Symmetry

14 pages, 9517 KiB

Open AccessEditor’s ChoiceArticle

A Family of 1D Chaotic Maps without Equilibria

by Marcin Lawnik, Lazaros Moysis and Christos Volos

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

Cited by 4 | Viewed by 1135

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

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

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

► Show Figures

Figure 1

17 pages, 1204 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Constantin Fetecau and Costică Moroşanu

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

Cited by 3 | Viewed by 876

Abstract

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

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

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

19 pages, 7215 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Cited by 1 | Viewed by 1173

Abstract

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

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

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

► Show Figures

Graphical abstract

26 pages, 16642 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Plamen G. Krastev

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

Cited by 11 | Viewed by 1374

Abstract

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

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

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

► Show Figures

Figure 1

19 pages, 2058 KiB

Open AccessEditor’s ChoiceArticle

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

by Mingqi Hu, Yanli Ren and Cien Chen

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

Cited by 1 | Viewed by 1544

Abstract

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

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

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

► Show Figures

Figure 1

12 pages, 6811 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Building an Equation of State Density Ladder

by Marc Salinas and Jorge Piekarewicz

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

Cited by 4 | Viewed by 905

Abstract

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

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

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

► Show Figures

Figure 1

18 pages, 324 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Expansion-Free Dissipative Fluid Spheres: Analytical Solutions

by Luis Herrera, Alicia Di Prisco and Justo Ospino

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

Cited by 8 | Viewed by 941

Abstract

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

Θ

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

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

Θ

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

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

30 pages, 3480 KiB

Open AccessFeature PaperEditor’s ChoiceReview

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

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

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

Cited by 9 | Viewed by 3188

Abstract

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

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

m_{0}

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

σ

, vector fields

(ω, ρ)

, and mesons with strangeness through the U(1)

_{A}

anomaly. In models with a large

m_{0}

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

σ

and vector fields

ω

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

_{A}

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

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

► Show Figures

Figure 1

27 pages, 13869 KiB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 4 | Viewed by 1303

Abstract

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

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

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

► Show Figures

Figure 1

28 pages, 825 KiB

Open AccessEditor’s ChoiceArticle

Near-Miss Symmetric Polyhedral Cages

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

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

Cited by 2 | Viewed by 1693

Abstract

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

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

P = 6

to

P = 20

with deformation of up to 10%. Full article

(This article belongs to the Section Mathematics)

► Show Figures

Figure 1

17 pages, 3212 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Classification of Blood Rheological Models through an Idealized Symmetrical Bifurcation

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

Symmetry 2023, 15(3), 630; https://doi.org/10.3390/sym15030630 - 02 Mar 2023

Cited by 5 | Viewed by 1902

Abstract

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

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

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

► Show Figures

Graphical abstract

15 pages, 313 KiB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 9 | Viewed by 1062

Abstract

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

η

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

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

η

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

η

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

(This article belongs to the Section Mathematics)

16 pages, 2144 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Viewed by 1140

Abstract

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

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

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

► Show Figures

Figure 1

22 pages, 1233 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Cited by 4 | Viewed by 1232

Abstract

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

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

H, A

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

\frac{E}{T}

). Thus, we examine the viability of

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

,

Z + \frac{E}{T}

and

h + \frac{E}{T}

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

t \bar{t}

,

V V

and

V h

production (where

V = W, Z

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

m_{A} \sim 1 - 2

TeV of the

m_{A}

vs.

tan β

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

5 σ

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

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

► Show Figures

Figure 1

10 pages, 2168 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Cited by 3 | Viewed by 2341

Abstract

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

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

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

► Show Figures

Figure 1

13 pages, 6325 KiB

Open AccessEditor’s ChoiceArticle

Electrochemical Studies of Azulene Modified Electrodes

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

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

Cited by 1 | Viewed by 1427

Abstract

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

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

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

► Show Figures

Figure 1

20 pages, 905 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Cited by 3 | Viewed by 1353

Abstract

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

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

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

► Show Figures

Figure 1

19 pages, 2126 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Teik-Cheng Lim

Symmetry 2023, 15(2), 462; https://doi.org/10.3390/sym15020462 - 09 Feb 2023

Cited by 3 | Viewed by 1368

Abstract

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

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

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

► Show Figures

Figure 1

21 pages, 380 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Potentials from the Polynomial Solutions of the Confluent Heun Equation

by Géza Lévai

Symmetry 2023, 15(2), 461; https://doi.org/10.3390/sym15020461 - 09 Feb 2023

Cited by 4 | Viewed by 1636

Abstract

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

z = 0

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

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

z = 0

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

H c (p, β, γ, δ, σ; z)

