Feb 2021

Cited by 22 | Viewed by 2237

Abstract

To address the problem that traditional stream ciphers are not sensitive to changes in the plaintext, a novel plaintext-related color image encryption scheme is proposed in this paper, which combines the 6-dimensional cellular neural network (CNN) and Chen’s chaotic system. This encryption scheme [...] Read more.

To address the problem that traditional stream ciphers are not sensitive to changes in the plaintext, a novel plaintext-related color image encryption scheme is proposed in this paper, which combines the 6-dimensional cellular neural network (CNN) and Chen’s chaotic system. This encryption scheme belongs to symmetric cryptography. In the proposed scheme, the initial key and switching function generated by the plaintext image are first utilized to control the CNN to complete the scrambling process. Then, Chen’s chaotic system is used to diffuse the scrambled image for realizing higher security. Finally, extensive performance evaluation is undertaken to validate the proposed scheme’s ability to offer the necessary security. Furthermore, the scheme is compared alongside state-of-the-art algorithms to establish its efficiency. Full article

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16 pages, 587 KiB

Open AccessEditor’s ChoiceArticle

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

by G. Fiorella Burgio, Hans-Josef Schulze, Isaac Vidaña and Jin-Biao Wei

Symmetry 2021, 13(3), 400; https://doi.org/10.3390/sym13030400 - 28 Feb 2021

Cited by 15 | Viewed by 3241

Abstract

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use [...] Read more.

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now,

2 . 14_{- 0.09}^{+ 0.10} M_{⊙}

for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5

M_{⊙}

deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility. Full article

(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)

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16 pages, 3495 KiB

Open AccessEditor’s ChoiceArticle

A Model Predictive Control with Preview-Follower Theory Algorithm for Trajectory Tracking Control in Autonomous Vehicles

by Ying Xu, Wentao Tang, Biyun Chen, Li Qiu and Rong Yang

Symmetry 2021, 13(3), 381; https://doi.org/10.3390/sym13030381 - 26 Feb 2021

Cited by 30 | Viewed by 3727

Abstract

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module [...] Read more.

Research on trajectory tracking is crucial for the development of autonomous vehicles. This paper presents a trajectory tracking scheme by utilizing model predictive control (MPC) and preview-follower theory (PFT), which includes a reference generation module and a MPC controller. The reference generation module could calculate reference lateral acceleration at the preview point by PFT to update state variables, and generate a reference yaw rate in each prediction point. Since the preview range is increased, PFT makes the calculation of yaw rate more accurate. Through physical constraints, the MPC controller can achieve the best tracking of the reference path. The MPC problem is formulated as a linear time-varying (LTV) MPC controller to achieve a predictive model from nonlinear vehicle dynamics to continuous online linearization. The MPC-PFT controller method performs well by increasing the effective length of the reference path. Compared with MPC and PFT controllers, the effectiveness and robustness of the proposed method are proved by simulations of two typical working conditions. Full article

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10 pages, 265 KiB

Open AccessEditor’s ChoiceArticle

Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function

by Alina Alb Lupaş and Georgia Irina Oros

Symmetry 2021, 13(2), 327; https://doi.org/10.3390/sym13020327 - 17 Feb 2021

Cited by 31 | Viewed by 2826

Abstract

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types [...] Read more.

Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. Full article

(This article belongs to the Section Mathematics)

24 pages, 544 KiB

Open AccessEditor’s ChoiceArticle

Coupling Hadron-Hadron Thresholds within a Chiral Quark Model Approach

by Pablo G. Ortega and David R. Entem

Symmetry 2021, 13(2), 279; https://doi.org/10.3390/sym13020279 - 6 Feb 2021

Cited by 16 | Viewed by 2334

Abstract

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the

X (3872)

was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state [...] Read more.

