Symmetry

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 - 5 Sep 2022

Cited by 3 | Viewed by 1482

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)

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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 1379

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)

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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 19 | Viewed by 3459

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 3227

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)

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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 - 5 Aug 2022

Cited by 9 | Viewed by 3794

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)

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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 3 | Viewed by 2042

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)

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18 pages, 4374 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Analysis of Drill-String Nonlinear Dynamics Using the Lumped-Parameter Method

by Lelya A. Khajiyeva, Igor V. Andrianov, Yuliya F. Sabirova and Askar K. Kudaibergenov

Symmetry 2022, 14(7), 1495; https://doi.org/10.3390/sym14071495 - 21 Jul 2022

Cited by 5 | Viewed by 1793

Abstract

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string [...] Read more.

This work aims at studying the nonlinear dynamics of drill strings using the lumped-parameter method (LPM). The study is based on the good consistency of the results of the test problem where the model of the longitudinal vibrations of a horizontal drill string with a static compressive load at the left end is considered. In this paper, this method is applied to discretize linear and nonlinear models of the lateral vibrations of a vertical drill string under the effect of a supersonic gas flow. The obtained results are verified with the previously published data. The optimal number of the drill-string partitions is determined using the developed application, which allows us to estimate the accuracy of the loaded data. The numerical solution of the model is obtained using the fourth-order Runge–Kutta method. The optimization of the numerical algorithm using parallel-programming tools is carried out, and the efficiency of the method is analyzed. Full article

(This article belongs to the Special Issue Dynamical Processes in Heterogeneous and Discrete Media)

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51 pages, 1322 KiB

Open AccessEditor’s ChoiceReview

Symmetric Mass Generation

by Juven Wang and Yi-Zhuang You

Symmetry 2022, 14(7), 1475; https://doi.org/10.3390/sym14071475 - 19 Jul 2022

Cited by 49 | Viewed by 4115

Abstract

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last [...] Read more.

The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG. Full article

(This article belongs to the Special Issue New Applications of Symmetry in Lattice Field Theory)

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20 pages, 316 KiB

Open AccessEditor’s ChoiceArticle

The Minimum-Norm Least Squares Solutions to Quaternion Tensor Systems

by Mengyan Xie, Qing-Wen Wang and Yang Zhang

Symmetry 2022, 14(7), 1460; https://doi.org/10.3390/sym14071460 - 17 Jul 2022

Cited by 7 | Viewed by 1416

Abstract

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system

A_{1} *_{N} X_{1} = C_{1},

A_{1} *_{N} X_{2} + A_{2} *_{N} X_{3} = C_{2},

[...] Read more.

In this paper, we investigate the minimum-norm least squares solution to a quaternion tensor system

A_{1} *_{N} X_{1} = C_{1},

A_{1} *_{N} X_{2} + A_{2} *_{N} X_{3} = C_{2},

E_{1} *_{N} X_{1} *_{M} F_{1} + E_{1} *_{N} X_{2} *_{M} F_{2} + E_{2} *_{N} X_{3} *_{M} F_{2} = D

by using the Moore–Penrose inverses of block tensors. As an application, we discuss the quaternion tensor system

A *_{N} X = C,

E *_{N} X *_{M} F = D

for minimum-norm least squares reducible solutions. To illustrate the results, we present an algorithm and a numerical example. Full article

(This article belongs to the Section Mathematics)

19 pages, 974 KiB

Open AccessEditor’s ChoiceArticle

SGXAP: SGX-Based Authentication Protocol in IoV-Enabled Fog Computing

by Tsu-Yang Wu, Xinglan Guo, Yeh-Cheng Chen, Saru Kumari and Chien-Ming Chen

Symmetry 2022, 14(7), 1393; https://doi.org/10.3390/sym14071393 - 6 Jul 2022

Cited by 34 | Viewed by 2060

Abstract

With the maturity and popularization of the Internet of Things, we saw the emergence of the Internet of Vehicles. This collects and processes real-time traffic information, alleviates traffic congestion, and realizes intelligent transportation. However, sensitive information, such as real-time driving data of vehicles, [...] Read more.

With the maturity and popularization of the Internet of Things, we saw the emergence of the Internet of Vehicles. This collects and processes real-time traffic information, alleviates traffic congestion, and realizes intelligent transportation. However, sensitive information, such as real-time driving data of vehicles, are transmitted on public channels, which are easily to steal and manipulate for attackers. In addition, vehicle communications are vulnerable to malicious attacks. Therefore, it is essential to design secure and efficient protocols. Many studies have adopted asymmetric cryptosystems and fog computing to in this environment, but most of them do not reflect the advantages of fog nodes, which share the computational burden of cloud servers. Therefore, it is challenging to design a protocol that effectively uses fog nodes. In this paper, we design an authentication protocol based on a symmetric encryption algorithm and fog computing in the Internet of Vehicles. In this protocol, we first propose a four-layer architecture that significantly reduces the computational burden of cloud servers. To resist several well-known attacks, we also apply Intel software guard extensions to our protocol. This is because it can resist privileged insider attacks. We prove the security of the proposed protocol through the Real-Or-Random model and informal analysis. We also compare the performance of the proposed protocol with recent protocols. The results show better security and a lower computational cost. Full article

(This article belongs to the Special Issue Information Security and Cryptology: Advanced Technologies in Symmetry/Asymmetry)

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34 pages, 3749 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Thinking Outside the Box: Numerical Relativity with Particles

by Stephan Rosswog, Peter Diener and Francesco Torsello

Symmetry 2022, 14(6), 1280; https://doi.org/10.3390/sym14061280 - 20 Jun 2022

Cited by 10 | Viewed by 6224

Abstract

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of [...] Read more.

The observation of gravitational waves from compact objects has now become an active part of observational astronomy. For a sound interpretation, one needs to compare such observations against detailed Numerical Relativity simulations, which are essential tools to explore the dynamics and physics of compact binary mergers. To date, essentially all simulation codes that solve the full set of Einstein’s equations are performed in the framework of Eulerian hydrodynamics. The exception is our recently developed Numerical Relativity code SPHINCS_BSSN which solves the commonly used BSSN formulation of the Einstein equations on a structured mesh and the matter equations via Lagrangian particles. We show here, for the first time, SPHINCS_BSSN neutron star merger simulations with piecewise polytropic approximations to four nuclear matter equations of state. In this set of neutron star merger simulations, we focus on perfectly symmetric binary systems that are irrotational and have 1.3

M_{⊙}

masses. We introduce some further methodological refinements (a new way of steering dissipation, an improved particle–mesh mapping), and we explore the impact of the exponent that enters in the calculation of the thermal pressure contribution. We find that it leaves a noticeable imprint on the gravitational wave amplitude (calculated via both quadrupole approximation and the

Ψ_{4}

formalism) and has a noticeable impact on the amount of dynamic ejecta. Consistent with earlier findings, we only find a few times

10^{- 3}

M_{⊙}

as dynamic ejecta in the studied equal mass binary systems, with softer equations of state (which are more prone to shock formation) ejecting larger amounts of matter. In all of the cases, we see a credible high-velocity (∼

0.5 \dots 0.7 c

) ejecta component of ∼

10^{- 4}

M_{⊙}

that is launched at contact from the interface between the two neutron stars. Such a high-velocity component has been suggested to produce an early, blue precursor to the main kilonova emission, and it could also potentially cause a kilonova afterglow. Full article

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

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27 pages, 17680 KiB

Open AccessEditor’s ChoiceReview

Impact of Molecular Symmetry/Asymmetry on Insulin-Sensitizing Treatments for Type 2 Diabetes

by Jessica Georgina Filisola-Villaseñor, María E. Aranda-Barradas, Susana Patricia Miranda-Castro, Jessica Elena Mendieta-Wejebe, Amaranta Sarai Valdez Guerrero, Selene Amasis Guillen Castro, Macario Martínez Castillo, Feliciano Tamay-Cach and Samuel Álvarez-Almazán

Symmetry 2022, 14(6), 1240; https://doi.org/10.3390/sym14061240 - 15 Jun 2022

Cited by 3 | Viewed by 3814

Abstract

Although the advantages and disadvantages of asymmetrical thiazolidinediones as insulin-sensitizers have been well-studied, the relevance of symmetry and asymmetry for thiazolidinediones and biguanides has scarcely been explored. Regarding symmetrical molecules, only one thiazolidinedione and no biguanides have been evaluated and proposed as an [...] Read more.

Although the advantages and disadvantages of asymmetrical thiazolidinediones as insulin-sensitizers have been well-studied, the relevance of symmetry and asymmetry for thiazolidinediones and biguanides has scarcely been explored. Regarding symmetrical molecules, only one thiazolidinedione and no biguanides have been evaluated and proposed as an antihyperglycemic agent for treating type 2 diabetes. Since molecular structure defines physicochemical, pharmacological, and toxicological properties, it is important to gain greater insights into poorly investigated patterns. For example, compounds with intrinsic antioxidant properties commonly have low toxicity. Additionally, the molecular symmetry and asymmetry of ligands are each associated with affinity for certain types of receptors. An advantageous response obtained in one therapeutic application may imply a poor or even adverse effect in another. Within the context of general patterns, each compound must be assessed individually. The current review aimed to summarize the available evidence for the advantages and disadvantages of utilizing symmetrical and asymmetrical thiazolidinediones and biguanides as insulin sensitizers in patients with type 2 diabetes. Other applications of these same compounds are also examined as well as the various uses of additional symmetrical molecules. More research is needed to exploit the potential of symmetrical molecules as insulin sensitizers. Full article

(This article belongs to the Special Issue Synthetic and Natural Compounds with Symmetry/Asymmetry in Medicinal and Environmental Chemistry)

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25 pages, 5431 KiB

Open AccessEditor’s ChoiceArticle

Lifetime and Dynamics of Natural Orbits around Titan

by Lucas S. Ferreira, Rafael Sfair and Antônio F. Bertachini A. Prado

Symmetry 2022, 14(6), 1243; https://doi.org/10.3390/sym14061243 - 15 Jun 2022

Cited by 8 | Viewed by 2034

Abstract

Considering the growing interest in sending probes to the natural satellite Titan, our work aims to investigate and map natural orbits around this moon. For that, we use mathematical models with forces that have symmetry/asymmetry phenomena, depending on the force, applied to orbits [...] Read more.