. One of these recovers the generalized Laguerre polynomials

L_{N}^{(α)}

, and another one the rationally extended

X_{1}

type Laguerre polynomials

{\hat{L}}_{N}^{(α)}

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

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

20 pages, 355 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Gravity as a Quantum Field Theory

by Roberto Percacci

Symmetry 2023, 15(2), 449; https://doi.org/10.3390/sym15020449 - 08 Feb 2023

Cited by 5 | Viewed by 2487

Abstract

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

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

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

33 pages, 11453 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Nonextensive Footprints in Dissipative and Conservative Dynamical Systems

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

Symmetry 2023, 15(2), 444; https://doi.org/10.3390/sym15020444 - 07 Feb 2023

Cited by 3 | Viewed by 1352

Abstract

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

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

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

► Show Figures

Figure 1

22 pages, 3802 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Making and Breaking—Insight into the Symmetry of Salen Analogues

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

Symmetry 2023, 15(2), 424; https://doi.org/10.3390/sym15020424 - 05 Feb 2023

Cited by 1 | Viewed by 1784

Abstract

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

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

ω

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

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

► Show Figures

Graphical abstract

35 pages, 542 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

More Insights into Symmetries in Multisymplectic Field Theories

by Arnoldo Guerra IV and Narciso Román-Roy

Symmetry 2023, 15(2), 390; https://doi.org/10.3390/sym15020390 - 01 Feb 2023

Cited by 4 | Viewed by 890

Abstract

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

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

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

12 pages, 3207 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Janina Kabatc-Borcz, Przemysław Czeleń and Agnieszka Skotnicka

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

Cited by 1 | Viewed by 1067

Abstract

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

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

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

► Show Figures

Figure 1

21 pages, 2060 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Ewa D. Raczyńska

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

Cited by 3 | Viewed by 890

Abstract

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

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

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

► Show Figures

Figure 1

20 pages, 756 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Popcorn Transitions and Approach to Conformality in Homogeneous Holographic Nuclear Matter

by Jesús Cruz Rojas, Tuna Demircik and Matti Järvinen

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

Cited by 9 | Viewed by 1977

Abstract

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

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

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

► Show Figures

Figure 1

23 pages, 1063 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Cristina Blaga, Paul Blaga and Tiberiu Harko

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

Cited by 5 | Viewed by 1217

Abstract

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

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

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

► Show Figures

Figure 1

10 pages, 1961 KiB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 5 | Viewed by 1715

Abstract

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

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

(This article belongs to the Section Life Sciences)

► Show Figures

Figure 1

12 pages, 698 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nanoscale Bending Dynamics in Mixed-Chain Lipid Membranes

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

Symmetry 2023, 15(1), 191; https://doi.org/10.3390/sym15010191 - 09 Jan 2023

Cited by 2 | Viewed by 1535

Abstract

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

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

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

► Show Figures

Figure 1

34 pages, 2488 KiB

Open AccessFeature PaperEditor’s ChoiceReview

The Proxy-SU(3) Symmetry in Atomic Nuclei

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

Symmetry 2023, 15(1), 169; https://doi.org/10.3390/sym15010169 - 06 Jan 2023

Cited by 9 | Viewed by 7189

Abstract

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

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

β

and

γ

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

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

► Show Figures

Figure 1

18 pages, 2415 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by József Cseh, Gábor Riczu and Judit Darai

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

Cited by 6 | Viewed by 1385

Abstract

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

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

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

► Show Figures

Figure 1

11 pages, 2622 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Mario Spagnuolo

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

Cited by 4 | Viewed by 1079

Abstract

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

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

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

► Show Figures

Figure 1

19 pages, 711 KiB

Open AccessEditor’s ChoiceArticle

SDSM: Secure Data Sharing for Multilevel Partnerships in IoT Based Supply Chain

by Chuntang Yu, Yongzhao Zhan and Muhammad Sohail

Symmetry 2022, 14(12), 2656; https://doi.org/10.3390/sym14122656 - 15 Dec 2022

Cited by 7 | Viewed by 1625

Abstract

Symmetric encryption algorithms enable rapid encryption of data in IoT based supply chains, which helps to alleviate the concerns of supply chain participants about privacy disclosure when sharing data. However, in supply chain management where multilevel partnerships exist universally, a pure symmetric encryption [...] Read more.