Heavy hadron spectroscopy was well understood within the naive quark model until the end of the past century. However, in 2003, the

X (3872)

was discovered, with puzzling properties difficult to understand in the simple naive quark model picture. This state made clear that excited states of heavy mesons should be coupled to two-meson states in order to understand not only the masses but, in some cases, unexpected decay properties. In this work, we will give an overview of a way in which the naive quark model can be complemented with the coupling to two hadron thresholds. This program has been already applied to the heavy meson spectrum with the chiral quark model, and we show some examples where thresholds are of special relevance. Full article

(This article belongs to the Special Issue Advances in Chiral Quark Models)

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14 pages, 2702 KiB

Open AccessEditor’s ChoiceArticle

Supramolecular Chirogenesis in Bis-Porphyrin: Crystallographic Structure and CD Spectra for a Complex with a Chiral Guanidine Derivative

by Irina Osadchuk, Nele Konrad, Khai-Nghi Truong, Kari Rissanen, Eric Clot, Riina Aav, Dzmitry Kananovich and Victor Borovkov

Symmetry 2021, 13(2), 275; https://doi.org/10.3390/sym13020275 - 5 Feb 2021

Cited by 8 | Viewed by 4036

Abstract

The complexation of (3aR,7aR)-N-(3,5-bis(trifluoromethyl)phenyl)octahydro-2H-benzo[d]imidazol-2-imine (BTI), as a guest, to ethane-bridged bis(zinc octaethylporphyrin), bis(ZnOEP), as a host, has been studied by means of ultraviolet-visible (UV-Vis) and circular dichroism (CD) absorption spectroscopies, single crystal X-ray [...] Read more.

The complexation of (3aR,7aR)-N-(3,5-bis(trifluoromethyl)phenyl)octahydro-2H-benzo[d]imidazol-2-imine (BTI), as a guest, to ethane-bridged bis(zinc octaethylporphyrin), bis(ZnOEP), as a host, has been studied by means of ultraviolet-visible (UV-Vis) and circular dichroism (CD) absorption spectroscopies, single crystal X-ray diffraction, and computational simulation. The formation of 1:2 host-guest complex was established by X-ray diffraction and UV-Vis titration studies. Two guest BTI molecules are located at the opposite sides of two porphyrin subunits of bis(ZnOEP) host, which is resting in the anti-conformation. The complexation of BTI molecules proceed via coordination of the imine nitrogens to the zinc ions of each porphyrin subunit of the host. Such supramolecular organization of the complex results in a screw arrangement of the two porphyrin subunits, inducing a strong CD signal in the Soret (B) band region. The corresponding DFT computational studies are in a good agreement with the experimental results and prove the presence of 1:2 host-guest complex as the major component in the solution (97.7%), but its optimized geometry differs from that observed in the solid-state. The UV-Vis and CD spectra simulated by using the solution-state geometry and the TD-DFT/ωB97X-D/cc-pVDZ + SMD (CH2Cl2) level of theory reproduced the experimentally obtained UV-Vis and CD spectra and confirmed the difference between the solid-state and solution structures. Moreover, it was shown that CD spectrum is very sensitive to the spatial arrangement of porphyrin subunits. Full article

(This article belongs to the Special Issue Chiral Auxiliaries and Chirogenesis II)

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21 pages, 10706 KiB

Open AccessEditor’s ChoiceArticle

Global Sensitivity Analysis of Quantiles: New Importance Measure Based on Superquantiles and Subquantiles

by Zdeněk Kala

Symmetry 2021, 13(2), 263; https://doi.org/10.3390/sym13020263 - 4 Feb 2021

Cited by 13 | Viewed by 6173

Abstract

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to [...] Read more.