Considering the growing interest in sending probes to the natural satellite Titan, our work aims to investigate and map natural orbits around this moon. For that, we use mathematical models with forces that have symmetry/asymmetry phenomena, depending on the force, applied to orbits around Titan. We evaluated the effects due to the gravitational attraction of the Saturn, together with the perturbative effects coming from the non-sphericity of Titan (the gravitational coefficient

J_{2}

) and the effects of the atmospheric drag present in the natural satellite. Lifetime maps were generated for different initial configurations of the orbit of the probe, which were analyzed in different scenarios of orbital perturbations. The results showed the existence of orbits surviving at least 20 years and conditions with shorter times, but sufficient to carry out possible missions, including the important polar orbits. Furthermore, the investigation of the oscillation rate of the altitude of the probe, called coefficient

Δ

, proposed in this work, showed orbital conditions that result in more minor oscillations in the altitude of the spacecraft. Full article

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

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14 pages, 625 KiB

Open AccessEditor’s ChoiceArticle

Using K-Means Clustering in Python with Periodic Boundary Conditions

by Alicja Miniak-Górecka, Krzysztof Podlaski and Tomasz Gwizdałła

Symmetry 2022, 14(6), 1237; https://doi.org/10.3390/sym14061237 - 14 Jun 2022

Cited by 5 | Viewed by 3818

Abstract

Periodic boundary conditions are natural in many scientific problems, and often lead to particular symmetries. Working with datasets that express periodicity properties requires special approaches when analyzing these phenomena. Periodic boundary conditions often help to solve or describe the problem in a much [...] Read more.

Periodic boundary conditions are natural in many scientific problems, and often lead to particular symmetries. Working with datasets that express periodicity properties requires special approaches when analyzing these phenomena. Periodic boundary conditions often help to solve or describe the problem in a much simpler way. The angular rotational symmetry is an example of periodic boundary conditions. This symmetry implies angular momentum conservation. On the other hand, clustering is one of the first and most basic methods used in data analysis. It is often a starting point when new data are acquired and understood. K-means clustering is one of the most commonly used clustering methods. It can be applied to many different situations with reasonably good results. Unfortunately, the original k-means approach does not cope well with the periodic properties of the data. For example, the original k-means algorithm treats a zero angle as very far from an angle that is 359 degrees. Periodic boundary conditions often change the classical distance measure and introduce an error in k-means clustering. In the paper, we discuss the problem of periodicity in the dataset and present a periodic k-means algorithm that modifies the original approach. Considering that many data scientists prefer on-the-shelf solutions, such as libraries available in Python, we present how easily they can incorporate periodicity into existing k-means implementation in the PyClustering library. It allows anyone to integrate periodic conditions without significant additional costs. The paper evaluates the described method using three different datasets: the artificial dataset, wind direction measurement, and the New York taxi service dataset. The proposed periodic k-means provides better results when the dataset manifests some periodic properties. Full article

(This article belongs to the Section Computer)

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24 pages, 3170 KiB

Open AccessEditor’s ChoiceReview

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

by Chong Wang, Xin Qiang, Menghui Xu and Tao Wu

Symmetry 2022, 14(6), 1219; https://doi.org/10.3390/sym14061219 - 13 Jun 2022

Cited by 34 | Viewed by 4437

Abstract

Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models [...] Read more.

Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested. Full article

(This article belongs to the Special Issue Advances in Computational Mechanics for Symmetrical Engineering Systems)

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14 pages, 7727 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Crystal Structure of Chiral Drug Prenalterol and Its Precursor Prone to Spontaneous Resolution

by Alexander A. Bredikhin, Robert R. Fayzullin and Zemfira A. Bredikhina

Symmetry 2022, 14(6), 1150; https://doi.org/10.3390/sym14061150 - 2 Jun 2022

Cited by 4 | Viewed by 1894

Abstract

Due to the chiral uniformity of proteins and carbohydrates, the basic building blocks of living matter, the mirror symmetry characteristics of drugs are of exceptional importance for medicinal chemistry. In this work, we present a new synthesis of the mono-enantiomeric chiral drug prenalterol [...] Read more.

Due to the chiral uniformity of proteins and carbohydrates, the basic building blocks of living matter, the mirror symmetry characteristics of drugs are of exceptional importance for medicinal chemistry. In this work, we present a new synthesis of the mono-enantiomeric chiral drug prenalterol 1 based on the symmetry-breaking phenomenon, namely, the spontaneous resolution of 4-hydroxyphenyl glycerol ether 2. The single crystal X-ray diffraction method was used to investigate both rac- and (S)-1 as well as (R)-2. A feature of the main crystal-forming supramolecular motif (SMM) for diol 2 is the participation of three different molecules representing different types of hydroxyl groups in the formation of its repeating unit. The type of prenalterol SMM, as in the case of the related drugs propranolol 3 and pindolol 4, appears to be a chirality driven property, and is dictated by the enantiomeric composition of the crystals. In single-enantiomeric forms, infinite one-dimensional chains are realized, organized around helical axes, while in racemates, zero-dimensional cycles are realized, organized around inversion symmetry elements. The results obtained again demonstrate the influence of the chiral polarization of a substance not only on the general (selection of a space group), but also on particular characteristics of matter crystal organization, namely selection of a specific SMM. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Medicinal Chemistry)

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12 pages, 2662 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

MCD and Induced CD of a Tetraphenoxyperylene-Based Dye in Chiral Solvents: An Experimental and Computational Study

by Simone Ghidinelli, Marco Fusè, Giuseppe Mazzeo, Sergio Abbate and Giovanna Longhi

Symmetry 2022, 14(6), 1108; https://doi.org/10.3390/sym14061108 - 28 May 2022

Cited by 3 | Viewed by 2398

Abstract

The magnetic circular dichroism (MCD) spectrum of N,N′-bis(2,6-diisopropylphenyl)-1,6,7,12-tetraphenoxyperylene-3,4:9,10-tetracarboxydiimide, also known as Lumogen Red 300 or ROT-300, has been recorded both in achiral and chiral solvents. The induced CD spectra in chiral solvents have, similarly, been recorded. A discussion of the spectroscopic response, both [...] Read more.

The magnetic circular dichroism (MCD) spectrum of N,N′-bis(2,6-diisopropylphenyl)-1,6,7,12-tetraphenoxyperylene-3,4:9,10-tetracarboxydiimide, also known as Lumogen Red 300 or ROT-300, has been recorded both in achiral and chiral solvents. The induced CD spectra in chiral solvents have, similarly, been recorded. A discussion of the spectroscopic response, both in CD and in MCD experiments, is presented in this paper. Both types of spectra have been predicted most satisfactorily by DFT calculations; the CD spectra were obtained by assuming the prevalence of one “enantiomeric” conformer and the same set of conformers could also be used for MCD, since “enantiomeric” structures present identically in MCD spectra. Full article

(This article belongs to the Special Issue Asymmetric Molecules and Chirality Recognition)

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13 pages, 3751 KiB

Open AccessEditor’s ChoiceArticle

Heat Flow Characteristics of Ferrofluid in Magnetic Field Patterns for Electric Vehicle Power Electronics Cooling

by Seong-Guk Hwang, Kunal Sandip Garud, Jae-Hyeong Seo and Moo-Yeon Lee

Symmetry 2022, 14(5), 1063; https://doi.org/10.3390/sym14051063 - 22 May 2022

Cited by 5 | Viewed by 3025

Abstract

The ferrofluid is a kind of nanofluid that has magnetization properties in addition to excellent thermophysical properties, which has resulted in an effective performance trend in cooling applications. In the present study, experiments are conducted to investigate the heat flow characteristics of ferrofluid [...] Read more.

The ferrofluid is a kind of nanofluid that has magnetization properties in addition to excellent thermophysical properties, which has resulted in an effective performance trend in cooling applications. In the present study, experiments are conducted to investigate the heat flow characteristics of ferrofluid based on thermomagnetic convection under the influence of different magnetic field patterns. The temperature and heat dissipation characteristics are compared for ferrofluid under the influence of no-magnet, I, L, and T magnetic field patterns. The results reveal that the heat gets accumulated within ferrofluid near the heating part in the case of no magnet, whereas the heat flows through ferrofluid under the influence of different magnetic field patterns without any external force. Owing to the thermomagnetic convection characteristic of ferrofluid, the heat dissipates from the heating block and reaches the cooling block by following the path of the I magnetic field pattern. However, in the case of the L and T magnetic field patterns, the thermomagnetic convection characteristic of ferrofluid drives the heat from the heating block to the endpoint location of the pattern instead of the cooling block. The asymmetrical heat dissipation in the case of the L magnetic field pattern and the symmetrical heat dissipation in the case of the T magnetic field pattern are observed following the magnetization path of ferrofluid in the respective cases. The results confirm that the direction of heat flow could be controlled based on the type of magnetic field pattern and its path by utilizing the thermomagnetic behavior of ferrofluid. The proposed lab-scale experimental set-up and results database could be utilized to design an automatic energy transport system for the cooling of power conversion devices in electric vehicles. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Advanced Research for Efficient Electric Vehicles)

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20 pages, 29741 KiB

Open AccessEditor’s ChoiceArticle

Design of a New Dimension-Changeable Hyperchaotic Model Based on Discrete Memristor

by Chengjing Wei, Guodong Li and Xiangliang Xu

Symmetry 2022, 14(5), 1019; https://doi.org/10.3390/sym14051019 - 17 May 2022

Cited by 12 | Viewed by 1980

Abstract

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic [...] Read more.