Symmetric encryption algorithms enable rapid encryption of data in IoT based supply chains, which helps to alleviate the concerns of supply chain participants about privacy disclosure when sharing data. However, in supply chain management where multilevel partnerships exist universally, a pure symmetric encryption scheme cannot provide efficient data sharing and fine-grained access control. To overcome these problems, this paper proposes a secure data sharing scheme (SDSM) for IoT based supply chains by combining blockchain and ciphertext-based attribute cryptography. This scheme supports the enforcement of fine-grained access control for different levels of partnerships. In addition, to identify partnerships, we propose a metric based on the historical transaction facts on the blockchain, where the level of partnerships among participants is automatically calculated by smart contracts. Finally, we introduce personalized attributes of participants in the ciphertext-based attribute encryption algorithm to support the construction of access policies that include partnerships, allowing for more fine-grained access control. Security analyses and simulation experiments show that our proposed scheme is secure, effective, and practical. Full article

(This article belongs to the Special Issue Advances in Internet of Things with Symmetric/Asymmetric Structure, Computing and Interaction)

► Show Figures

Figure 1

58 pages, 2239 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Dynamic Load Balancing Techniques in the IoT: A Review

by Dimitris Kanellopoulos and Varun Kumar Sharma

Symmetry 2022, 14(12), 2554; https://doi.org/10.3390/sym14122554 - 02 Dec 2022

Cited by 13 | Viewed by 5823

Abstract

The Internet of things (IoT) extends the Internet space by allowing smart things to sense and/or interact with the physical environment and communicate with other physical objects (or things) around us. In IoT, sensors, actuators, smart devices, cameras, protocols, and cloud services are [...] Read more.

The Internet of things (IoT) extends the Internet space by allowing smart things to sense and/or interact with the physical environment and communicate with other physical objects (or things) around us. In IoT, sensors, actuators, smart devices, cameras, protocols, and cloud services are used to support many intelligent applications such as environmental monitoring, traffic monitoring, remote monitoring of patients, security surveillance, and smart home automation. To optimize the usage of an IoT network, certain challenges must be addressed such as energy constraints, scalability, reliability, heterogeneity, security, privacy, routing, quality of service (QoS), and congestion. To avoid congestion in IoT, efficient load balancing (LB) is needed for distributing traffic loads among different routes. To this end, this survey presents the IoT architectures and the networking paradigms (i.e., edge–fog–cloud paradigms) adopted in these architectures. Then, it analyzes and compares previous related surveys on LB in the IoT. It reviews and classifies dynamic LB techniques in the IoT for cloud and edge/fog networks. Lastly, it presents some lessons learned and open research issues. Full article

(This article belongs to the Special Issue Advances in Electrical Engineering, Computing, and Symmetry)

► Show Figures

Figure 1

21 pages, 2952 KiB

Open AccessEditor’s ChoiceArticle

Fractional Stefan Problem Solving by the Alternating Phase Truncation Method

by Agata Chmielowska and Damian Słota

Symmetry 2022, 14(11), 2287; https://doi.org/10.3390/sym14112287 - 01 Nov 2022

Cited by 4 | Viewed by 1246

Abstract

The aim of this paper is the adaptation of the alternating phase truncation (APT) method for solving the two-phase time-fractional Stefan problem. The aim was to determine the approximate temperature distribution in the domain with the moving boundary between the solid and the [...] Read more.

The aim of this paper is the adaptation of the alternating phase truncation (APT) method for solving the two-phase time-fractional Stefan problem. The aim was to determine the approximate temperature distribution in the domain with the moving boundary between the solid and the liquid phase. The adaptation of the APT method is a kind of method that allows us to consider the enthalpy distribution instead of the temperature distribution in the domain. The method consists of reducing the whole considered domain to liquid phase by adding sufficient heat at each point of the solid and then, after solving the heat equation transformed to the enthalpy form in the obtained region, subtracting the heat that has been added. Next the whole domain is reduced to the solid phase by subtracting the sufficient heat from each point of the liquid. The heat equation is solved in the obtained region and, after that, the heat that had been subtracted is added at the proper points. The steps of the APT method were adapted to solve the equations with the fractional derivatives. The paper includes numerical examples illustrating the application of the described method. Full article

(This article belongs to the Special Issue Trends in Fractional Modelling in Science and Innovative Technologies)

► Show Figures

Figure 1

13 pages, 508 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Pseudo-Conformal Sound Speed in the Core of Compact Stars

by Mannque Rho

Symmetry 2022, 14(10), 2154; https://doi.org/10.3390/sym14102154 - 14 Oct 2022

Cited by 9 | Viewed by 1035

Abstract

By implementing the putative “hadron-quark continuity” conjectured in QCD in terms of skyrmion-half-skyrmion topological change in an effective field theory for dense matter, we argue that (quasi-)baryons could “masquerade” deconfined quarks in the interior of compact stars. We interpret this phenomenon as a [...] Read more.