The article introduces quantile deviation l as a new sensitivity measure based on the difference between superquantile and subquantile. New global sensitivity indices based on the square of l are presented. The proposed sensitivity indices are compared with quantile-oriented sensitivity indices subordinated to contrasts and classical Sobol sensitivity indices. The comparison is performed in a case study using a non-linear mathematical function, the output of which represents the elastic resistance of a slender steel member under compression. The steel member has random imperfections that reduce its load-carrying capacity. The member length is a deterministic parameter that significantly changes the sensitivity of the output resistance to the random effects of input imperfections. The comparison of the results of three types of global sensitivity analyses shows the rationality of the new quantile-oriented sensitivity indices, which have good properties similar to classical Sobol indices. Sensitivity indices subordinated to contrasts are the least comprehensible because they exhibit the strongest interaction effects between inputs. However, using total indices, all three types of sensitivity analyses lead to approximately the same conclusions. The similarity of the results of two quantile-oriented and Sobol sensitivity analysis confirms that Sobol sensitivity analysis is empathetic to the structural reliability and that the variance is one of the important characteristics significantly influencing the low quantile of resistance. Full article

(This article belongs to the Special Issue Symmetric and Asymmetric Data in Solution Models)

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12 pages, 1704 KiB

Open AccessEditor’s ChoiceArticle

Self-Assembly of Hydrogen-Bonded Cage Tetramers of Phosphonic Acid

by Ivan S. Giba and Peter M. Tolstoy

Symmetry 2021, 13(2), 258; https://doi.org/10.3390/sym13020258 - 4 Feb 2021

Cited by 9 | Viewed by 3094

Abstract

The self-association of phosphonic acids with general formula RP(O)(OH)₂ in solution state remains largely unexplored. The general understanding is that such molecules form multiple intermolecular hydrogen bonds, but the stoichiometry of self-associates and the bonding motifs are unclear. In this work, we [...] Read more.

The self-association of phosphonic acids with general formula RP(O)(OH)₂ in solution state remains largely unexplored. The general understanding is that such molecules form multiple intermolecular hydrogen bonds, but the stoichiometry of self-associates and the bonding motifs are unclear. In this work, we report the results of the study of self-association of tert-butylphosphonic acid using low temperature liquid-state ¹H and ³¹P NMR spectroscopy (100 K; CDF₃/CDF₂Cl) and density functional theory (DFT) calculations. For the first time, we demonstrate conclusively that polar aprotic medium tert-butylphosphonic acid forms highly symmetric cage-like tetramers held by eight OHO hydrogen bonds, which makes the complex quite stable. In these associates. each phosphonic acid molecule is bonded to three other molecules by forming two hydrogen bonds as proton donor and two hydrogen bonds as proton acceptor. Though the structure of such cage-like tetramers is close to tetrahedral, the formal symmetry of the self-associate is C₂. Full article

(This article belongs to the Special Issue Exploring Inter- and Intramolecular Interactions as Building Blocks of Larger Systems)

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9 pages, 276 KiB

Open AccessEditor’s ChoiceArticle

Historical Introduction to Chiral Quark Models

by Francisco Fernández and Jorge Segovia

Symmetry 2021, 13(2), 252; https://doi.org/10.3390/sym13020252 - 2 Feb 2021

Cited by 10 | Viewed by 2074

Abstract

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to [...] Read more.

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature. Full article

(This article belongs to the Section Physics)

15 pages, 275 KiB

Open AccessEditor’s ChoiceArticle

Adjoint Operations in Twist-Products of Lattices

by Ivan Chajda and Helmut Länger

Symmetry 2021, 13(2), 253; https://doi.org/10.3390/sym13020253 - 2 Feb 2021

Cited by 1 | Viewed by 2195

Abstract

Given an integral commutative residuated lattices

L = (L, \lor, \land)

, its full twist-product

(L^{2}, ⊔, ⊓)

can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and [...] Read more.

Given an integral commutative residuated lattices

L = (L, \lor, \land)

, its full twist-product

(L^{2}, ⊔, ⊓)

can be endowed with two binary operations ⊙ and ⇒ introduced formerly by M. Busaniche and R. Cignoli as well as by C. Tsinakis and A. M. Wille such that it becomes a commutative residuated lattice. For every

a \in L

we define a certain subset

P_{a} (L)

of

L^{2}

. We characterize when

P_{a} (L)

is a sublattice of the full twist-product

(L^{2}, ⊔, ⊓)