The application of a memristor in chaotic circuits is increasingly becoming a popular research topic. The influence of a memristor on the dynamics of chaotic systems is worthy of further exploration. In this paper, a multi-dimensional closed-loop coupling model based on a Logistic map and Sine map (CLS) is proposed. The new chaotic model is constructed by cascade operation in which the output of the Logistic map is used as the input of the Sine map. Additionally, the one-dimensional map is extended to any dimension through the coupling modulation. In order to further increase the complexity and stability of CLS, the discrete memristor model is introduced to construct a discrete memristor-based coupling model with a Logistic map and a Sine map (MCLS). By analyzing the Lyapunov exponents, bifurcation diagram, complexity, and the 0–1 test result, the comparison result between CLS and MCLS is obtained. The dynamics performance analysis shows that the Lyapunov exponents and bifurcation diagrams present symmetrical distribution with variations of some parameters. The MCLS has parameters whose values can be set in a wider range and can generate more complex and more stable chaotic sequences. It proves that the proposed discrete memristor-based closed-loop coupling model can produce any higher dimension hyperchaotic system and the discrete memristor model can effectively improve the performance of discrete chaotic map and make this hyperchaotic system more stable. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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19 pages, 12439 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Recent Progress of Squaraine-Based Fluorescent Materials and Their Biomedical Applications

by Weiguo Qiao and Zhong’an Li

Symmetry 2022, 14(5), 966; https://doi.org/10.3390/sym14050966 - 9 May 2022

Cited by 13 | Viewed by 5585

Abstract

Squaraines (SQs) are unusual cyanine dyes with a unique resonance-stabilized zwitterionic structure. These dyes have attracted significant attention in the fields of organic electronics and organic photonics, due to their facile synthesis, intense and narrow visible and near-infrared absorption/emission, high photostability, low biotoxicity, [...] Read more.

Squaraines (SQs) are unusual cyanine dyes with a unique resonance-stabilized zwitterionic structure. These dyes have attracted significant attention in the fields of organic electronics and organic photonics, due to their facile synthesis, intense and narrow visible and near-infrared absorption/emission, high photostability, low biotoxicity, etc. In this review, we summarize the recent progress of SQ-based fluorescent materials and their biomedical applications. After a brief introduction to SQs, general synthetic routes and design principles of SQ-based fluorescent materials, as well as their aggregation-induced luminescence behaviors, are discussed. Subsequently, their biomedical applications for cell imaging and as fluorescent sensors and therapeutic agents are introduced. Finally, a summary and perspective are given for promoting the development of SQs-based fluorescent materials. Full article

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

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21 pages, 844 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Structural Brain Asymmetries for Language: A Comparative Approach across Primates

by Yannick Becker and Adrien Meguerditchian

Symmetry 2022, 14(5), 876; https://doi.org/10.3390/sym14050876 - 25 Apr 2022

Cited by 5 | Viewed by 8333

Abstract

Humans are the only species that can speak. Nonhuman primates, however, share some ‘domain-general’ cognitive properties that are essential to language processes. Whether these shared cognitive properties between humans and nonhuman primates are the results of a continuous evolution [homologies] or of a [...] Read more.

Humans are the only species that can speak. Nonhuman primates, however, share some ‘domain-general’ cognitive properties that are essential to language processes. Whether these shared cognitive properties between humans and nonhuman primates are the results of a continuous evolution [homologies] or of a convergent evolution [analogies] remain difficult to demonstrate. However, comparing their respective underlying structure—the brain—to determinate their similarity or their divergence across species is critical to help increase the probability of either of the two hypotheses, respectively. Key areas associated with language processes are the Planum Temporale, Broca’s Area, the Arcuate Fasciculus, Cingulate Sulcus, The Insula, Superior Temporal Sulcus, the Inferior Parietal lobe, and the Central Sulcus. These structures share a fundamental feature: They are functionally and structurally specialised to one hemisphere. Interestingly, several nonhuman primate species, such as chimpanzees and baboons, show human-like structural brain asymmetries for areas homologous to key language regions. The question then arises: for what function did these asymmetries arise in non-linguistic primates, if not for language per se? In an attempt to provide some answers, we review the literature on the lateralisation of the gestural communication system, which may represent the missing behavioural link to brain asymmetries for language area’s homologues in our common ancestor. Full article

(This article belongs to the Special Issue Cognitive and Neurophysiological Models of Brain Asymmetry)

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76 pages, 4149 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Cerebral Polymorphisms for Lateralisation: Modelling the Genetic and Phenotypic Architectures of Multiple Functional Modules

by Chris McManus

Symmetry 2022, 14(4), 814; https://doi.org/10.3390/sym14040814 - 14 Apr 2022

Cited by 14 | Viewed by 13883

Abstract

Recent fMRI and fTCD studies have found that functional modules for aspects of language, praxis, and visuo-spatial functioning, while typically left, left and right hemispheric respectively, frequently show atypical lateralisation. Studies with increasing numbers of modules and participants are finding increasing numbers of [...] Read more.

Recent fMRI and fTCD studies have found that functional modules for aspects of language, praxis, and visuo-spatial functioning, while typically left, left and right hemispheric respectively, frequently show atypical lateralisation. Studies with increasing numbers of modules and participants are finding increasing numbers of module combinations, which here are termed cerebral polymorphisms—qualitatively different lateral organisations of cognitive functions. Polymorphisms are more frequent in left-handers than right-handers, but it is far from the case that right-handers all show the lateral organisation of modules described in introductory textbooks. In computational terms, this paper extends the original, monogenic McManus DC (dextral-chance) model of handedness and language dominance to multiple functional modules, and to a polygenic DC model compatible with the molecular genetics of handedness, and with the biology of visceral asymmetries found in primary ciliary dyskinesia. Distributions of cerebral polymorphisms are calculated for families and twins, and consequences and implications of cerebral polymorphisms are explored for explaining aphasia due to cerebral damage, as well as possible talents and deficits arising from atypical inter- and intra-hemispheric modular connections. The model is set in the broader context of the testing of psychological theories, of issues of laterality measurement, of mutation-selection balance, and the evolution of brain and visceral asymmetries. Full article

(This article belongs to the Special Issue Cognitive and Neurophysiological Models of Brain Asymmetry)

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49 pages, 14068 KiB

Open AccessEditor’s ChoiceReview

Overview: State-of-the-Art in the Energy Harvesting Based on Piezoelectric Devices for Last Decade

by Ivan A. Parinov and Alexander V. Cherpakov

Symmetry 2022, 14(4), 765; https://doi.org/10.3390/sym14040765 - 7 Apr 2022

Cited by 20 | Viewed by 4565

Abstract

Technologies of energy harvesting have been developed intensively since the beginning of the twenty-first century, presenting themselves as alternatives to traditional energy sources (for instance, batteries) for small-dimensional and low-power electronics. Batteries have numerous shortcomings connected, for example, with restricted service life and [...] Read more.

Technologies of energy harvesting have been developed intensively since the beginning of the twenty-first century, presenting themselves as alternatives to traditional energy sources (for instance, batteries) for small-dimensional and low-power electronics. Batteries have numerous shortcomings connected, for example, with restricted service life and the necessity of periodic recharging/replacement that create significant problems for portative and remote devices and for power equipment. Environmental energy covers solar, thermal, and oscillation energy. By this, the vibration energy exists continuously around us due to the operation of numerous artificial structures and mechanisms. Different materials (including piezoelectrics) and conversion mechanisms can transform oscillation energy into electrical energy for use in many devices of energy harvesting. Piezoelectric transducers possessing electric mechanical coupling and demonstrating a high density of power in comparison with electromagnetic and electrostatic sensors are broadly applied for the generation of energy from different oscillation energy sources. For the last decade, novel piezoelectric materials, transformation mechanisms, electrical circuits, and experimental and theoretical approaches with results of computer simulation have been developed for improving different piezoelectric devices of energy harvesting. This overview presents results, obtained in the area of piezoelectric energy harvesting for the last decade, including a wide spectrum of experimental, analytical, and computer simulation investigations. Full article

(This article belongs to the Special Issue Advances in Energy Harvesting, Metamaterials, and Their Integrated Multifunctional Systems)

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10 pages, 1040 KiB

Open AccessEditor’s ChoiceArticle

Asymmetry in Muscle Strength, Dynamic Balance, and Range of Motion in Adult Symptomatic Hip Dysplasia

by Haifang Wang, Hailong Yu, Yonghwan Kim and Tingting Chen

Symmetry 2022, 14(4), 748; https://doi.org/10.3390/sym14040748 - 5 Apr 2022

Cited by 7 | Viewed by 2943

Abstract

Hip dysplasia (HD) is a typical developmental abnormality of the hip joint, and discomfort is often found in adulthood. This study compared patients with symptomatic HD in muscle strength, dynamic balance, and range of motion (ROM) with healthy individuals. Patients included those who [...] Read more.