By implementing the putative “hadron-quark continuity” conjectured in QCD in terms of skyrmion-half-skyrmion topological change in an effective field theory for dense matter, we argue that (quasi-)baryons could “masquerade” deconfined quarks in the interior of compact stars. We interpret this phenomenon as a consequence of possible interplay between hidden scale symmetry and hidden local symmetry at high density. A surprising spin-off of the emerging symmetry that we call “pseudo-conformality” is that the long-standing puzzle of the quenched

g_{A} \approx 1

in nuclei can be given a simple resolution by the way the hidden symmetries impact nuclear dynamics at low density. Full article

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

► Show Figures

Figure 1

12 pages, 8582 KiB

Open AccessEditor’s ChoiceArticle

Design and Robustness Evaluation of Valley Topological Elastic Wave Propagation in a Thin Plate with Phononic Structure

by Motoki Kataoka, Masaaki Misawa and Kenji Tsuruta

Symmetry 2022, 14(10), 2133; https://doi.org/10.3390/sym14102133 - 13 Oct 2022

Cited by 5 | Viewed by 1822

Abstract

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic [...] Read more.

Based on the concept of band topology in phonon dispersion, we designed a topological phononic crystal in a thin plate for developing an efficient elastic waveguide. Despite that various topological phononic structures have been actively proposed, a quantitative design strategy of the phononic band and its robustness assessment in an elastic regime are still missing, hampering the realization of topological acoustic devices. We adopted a snowflake-like structure for the crystal unit cell and determined the optimal structure that exhibited the topological phase transition of the planar phononic crystal by changing the unit cell structure. The bandgap width could be adjusted by varying the length of the snow-side branch, and a topological phase transition occurred in the unit cell structure with threefold rotational symmetry. Elastic waveguides based on edge modes appearing at interfaces between crystals with different band topologies were designed, and their transmission efficiencies were evaluated numerically and experimentally. The results demonstrate the robustness of the elastic wave propagation in thin plates. Moreover, we experimentally estimated the backscattering length, which measures the robustness of the topologically protected propagating states against structural inhomogeneities. The results quantitatively indicated that degradation of the immunization against the backscattering occurs predominantly at the corners in the waveguides, indicating that the edge mode observed is a relatively weak topological state. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

23 pages, 1790 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Prospects for Heavy Neutral SUSY HIGGS Scalars in the hMSSM and Natural SUSY at LHC Upgrades

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

Symmetry 2022, 14(10), 2061; https://doi.org/10.3390/sym14102061 - 03 Oct 2022

Cited by 9 | Viewed by 1046

Abstract

We examine production and decay of heavy neutral SUSY Higgs bosons

p p \to H, A \to τ \bar{τ}

within the hMSSM and compare against a perhaps more plausible natural supersymmetry scenario dubbed

m_{h}^{125} (nat)

which allows [...] Read more.

We examine production and decay of heavy neutral SUSY Higgs bosons

p p \to H, A \to τ \bar{τ}

within the hMSSM and compare against a perhaps more plausible natural supersymmetry scenario dubbed

m_{h}^{125} (nat)

which allows for a natural explanation for

m_{w e a k} ≃ m_{W, Z, h} \sim 100

GeV while maintaining

m_{h} ≃ 125

GeV. We evaluate signal against various Standard Model backgrounds from

γ, Z \to τ \bar{τ}

,

t \bar{t}

and vector boson pair production

V V

. We combine the transverse mass method for back-to-back (BtB) taus along with the ditau mass peak

m_{τ τ}

method for acollinear taus as our signal channels. This technique ultimately gives a boost to the signal significance over the standard technique of using just the BtB signal channel. We evaluate both the 95% CL exclusion and

5 σ

discovery reach in the

m_{A}

vs.