. In this case

P_{a} (L)

together with some natural antitone involution

^{'}

becomes a pseudo-Kleene lattice. If

L

is distributive then

(P_{a} (L), ⊔, ⊓,^{'})

becomes a Kleene lattice. We present sufficient conditions for

P_{a} (L)

being a subalgebra of

(L^{2}, ⊔, ⊓, ⊙, \Rightarrow)

and thus for ⊙ and ⇒ being a pair of adjoint operations on

P_{a} (L)

. Finally, we introduce another pair ⊙ and ⇒ of adjoint operations on the full twist-product of a bounded commutative residuated lattice such that the resulting algebra is a bounded commutative residuated lattice satisfying the double negation law, and we investigate when

P_{a} (L)

is closed under these new operations. Full article

(This article belongs to the Section Mathematics)

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25 pages, 3327 KiB

Open AccessEditor’s ChoiceArticle

An Improved Whale Optimization Algorithm with Random Evolution and Special Reinforcement Dual-Operation Strategy Collaboration

by Qibing Jin, Zhonghua Xu and Wu Cai

Symmetry 2021, 13(2), 238; https://doi.org/10.3390/sym13020238 - 31 Jan 2021

Cited by 29 | Viewed by 3779

Abstract

In view of the slow convergence speed, difficulty of escaping from the local optimum, and difficulty maintaining the stability associated with the basic whale optimization algorithm (WOA), an improved WOA algorithm (REWOA) is proposed based on dual-operation strategy collaboration. Firstly, different evolutionary strategies [...] Read more.

In view of the slow convergence speed, difficulty of escaping from the local optimum, and difficulty maintaining the stability associated with the basic whale optimization algorithm (WOA), an improved WOA algorithm (REWOA) is proposed based on dual-operation strategy collaboration. Firstly, different evolutionary strategies are integrated into different dimensions of the algorithm structure to improve the convergence accuracy and the randomization operation of the random Gaussian distribution is used to increase the diversity of the population. Secondly, special reinforcements are made to the process involving whales searching for prey to enhance their exclusive exploration or exploitation capabilities, and a new skip step factor is proposed to enhance the optimizer’s ability to escape the local optimum. Finally, an adaptive weight factor is added to improve the stability of the algorithm and maintain a balance between exploration and exploitation. The effectiveness and feasibility of the proposed REWOA are verified with the benchmark functions and different experiments related to the identification of the Hammerstein model. Full article

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10 pages, 2216 KiB

Open AccessEditor’s ChoiceArticle

Bootstrapped Motion of an Agent on an Adaptive Resource Landscape

by Trung V. Phan, Gao Wang, Liyu Liu and Robert H. Austin

Symmetry 2021, 13(2), 225; https://doi.org/10.3390/sym13020225 - 29 Jan 2021

Cited by 7 | Viewed by 2428

Abstract

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. [...] Read more.

We theoretically show that isolated agents that locally and symmetrically consume resources and sense positive resource gradients can generate constant motion via bootstrapped resource gradients in the absence of any externally imposed gradients, and we show a realization of this motion using robots. This self-generated agent motion can be coupled with neighboring agents to act as a spontaneously broken symmetry seed for emergent collective dynamics. We also show that in a sufficiently weak externally imposed gradient, it is possible for an agent to move against an external resource gradient due to the local resource depression on the landscape created by an agent. This counter-intuitive boot-strapped motion against an external gradient is demonstrated with a simple robot system on an light-emitting diode (LED) light-board. Full article

(This article belongs to the Special Issue Emergent Order Parameters in Complex Biophysical Systems)

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26 pages, 5952 KiB

Open AccessEditor’s ChoiceArticle

An Improved Whale Algorithm for Support Vector Machine Prediction of Photovoltaic Power Generation

by Yu-Wei Liu, Huan Feng, Heng-Yi Li and Ling-Ling Li

Symmetry 2021, 13(2), 212; https://doi.org/10.3390/sym13020212 - 28 Jan 2021

Cited by 16 | Viewed by 2305

Abstract

Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically [...] Read more.