Hip dysplasia (HD) is a typical developmental abnormality of the hip joint, and discomfort is often found in adulthood. This study compared patients with symptomatic HD in muscle strength, dynamic balance, and range of motion (ROM) with healthy individuals. Patients included those who complained of unilateral pain although the lateral center edge angle (LCEA) exhibited bilateral abnormality. Participants (n = 95; men: 46, women: 49) were divided into symptomatic and asymptomatic sides, and a healthy group without a history of hip joint disease (n = 70; men: 30, women: 40) was compared. Hip flexion, extension, abduction, and adduction were performed at an angular velocity of 30°/s using an isokinetic strength test device. The Y-balance test was conducted to measure dynamic balance, and ROM was measured using an electronic goniometer to evaluate flexion, extension, adduction, abduction, and internal and external rotations. In addition, the pain visual analog scale (VAS) and hip and groin outcome scale (HAGOS), a subjective evaluation of the hip joint, were evaluated. ROM (flexion, abduction, internal rotation, and external rotation) was significantly decreased in the HD symptomatic sides of men and women compared to those of the healthy group and the asymptomatic side, and the dynamic balance, flexion, and abduction muscle strength were also lower on the symptomatic sides. Although the LCEA of the HD asymptomatic side was lower than that of the healthy group, there were no significant differences in VAS, flexion, extension, abduction ROM, and extension strength compared to those of healthy individuals. In conclusion, patients with HD were mostly bilateral, and on the symptomatic side, there was a decrease in ROM, dynamic balance, and muscle strength; however, on the asymptomatic side, the function was relatively close to normal. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Study in Clinical Rehabilitation, Exercise Science, Clinical Biomechanics, and Biomedical Engineering: Technologies, Advances, and Applications)

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15 pages, 365 KiB

Open AccessFeature PaperEditor’s ChoiceReview

Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview

by Sergei D. Odintsov, Vasilis K. Oikonomou and Ratbay Myrzakulov

Symmetry 2022, 14(4), 729; https://doi.org/10.3390/sym14040729 - 3 Apr 2022

Cited by 45 | Viewed by 3316

Abstract

In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects [...] Read more.

In this work, we shall exhaustively study the effects of modified gravity on the energy spectrum of the primordial gravitational waves background. S. Weinberg has also produced significant works related to the primordial gravitational waves, with the most important one being the effects of neutrinos on primordial gravitational waves. With this short review, our main aim is to gather all the necessary information for studying the effects of modified gravity on primordial gravitational waves in a concrete and quantitative way and in a single paper. After reviewing all the necessary techniques for extracting the general relativistic energy spectrum, and how to obtain, in a WKB way, the modified gravity damping or amplifying factor, we concentrate on specific forms of modified gravity of interest. The most important parameter involved for the calculation of the effects of modified gravity on the energy spectrum is the parameter

a_{M}

, which we calculate for the cases of

f (R, ϕ)

gravity, Chern–Simons-corrected

f (R, ϕ)

gravity, Einstein–Gauss–Bonnet-corrected

f (R, ϕ)

gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected

f (R, ϕ)

gravity. The exact form of

a_{M}

is presented explicitly for the first time in the literature. With regard to Einstein–Gauss–Bonnet-corrected

f (R, ϕ)

gravity, and higher derivative extended Einstein–Gauss–Bonnet-corrected

f (R, ϕ)

gravity theories, we focus on the case in which the gravitational wave propagating speed is equal to that of light in a vacuum. We provide expressions for

a_{M}

expressed in terms of the cosmic time and in terms of the redshift, which can be used directly for the numerical calculation of the effect of modified gravity on the primordial gravitational wave energy spectrum. Full article

(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)

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20 pages, 5749 KiB

Open AccessEditor’s ChoiceArticle

Exploration of Temperature Distribution through a Longitudinal Rectangular Fin with Linear and Exponential Temperature-Dependent Thermal Conductivity Using DTM-Pade Approximant

by Ravikumar Shashikala Varun Kumar, Rangaswamy Naveen Kumar, Ganeshappa Sowmya, Ballajja Chandrappa Prasannakumara and Ioannis E. Sarris

Symmetry 2022, 14(4), 690; https://doi.org/10.3390/sym14040690 - 26 Mar 2022

Cited by 25 | Viewed by 3657

Abstract

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying [...] Read more.

The present study elaborates on the thermal distribution and efficiency of a longitudinal rectangular fin with exponentially varying temperature-dependent thermal conductivity and heat transfer coefficient concerning internal heat generation. Also, the thermal distribution of a fin is comparatively studied for both exponentially varying temperature-dependent thermal conductivity and linearly varying temperature-dependent thermal conductivity. Further, the thermal distribution of a longitudinal fin is examined by using ANSYS software with different fin materials. Many physical mechanisms can be explained by ordinary differential equations (ODEs) with symmetrical behavior, the significance of which varies based on the perspective. The governing equation of the considered problem is reduced to a non-linear ODE with the assistance of dimensionless terms. The resultant equation is solved analytically using the DTM-Pade approximant and is also solved numerically using Runge-Kutta Fehlberg’s fourth-fifth (RKF-45) order method. The features of dimensionless parameters influencing the fin efficiency and temperature profile are discussed through graphical representation for exponentially and linearly varying temperature-dependent thermal conductivity. This study ensures that the temperature field enhances for the higher magnitude of thermal conductivity parameter, whereas it diminishes for diverse values of the thermo-geometric parameter. Also, greater values of heat generation and heat transfer parameters enhance the temperature profile. Highlight: Thermal distribution through a rectangular profiled straight fin is examined. Linear and non-linear thermal properties are considered. The combined impact of conduction, convection, and internal heat generation is taken for modeling the energy equation of the fin. Thermal simulation is performed for Aluminum Alloy 6061 (AA 6061) and Cast Iron using ANSYS. Full article

(This article belongs to the Special Issue Solid Mechanics and Mechanical Mechanics)

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13 pages, 3012 KiB

Open AccessFeature PaperEditor’s ChoiceReview

How Symmetry Influences the Dissociation of Protonated Cyclic Peptides

by Ariel F. Pérez-Mellor, Riccardo Spezia and Anne Zehnacker

Symmetry 2022, 14(4), 679; https://doi.org/10.3390/sym14040679 - 25 Mar 2022

Cited by 4 | Viewed by 2251

Abstract

Protonated cyclic dipeptides undergo collision-induced dissociation, and this reaction mechanism strongly depends on the symmetry and the nature of the residues. We review the main dissociation mechanism for a series of cyclic dipeptides, obtained through chemical dynamics simulations. The systems range from the [...] Read more.

Protonated cyclic dipeptides undergo collision-induced dissociation, and this reaction mechanism strongly depends on the symmetry and the nature of the residues. We review the main dissociation mechanism for a series of cyclic dipeptides, obtained through chemical dynamics simulations. The systems range from the symmetrical cyclo-(glycyl-glycyl), with two possible symmetrical protonation sites located on the peptide ring, to cyclo-(tyrosyl-prolyl), where the symmetry of protonation sites on the peptide ring is broken by the dissimilar nature of the different residues. Finally, cyclo-(phenylalanyl-histidyl) shows a completely asymmetric situation, with the proton located on one of the dipeptide side chains, which explains the peculiar fragmentation mechanism induced by shuttling the proton, whose efficiency is strongly dependent on the relative chirality of the residues. Full article

(This article belongs to the Special Issue Asymmetric Molecules and Chirality Recognition)

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15 pages, 2266 KiB

Open AccessEditor’s ChoiceArticle

From Memristor-Modeled Jerk System to the Nonlinear Systems with Memristor

by Xianming Wu, Shaobo He, Weijie Tan and Huihai Wang

Symmetry 2022, 14(4), 659; https://doi.org/10.3390/sym14040659 - 24 Mar 2022

Cited by 8 | Viewed by 2463

Abstract

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the [...] Read more.

Based on the proposed generalized memristor, a new jerk system is proposed. The complex dynamics of the system are investigated by means of bifurcation diagrams, Lyapunov exponents, and MSampEn, and rich dynamics are observed. Moreover, the circuits of the generalized memristor and the jerk system are physically implemented in the hardware level. The experimental results show that the memristor circuit can generate “8”-shaped pinched hysteresis loops, and the observed attractors match well with the numerical simulations results. In this paper, we summarize nonlinear systems with memristors in the references. It indicates that there are two symmetry methods to find a memristor model in nonlinear systems. However, some of them cannot be realized using the memristor devices, although a memristor model can be found. For example, the famous Lorenz system contains a memristor function, but it cannot be realized using the memristor device. The principles regarding whether nonlinear systems with a memristor function can be realized using a memristor device are discussed. Full article

(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)

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19 pages, 9170 KiB

Open AccessEditor’s ChoiceArticle

Evolution of Microstructure, Texture and Corrosion Properties of Additively Manufactured AlSi10Mg Alloy Subjected to Equal Channel Angular Pressing (ECAP)

by Przemysław Snopiński, Anna Woźniak, Dariusz Łukowiec, Krzysztof Matus, Tomasz Tański, Stanislav Rusz and Ondřej Hilšer

Symmetry 2022, 14(4), 674; https://doi.org/10.3390/sym14040674 - 24 Mar 2022

Cited by 13 | Viewed by 2520

Abstract

In the selective laser melting process (SLM), the region irradiated by the laser beam is melted and quickly solidified, forming solidification lines (laser scan tracks) with symmetrical shapes. Because of the unique (rapid) crystallization conditions, the subgrain structures, typically observed inside these solidification [...] Read more.