tan β

plane for present LHC with 139 fb⁻¹, Run 3 with 300 fb⁻¹ and high luminosity LHC (HL-LHC) with 3000 fb⁻¹ of integrated luminosity. For

tan β = 10

, the exclusion limits range up to

m_{A} \sim 1

, 1.1 and 1.4 TeV, respectively. These may be compared to the range of

m_{A}

values gleaned from a statistical analysis of the string landscape wherein

m_{A}

can range up to

\sim 8

TeV. Full article

(This article belongs to the Special Issue Higgs Boson and Supersymmetry: 10th Anniversary of the Discovery of the Higgs Boson)

► Show Figures

Figure 1

26 pages, 7028 KiB

Open AccessEditor’s ChoiceArticle

A Triple-Structure Network Model Based upon MobileNet V1 and Multi-Loss Function for Facial Expression Recognition

by Baojin Han, Min Hu, Xiaohua Wang and Fuji Ren

Symmetry 2022, 14(10), 2055; https://doi.org/10.3390/sym14102055 - 02 Oct 2022

Cited by 5 | Viewed by 2551

Abstract

Existing facial expression recognition methods have some drawbacks. For example, it becomes difficult for network learning on cross-dataset facial expressions, multi-region learning on an image did not extract the overall image information, and a frequency multiplication network did not take into account the [...] Read more.

Existing facial expression recognition methods have some drawbacks. For example, it becomes difficult for network learning on cross-dataset facial expressions, multi-region learning on an image did not extract the overall image information, and a frequency multiplication network did not take into account the inter-class and intra-class features in image classification. In order to deal with the above problems, in our current research, we raise a symmetric mode to extract the inter-class features and intra-class diversity features, and then propose a triple-structure network model based upon MobileNet V1, which is trained via a new multi-branch loss function. Such a proposed network consists of triple structures, viz., a global branch network, an attention mechanism branch network, and a diversified feature learning branch network. To begin with, the global branch network is used to extract the global features of the facial expression images. Furthermore, an attention mechanism branch network concentrates to extract inter-class features. In addition, the diversified feature learning branch network is utilized to extract intra-class diverse features. The network training is performed by using multiple loss functions to decrease intra-class differences and inter-class similarities. Finally, through ablation experiments and visualization, the intrinsic mechanism of our triple-structure network model is proved to be very reasonable. Experiments on the KDEF, MMI, and CK+ datasets show that the accuracy of facial expression recognition using the proposed model is 1.224%, 13.051%, and 3.085% higher than that using MC-loss (VGG16), respectively. In addition, related comparison tests and analyses proved that our raised triple-structure network model reaches better performance than dozens of state-of-the-art methods. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)

► Show Figures

Figure 1

27 pages, 10857 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Influence of Centrifugal Buoyancy in Thermal Convection within a Rotating Spherical Shell

by Hidemoto Satake and Toshio Tagawa

Symmetry 2022, 14(10), 2021; https://doi.org/10.3390/sym14102021 - 26 Sep 2022

Cited by 2 | Viewed by 2056

Abstract

The dynamo action, which is of importance in the study of the geomagnetism mechanism, is considered to be caused by the convection structure formed inside a rotating spherical shell. This convection structure elongated in the rotation axis is generated by the action of [...] Read more.

The dynamo action, which is of importance in the study of the geomagnetism mechanism, is considered to be caused by the convection structure formed inside a rotating spherical shell. This convection structure elongated in the rotation axis is generated by the action of both heat and rotation on the fluid inside a spherical shell. In this study, we analyzed thermal convection in such a rotating spherical shell and attempted to understand the phenomenon of this convective structure. It is known that each value of the Prandtl number, the Ekman number and the Rayleigh number and their balance are important for the generation of such convective structure. We fixed these three parameters and considered the effect of centrifugal buoyancy as the Froude number additionally. To investigate how the effects of centrifugal buoyancy affect the convective structure, we carried out both three-dimensional numerical simulations and linear stability analyses. In particular, we focused on the transition from axisymmetric flow to non-axisymmetric flow having wavenumbers in the toroidal direction and investigated both growth rate and phase velocity of the disturbance. It was found that axisymmetric flow tends to be maintained as the effect of centrifugal buoyancy increases. Full article

(This article belongs to the Special Issue Symmetry in Fluid Flow II)

► Show Figures

Figure 1

27 pages, 430 KiB

Open AccessEditor’s ChoiceArticle

Proportional Caputo Fractional Differential Inclusions in Banach Spaces

by Abdelkader Rahmani, Wei-Shih Du, Mohammed Taha Khalladi, Marko Kostić and Daniel Velinov

Symmetry 2022, 14(9), 1941; https://doi.org/10.3390/sym14091941 - 18 Sep 2022

Cited by 5 | Viewed by 1269

Abstract

In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order

α \in (0, 1)

for a continuous (locally integrable) function

u : [0, \infty) \to E

, where E is a [...] Read more.