Accurate prediction of photovoltaic power is conducive to the application of clean energy and sustainable development. An improved whale algorithm is proposed to optimize the Support Vector Machine model. The characteristic of the model is that it needs less training data to symmetrically adapt to the prediction conditions of different weather, and has high prediction accuracy in different weather conditions. This study aims to (1) select light intensity, ambient temperature and relative humidity, which are strictly related to photovoltaic output power as the input data; (2) apply wavelet soft threshold denoising to preprocess input data to reduce the noise contained in input data to symmetrically enhance the adaptability of the prediction model in different weather conditions; (3) improve the whale algorithm by using tent chaotic mapping, nonlinear disturbance and differential evolution algorithm; (4) apply the improved whale algorithm to optimize the Support Vector Machine model in order to improve the prediction accuracy of the prediction model. The experiment proves that the short-term prediction model of photovoltaic power based on symmetry concept achieves ideal accuracy in different weather. The systematic method for output power prediction of renewable energy is conductive to reducing the workload of predicting the output power and to promoting the application of clean energy and sustainable development. Full article

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47 pages, 5068 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics

by Dietrich Haase, Gunter Hermann, Jörn Manz, Vincent Pohl and Jean Christophe Tremblay

Symmetry 2021, 13(2), 205; https://doi.org/10.3390/sym13020205 - 27 Jan 2021

Cited by 11 | Viewed by 3023

Abstract

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D_6h [...] Read more.

Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D_6h and D_4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses. Full article

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

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22 pages, 2529 KiB

Open AccessEditor’s ChoiceArticle

Probing the Nuclear Equation of State from the Existence of a ∼2.6 M_⊙ Neutron Star: The GW190814 Puzzle

by Alkiviadis Kanakis-Pegios, Polychronis S. Koliogiannis and Charalampos C. Moustakidis

Symmetry 2021, 13(2), 183; https://doi.org/10.3390/sym13020183 - 24 Jan 2021

Cited by 37 | Viewed by 3251

Abstract

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass

\sim {2.59}_{- 0.09}^{+ 0.08} M_{⊙}

, as a component of a system where the main companion was a black hole with mass

\sim 23 M_{⊙}

. [...] Read more.

On 14 August 2019, the LIGO/Virgo collaboration observed a compact object with mass

\sim {2.59}_{- 0.09}^{+ 0.08} M_{⊙}

, as a component of a system where the main companion was a black hole with mass

\sim 23 M_{⊙}

. A scientific debate initiated concerning the identification of the low mass component, as it falls into the neutron star–black hole mass gap. The understanding of the nature of GW190814 event will offer rich information concerning open issues, the speed of sound and the possible phase transition into other degrees of freedom. In the present work, we made an effort to probe the nuclear equation of state along with the GW190814 event. Firstly, we examine possible constraints on the nuclear equation of state inferred from the consideration that the low mass companion is a slow or rapidly rotating neutron star. In this case, the role of the upper bounds on the speed of sound is revealed, in connection with the dense nuclear matter properties. Secondly, we systematically study the tidal deformability of a possible high mass candidate existing as an individual star or as a component one in a binary neutron star system. As the tidal deformability and radius are quantities very sensitive on the neutron star equation of state, they are excellent counters on dense matter properties. We conjecture that similar isolated neutron stars or systems may exist in the universe and their possible future observation will shed light on the maximum neutron star mass problem. Full article

(This article belongs to the Special Issue The Nuclear Physics of Neutron Stars)

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20 pages, 623 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nucleon Structure and Spin Effects in Elastic Hadron Scattering

by Oleg Selyugin

Symmetry 2021, 13(2), 164; https://doi.org/10.3390/sym13020164 - 21 Jan 2021

Cited by 6 | Viewed by 1878

Abstract

Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic

p p

scattering, and spin-dependent differential cross sections and spin correlation parameters are calculated. The spin [...] Read more.