In the selective laser melting process (SLM), the region irradiated by the laser beam is melted and quickly solidified, forming solidification lines (laser scan tracks) with symmetrical shapes. Because of the unique (rapid) crystallization conditions, the subgrain structures, typically observed inside these solidification lines, could also have variable geometric symmetrical patterns, e.g., cellular, pentagonal, or hexagonal cellular. The existence of such distinctive microstructures in SLM-made alloys has a significant impact on their superior mechanical and corrosion properties. Thus, any modification of this symmetrical microstructure (due to post-processing) can degrade or improve the properties of SLM-fabricated alloys. This study presents the experimental results on the effects of heat treatment and ECAP on microstructure modification and corrosion behavior of SLM-fabricated AlSi10Mg alloy. Light microscopy, scanning electron microscopy (SEM), electron backscattered diffraction (EBSD), and X-ray diffraction (XRD) were used for microstructural analysis. The corrosion properties of the given samples were determined using open-circuit potential (OCP), potentiodynamic polarization, and electrochemical impedance spectroscopy (EIS) techniques. EBSD observations showed that the imposed strain resulted in an obvious reduction in grain size to ~1.42 µm and ~0.24 µm after the first and second ECAP passes, respectively. Electrochemical tests revealed that the corrosion resistance of the ECAP-processed AlSi10Mg alloy improved significantly, which was confirmed by a nobler E_corr and lower I_corr values, and higher polarization resistance. The final results indicated that the strain-induced crystalline defects provided more nucleation sites for the formation of a denser and thicker oxide film, thus enhancing the corrosion resistance of the AlSi10Mg alloy. Full article

(This article belongs to the Special Issue Advances in Materials Science with Symmetry/Asymmetry)

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27 pages, 17811 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Symmetry Constraints on Spin Order Transfer in Parahydrogen-Induced Polarization (PHIP)

by Andrey N. Pravdivtsev, Danila A. Barskiy, Jan-Bernd Hövener and Igor V. Koptyug

Symmetry 2022, 14(3), 530; https://doi.org/10.3390/sym14030530 - 4 Mar 2022

Cited by 5 | Viewed by 3299

Abstract

It is well known that the association of parahydrogen (pH₂) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed [...] Read more.

It is well known that the association of parahydrogen (pH₂) with an unsaturated molecule or a transient metalorganic complex can enhance the intensity of NMR signals; the effect is known as parahydrogen-induced polarization (PHIP). During recent decades, numerous methods were proposed for converting pH₂-derived nuclear spin order to the observable magnetization of protons or other nuclei of interest, usually ¹³C or ¹⁵N. Here, we analyze the constraints imposed by the topological symmetry of the spin systems on the amplitude of transferred polarization. We find that in asymmetric systems, heteronuclei can be polarized to 100%. However, the amplitude drops to 75% in A₂BX systems and further to 50% in A₃B₂X systems. The latter case is of primary importance for biological applications of PHIP using sidearm hydrogenation (PHIP-SAH). If the polarization is transferred to the same type of nuclei, i.e., ¹H, symmetry constraints impose significant boundaries on the spin-order distribution. For AB, A₂B, A₃B, A₂B₂, AA’(AA’) systems, the maximum average polarization for each spin is 100%, 50%, 33.3%, 25%, and 0, respectively, (where A and B (or A’) came from pH₂). Remarkably, if the polarization of all spins in a molecule is summed up, the total polarization grows asymptotically with ~1.27

\sqrt{N}

and can exceed 2 in the absence of symmetry constraints (where

N

is the number of spins). We also discuss the effect of dipole–dipole-induced pH₂ spin-order distribution in heterogeneous catalysis or nematic liquid crystals. Practical examples from the literature illustrate our theoretical analysis. Full article

(This article belongs to the Special Issue Symmetry Principles in the Nuclear Magnetic Resonance)

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18 pages, 5222 KiB

Open AccessEditor’s ChoiceArticle

Position-Aware Guided Hiding Data Scheme with Reversibility and Adaptivity for Dual Images

by Chin-Chen Chang, Guo-Dong Su, Chia-Chen Lin and Yung-Hui Li

Symmetry 2022, 14(3), 509; https://doi.org/10.3390/sym14030509 - 2 Mar 2022

Cited by 4 | Viewed by 1656

Abstract

Reversible data hiding (RDH) in dual images is a technique that shares secret messages into two similar shadow images, while the secret messages and the cover image can be restored only when those two shadows are gathered simultaneously. In this paper, a novel [...] Read more.

Reversible data hiding (RDH) in dual images is a technique that shares secret messages into two similar shadow images, while the secret messages and the cover image can be restored only when those two shadows are gathered simultaneously. In this paper, a novel turtle shell-based RDH hiding scheme based on the symmetric property is presented in order to increase the embedding capacity and maintain good visual quality in dual images under the guidance of position-aware. First, we classify each pixel pair into one of four types according to their locations and then determine a sunflower area centered around it in order to construct the combination of positions and the embedding table. Using the embedding table, the secret messages are concealed into a cover image by generating two shadow images. At the decoder’s side, the complete restoration of the secret messages and the cover image can be accomplished by identifying the position relationship between the two stego-pixel pairs. The experimental results confirmed that the proposed position-aware guided RDH scheme is superior to some of the relevant works on the aspects of embedding capacity or image quality. In addition, the proposed scheme provides a secure communication that can effectively resist attacks on the pixel value difference histogram, relative entropy, and regular singular analysis. Full article

(This article belongs to the Special Issue Information Security and Cryptology: Advanced Technologies in Symmetry/Asymmetry)

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62 pages, 6768 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Neutron Stars with Baryon Number Violation, Probing Dark Sectors

by Jeffrey M. Berryman, Susan Gardner and Mohammadreza Zakeri

Symmetry 2022, 14(3), 518; https://doi.org/10.3390/sym14030518 - 2 Mar 2022

Cited by 28 | Viewed by 7056

Abstract

The neutron lifetime anomaly has been used to motivate the introduction of new physics with hidden-sector particles coupled to baryon number, and on which neutron stars provide powerful constraints. Although the neutron lifetime anomaly may eventually prove to be of mundane origin, we [...] Read more.

The neutron lifetime anomaly has been used to motivate the introduction of new physics with hidden-sector particles coupled to baryon number, and on which neutron stars provide powerful constraints. Although the neutron lifetime anomaly may eventually prove to be of mundane origin, we use it as motivation for a broader review of the ways that baryon number violation, be it real or apparent, and dark sectors can intertwine and how neutron star observables, both present and future, can constrain them. Full article

(This article belongs to the Special Issue The Neutron Physics - Dark Matter Connection: Bridge Through the Baryon Symmetry Violation)

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13 pages, 289 KiB

Open AccessEditor’s ChoiceArticle

Some Results in the Theory of a Cosserat Thermoelastic Body with Microtemperatures and Inner Structure

by Marin Marin, Sorin Vlase, Eduard M. Craciun, Nicolae Pop and Ioan Tuns

Symmetry 2022, 14(3), 511; https://doi.org/10.3390/sym14030511 - 2 Mar 2022

Cited by 6 | Viewed by 2274

Abstract

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context is transformed in a temporally evolutionary equation on a Hilbert space. Using some results from the theory of [...] Read more.

This study is concerned with the theory of Cosserat thermoelastic media, whose micro-particles possess microtemperatures. The mixed initial boundary value problem considered in this context is transformed in a temporally evolutionary equation on a Hilbert space. Using some results from the theory of semigroups, the existence and uniqueness of solution is proved. In the same manner, it approached the continuous dependence of the solution upon initial data and loads. From what we have studied, neither on the internet nor in the databases, we have not found qualitative issues addressed regarding the mixed problem in the context of the theory of thermoelasticity of Cosserat environments, in which the contribution of inner structure and microtemperatures are taken into account. Full article

(This article belongs to the Section Mathematics)

22 pages, 6035 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Improved Search for Neutron to Mirror-Neutron Oscillations in the Presence of Mirror Magnetic Fields with a Dedicated Apparatus at the PSI UCN Source

by Nicholas J. Ayres, Zurab Berezhiani, Riccardo Biondi, Georg Bison, Kazimierz Bodek, Vira Bondar, Pin-Jung Chiu, Manfred Daum, Reza Tavakoli Dinani, Cornelis B. Doorenbos, Solange Emmenegger, Klaus Kirch, Victoria Kletzl, Jochen Krempel, Bernhard Lauss, Duarte Pais, Ingo Rienäcker, Dieter Ries, Nicola Rossi, Dagmara Rozpedzik, Philipp Schmidt-Wellenburg, Kazuo S. Tanaka, Jacek Zejma, Nathalie Ziehl and Geza Zsigmond Show full author list Hide full author list

Symmetry 2022, 14(3), 503; https://doi.org/10.3390/sym14030503 - 1 Mar 2022

Cited by 18 | Viewed by 6132

Abstract

While the international nEDM collaboration at the Paul Scherrer Institut (PSI) took data in 2017 that covered a considerable fraction of the parameter space of claimed potential signals of hypothetical neutron (n) to mirror-neutron (

n^{'}

) transitions, it could [...] Read more.