In this work, we introduce the notion of a (weak) proportional Caputo fractional derivative of order

α \in (0, 1)

for a continuous (locally integrable) function

u : [0, \infty) \to E

, where E is a complex Banach space. In our definition, we do not require that the function

u (\cdot)

is continuously differentiable, which enables us to consider the wellposedness of the corresponding fractional relaxation problems in a much better theoretical way. More precisely, we systematically investigate several new classes of (degenerate) fractional solution operator families connected with the use of this type of fractional derivatives, obeying the multivalued linear approach to the abstract Volterra integro-differential inclusions. The quasi-periodic properties of the proportional fractional integrals as well as the existence and uniqueness of almost periodic-type solutions for various classes of proportional Caputo fractional differential inclusions in Banach spaces are also considered. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Analysis and Boundary Value Problems)

24 pages, 2094 KiB

Open AccessEditor’s ChoiceArticle

Anti-Symmetric Medium Chirality Leading to Symmetric Field Helicity in Response to a Pair of Circularly Polarized Plane Waves in Counter-Propagating Configuration

by Hyoung-In Lee

Symmetry 2022, 14(9), 1895; https://doi.org/10.3390/sym14091895 - 10 Sep 2022

Cited by 4 | Viewed by 1411

Abstract

We examine how a chiral medium responds to a pair of plane waves of circular polarizations. To this goal, we assume the chiral medium to be spatially homogeneous for simplicity. By assuming the medium to be a lossless, we provide analytic formulas of [...] Read more.

We examine how a chiral medium responds to a pair of plane waves of circular polarizations. To this goal, we assume the chiral medium to be spatially homogeneous for simplicity. By assuming the medium to be a lossless, we provide analytic formulas of key bilinear parameters such as the pair of electromagnetic and reactive Poynting vectors in addition to the pair of electromagnetic and reactive helicities. By examining two obliquely colliding plane waves, we learned that most of those key parameters are asymmetric with respect to the medium chirality. Only for a counter-propagating pair, some of those key parameters are found to exhibit symmetry with respect to the medium chirality. We will discuss the implications of those asymmetries and symmetries from the viewpoints of typical applications in optics and physics. Full article

(This article belongs to the Special Issue Symmetry in Integrable Systems: Theory and Application)

► Show Figures

Figure 1

16 pages, 490 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The QCD Adler Function and the Muon g − 2 Anomaly from Renormalons

by Alessio Maiezza and Juan Carlos Vasquez

Symmetry 2022, 14(9), 1878; https://doi.org/10.3390/sym14091878 - 08 Sep 2022

Cited by 3 | Viewed by 1458

Abstract

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough [...] Read more.

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon’s anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon’s anomalous magnetic moment and the experimental value obtained by the most recent muon

g - 2

collaboration. The latter shows that the Adler function’s new representation can also be consistent with recent lattice determinations. Full article

(This article belongs to the Section Physics)

► Show Figures

Figure 1

63 pages, 1303 KiB

Open AccessFeature PaperEditor’s ChoiceReview

New Developments in Relativistic Magnetohydrodynamics

by Koichi Hattori, Masaru Hongo and Xu-Guang Huang

Symmetry 2022, 14(9), 1851; https://doi.org/10.3390/sym14091851 - 05 Sep 2022

Cited by 22 | Viewed by 7905

Abstract

Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark–gluon plasma in heavy-ion collisions to matters in supernova, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such [...] Read more.

Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark–gluon plasma in heavy-ion collisions to matters in supernova, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such as a formulation of RMHD from the perspective of magnetic flux conservation using the entropy–current analysis, the nonequilibrium statistical operator approach applied to quantum electrodynamics, and the relativistic kinetic theory. We discuss how the transport coefficients in RMHD are computed in kinetic theory and perturbative quantum field theories. We also explore the collective modes and instabilities in RMHD with a special emphasis on the role of chirality in a parity-odd plasma. We also give some future prospects of RMHD, including the interaction with spin hydrodynamics and the new kinetic framework with magnetic flux conservation. Full article

(This article belongs to the Special Issue Relativistic Hydrodynamics and Symmetry: Theory, Methods and Applications)