Soft diffraction phenomena in elastic nucleon scattering are considered from the viewpoint of the spin dependence of the interaction potential. Spin-dependent pomeron effects are analyzed for elastic

p p

scattering, and spin-dependent differential cross sections and spin correlation parameters are calculated. The spin correlation parameter

A_{N}

is examined on the basis of experimental data from

\sqrt{s} = 4.9

GeV up to

23.4

GeV in the framework of the extended High Energy Generalized Structure (HEGS) model. It is shown that the existing experimental data of proton-proton and proton-antiproton elastic scattering at high energy in the region of the diffraction minimum and at large momentum transfer give the support of the existence of the energy-independent part of the hadron spin flip amplitude. Full article

(This article belongs to the Special Issue Advances in Spin Physics)

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17 pages, 15366 KiB

Open AccessEditor’s ChoiceArticle

The Symmetric Nature of the Position Distribution of the Human Body Center of Gravity during Propelling Manual Wheelchairs with Innovative Propulsion Systems

by Bartosz Wieczorek, Mateusz Kukla and Łukasz Warguła

Symmetry 2021, 13(1), 154; https://doi.org/10.3390/sym13010154 - 19 Jan 2021

Cited by 14 | Viewed by 3614

Abstract

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a [...] Read more.

Objective: The main objective of the tests conducted was to analyze the position variability of the human body’s center of gravity during propelling the wheelchair, and to demonstrate the properties enabling the description of this variability by means of plane figures with a symmetry axis. A secondary objective was to show the impact of the used manual propulsion type and the wheelchair inclination angle in relation to the plane on the dimensions of the position variability areas of the center of gravity. Method and materials: Three patients participated in the research representing 50 centiles of anthropometric dimensions. Each patient carried out fifteen measurement tests on three wheelchairs for three inclination angles of the wheelchair frame in relation to the level. Each measurement test consisted of five propulsion cycles for which the positions of the center of gravity were determined with the sampling frequency of 100 Hz. The measured positions of the center of gravity were approximated with ellipses containing 95.4% of the measurements conducted, assuming their dimension scaling basis in the form of the double value of standard deviation defined based on the registered results. Results: Based on the measurements conducted, the average values of five ellipses parameters were determined for nine cases in which a variable was the type of wheelchair propulsion and its inclination angle in relation to the level. The area of the highest variability of the position of the center of gravity was measured for the wheelchair with a multispeed transmission. The average dimensions of the ellipse semi-axis amounted to 108.53 mm for the semi-axis a and 29.75 for the semi-axis b, the average position of the ellipse center amounted to x = 114.51 mm and y = −10.53 mm, and the average inclination angle of the ellipse α amounted to −6.92°. The area of the lowest variability of the position of the center of gravity was measured for the wheelchair with a hybrid transmission. In this case, the average dimensions of the ellipse semi-axis amounted to 64.07 mm for the semi-axis a and 33.85 for the semi-axis b; whereas, the average position of the ellipse center amounted to x = 245.13 mm and y = −28.24 mm, and the average inclination angle of the ellipse α amounted to −0.56°. Full article

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20 pages, 1204 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Discrete-Time Pole-Region Robust Controller for Magnetic Levitation Plant

by Mária Hypiusová and Danica Rosinová

Symmetry 2021, 13(1), 142; https://doi.org/10.3390/sym13010142 - 16 Jan 2021

Cited by 8 | Viewed by 2563

Abstract

Robust pole-placement based on convex

D_{R}

-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is [...] Read more.

Robust pole-placement based on convex

D_{R}

-regions belongs to the efficient control design techniques for real systems, providing computationally tractable pole-placement design algorithms. The problem arises in the discrete-time domain when the relative damping is prescribed since the corresponding discrete-time domain is non-convex, having a “cardioid” shape. In this paper, we further develop our recent results on the inner convex approximations of the cardioid, present systematical analysis of its design parameters and their influence on the corresponding closed loop performance (measured by standard integral of absolute error (IAE) and Total Variance criteria). The application of a robust controller designed with the proposed convex approximation of the discrete-time pole region is illustrated and evaluated on a real laboratory magnetic levitation plant. Full article

(This article belongs to the Special Issue PID Control and Symmetry)

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