While the international nEDM collaboration at the Paul Scherrer Institut (PSI) took data in 2017 that covered a considerable fraction of the parameter space of claimed potential signals of hypothetical neutron (n) to mirror-neutron (

n^{'}

) transitions, it could not test all claimed signal regions at various mirror magnetic fields. Therefore, a new study of

n - n^{'}

oscillations using stored ultracold neutrons (UCNs) is underway at PSI, considerably expanding the reach in parameter space of mirror magnetic fields (

B^{'}

) and oscillation time constants (

τ_{n n^{'}}

). The new apparatus is designed to test for the anomalous loss of stored ultracold neutrons as a function of an applied magnetic field. The experiment is distinguished from its predecessors by its very large storage vessel (1.47 m³), enhancing its statistical sensitivity. In a test experiment in 2020 we have demonstrated the capabilities of our apparatus. However, the full analysis of our recent data is still pending. Based on already demonstrated performance, we will reach sensitivity to oscillation times

τ_{n n^{'}} / \sqrt{cos (β)}

well above a hundred seconds, with

β

being the angle between

B^{'}

and the applied magnetic field B. The scan of B will allow the finding or the comprehensive exclusion of potential signals reported in the analysis of previous experiments and suggested to be consistent with neutron to mirror-neutron oscillations. Full article

(This article belongs to the Special Issue The Neutron Physics - Dark Matter Connection: Bridge Through the Baryon Symmetry Violation)

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10 pages, 1365 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Search for Cosmic Ray Bursts at 0.1 PeV with a Small Air Shower Array

by Roger Clay, Jassimar Singh, Piotr Homola, Olaf Bar, Dmitry Beznosko, Apoorva Bhatt, Gopal Bhatta, Łukasz Bibrzycki, Nikolay Budnev, David E. Alvarez-Castillo, Niraj Dhital, Alan R. Duffy, Michał Frontczak, Dariusz Góra, Alok C. Gupta, Bartosz Łozowski, Mikhail V. Medvedev, Justyna Mędrala, Justyna Miszczyk, Michał Niedźwiecki, Marcin Piekarczyk, Krzysztof Rzecki, Jilberto Zamora-Saa, Katarzyna Smelcerz, Karel Smolek, Tomasz Sośnicki, Jaroslaw Stasielak, Sławomir Stuglik, Oleksandr Sushchov, Arman Tursunov and Tadeusz Wibig Show full author list Hide full author list

Symmetry 2022, 14(3), 501; https://doi.org/10.3390/sym14030501 - 1 Mar 2022

Cited by 6 | Viewed by 2854

Abstract

The Cosmic Ray Extremely Distributed Observatory (CREDO) pursues a global research strategy dedicated to the search for correlated cosmic rays, so-called Cosmic Ray Ensembles (CRE). Its general approach to CRE detection does not involve any a priori considerations, and its search strategy encompasses [...] Read more.

The Cosmic Ray Extremely Distributed Observatory (CREDO) pursues a global research strategy dedicated to the search for correlated cosmic rays, so-called Cosmic Ray Ensembles (CRE). Its general approach to CRE detection does not involve any a priori considerations, and its search strategy encompasses both spatial and temporal correlations, on different scales. Here we search for time clustering of the cosmic ray events collected with a small sea-level extensive air shower array at the University of Adelaide. The array consists of seven one-square-metre scintillators enclosing an area of 10 m × 19 m. It has a threshold energy ~0.1 PeV, and records cosmic ray showers at a rate of ~6 mHz. We have examined event arrival times over a period of over 2.5 years in two equipment configurations (without and with GPS timing), recording ~300 k events and ~100 k events. We determined the event time spacing distributions between individual events and the distributions of time periods which contained specific numbers of multiple events. We find that the overall time distributions are as expected for random events. The distribution which was chosen a priori for particular study was for time periods covering five events (four spacings). Overall, these distributions fit closely with expectation, but there are two outliers of short burst periods in data for each configuration. One of these outliers contains eight events within 48 s. The physical characteristics of the array will be discussed together with the analysis procedure, including a comparison between the observed time distributions and expectation based on randomly arriving events. Full article

(This article belongs to the Special Issue Symmetry in Cosmic Ray Detections)

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14 pages, 1441 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

A Search for Neutron to Mirror Neutron Oscillation Using Neutron Electric Dipole Moment Measurements

by Prajwal Mohanmurthy, Albert R. Young, Jeff A. Winger and Geza Zsigmond

Symmetry 2022, 14(3), 487; https://doi.org/10.3390/sym14030487 - 28 Feb 2022

Cited by 9 | Viewed by 2597

Abstract

Baryon number violation is a key ingredient of baryogenesis. It has been hypothesized that there could also be a parity-conjugated copy of the standard model particles, called mirror particles. The existence of such a mirror universe has specific testable implications, especially in the [...] Read more.

Baryon number violation is a key ingredient of baryogenesis. It has been hypothesized that there could also be a parity-conjugated copy of the standard model particles, called mirror particles. The existence of such a mirror universe has specific testable implications, especially in the domain of neutral particle oscillation, viz. the baryon number violating neutron to mirror-neutron (

n - n^{'}

) oscillation. Consequently, there were many experiments that have searched for

n - n^{'}

oscillation, and imposed constraints upon the parameters that describe it. Recently, further analysis on some of these results have identified anomalies which could point to the detection of

n - n^{'}

oscillation. All the previous efforts searched for

n - n^{'}

oscillation by comparing the relative number of ultracold neutrons that survive after a period of storage for one or both of the two cases: (i) comparison of zero applied magnetic field to a non-zero applied magnetic field, and (ii) comparison where the orientation of the applied magnetic field was reversed. However,

n - n^{'}

oscillations also lead to variations in the precession frequency of polarized neutrons upon flipping the direction of the applied magnetic field. Precession frequencies are measured, very precisely, by experiments searching for the electric dipole moment. For the first time, we used the data from the latest search for the neutron electric dipole moment to constrain

n - n^{'}

oscillation. After compensating for the systematic effects that affect the ratio of precession frequencies of ultracold neutrons and cohabiting

^{199}

Hg-atoms, chief among which was due to their motion in non-uniform magnetic field, we constrained any further perturbations due to

n - n^{'}

oscillation. We thereby provide a lower limit on the

n - n^{'}

oscillation time constant of

τ_{n n^{'}} / \sqrt{| cos (β) |} > 5.7 s, 0.36 T^{'} < B^{'} < 1.01 T^{'}

(95% C.L.), where

β

is the angle between the applied magnetic field and the ambient mirror magnetic field. This constraint is the best available in the range of

0.36 T^{'} < B^{'} < 0.40 T^{'}

. Full article

(This article belongs to the Special Issue The Neutron Physics - Dark Matter Connection: Bridge Through the Baryon Symmetry Violation)

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13 pages, 1022 KiB

Open AccessEditor’s ChoiceSystematic Review

Genetic Factors That Affect Asymmetric Mandibular Growth—A Systematic Review

by Alicja Babczyńska, Beata Kawala and Michał Sarul

Symmetry 2022, 14(3), 490; https://doi.org/10.3390/sym14030490 - 28 Feb 2022

Cited by 6 | Viewed by 3036

Abstract

Facial asymmetry is a feature that occurs to a greater or lesser extent in the general population. As its severity is usually slight, facial asymmetry may not be noticeable to the patient. However, there are cases when severe facial asymmetry not only affects [...] Read more.

Facial asymmetry is a feature that occurs to a greater or lesser extent in the general population. As its severity is usually slight, facial asymmetry may not be noticeable to the patient. However, there are cases when severe facial asymmetry not only affects the facial aesthetics by distorting facial proportions, but also contributes to problems related to the function of the stomatognathic system. The nodal signalling pathway appears to be of particular importance in the process of mandibular asymmetry, as it affects not only structures formed from the first pharyngeal arch, but also other organs, such as the heart and lungs. Following the evaluation of the available literature, the inheritance of mandibular asymmetry is a very complex and multifactorial process, and the genes whose altered expression appears to be a more important potential aetiological factor for asymmetry include PITX2, ACTN3, ENPP1 and ESR1. This systematic review attempts to systematise the available literature concerning the impact of signalling pathway disruption, including the disruption of the nodal signalling pathway, on the development of mandibular asymmetry. Full article

(This article belongs to the Special Issue Dentofacial Asymmetry — Challenges and Perspectives)

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23 pages, 1034 KiB

Open AccessEditor’s ChoiceArticle

Infrasonic, Acoustic and Seismic Waves Produced by the Axion Quark Nuggets

by Dmitry Budker, Victor V. Flambaum and Ariel Zhitnitsky

Symmetry 2022, 14(3), 459; https://doi.org/10.3390/sym14030459 - 24 Feb 2022

Cited by 11 | Viewed by 2108

Abstract

We advocate the idea that Axion Quark Nuggets (AQN) hitting the Earth can be detected by analysing the infrasound, acoustic, and seismic waves which always accompany their passage in the atmosphere and underground. Our estimates for the infrasonic frequency

ν ≃ 5

Hz [...] Read more.

We advocate the idea that Axion Quark Nuggets (AQN) hitting the Earth can be detected by analysing the infrasound, acoustic, and seismic waves which always accompany their passage in the atmosphere and underground. Our estimates for the infrasonic frequency

ν ≃ 5

Hz and overpressure

δ p \sim 0.3

Pa for relatively large size dark matter (DM) nuggets suggest that sensitivity of presently available instruments is already sufficient to detect very intense (but very rare) events today with existing technology. A study of much more frequent but less intense events requires a new type of instrument. We propose a detection strategy for a systematic study to search for such relatively weak and frequent events by using distributed acoustic sensing and briefly mention other possible detection methods. Full article

(This article belongs to the Special Issue The Dark Universe: The Harbinger of a Major Discovery)

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48 pages, 2788 KiB

Open AccessEditor’s ChoiceReview

Chirality in Organic and Mineral Systems: A Review of Reactivity and Alteration Processes Relevant to Prebiotic Chemistry and Life Detection Missions

by Carina Lee, Jessica M. Weber, Laura E. Rodriguez, Rachel Y. Sheppard, Laura M. Barge, Eve L. Berger and Aaron S. Burton

Symmetry 2022, 14(3), 460; https://doi.org/10.3390/sym14030460 - 24 Feb 2022

Cited by 17 | Viewed by 12327

Abstract

Chirality is a central feature in the evolution of biological systems, but the reason for biology’s strong preference for specific chiralities of amino acids, sugars, and other molecules remains a controversial and unanswered question in origins of life research. Biological polymers tend toward [...] Read more.