► Show Figures

Figure 1

21 pages, 11808 KiB

Open AccessEditor’s ChoiceArticle

A High-Performance Compound Control Method for a Three-Axis Inertially Stabilized Platform under Multiple Disturbances

by Xusheng Lei, Fa Fu and Rui Wang

Symmetry 2022, 14(9), 1848; https://doi.org/10.3390/sym14091848 - 05 Sep 2022

Cited by 2 | Viewed by 1315

Abstract

Symmetry is presented in the frame structure, modeling, and disturbance analysis of the three-axis inertially stabilized platform (ISP), which affects the control performance of the ISP. To realize high-performance control for the ISP, a nonlinear dynamic model based on the geographic coordinates and [...] Read more.

Symmetry is presented in the frame structure, modeling, and disturbance analysis of the three-axis inertially stabilized platform (ISP), which affects the control performance of the ISP. To realize high-performance control for the ISP, a nonlinear dynamic model based on the geographic coordinates and a compound control method based on the adaptive extended state observer (ESO) and adaptive back-stepping integral sliding mode control (SMC) are proposed. The nonlinear dynamic model based on geographic coordinates could avoid the degradation of measurement and control performance due to complex coordinate transformations. An adaptive ESO (AESO) has been developed to estimate the unknown disturbances of ISP. With the information from the ISP system, the adaptive bandwidth of AESO can deal with the peaking phenomenon without introducing excessive noise. Furthermore, based on the integral sliding mode, the adaptation laws of parameter uncertainty and disturbance estimation compensation have been developed for the back-stepping integral SMC method, which can reduce the estimation burden and improve the disturbance estimation accuracy of AESO. The asymptotic stability of the compound control method has been proven by the Lyapunov stability theory. Through a series of simulations and experiments, the effectiveness of the compound method is validated. Full article

(This article belongs to the Special Issue Numerical Simulation and Control of Mechanical and Mechatronic Systems)

► Show Figures

Figure 1

23 pages, 15034 KiB

Open AccessEditor’s ChoiceArticle

Low Thrust Propelled Close Approach Maneuvers

by Alessandra F. S. Ferreira, Antonio Elipe, Rodolpho V. De Moraes, Antônio F. B. A. Prado, Othon C. Winter and Vivian M. Gomes

Symmetry 2022, 14(9), 1786; https://doi.org/10.3390/sym14091786 - 27 Aug 2022

Cited by 2 | Viewed by 1228

Abstract

The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a “gravity assisted” maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the [...] Read more.

The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a “gravity assisted” maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the gravity of this body to change its trajectory. This approach trajectory has symmetry with respect to the periapsis line when observed from a reference frame fixed in the approached body. There is also a more complex maneuver, when the passage by the celestial body is combined with the application of propulsion, either to give extra energy to the spacecraft or to help to satisfy other constraints required by the mission, like passing by a giving point or region in space. The main object of this study is to measure the efficiency of the application of a continuous thrust combined with the “gravity assisted” maneuver. The effect of this combination is analyzed using maps that give the energy variation of the spacecraft as function of the parameters related to the maneuver. This analysis is made from the point of view of the variation of energy of the spacecraft with respect to the main body of the system. The continuous thrust is applied in the different regions of the trajectory to evaluate the effects of the locations of the thrusting arcs in the variations of energy. The effects of the variations of the direction of the thrust are also studied. This type of combined maneuver may be used to give extra energy to the spacecraft and keeping control of the trajectory during the close approach to better position the spacecraft to complete the mission. Full article

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

► Show Figures

Figure 1

24 pages, 406 KiB

Open AccessEditor’s ChoiceReview

Dynamics of Open Quantum Systems—Markovian Semigroups and Beyond

by Artur Czerwinski

Symmetry 2022, 14(8), 1752; https://doi.org/10.3390/sym14081752 - 22 Aug 2022

Cited by 18 | Viewed by 3240

Abstract

The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components [...] Read more.