Chirality is a central feature in the evolution of biological systems, but the reason for biology’s strong preference for specific chiralities of amino acids, sugars, and other molecules remains a controversial and unanswered question in origins of life research. Biological polymers tend toward homochiral systems, which favor the incorporation of a single enantiomer (molecules with a specific chiral configuration) over the other. There have been numerous investigations into the processes that preferentially enrich one enantiomer to understand the evolution of an early, racemic, prebiotic organic world. Chirality can also be a property of minerals; their interaction with chiral organics is important for assessing how post-depositional alteration processes could affect the stereochemical configuration of simple and complex organic molecules. In this paper, we review the properties of organic compounds and minerals as well as the physical, chemical, and geological processes that affect organic and mineral chirality during the preservation and detection of organic compounds. We provide perspectives and discussions on the reactions and analytical techniques that can be performed in the laboratory, and comment on the state of knowledge of flight-capable technologies in current and future planetary missions, with a focus on organics analysis and life detection. Full article

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

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26 pages, 18774 KiB

Open AccessEditor’s ChoiceReview

Lamellar Tetragonal Symmetry of Amphiphilic Thermotropic Ionic Liquid Crystals in the Framework of Other Closely Related Highly Ordered Structures

by Michael Arkas, Marilina Douloudi, Michail Vardavoulias and Theodora Katsika

Symmetry 2022, 14(2), 394; https://doi.org/10.3390/sym14020394 - 16 Feb 2022

Cited by 4 | Viewed by 3054

Abstract

An overview of the chemical compounds forming the rare smectic T phases is presented with references to the historical context. Thermodynamics (transition temperatures, enthalpies) along with the factors (stereochemical constraints, electrostatic interactions, aliphatic chain stacking, intermolecular forces) contributing to the adoption of tetragonal [...] Read more.

An overview of the chemical compounds forming the rare smectic T phases is presented with references to the historical context. Thermodynamics (transition temperatures, enthalpies) along with the factors (stereochemical constraints, electrostatic interactions, aliphatic chain stacking, intermolecular forces) contributing to the adoption of tetragonal scaffolds are also discussed. Characteristic optical microscopy textures and X-ray diffraction patterns are presented. In parallel, a comparison of the geometrical parameters such as distances between atoms, molecular areas, volumes, and lattice parameters with the closest two-dimensional and three-dimensional organizations, is performed. Full article

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

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19 pages, 1220 KiB

Open AccessEditor’s ChoiceArticle

Attaching Onto or Inserting Into an Intramolecular Hydrogen Bond: Exploring and Controlling a Chirality-Dependent Dilemma for Alcohols

by Manuel Lange, Elisabeth Sennert and Martin A. Suhm

Symmetry 2022, 14(2), 357; https://doi.org/10.3390/sym14020357 - 11 Feb 2022

Cited by 4 | Viewed by 2287

Abstract

Prereactive complexes in noncovalent organocatalysis are sensitive to the relative chirality of the binding partners and to hydrogen bond isomerism. Both effects are present when a transiently chiral alcohol docks on a chiral

α

-hydroxy ester, turning such 1:1 complexes into elementary, non-reactive [...] Read more.

Prereactive complexes in noncovalent organocatalysis are sensitive to the relative chirality of the binding partners and to hydrogen bond isomerism. Both effects are present when a transiently chiral alcohol docks on a chiral

α

-hydroxy ester, turning such 1:1 complexes into elementary, non-reactive model systems for chirality induction in the gas phase. With the help of linear infrared and Raman spectroscopy in supersonic jet expansions, conformational preferences are investigated for benzyl alcohol in combination with methyl lactate, also exploring p-chlorination of the alcohol and the achiral homolog methyl glycolate to identify potential London dispersion and chirality effects on the energy sequence. Three of the four combinations prefer barrierless complexation via the hydroxy group of the ester (association). In contrast, the lightest complex predominantly shows insertion into the intramolecular hydrogen bond, such as the analogous lactate and glycolate complexes of methanol. The experimental findings are rationalized with computations, and a uniform helicality induction in the alcohol by the lactate is predicted, independent of insertion into or association with the internal lactate hydrogen bond. p-chlorination of benzyl alcohol has a stabilizing effect on association because the insertion motif prevents a close contact between the chlorine and the hydroxy ester. After simple anharmonicity and substitution corrections, the B3LYP-D3 approach offers a fairly systematic description of the known spectroscopic data on alcohol complexes with

α

-hydroxy esters. Full article

(This article belongs to the Special Issue Asymmetric Molecules and Chirality Recognition)

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10 pages, 855 KiB

Open AccessEditor’s ChoiceArticle

Bayesian Interval Estimation for the Two-Parameter Exponential Distribution Based on the Right Type II Censored Sample

by Shu-Fei Wu

Symmetry 2022, 14(2), 352; https://doi.org/10.3390/sym14020352 - 10 Feb 2022

Cited by 5 | Viewed by 1980

Abstract

The Bayesian interval estimation of the scale parameter for two-parameter exponential distribution is proposed based on the right type II censored sample. Under this type of censoring, two methods of Bayesian joint confidence region of the two parameters are also proposed. The simulation [...] Read more.

The Bayesian interval estimation of the scale parameter for two-parameter exponential distribution is proposed based on the right type II censored sample. Under this type of censoring, two methods of Bayesian joint confidence region of the two parameters are also proposed. The simulation results show that the Bayesian method has a higher coverage probability than the existing method, so the Bayesian method is recommended for use. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. The predictive interval of the future observation based on the right type II censored sample is also provided. One biometrical example is given to illustrate the proposed methods for the Bayesian interval estimations and prediction interval. Full article

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

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15 pages, 2620 KiB

Open AccessEditor’s ChoiceArticle

Interface Asymmetry Induced and Surface Pressure Controlled Valence Tautomerism in Monolayers of bis-Phthalocyaninates of Lanthanides

by Daria S. Kutsybala, Alexander V. Shokurov, Alexander G. Martynov, Alexey V. Yagodin, Vladimir V. Arslanov, Yulia G. Gorbunova and Sofiya L. Selektor

Symmetry 2022, 14(2), 340; https://doi.org/10.3390/sym14020340 - 7 Feb 2022

Cited by 6 | Viewed by 1886

Abstract

Supramolecular systems based on transition metal complexes capable of reversible redox isomerization due to intramolecular electron transfer are one of the most interesting objects from the viewpoint of molecular switches’ design. In the present work, a comparative analysis of valence transformation of lanthanide [...] Read more.

Supramolecular systems based on transition metal complexes capable of reversible redox isomerization due to intramolecular electron transfer are one of the most interesting objects from the viewpoint of molecular switches’ design. In the present work, a comparative analysis of valence transformation of lanthanide complexes (Sm, Er, Tm and Yb) with donor-substituted bis-phthalocyaninates occurring during the formation and compression–extension of Langmuir monolayers was carried out using data of UV–Vis–NIR spectroscopy. It is shown that the numerical values of the Q-band positions in the absorption spectra for the extended monolayers of the complexes under study depend linearly on the ionic radius of the metal center, if the metals have an oxidation state of +2. This makes it possible to draw a direct analogy between the behavior of the studied compounds and analogous europium and cerium complexes, for which direct evidence of the valence tautomerism in such planar systems was obtained earlier. This led to the conclusion that the intramolecular electron transfer from the phthalocyanine ligand to the central metal ion [Ln³⁺(R₄Pc²⁻)(R₄Pc^•−)]⁰→[Ln²⁺(R₄Pc^•−)₂]⁰ occurs when solutions of donor-substituted bis-phthalocyaninates of samarium, erbium, thulium, and ytterbium are deposited onto the water subphase, and the reverse redox-isomeric transition is observed in most cases when the monolayer is compressed to high surface pressures. The first of these switches is related to the asymmetry of the air/water interface, and the second one is controlled by the lateral compression–expansion of the monolayer. It has been demonstrated that when bis-phthalocyanine monolayers of lanthanides with variable valence are transferred to solid substrates, the valence state of the metal center, and consequently, the redox-isomeric state of the complex, do not change. This means that we are able to form films with a predetermined state of the complex. Note that the redox-isomeric state of complexes should affect the entire range of physicochemical properties of such films. Full article

(This article belongs to the Special Issue Spin Crossover and Valence Tautomerism: Symmetry Aspects)

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53 pages, 2604 KiB

Open AccessEditor’s ChoiceReview

Low-Energy Interactions of Mesons with Participation of the First Radially Excited States in U(3) × U(3) NJL Model

by Mikhail Konstantinovich Volkov, Aleksey Aleksandrovich Pivovarov and Kanat Nurlan

Symmetry 2022, 14(2), 308; https://doi.org/10.3390/sym14020308 - 2 Feb 2022

Cited by 11 | Viewed by 2044

Abstract

The

U (3) \times U (3)

chiral symmetric NJL model describing pseudoscalar, vector, and axial-vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to [...] Read more.

The

U (3) \times U (3)

chiral symmetric NJL model describing pseudoscalar, vector, and axial-vector mesons in both the ground state and first radially excited states is shortly presented in this review. In this model, it is possible to describe a large number of low-energy interactions of mesons,

τ

lepton decays into mesons, and processes of meson production in electron–positron annihilations in satisfactory agreement with the experiments. In describing a number of processes, it turned out to be necessary to take into account the interactions of mesons in the final state. Full article

(This article belongs to the Special Issue Symmetry in Quantum Field Theory, Critical Behavior Theory and Stochastic Dynamics)

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8 pages, 499 KiB

Open AccessEditor’s ChoiceArticle

The Cosmological Constant as Event Horizon

by Enrique Gaztanaga

Symmetry 2022, 14(2), 300; https://doi.org/10.3390/sym14020300 - 1 Feb 2022

Cited by 11 | Viewed by 3613

Abstract

General Relativity allows for a cosmological constant (

Λ

) which has inspired models of cosmic Inflation and Dark Energy. We show instead that

r_{Λ} = \sqrt{3 / Λ}

corresponds to an event horizon: a causal boundary term in the action. Our [...] Read more.

General Relativity allows for a cosmological constant (

Λ

) which has inspired models of cosmic Inflation and Dark Energy. We show instead that

r_{Λ} = \sqrt{3 / Λ}

corresponds to an event horizon: a causal boundary term in the action. Our Universe is expanding inside its Schwarzschild radius

r_{S} = r_{Λ} = 2 G M

, which could have originated from a uniform free falling cloud of mass M that collapsed as a Black Hole (BH) 25 Gyrs ago. Such a BH Universe allows for large-scale structure formation without the need of Inflation or Dark Energy. Full article

(This article belongs to the Special Issue Fundamental Constants in Cosmology)

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27 pages, 5203 KiB

Open AccessEditor’s ChoiceReview

Functional Chirality: From Small Molecules to Supramolecular Assemblies

by Alaa Adawy

Symmetry 2022, 14(2), 292; https://doi.org/10.3390/sym14020292 - 1 Feb 2022

Cited by 17 | Viewed by 7579

Abstract

Many structures in nature look symmetric, but this is not completely accurate, because absolute symmetry is close to death. Chirality (handedness) is one form of living asymmetry. Chirality has been extensively investigated at different levels. Many rules were coined in attempts made for [...] Read more.

Many structures in nature look symmetric, but this is not completely accurate, because absolute symmetry is close to death. Chirality (handedness) is one form of living asymmetry. Chirality has been extensively investigated at different levels. Many rules were coined in attempts made for many decades to have control over the selection of handedness that seems to easily occur in nature. It is certain that if good control is realized on chirality, the roads will be ultimately open towards numerous developments in pharmaceutical, technological, and industrial applications. This tutorial review presents a report on chirality from single molecules to supramolecular assemblies. The realized functions are still in their infancy and have been scarcely converted into actual applications. This review provides an overview for starters in the chirality field of research on concepts, common methodologies, and outstanding accomplishments. It starts with an introductory section on the definitions and classifications of chirality at the different levels of molecular complexity, followed by highlighting the importance of chirality in biological systems and the different means of realizing chirality and its inversion in solid and solution-based systems at molecular and supramolecular levels. Chirality-relevant important findings and (bio-)technological applications are also reported accordingly. Full article

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

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11 pages, 628 KiB

Open AccessEditor’s ChoiceSystematic Review

A Systematic Review of Non-Pharmacological Interventions to Improve Gait Asymmetries in Neurological Populations

by Krista G. Meder, Chanel T. LoJacono and Christopher K. Rhea

Symmetry 2022, 14(2), 281; https://doi.org/10.3390/sym14020281 - 30 Jan 2022

Cited by 7 | Viewed by 3110

Abstract

Gait asymmetries are commonly observed in neurological populations and linked to decreased gait velocity, balance decrements, increased fall risk, and heightened metabolic cost. Interventions designed to improve gait asymmetries have varying methods and results. The purpose of this systematic review was to investigate [...] Read more.

Gait asymmetries are commonly observed in neurological populations and linked to decreased gait velocity, balance decrements, increased fall risk, and heightened metabolic cost. Interventions designed to improve gait asymmetries have varying methods and results. The purpose of this systematic review was to investigate non-pharmacological interventions to improve gait asymmetries in neurological populations. Keyword searches were conducted using PubMed, CINAHL, and Academic Search Complete. The search yielded 14 studies for inclusion. Gait was assessed using 3D motion capture systems (n = 7), pressure-sensitive mats (e.g., GAITRite; n = 5), and positional sensors (n = 2). The gait variables most commonly analyzed for asymmetry were step length (n = 11), stance time (n = 9), and swing time (n = 5). Interventions to improve gait asymmetries predominantly used gait training techniques via a split-belt treadmill (n = 6), followed by insoles/orthoses (n = 3). The literature suggests that a wide range of methods can be used to improve spatiotemporal asymmetries. However, future research should further examine kinematic and kinetic gait asymmetries. Additionally, researchers should explore the necessary frequency and duration of various intervention strategies to achieve the greatest improvement in gait asymmetries, and to determine the best symmetry equation for quantifying gait asymmetries. Full article

(This article belongs to the Special Issue Symmetry and Asymmetry in Sport Sciences)

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14 pages, 569 KiB

Open AccessEditor’s ChoiceArticle

Improving the Statistical Qualities of Pseudo Random Number Generators

by Rafael Álvarez, Francisco Martínez and Antonio Zamora

Symmetry 2022, 14(2), 269; https://doi.org/10.3390/sym14020269 - 29 Jan 2022

Cited by 6 | Viewed by 2384

Abstract

Pseudo random and true random sequence generators are important components in many scientific and technical fields, playing a fundamental role in the application of the Monte Carlo methods and stochastic simulation. Unfortunately, the quality of the sequences produced by these generators are not [...] Read more.

Pseudo random and true random sequence generators are important components in many scientific and technical fields, playing a fundamental role in the application of the Monte Carlo methods and stochastic simulation. Unfortunately, the quality of the sequences produced by these generators are not always ideal in terms of randomness for many applications. We present a new nonlinear filter design that improves the output sequences of common pseudo random generators in terms of statistical randomness. Taking inspiration from techniques employed in symmetric ciphers, it is based on four seed-dependent substitution boxes, an evolving internal state register, and the combination of different types of operations with the aim of diffusing nonrandom patterns in the input sequence. For statistical analysis we employ a custom initial battery of tests and well-regarded comprehensive packages such as TestU01 and PractRand. Analysis results show that our proposal achieves excellent randomness characteristics and can even transform nonrandom sources (such as a simple counter generator) into perfectly usable pseudo random sequences. Furthermore, performance is excellent while storage consumption is moderate, enabling its implementation in embedded or low power computational platforms. Full article

(This article belongs to the Section Computer)

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12 pages, 322 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus

by Zine El Abiddine Fellah, Mohamed Fellah, Rémi Roncen, Nicholas O. Ongwen, Erick Ogam and Claude Depollier

Symmetry 2022, 14(2), 233; https://doi.org/10.3390/sym14020233 - 25 Jan 2022

Cited by 7 | Viewed by 2458

Abstract

A fractional-order wave equation is established and solved for a space of three dimensions using spherical coordinates. An equivalent fluid model is used in which the acoustic wave propagates only in the fluid saturating the porous medium; this model is a special case [...] Read more.

A fractional-order wave equation is established and solved for a space of three dimensions using spherical coordinates. An equivalent fluid model is used in which the acoustic wave propagates only in the fluid saturating the porous medium; this model is a special case of Biot’s theory obtained by the symmetry of the Lagrangian (invariance by translation and rotation). The basic solution of the wave equation is obtained in the time domain by analytically calculating Green’s function of the porous medium and using the properties of the Laplace transforms. Fractional derivatives are used to describe, in the time domain, the fluid–structure interactions, which are of the inertial, viscous, and thermal kind. The solution to the fractional-order wave equation represents the radiation field in the porous medium emitted by a point source. An important result obtained in this study is that the solution of the fractional equation is expressed by recurrence relations that are the consequence of the modified Bessel function of the third kind, which represents a physical solution of the wave equation. This theoretical work with analytical results opens up prospects for the resolution of forward and inverse problems allowing the characterization of a porous medium using spherical waves. Full article

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

13 pages, 567 KiB

Open AccessEditor’s ChoiceArticle

Neutron-Mirror Neutron Oscillations in Absorbing Matter

by Yuri Kamyshkov, James Ternullo, Louis Varriano and Zurab Berezhiani

Symmetry 2022, 14(2), 230; https://doi.org/10.3390/sym14020230 - 25 Jan 2022

Cited by 10 | Viewed by 2409

Abstract

The possibility that a neutron can be transformed to a hidden sector particle remains intriguingly open. Proposed theoretical models conjecture that the hidden sector can be represented by a mirror sector, and the neutron n can oscillate into its sterile mirror twin [...] Read more.

The possibility that a neutron can be transformed to a hidden sector particle remains intriguingly open. Proposed theoretical models conjecture that the hidden sector can be represented by a mirror sector, and the neutron n can oscillate into its sterile mirror twin

n^{'}

, exactly or nearly degenerate in mass with n. Oscillations

n - n^{'}

can take place in vacuum or in an environment containing regular matter and a magnetic field, in which only the neutron will be subject to interactions with the environment. We describe the propagation of the oscillating

n - n^{'}

system in a cold neutron beam passing through dense absorbing materials in connection to the possible regeneration type of experiments, where the effect of

n \to n^{'} \to n

transformation can be observed. Full article

(This article belongs to the Special Issue The Neutron Physics - Dark Matter Connection: Bridge Through the Baryon Symmetry Violation)

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