The idea of an open quantum system was introduced in the 1950s as a response to the problems encountered in areas such as nuclear magnetic resonance and the decay of unstable atoms. Nowadays, dynamical models of open quantum systems have become essential components in many applications of quantum mechanics. This paper provides an overview of the fundamental concepts of open quantum systems. All underlying definitions, algebraic methods and crucial theorems are presented. In particular, dynamical semigroups with corresponding time-independent generators are characterized. Furthermore, evolution models that induce memory effects are discussed. Finally, measures of non-Markovianity are recapped and interpreted from a perspective of physical relevance. Full article

(This article belongs to the Special Issue Memory, Non-markovianity, Nonlocality, and Storage Processes: Multidisciplinary Classical and Quantum Aspects)

18 pages, 1163 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Multi-Fractional Brownian Motion: Estimating the Hurst Exponent via Variational Smoothing with Applications in Finance

by Luca Di Persio and Gianni Turatta

Symmetry 2022, 14(8), 1657; https://doi.org/10.3390/sym14081657 - 11 Aug 2022

Cited by 2 | Viewed by 2910

Abstract

Beginning with the basics of the Wiener process, we consider limitations characterizing the “Brownian approach” in analyzing real phenomena. This leads us to first consider the fractional Brownian motion (fBm)—also discussing the Wood–Chan fast algorithm to generate sample paths—to then focus on multi-fBm [...] Read more.

Beginning with the basics of the Wiener process, we consider limitations characterizing the “Brownian approach” in analyzing real phenomena. This leads us to first consider the fractional Brownian motion (fBm)—also discussing the Wood–Chan fast algorithm to generate sample paths—to then focus on multi-fBm and methods to generate its trajectories. This is heavily linked to the Hurst exponent study, which we link to real data, firstly considering an absolute moment method, allowing us to obtain raw estimates, to then consider variational calculus approaches allowing to smooth it. The latter smoothing tool was tested in accuracy on synthetic data, comparing it with the exponential moving average method. Previous analyses and results were exploited to develop a forecasting procedure applied to the real data of foreign exchange rates from the Forex market. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Study with PDE)

► Show Figures

Figure 1

14 pages, 3137 KiB

Open AccessEditor’s ChoiceArticle

Using XAI for Deep Learning-Based Image Manipulation Detection with Shapley Additive Explanation

by Savita Walia, Krishan Kumar, Saurabh Agarwal and Hyunsung Kim

Symmetry 2022, 14(8), 1611; https://doi.org/10.3390/sym14081611 - 05 Aug 2022

Cited by 7 | Viewed by 3456

Abstract

In the arena of image forensics, detecting manipulations in an image is extremely significant because of the use of images in different fields. Various detection techniques have been suggested in the literature that are based on digging out the features from images to [...] Read more.

In the arena of image forensics, detecting manipulations in an image is extremely significant because of the use of images in different fields. Various detection techniques have been suggested in the literature that are based on digging out the features from images to unveil the traces left by manipulation operations. In this paper, a deep learning-based approach is proposed in which a residual network is used to learn deep, complex features from preprocessed images for classification into authentic and forged images. There is statistical symmetry in similar types of images and asymmetry in different types of images. The proposed scheme can highlight the statistical asymmetry between authentic and forged images. In the proposed scheme, firstly, an RGB image is analyzed for different JPEG compression levels. The obtained difference between the error levels is used to extract enhanced LBP code. Then, the scale- and direction-invariant LBP (SD-LBP) code is transformed into SD-LBP feature maps to feed to a deep residual network. Next, the concept of explainable artificial intelligence (XAI) is used to help provide explanations and interpret the output, thereby raising the credibility of the proposed approach. The unique feature selection approach employed is the kernel SHAP method, which is focused on the Shapley values. This technique is used to pinpoint the specific characteristics that are responsible for the aberrant behavior of the forged images dataset. Later, the deep learning-based model is trained and validated using these feature sets. A pre-activation version of ResNet-50 architecture is used that achieved an accuracy of 99.31%, 99.52%, 98.05%, and 99.10% on CASIA v1, CASIA v2, IMD 2020, and DVMM datasets, respectively. The capability of the pretrained residual network and rich textural features, which are scale- and direction-invariant, helps to expand the detection accuracy of the proposed approach. The results confirmed that the method either produced competitive results or outperformed existing methods. Full article

(This article belongs to the Section Computer)

► Show Figures

Figure 1

19 pages, 1268 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Stability of a Hydrodynamic Bravais Lattice

by Miles M. P. Couchman, Davis J. Evans and John W. M. Bush

Symmetry 2022, 14(8), 1524; https://doi.org/10.3390/sym14081524 - 26 Jul 2022

Cited by 2 | Viewed by 1906

Abstract

We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of [...] Read more.

We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart. Full article

(This article belongs to the Special Issue Symmetry and Symmetry-Breaking in Fluid Dynamics)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Editor’s Choice Articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI