Symmetry

16 pages, 877 KB

Open AccessEditor’s ChoiceArticle

Explanatory Model for Elite Canoeists’ Performance Using a Functional Electromechanical Dynamometer Based on Detected Lateral Asymmetry

by Tania Álvarez-Yates, Mario Iglesias-Caamaño, Alba Cuba-Dorado, Virginia Serrano-Gómez, Victor Ferreira-Lima, Fábio Yuzo Nakamura and Oscar García-García

Symmetry 2024, 16(3), 347; https://doi.org/10.3390/sym16030347 - 14 Mar 2024

Cited by 6 | Viewed by 2919

Abstract

Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for [...] Read more.

Canoe modality in flatwater canoeing has a clear asymmetrical nature. This study aimed (1) to determine the magnitude and direction of neuromuscular properties, range of motion (ROM) and lower-limb strength asymmetries in female and male canoeists; (2) to establish sex-individualized asymmetry thresholds for canoeists’ neuromuscular properties, ROM and lower-limb strength; and (3) to determine the relationship of canoeists’ neuromuscular properties, ROM and lower-limb strength asymmetries with a specific canoe–dynamometer performance test. Twenty-one international canoeists were assessed through tensiomyography (TMG), ROM, lower-limb explosive strength, and a specific canoe incremental dynamometric test. The magnitude of asymmetry assessed through TMG and ROM was not modulated either by sex or performance level (international medal vs. non-medal). Females showed greater asymmetry than males on muscle tone of the erector spinae towards non-stroke side (22.75% vs. 9.72%) and the tibialis anterior (30.97% vs. 16.29%), and Fmax in explosive leg press (2.41% vs. 0.63%) towards the stroke side. International medalists showed greater asymmetry in semitendinosus contraction time towards non-stroke side (20.51% vs. 9.43%) and reached Vmax earlier in explosive leg press towards stroke side leg (19.20% vs. 9.40%). A greater asymmetry in Fmax and in Vm, and a smaller asymmetry in Tvmax and in leg press showed a small predictive capacity for canoeists’ performance on a specific canoe incremental dynamometry test. Reporting reference data from world-class canoeists’ asymmetries can be of great importance for coaches to periodically control lateral asymmetry. Full article

(This article belongs to the Section Life Sciences)

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20 pages, 18983 KB

Open AccessEditor’s ChoiceArticle

A Lagrangian Analysis of Tip Leakage Vortex in a Low-Speed Axial Compressor Rotor

by Jiexuan Hou, Yangwei Liu and Yumeng Tang

Symmetry 2024, 16(3), 344; https://doi.org/10.3390/sym16030344 - 13 Mar 2024

Cited by 7 | Viewed by 2404

Abstract

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent [...] Read more.

A Lagrangian method is introduced to analyze the tip leakage vortex (TLV) behavior in a low-speed axial compressor rotor. The finite-time Lyapunov exponent (FTLE) fields are calculated based on the delayed detached-eddy simulation (DDES) results and identifying the FTLE ridges as Lagrangian coherent structures (LCSs). The computational method of the FTLE field in three-dimensional unsteady flow fields is discussed and then applied to the instantaneous flow fields at both the design and near-stall conditions. Results show that the accuracy of the particle trajectory and the density of the initial grid of the particle trajectory greatly affect the results of the FTLE field and, thus, the LCSs. Compared to the Eulerian Q method, which is calculated based on the symmetric and anti-symmetric components of the local velocity gradient tensor, the Lagrangian method has great potential in unraveling the mechanism of complex vortex structures. The LCSs show a transport barrier between the TLV and the secondary TLV, indicating two separate vortices. The aLCSs show the bubble-like and bar-like structure in the isosurfaces corresponding to the bubble and spiral breakdown patterns. Full article

(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)

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14 pages, 1755 KB

Open AccessEditor’s ChoiceArticle

Partial Control and Beyond: Controlling Chaotic Transients with the Safety Function

by Rubén Capeáns and Miguel A. F. Sanjuan

Symmetry 2024, 16(3), 338; https://doi.org/10.3390/sym16030338 - 11 Mar 2024

Cited by 4 | Viewed by 2157

Abstract

Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent [...] Read more.

Chaotic dynamical systems often exhibit transient chaos, where trajectories behave chaotically for a short amount of time before escaping to an external attractor. Sustaining transient chaotic dynamics under disturbances is challenging yet desirable for many applications. The partial control approach exploits the inherent symmetry and geometric structure of chaotic saddles, the topological object responsible of transient chaos, to enable surprising control with only small perturbations. Here, we review the latest findings in partial control techniques with the aim to sustain chaos or accelerate escapes by exploiting these intricate invariant sets. We introduce the fundamental concept of safe sets regions where orbits persist despite noise. This paper presents recent generalizations through safety functions and escape functions that automatically find the minimum control needed. Efficient numerical algorithms are presented and several examples of application are illustrated. Rather than eliminating chaos entirely, partial control techniques provide a framework to reliably control transient chaotic dynamics with minimal interventions. This approach has promising applications across diverse fields including physics, engineering, biology, and more. Full article

(This article belongs to the Special Issue Selected Papers on Nonlinear Dynamics)

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24 pages, 2695 KB

Open AccessEditor’s ChoiceArticle

Implicit and Explicit Preferences for Golden Ratio

by Claudia Salera, Camilla Vallebella, Marco Iosa and Anna Pecchinenda

Symmetry 2024, 16(3), 333; https://doi.org/10.3390/sym16030333 - 9 Mar 2024

Cited by 5 | Viewed by 8648

Abstract

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in [...] Read more.

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of the golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for the golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking them to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimatum Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in Life Sciences: Feature Papers 2024)

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15 pages, 3848 KB

Open AccessEditor’s ChoiceArticle

Unsymmetrical and C₃-Symmetrical Partially Fluorinated Hexaarylbenzenes: Effect of Terminal Alkoxy Chain Length on Photophysical and Thermophysical Behavior

by Yizhou Wang, Shigeyuki Yamada, Motohiro Yasui and Tsutomu Konno

Symmetry 2024, 16(3), 314; https://doi.org/10.3390/sym16030314 - 6 Mar 2024

Viewed by 2801

Abstract

Solution-state photoluminescence (PL) is affected by the electronic state; however, solid-state PL varies widely depending on the aggregated state. Although the synthesis and photophysical properties of unsymmetrical and C₃-symmetrical hexaarylbenzenes (HABs) have been reported, the influence of their terminal alkoxy chains [...] Read more.

Solution-state photoluminescence (PL) is affected by the electronic state; however, solid-state PL varies widely depending on the aggregated state. Although the synthesis and photophysical properties of unsymmetrical and C₃-symmetrical hexaarylbenzenes (HABs) have been reported, the influence of their terminal alkoxy chains on their physical properties remains unclear. Therefore, we synthesized a series of unsymmetrical and C₃-symmetrical partially fluorinated HABs with different alkoxy chains and investigated the effects of alkoxy chain length on the thermophysical and photophysical properties. While investigating phase transition behavior, the ethoxy-substituted unsymmetrical derivative revealed a columnar liquid-crystalline phase, whereas the other derivatives only exhibited a phase transition between crystalline and isotropic phases. While evaluating PL behavior, both the unsymmetrical and C₃-symmetrical analogs exhibited relatively strong blue PL, independent of the alkoxy chain length. Through-space π-conjugation caused the PL spectra of C₃-symmetrical derivatives to redshift compared to those of unsymmetrical derivatives. Partially fluorinated HABs exhibited relatively strong fluorescence, even in the crystalline state, depending on the alkoxy chain length, owing to the formation of various aggregated structures. Crystalline fluorinated HABs exhibited photochromism, resulting in the appearance of long-wavelength PL bands when exposed to ultraviolet (UV) irradiation, making them promising candidates for PL sensing materials for UV detection. Full article

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

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32 pages, 448 KB

Open AccessEditor’s ChoiceArticle

Quantization of a New Canonical, Covariant, and Symplectic Hamiltonian Density

by David Chester, Xerxes D. Arsiwalla, Louis H. Kauffman, Michel Planat and Klee Irwin

Symmetry 2024, 16(3), 316; https://doi.org/10.3390/sym16030316 - 6 Mar 2024

Cited by 8 | Viewed by 2206

Abstract

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the [...] Read more.

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl’s theory. Compared with Dirac’s Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras. Full article

(This article belongs to the Section Physics)

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25 pages, 897 KB

Open AccessEditor’s ChoiceArticle

Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation

by Mariusz Ciesielski

Symmetry 2024, 16(2), 252; https://doi.org/10.3390/sym16020252 - 18 Feb 2024

Cited by 6 | Viewed by 2687

Abstract

Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, [...] Read more.

Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented. Full article

(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)

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21 pages, 895 KB

Open AccessEditor’s ChoiceReview

Analysis of

B_{(s)}^{0}

→ μ⁺μ⁻ Decays at the Large Hadron Collider

by Kai-Feng Chen, Titus Mombächer and Umberto De Sanctis

Symmetry 2024, 16(2), 251; https://doi.org/10.3390/sym16020251 - 18 Feb 2024

Cited by 3 | Viewed by 2273

Abstract

This article reviews the most recent measurements of

B_{(s)}^{0}

→ μ⁺μ⁻ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of [...] Read more.

This article reviews the most recent measurements of

B_{(s)}^{0}

→ μ⁺μ⁻ decay properties at the Large Hadron Collider (LHC) which are the most precise to date. The measurements of the branching fraction and effective lifetime of the

B_{s}^{0}

→ μ⁺μ⁻ decay by the ATLAS, CMS, and LHCb collaborations, as well as the search for

B^{0}

→ μ⁺μ⁻ decays, are summarized with a focus on the experimental challenges. Furthermore, prospects are given for these measurements and new observables that become accessible with the foreseen amounts of data by the end of the LHC. Full article

(This article belongs to the Special Issue Symmetries and Anomalies in Flavour Physics)

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15 pages, 2129 KB

Open AccessEditor’s ChoiceArticle

g.ridge: An R Package for Generalized Ridge Regression for Sparse and High-Dimensional Linear Models

by Takeshi Emura, Koutarou Matsumoto, Ryuji Uozumi and Hirofumi Michimae

Symmetry 2024, 16(2), 223; https://doi.org/10.3390/sym16020223 - 12 Feb 2024

Cited by 6 | Viewed by 4557

Abstract

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to [...] Read more.

Ridge regression is one of the most popular shrinkage estimation methods for linear models. Ridge regression effectively estimates regression coefficients in the presence of high-dimensional regressors. Recently, a generalized ridge estimator was suggested that involved generalizing the uniform shrinkage of ridge regression to non-uniform shrinkage; this was shown to perform well in sparse and high-dimensional linear models. In this paper, we introduce our newly developed R package “g.ridge” (first version published on 7 December 2023) that implements both the ridge estimator and generalized ridge estimator. The package is equipped with generalized cross-validation for the automatic estimation of shrinkage parameters. The package also includes a convenient tool for generating a design matrix. By simulations, we test the performance of the R package under sparse and high-dimensional settings with normal and skew-normal error distributions. From the simulation results, we conclude that the generalized ridge estimator is superior to the benchmark ridge estimator based on the R package “glmnet”. Hence the generalized ridge estimator may be the most recommended estimator for sparse and high-dimensional models. We demonstrate the package using intracerebral hemorrhage data. Full article

(This article belongs to the Special Issue Research Topics Related to Skew-Symmetric Distributions)

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33 pages, 1158 KB

Open AccessEditor’s ChoiceReview

Direct Detection of Dark Matter: A Critical Review

by Marcin Misiaszek and Nicola Rossi

Symmetry 2024, 16(2), 201; https://doi.org/10.3390/sym16020201 - 8 Feb 2024

Cited by 38 | Viewed by 15311

Abstract

The nature of dark matter in the Universe is one of the hardest unsolved problems in modern physics. Indeed, on one hand, the overwhelming indirect evidence from astrophysics seems to leave no doubt about its existence; on the other hand, direct search experiments, [...] Read more.

The nature of dark matter in the Universe is one of the hardest unsolved problems in modern physics. Indeed, on one hand, the overwhelming indirect evidence from astrophysics seems to leave no doubt about its existence; on the other hand, direct search experiments, especially those conducted with low-background detectors in underground laboratories all over the world, seem to deliver only null results with a few debated exceptions. Furthermore, the lack of predicted candidates on the LHC energy scale has made this dichotomy even more puzzling. We will recall the most important phases of this novel branch of experimental astro-particle physics, analyzing the interconnections among the main projects involved in this challenging quest, and we will draw conclusions slightly different from how the problem is commonly understood. Full article

(This article belongs to the Section Physics)

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20 pages, 974 KB

Open AccessEditor’s ChoiceArticle

Exploring Footedness, Throwing Arm, and Handedness as Predictors of Eyedness Using Cluster Analysis and Machine Learning: Implications for the Origins of Behavioural Asymmetries

by Paul Rodway, Curtis Rodway and Astrid Schepman

Symmetry 2024, 16(2), 177; https://doi.org/10.3390/sym16020177 - 2 Feb 2024

Cited by 3 | Viewed by 3420

Abstract

Behavioural asymmetries displayed by individuals, such as hand preference and foot preference, tend to be lateralized in the same direction (left or right). This may be because their co-ordination conveys functional benefits for a variety of motor behaviours. To explore the potential functional [...] Read more.

Behavioural asymmetries displayed by individuals, such as hand preference and foot preference, tend to be lateralized in the same direction (left or right). This may be because their co-ordination conveys functional benefits for a variety of motor behaviours. To explore the potential functional relationship between key motor asymmetries, we examined whether footedness, handedness, or throwing arm was the strongest predictor of eyedness. Behavioural asymmetries were measured by self-report in 578 left-handed and 612 right-handed individuals. Cluster analysis of the asymmetries revealed four handedness groups: consistent right-handers, left-eyed right-handers, consistent left-handers, and inconsistent left-handers (who were left-handed but right-lateralized for footedness, throwing and eyedness). Supervised machine learning models showed the importance of footedness, in addition to handedness, in determining eyedness. In right-handers, handedness was the best predictor of eyedness, followed closely by footedness, and for left-handers it was footedness. Overall, predictors were more informative in predicting eyedness for individuals with consistent lateral preferences. Implications of the findings in relation to the origins and genetics of handedness and sports training are discussed. Findings are related to fighting theories of handedness and to bipedalism, which evolved after manual dexterity, and which may have led to some humans being right-lateralized for ballistic movements and left-lateralized for hand dexterity. Full article

(This article belongs to the Section Life Sciences)

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14 pages, 916 KB

Open AccessEditor’s ChoiceArticle

A Forecast of the Sensitivity of the DALI Experiment to Galactic Axion Dark Matter

by Juan F. Hernández-Cabrera, Javier De Miguel, Enrique Joven Álvarez, E. Hernández-Suárez, J. Alberto Rubiño-Martín and Chiko Otani

Symmetry 2024, 16(2), 163; https://doi.org/10.3390/sym16020163 - 30 Jan 2024

Cited by 5 | Viewed by 3385

Abstract

The axion is a long-postulated boson that can simultaneously solve two fundamental problems of modern physics: the charge–parity symmetry problem in the strong interaction and the enigma of dark matter. In this work, we estimate, by means of Monte Carlo simulations, the sensitivity [...] Read more.

The axion is a long-postulated boson that can simultaneously solve two fundamental problems of modern physics: the charge–parity symmetry problem in the strong interaction and the enigma of dark matter. In this work, we estimate, by means of Monte Carlo simulations, the sensitivity of the Dark-photons & Axion-Like particles Interferometer (DALI), a new-generation Fabry–Pérot haloscope proposed to probe axion dark matter in the 25–250

μ

eV band. Full article

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

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16 pages, 1031 KB

Open AccessEditor’s ChoiceArticle

Symmetry Breaking and Dynamic Transition in the Negative Mass Term Klein–Gordon Equations

by Ferenc Márkus and Katalin Gambár

Symmetry 2024, 16(2), 144; https://doi.org/10.3390/sym16020144 - 26 Jan 2024

Cited by 4 | Viewed by 1653

Abstract

Through the discussion of three physical processes, we show that the Klein–Gordon equations with a negative mass term describe special dynamics. In the case of two classical disciplines—mechanics and thermodynamics—the Lagrangian-based mathematical description is the same, even though the nature of the investigated [...] Read more.

Through the discussion of three physical processes, we show that the Klein–Gordon equations with a negative mass term describe special dynamics. In the case of two classical disciplines—mechanics and thermodynamics—the Lagrangian-based mathematical description is the same, even though the nature of the investigated processes seems completely different. The unique feature of this type of equation is that it contains wave propagation and dissipative behavior in one framework. The dissipative behavior appears through a repulsive potential. The transition between the two types of dynamics can be specified precisely, and its physical meaning is clear. The success of the two descriptions inspires extension to the case of electrodynamics. We reverse the suggestion here. We create a Klein–Gordon equation with a negative mass term, but first, we modify Maxwell’s equations. The repulsive interaction that appears here results in a charge spike. However, the Coulomb interaction limits this. The charge separation is also associated with the high-speed movement of the charged particle localized in a small space domain. As a result, we arrive at a picture of a fast vibrating phenomenon with an electromagnetism-related Klein–Gordon equation with a negative mass term. The calculated maximal frequency value

ω = 1.74 \times 10^{21}

1/s. Full article

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

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31 pages, 2565 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Revisiting de Broglie’s Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework

by David Darrow and John W. M. Bush

Symmetry 2024, 16(2), 149; https://doi.org/10.3390/sym16020149 - 26 Jan 2024

Cited by 9 | Viewed by 4844

Abstract

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with [...] Read more.

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation

p = ℏ k

at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article

(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)

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13 pages, 3286 KB

Open AccessEditor’s ChoiceArticle

Temperature-Dependent Phase Variations in Van Der Waals CdPS₃ Revealed by Raman Spectroscopy

by Sharidya Rahman, Hieu Ngyuen, Daniel Macdonald and Yuerui Lu

Symmetry 2024, 16(2), 140; https://doi.org/10.3390/sym16020140 - 24 Jan 2024

Cited by 4 | Viewed by 3085

Abstract

In addition to graphene, the transition metal dichalcogenides, black phosphorus and multiple other layered materials have undergone immense investigations. Among them, metal thiophosphates (MPS_x) have emerged as a promising material for various applications. While several layered metal thiophosphates with general-formula MPS [...] Read more.

In addition to graphene, the transition metal dichalcogenides, black phosphorus and multiple other layered materials have undergone immense investigations. Among them, metal thiophosphates (MPS_x) have emerged as a promising material for various applications. While several layered metal thiophosphates with general-formula MPS_x have been scrutinized extensively, van der Waals (vdW) CdPS₃ has been overlooked in the literature. Here we report on the extensive Raman scattering of layered CdPS₃, showing structural phase transition at a low temperature. The emergence of multiple new peaks at low frequency and a significant shift in peak position with temperature implied a probable change in crystal symmetry from trigonal D_3d to triclinic C_i below the phase transition temperature, T_K~180 K. In addition, we also showed a p-type performance of CdPS₃ FET fabricated using Au electrodes. This work adds CdPS₃ to the list of potential layered materials for energy application. Full article

(This article belongs to the Special Issue Symmetry/Asymmetry in 2D Materials)

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13 pages, 2726 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Revisiting the Absolute Configuration of Peyssonnoside A Using Vibrational Circular Dichroism Spectroscopy

by Andrew R. Puente, Bhuwan Khatri Chhetri, Julia Kubanek and Prasad L. Polavarapu

Symmetry 2024, 16(2), 133; https://doi.org/10.3390/sym16020133 - 23 Jan 2024

Viewed by 3202

Abstract

Peyssonnoside A is an unusual natural product consisting of a diterpene unit and a sulfonated monosaccharide. The experimental and theoretical comparison of Optical Rotatory Dispersion (ORD) and quantitative Nuclear Magnetic Resonance (NMR) data provided strong evidence for the stereochemistry of the diterpene unit. [...] Read more.

Peyssonnoside A is an unusual natural product consisting of a diterpene unit and a sulfonated monosaccharide. The experimental and theoretical comparison of Optical Rotatory Dispersion (ORD) and quantitative Nuclear Magnetic Resonance (NMR) data provided strong evidence for the stereochemistry of the diterpene unit. However, predicted Vibrational Circular Dichroism (VCD) spectra of Peyssonnoside A at the B3LYP/6-311++G(2d,2p) level showed poor correlation to the corresponding experimental spectra, preventing independent absolute configuration (AC) determination from VCD analysis. New calculations using the B3PW91 functional and the 6-311G(3df,2pd) basis set suggest that we can now independently and confidently assign the AC of Peyssonnoside A through VCD analyses. The use of f-polarization functions is responsible for the current successful assignment, compared to previously failed VCD analysis. This study highlights two important points: (a) the importance of using multiple levels of theories for satisfactorily reproducing the experimental spectra and (b) for quantitative comparisons using similarity indices, it is important to consider not only the VCD spectra but also the corresponding absorption spectra. Full article

(This article belongs to the Special Issue From Nanoclusters to Nanoparticles: Symmetry, Theory, Experiments, and Applications)

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15 pages, 13929 KB

Open AccessEditor’s ChoiceArticle

Effects of KoBo-Processing and Subsequent Annealing Treatment on Grain Boundary Network and Texture Development in Laser Powder Bed Fusion (LPBF) AlSi10Mg Alloy

by Przemysław Snopiński

Symmetry 2024, 16(1), 122; https://doi.org/10.3390/sym16010122 - 19 Jan 2024

Cited by 7 | Viewed by 2668

Abstract

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties [...] Read more.

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties that differ from bulk crystalline domains. Their effects on material properties, including mechanical strength, corrosion resistance, and electrical conductivity, make grain boundaries a focus of intense scientific investigation. In this study, the microstructural transformation of an AlSi10Mg alloy subjected to KoBo extrusion and subsequent annealing is investigated. A notable discovery is the effectiveness of a strain-annealing method for grain boundary engineering (GBE) of the LPBF AlSi10Mg alloy. In particular, this study shows a significant increase in the population of coincidence site lattice boundaries (CSL), which embody the symmetry of the crystal lattice structure. These boundaries, which are characterised by a high degree of symmetry, contribute to their special properties compared to random grain boundaries. The experimental results emphasise the crucial role of strain-induced boundary migration (SIBM) in the development of a brass texture in the microstructure of the alloy after annealing. In addition, the presented results demonstrate the feasibility of applying GBE to materials with high stacking fault energy (SFE), which opens up new possibilities for optimizing their properties. Full article

(This article belongs to the Special Issue Symmetry in Mechanical Engineering: Properties and Applications)

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19 pages, 6448 KB

Open AccessEditor’s ChoiceArticle

Constraints on Phase Transitions in Neutron Star Matter

by Len Brandes and Wolfram Weise

Symmetry 2024, 16(1), 111; https://doi.org/10.3390/sym16010111 - 18 Jan 2024

Cited by 23 | Viewed by 3392

Abstract

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known [...] Read more.

Recent inference results of the sound velocity in the cores of neutron stars are summarized. Implications for the equation of state and the phase structure of highly compressed baryonic matter are discussed. In view of the strong constraints imposed by the heaviest known pulsars, the equation of state must be very stiff in order to ensure the stability of these extreme objects. This required stiffness limits the possible appearance of phase transitions in neutron star cores. For example, a Bayes factor analysis quantifies strong evidence for squared sound velocities

c_{s}^{2} > 0.1

in the cores of 2.1 solar-mass and lighter neutron stars. Only weak first-order phase transitions with a small phase coexistence density range

Δ ρ / ρ < 0.2

(at the 68% level) in a Maxwell construction still turn out to be possible within neutron stars. The central baryon densities in even the heaviest neutron stars do not exceed five times the density of normal nuclear matter. In view of these data-based constraints, much discussed issues such as the quest for a phase transition towards restored chiral symmetry and the active degrees of freedom in cold and dense baryonic matter, are reexamined. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars II: Emergence of Symmetries in Strong Nuclear Correlations)

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23 pages, 381 KB

Open AccessEditor’s ChoiceArticle

Noether Symmetry Analysis of the Klein–Gordon and Wave Equations in Bianchi I Spacetime

by Ugur Camci

Symmetry 2024, 16(1), 115; https://doi.org/10.3390/sym16010115 - 18 Jan 2024

Cited by 6 | Viewed by 2256

Abstract

We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A [...] Read more.

We investigate the Noether symmetries of the Klein–Gordon Lagrangian for Bianchi I spacetime. This is accomplished using a set of new Noether symmetry relations for the Klein–Gordon Lagrangian of Bianchi I spacetime, which reduces to the wave equation in a special case. A detailed Noether symmetry analysis of the Klein–Gordon and the wave equations for Bianchi I spacetime is presented, and the corresponding conservation laws are derived. Full article

(This article belongs to the Special Issue Noether and Space-Time Symmetries in Physics—Volume Ⅱ)

13 pages, 336 KB

Open AccessEditor’s ChoiceArticle

Mapping GENERIC Hydrodynamics into Carter’s Multifluid Theory

by Lorenzo Gavassino

Symmetry 2024, 16(1), 78; https://doi.org/10.3390/sym16010078 - 6 Jan 2024

Cited by 5 | Viewed by 1851

Abstract

We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter; this allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that in the limit of infinite heat conductivity, [...] Read more.

We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter; this allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that in the limit of infinite heat conductivity, GENERIC heat conduction reduces to the relativistic two-fluid model for superfluidity. This surprising “crossover” is a consequence of relativistic causality: if diffusion happens too fast, all the diffusing charge cumulates on the surface of the light cone, and it eventually travels at the speed of light like a wave. Our analysis is non-perturbative and carried out in a fully non-linear regime. Full article

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

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18 pages, 1956 KB

Open AccessEditor’s ChoiceArticle

Modifying Hellwig’s Method for Multi-Criteria Decision-Making with Mahalanobis Distance for Addressing Asymmetrical Relationships

by Ewa Roszkowska

Symmetry 2024, 16(1), 77; https://doi.org/10.3390/sym16010077 - 6 Jan 2024

Cited by 5 | Viewed by 2538

Abstract

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, [...] Read more.

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig’s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig’s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig’s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable tool for decision-makers in real-life situations. It enables the evaluation of alternatives by considering interactions between criteria, providing a more comprehensive perspective for decision-making. Full article

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

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18 pages, 4133 KB

Open AccessFeature PaperEditor’s ChoiceArticle

Synthesis and Structural Elucidation of P-stereogenic Coumarins

by Kamil F. Dziuba, Sławomir Frynas, Anna E. Kozioł and Katarzyna Szwaczko

Symmetry 2024, 16(1), 73; https://doi.org/10.3390/sym16010073 - 5 Jan 2024

Cited by 3 | Viewed by 2720

Abstract

This paper presents the general synthesis of a comprehensive group of P-chiral phosphinyl derivatives with a natural coumarin-type motif. A chiral substituent was attached at the third position of the coumarin molecule via the Knoevenagel procedure using readily available P-chiral phoshinylacetic acid esters [...] Read more.

This paper presents the general synthesis of a comprehensive group of P-chiral phosphinyl derivatives with a natural coumarin-type motif. A chiral substituent was attached at the third position of the coumarin molecule via the Knoevenagel procedure using readily available P-chiral phoshinylacetic acid esters without loss of enantiomeric purity. The application of salicylaldehyde-based derivatives allowed the incorporation of substituents of different electron character into the backbone of these coumarins making them suitable for subsequent chemical modifications. As a result, we gained access to six achiral (2a–g) and a large number ((S_p)-4a–f, (S_p)-6a–e and (R_p)-8a) of new potential chiral ligand precursors, pharmaceuticals, etc. with an imbedded phosphinyl group with evidenced biological activity based on the natural coumarin backbone. The molecular structure, including absolute configuration, was determined for seven compounds. Full article

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

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30 pages, 7507 KB

Open AccessEditor’s ChoiceArticle

Data-Tracking in Blockchain Utilizing Hash Chain: A Study of Structured and Adaptive Process

by Sungbeen Kim and Dohoon Kim

Symmetry 2024, 16(1), 62; https://doi.org/10.3390/sym16010062 - 3 Jan 2024

Cited by 8 | Viewed by 5718

Abstract

This study presents a series of structured and adaptive processes aimed at tracking and verifying transactions recorded on the blockchain. Permissioned blockchains are employed across diverse enterprises for various purposes, including data recording, management, the utilization of blockchain services, and authentication. However, the [...] Read more.

This study presents a series of structured and adaptive processes aimed at tracking and verifying transactions recorded on the blockchain. Permissioned blockchains are employed across diverse enterprises for various purposes, including data recording, management, the utilization of blockchain services, and authentication. However, the processes of data tracking and transactions incur substantial resource and time expenditure. Furthermore, there is potential for information asymmetry within the blockchain ledger due to data breach attacks. Consequently, we propose a contract structured as a hash chain to mitigate resource and time consumption in the tracking and verification processes by organizing transaction hash values and content in a hash chain format based on cryptography. We generate a hash chain for the recorded transactions along the process line and expedite the tracking and verification process by navigating the relevant hash chain. This approach achieves faster and more accurate tracking procedures compared to conventional transaction tracking processes, simultaneously maintaining data symmetry within the blockchain ledger. We conduct a comparative analysis of a contract-based hash-chain-employing structure and two contracts related to tracking in terms of tracking time, CPU usage, and network traffic, among other metrics. The findings suggest that structuring transaction data in the form of a hash chain significantly enhances the efficiency and integrity of the data-tracking and verification processes. Consequently, in this study, we advocate for the adoption of contracts based on the hash chain format when leveraging the blockchain for tracking and verification purposes across various institutions. Full article

(This article belongs to the Special Issue Cryptography and Blockchain Technologies—Present Applications and Future Researches)

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13 pages, 4083 KB

Open AccessEditor’s ChoiceReview

Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision

by Yupeng Leng, Chengming He, Qian Wang, Zhixia He, Nigel Simms and Peng Zhang

Symmetry 2024, 16(1), 47; https://doi.org/10.3390/sym16010047 - 29 Dec 2023

Cited by 2 | Viewed by 3832

Abstract

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on [...] Read more.

Binary droplet collision is a basic fluid phenomenon for many spray processes in nature and industry involving lots of discrete droplets. It exists an inherent mirror symmetry between two colliding droplets. For specific cases of the collision between two identical droplets, the head-on collision and the off-center collision, respectively, show the axisymmetric and rotational symmetry characteristics, which is useful for the simplification of droplet collision modeling. However, for more general cases of the collision between two droplets involving the disparities of size ratio, surface tension, viscosity, and self-spin motions, the axisymmetric and rotational symmetry droplet deformation and inner flow tend to be broken, leading to many distinct phenomena that cannot occur for the collision between two identical droplets owing to the mirror symmetry. This review focused on interpreting the asymmetric droplet deformation and the collision-induced internal mixing that was affected by those symmetry breaking factors, such as size ratio effects, Marangoni Effects, non-Newtonian effects, and droplet self-spin motion. It helps to understand the droplet internal mixing for hypergolic propellants in the rocket engineering and microscale droplet reactors in the biological engineering, and the modeling of droplet collision in real combustion spray processes. Full article

(This article belongs to the Special Issue Symmetry in Aerospace Sciences and Applications)

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38 pages, 7240 KB

Open AccessEditor’s ChoiceArticle

Challenges of Engineering Applications of Descriptive Geometry

by Zsuzsa Balajti

Symmetry 2024, 16(1), 50; https://doi.org/10.3390/sym16010050 - 29 Dec 2023

Cited by 9 | Viewed by 6455

Abstract

Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection [...] Read more.

Descriptive geometry has indispensable applications in many engineering activities. A summary of these is provided in the first chapter of this paper, preceded by a brief introduction into the methods of representation and mathematical recognition related to our research area, such as projection perpendicular to a single plane, projection images created by perpendicular projection onto two mutually perpendicular image planes, but placed on one plane, including the research of curves and movements, visual representation and perception relying on a mathematical approach, and studies on toothed driving pairs and tool geometry in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, for which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Our aim was to examine the spatial variation in the wear of the tool edge and the machining of the components of toothed drive pairs using two cameras. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the searching for the right projection direction, and positioning cameras appropriately. A special method of enumerating the possible infinite viewpoints for the reconstruction of tool surface edge curves is presented in the second part of this paper. In the case of the monitoring the shape geometry, taking into account the interchangeability of the projection directions, i.e., the property of symmetry, all images made from two perpendicular directions were taken into account. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. A new criterion was formulated for the tested tooth edge of the hob to take into account the shading of the tooth next to it. The analysis and some of the results of the Monge mapping, suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, namely defining the conditions for camera placements that ensure reconstructibility are also presented. Taking physical shadowing into account, conclusions can be drawn about the degree of distortion of the machined surface from the spatial deformation of the edge curve of the tool reconstructed with correctly positioned cameras. Full article

(This article belongs to the Special Issue Challenges and Trends in the Application of Descriptive Geometry Field under the Current Paradigm of Computer – Assisted Design (CAD))

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13 pages, 3131 KB

Open AccessEditor’s ChoiceArticle

Stereoselectivity in Butadiene Polymerization Promoted by Using Ziegler–Natta Catalysts Based on (Anilidomethyl)pyridine Group (IV) Complexes

by Stefano Milione and Stefania Pragliola

Symmetry 2024, 16(1), 18; https://doi.org/10.3390/sym16010018 - 22 Dec 2023

Viewed by 3445

Abstract

The stereoselective polymerization of conjugated dienes promoted by using transition metal complexes has attracted much interest in both industrial and academic environments for the relevance of polydienes as synthetic rubbers and for the challenging reaction mechanisms. Among the different transition metal complexes, those [...] Read more.

The stereoselective polymerization of conjugated dienes promoted by using transition metal complexes has attracted much interest in both industrial and academic environments for the relevance of polydienes as synthetic rubbers and for the challenging reaction mechanisms. Among the different transition metal complexes, those based on group IV have been demonstrated to be versatile and efficient catalysts. Titanium complexes are generally more active than zirconium complexes. A rare exception to this trend is represented by a series of Zr(IV) complexes supported by (anilidomethyl)pyridine ligands that, after activation by using Al(iBu₂H)/MAO, were found to be highly active affording exclusively cis-1,4-polybutadiene. To rationalize this unexpected trend and to obtain more insights into the parameters that control the reactivity of group IV complexes, a theoretical investigation of the entire polymerization mechanism, employing density functional methods, was undertaken. In the framework of the widely accepted polymerization scheme, the different intermediates featuring h⁴ (both cis and trans) coordination of the monomer and h¹ or h³ (syn or anti)allyl coordination of the growing chain were scrutinized. Subsequently, the effects of the metal center on the free-energy profiles of the elementary steps involved in the reaction were examined. The results presented herein aim to achieve a better knowledge of the influence of the metal on the polymerization rates and on the stereoselectivity of the reaction. Full article

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

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12 pages, 2651 KB

Open AccessEditor’s ChoiceArticle

Chiral Separation of Vildagliptin by Capillary Electrophoresis—The Study of Enantiomeric Complexation

by Lajos Attila Papp, Gabriel Hancu, Zoltán István Szabó, Blanka Székely-Szentmiklósi, Tamás Gáti, Béla Fiser, Márta Kraszni and Gergő Tóth

Symmetry 2024, 16(1), 17; https://doi.org/10.3390/sym16010017 - 22 Dec 2023

Cited by 2 | Viewed by 2811

Abstract

Vildagliptin (VIL) is a dipeptidyl peptidase-4 inhibitor used in the treatment of type 2 diabetes mellitus; in therapy, it is available as the enantiomerically pure S-VIL, the other enantiomer R-VIL being considered as an enantiomeric impurity. A systematic screening of 16 [...] Read more.

Vildagliptin (VIL) is a dipeptidyl peptidase-4 inhibitor used in the treatment of type 2 diabetes mellitus; in therapy, it is available as the enantiomerically pure S-VIL, the other enantiomer R-VIL being considered as an enantiomeric impurity. A systematic screening of 16 cyclodextrin (CD) derivatives as chiral selectors was performed at three pH levels using phosphate (pH 2.5, pH 7.0) and acetate (pH 4.5) buffers. Method optimization employed an experimental design approach, systematically investigating the effect of buffer and CD concentration, buffer pH, capillary temperature, and applied voltage on the chiral resolution and analysis time. The method’s analytical performance was thoroughly assessed and subsequently employed for determining the enantiomeric purity of VIL in a pharmaceutical formulation. The properties of the inclusion complexes, such as stoichiometry and atomic level intermolecular host–guest interactions were studied by NMR measurements and molecular modeling. Native α-CD at acidic pH has demonstrated its exceptional suitability for the separation of VIL enantiomers with a favorable migration order (R-VIL followed by S-VIL). The optimized analytical conditions (75 mM acetate buffer, pH 4.5, containing 50 mM α-CD, 18 kV applied voltage, and 15 °C capillary temperature) provided a baseline separation of VIL enantiomers within 9 min. The developed method represents a cost-effective alternative to the enantiomeric impurity control of VIL. Symmetry is often a fundamental aspect of molecular structures and interactions, and our detailed analysis of the chiral recognition process contributes to the understanding of symmetry-related aspects in molecular systems. This developed method not only offers a cost-effective alternative for the enantiomeric impurity control of VIL but also provides valuable information regarding the mechanism of the chiral recognition process, aligning with the broader themes of symmetry in molecular sciences. Full article

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

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17 pages, 3723 KB

Open AccessFeature PaperEditor’s ChoiceReview

Synthesis of Axially Chiral Boron Compounds

by Ana Maria Faisca Phillips and Armando J. L. Pombeiro

Symmetry 2024, 16(1), 11; https://doi.org/10.3390/sym16010011 - 21 Dec 2023

Cited by 5 | Viewed by 4398

Abstract

Boron-doped organic compounds display unique properties as a result of the presence of an empty p orbital on boron and the ability to switch between a trigonal planar and a tetrahedral geometry. In recent years, they have found several applications not only as [...] Read more.

Boron-doped organic compounds display unique properties as a result of the presence of an empty p orbital on boron and the ability to switch between a trigonal planar and a tetrahedral geometry. In recent years, they have found several applications not only as synthetic reagents, e.g., in the Suzuki–Miyaura reaction, but also as pharmaceuticals and as specialized materials due to their optical and electronic properties. Some boron compounds may exist as atropisomers, and these rotamers may have different properties according to their sense of rotation. Synthetic strategies to separate them and, more recently, to obtain them in an asymmetric manner are becoming popular. In this review, we survey the literature on this emerging field of research. Full article

(This article belongs to the Special Issue Chemistry and Symmetry/Asymmetry: Feature Papers 2023)

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21 pages, 5210 KB

Open AccessEditor’s ChoiceArticle

The Effect of the Stationary Phase on Resolution in the HPLC-Based Separation of Racemic Mixtures Using Vancomycin as a Chiral Selector: A Case Study with Profen Nonsteroidal Anti-Inflammatory Drugs

by Dehbiya Gherdaoui, Madiha Melha Yahoum, Selma Toumi, Hichem Tahraoui, Fatma Bouazza, Sonia Lefnaoui, Abdelhamid Zeghdaoui, Abdeltif Amrane, Bassem Jaouadi and Jie Zhang

Symmetry 2023, 15(12), 2154; https://doi.org/10.3390/sym15122154 - 4 Dec 2023

Cited by 2 | Viewed by 4310

Abstract

Chiral resolution is a technique of choice, making it possible to obtain asymmetric and enantiomerically pure compounds from a racemic mixture. This study investigated the behavior of vancomycin when used as a chiral additive in high-performance liquid chromatography (HPLC) to separate enantiomers of [...] Read more.

Chiral resolution is a technique of choice, making it possible to obtain asymmetric and enantiomerically pure compounds from a racemic mixture. This study investigated the behavior of vancomycin when used as a chiral additive in high-performance liquid chromatography (HPLC) to separate enantiomers of nonsteroidal anti-inflammatory drugs (NSAIDs), including ketoprofen, ibuprofen, flurbiprofen, and naproxen enantiomeric impurities. We compared two achiral stationary phases (C18 and NH₂) to assess the impact of mobile phase composition and stationary phase on the vancomycin retention time in the racemic resolution of drug enantiomers. Our results demonstrated the successful enantioseparation of all drugs using vancomycin in the mobile phase (phosphate buffer 0.05 M/2-propanol, 50/50) with an NH₂ column. This enhanced separation on the NH₂ column resulted from the chromatography system’s efficiency and vancomycin dimers’ stereoselective interaction on the NH₂ surface. This study underscores the importance of stationary phase selection in the chiral resolution of NSAIDs with vancomycin as a chiral additive. It offers valuable insights for future research and development of NSAID chiral separation methods, highlighting potential vancomycin applications in this context. Full article

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

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20 pages, 24078 KB

Open AccessEditor’s ChoiceArticle

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

by Lazaros Moysis, Marcin Lawnik, Christos Volos, Murilo S. Baptista and Sotirios K. Goudos

Symmetry 2023, 15(12), 2138; https://doi.org/10.3390/sym15122138 - 1 Dec 2023

Cited by 9 | Viewed by 3684

Abstract

Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase [...] Read more.

Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase the statistical characteristics suitable for each application. This may often be hard to achieve, as the design of maps with tunable statistical properties is not a trivial task. Motivated by this, the present study explores the task of constructing maps, where the statistical measures like the mean value can be appropriately controlled by tuning the map’s parameters. For this, a family of piecewise maps is considered, with three control parameters that affect the endpoint interpolations. Numerous examples are given, and the maps are studied through a collection of numerical simulations. The maps can indeed achieve a range of values for their statistical mean. Such maps may find extensive use in relevant chaos-based applications. To showcase this, the problem of chaotic path surveillance is considered as a potential application of the designed maps. Here, an autonomous agent follows a predefined trajectory but maneuvers around it in order to imbue unpredictability to potential hostile observers. The trajectory inherits the randomness of the chaotic map used as a seed, which results in chaotic motion patterns. Simulations are performed for the designed strategy. Full article

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

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12 pages, 2354 KB

Open AccessEditor’s ChoiceArticle

Chemical Composition Optimization of Biocompatible Non-Equiatomic High-Entropy Alloys Using Machine Learning and First-Principles Calculations

by Gengzhu Zhou, Zili Zhang, Renyao Feng, Wenjie Zhao, Shenyou Peng, Jia Li, Feifei Fan and Qihong Fang

Symmetry 2023, 15(11), 2029; https://doi.org/10.3390/sym15112029 - 8 Nov 2023

Cited by 2 | Viewed by 2879

Abstract

Obtaining a suitable chemical composition for high-entropy alloys (HEAs) with superior mechanical properties and good biocompatibility is still a formidable challenge through conventional trial-and-error methods. Here, based on a large amount of experimental data, a machine learning technique may be used to establish [...] Read more.

Obtaining a suitable chemical composition for high-entropy alloys (HEAs) with superior mechanical properties and good biocompatibility is still a formidable challenge through conventional trial-and-error methods. Here, based on a large amount of experimental data, a machine learning technique may be used to establish the relationship between the composition and the mechanical properties of the biocompatible HEAs. Subsequently, first-principles calculations are performed to verify the accuracy of the prediction results from the machine learning model. The predicted Young’s modulus and yield strength of HEAs performed very well in the previous experiments. In addition, the effect on the mechanical properties of alloying an element is investigated in the selected Ti-Zr-Hf-Nb-Ta HEA with the high crystal symmetry. Finally, the Ti₈-Zr₂₀-Hf₁₆-Nb₃₅-Ta₂₁ HEA predicted by the machine learning model exhibits a good combination of biocompatibility and mechanical performance, attributed to a significant electron flow and charge recombination. This work reveals the importance of these strategies, combined with machine learning and first-principles calculations, on the development of advanced biocompatible HEAs. Full article

(This article belongs to the Special Issue Mechanical Properties of Materials and Symmetry/Asymmetry)

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23 pages, 618 KB

Open AccessEditor’s ChoiceArticle

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

by Daniel Condurache and Ionuț Popa

Symmetry 2023, 15(11), 2011; https://doi.org/10.3390/sym15112011 - 1 Nov 2023

Cited by 2 | Viewed by 1905

Abstract

The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these [...] Read more.

The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)

15 pages, 7649 KB

Open AccessEditor’s ChoiceArticle

Research on Optimal Scheduling Strategy of Microgrid Considering Electric Vehicle Access

by Zhimin Wu, Yang Zou, Feng Zheng and Ning Liang

Symmetry 2023, 15(11), 1993; https://doi.org/10.3390/sym15111993 - 28 Oct 2023

Cited by 13 | Viewed by 2646

Abstract

The random output of renewable energy and the disorderly grid connection of electric vehicles (EV) will pose challenges to the safe and stable operation of the power system. In order to ensure the reliability and symmetry of the microgrid operation, this paper proposes [...] Read more.

The random output of renewable energy and the disorderly grid connection of electric vehicles (EV) will pose challenges to the safe and stable operation of the power system. In order to ensure the reliability and symmetry of the microgrid operation, this paper proposes a microgrid optimization scheduling strategy considering the access of EVs. Firstly, in order to reduce the impact of random access to EVs on power system operation, a schedulable model of an EV cluster is constructed based on the Minkowski sum. Then, based on the wavelet neural network (WNN), the renewable energy output is predicted to reduce the influence of its output fluctuation on the operation of the power system. Considering the operation constraints of each unit in the microgrid, the network active power loss and node voltage deviation are taken as the optimization objectives, and the established microgrid model is equivalently transformed via second-order cone relaxation to improve its solution efficiency. Based on network reconfiguration and flexible load participation in demand response, the economy and reliability of system operation are improved. Finally, the feasibility and effectiveness of the proposed method are verified based on the simulation examples. Full article

(This article belongs to the Special Issue Advanced Technologies in Power Quality and Power Disturbance Data Application)

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19 pages, 532 KB

Open AccessEditor’s ChoiceArticle

Shifting Pattern Biclustering and Boolean Reasoning Symmetry

by Marcin Michalak and Jesús S. Aguilar-Ruiz

Symmetry 2023, 15(11), 1977; https://doi.org/10.3390/sym15111977 - 26 Oct 2023

Cited by 2 | Viewed by 2404

Abstract

There are several goals of the two-dimensional data analysis: one may be interested in searching for groups of similar objects (clustering), another one may be focused on searching for some dependencies between a specified one and other variables (classification, regression, associate rules induction), [...] Read more.

There are several goals of the two-dimensional data analysis: one may be interested in searching for groups of similar objects (clustering), another one may be focused on searching for some dependencies between a specified one and other variables (classification, regression, associate rules induction), and finally, some may be interested in serching for well-defined patterns in the data called biclusters. It was already proved that there exists a mathematically proven symmetry between some patterns in the matrix and implicants of data-defined Boolean function. This paper provides the new look for a specific pattern search—the pattern named the

δ

-shifting pattern. The shifting pattern is interesting, as it accounts for constant fluctuations in data, i.e., it captures situations in which all the values in the pattern move up or down for one dimension, maintaining the range amplitude for all the dimensions. Such a behavior is very common in real data, e.g., in the analysis of gene expression data. In such a domain, a subset of genes might go up or down for a subset of patients or experimental conditions, identifying functionally coherent categories. A

δ

-shifting pattern meets the necessity of shifting pattern induction together with the bias of the real values acquisition where the original shifts may be disturbed with some outer conditions. Experiments with a real dataset show the potential of our approach at finding biclusters with

δ

-shifting patterns, providing excellent performance. It was possible to find the

12 \times 9

pattern in the

112 \times 9

input data with

M S R = 0.00653

. The experiments also revealed that

δ

-shifting patterns are quite difficult to be found by some well-known methods of biclustering, as these are not designed to focus on shifting patterns—results comparable due to

M S R

had much more variability (in terms of

δ

) than patterns found with Boolean reasoning. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis II)

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15 pages, 1698 KB

Open AccessEditor’s ChoiceArticle

Deep Learning-Based Cross-Layer Power Allocation for Downlink Cell-Free Massive Multiple-Input–Multiple-Output Video Communication Systems

by Wen-Yen Lin, Tin-Hao Chang and Shu-Ming Tseng

Symmetry 2023, 15(11), 1968; https://doi.org/10.3390/sym15111968 - 24 Oct 2023

Cited by 7 | Viewed by 2408

Abstract

We propose a deep learning-based cross-layer power allocation method for asymmetric cell-free massive MIMO video communication systems. The proposed cross-layer approach considers physical layer channel state information (CSI) and the application layer rate distortion (RD) function, and it aims to enhance video quality [...] Read more.

We propose a deep learning-based cross-layer power allocation method for asymmetric cell-free massive MIMO video communication systems. The proposed cross-layer approach considers physical layer channel state information (CSI) and the application layer rate distortion (RD) function, and it aims to enhance video quality in terms of peak signal-to-noise ratio (PSNR). Our study develops a decentralized deep neural network (DNN) model to capture intricate system patterns, enabling accurate and efficient power allocation decisions. The proposed cross-layer approach includes unsupervised and hybrid (supervised/unsupervised) learning models. The numerical results show that the hybrid method achieves convergence with just 50% of the iterations required by the unsupervised learning model and that it achieves a 1 dB gain in PSNR over the baseline physical layer scheme. Full article

(This article belongs to the Special Issue Symmetry in Antenna Theory and Design)

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37 pages, 9517 KB

Open AccessEditor’s ChoiceReview

A Review of Uncertainty-Based Multidisciplinary Design Optimization Methods Based on Intelligent Strategies

by Chong Wang, Haoran Fan and Xin Qiang

Symmetry 2023, 15(10), 1875; https://doi.org/10.3390/sym15101875 - 6 Oct 2023

Cited by 10 | Viewed by 5877

Abstract

The design of aerospace systems is recognized as a complex interdisciplinary process. Many studies have shown that the exchange of information among multiple disciplines often results in strong coupling and nonlinearity characteristics in system optimization. Meanwhile, inevitable multi-source uncertainty factors continuously accumulate during [...] Read more.

The design of aerospace systems is recognized as a complex interdisciplinary process. Many studies have shown that the exchange of information among multiple disciplines often results in strong coupling and nonlinearity characteristics in system optimization. Meanwhile, inevitable multi-source uncertainty factors continuously accumulate during the optimization process, greatly compromising the system’s robustness and reliability. In this context, uncertainty-based multidisciplinary design optimization (UMDO) has emerged and has been preliminarily applied in aerospace practices. However, it still encounters major challenges, including the complexity of multidisciplinary analysis modeling, and organizational and computational complexities of uncertainty analysis and optimization. Extensive research has been conducted recently to address these issues, particularly uncertainty analysis and artificial intelligence strategies. The former further enriches the UMDO technique, while the latter makes outstanding contributions to addressing the computational complexity of UMDO. With the aim of providing an overview of currently available methods, this paper summarizes existing state-of-the art UMDO technologies, with a special focus on relevant intelligent optimization strategies. Full article

(This article belongs to the Section Engineering and Materials)

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35 pages, 5686 KB

Open AccessEditor’s ChoiceArticle

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

by Nikolay Hinov

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

Cited by 4 | Viewed by 2622

Abstract

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

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

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

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15 pages, 481 KB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Paola Marziani

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

Cited by 8 | Viewed by 3265

Abstract

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

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

β

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

M_{BH} ≳ 10^{8.7}

M

_{⊙}

. Full article

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

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20 pages, 727 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 5 | Viewed by 3219

Abstract

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

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

^{- 4}

mL·L

^{- 1}

and 10

^{- 3}

mL·L

^{- 1}

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

^{- 1}

and 100 mg·L

^{- 1}

) and the same treatment (with concentrations 5 × 10

^{- 3}

mL·L

^{- 1}

and 10

^{- 2}

mL·L

^{- 1}

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

^{- 1}

and 300 mg·L

^{- 1}

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

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

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10 pages, 329 KB

Open AccessEditor’s ChoiceArticle

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

by Reinhard Alkofer

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

Cited by 8 | Viewed by 3145

Abstract

Dynamical chiral symmetry breaking (D

χ

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

Dynamical chiral symmetry breaking (D

χ

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

χ

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

χ

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

χ

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

χ

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

χ

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

χ

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

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

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22 pages, 5890 KB

Open AccessEditor’s ChoiceArticle

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

by Lior Shamir

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

Cited by 5 | Viewed by 5974

Abstract

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

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

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

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20 pages, 7507 KB

Open AccessEditor’s ChoiceArticle

Numerical Investigation of Cavitation Bubble Jet Dynamics near a Spherical Particle

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

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

Cited by 12 | Viewed by 3328

Abstract

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

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

(This article belongs to the Section Physics)

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20 pages, 10233 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 2 | Viewed by 1615

Abstract

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

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

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

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15 pages, 387 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 10 | Viewed by 4486

Abstract

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

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

ξ

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

ϕ

and the Gauss–Bonnet topological term

G

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

F (G, ϕ)

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

(This article belongs to the Section Physics)

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22 pages, 8642 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 4 | Viewed by 2384

Abstract

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

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

(This article belongs to the Section Computer)

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18 pages, 3206 KB

Open AccessEditor’s ChoiceArticle

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

by Zhenpeng Ge and Hongfeng Wang

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

Cited by 6 | Viewed by 2214

Abstract

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

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

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

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18 pages, 427 KB

Open AccessFeature PaperEditor’s ChoiceArticle

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

by Jacob Benesty, Constantin Paleologu and Laura-Maria Dogariu

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

Cited by 3 | Viewed by 4202

Abstract

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

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

(This article belongs to the Section Engineering and Materials)

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22 pages, 997 KB

Open AccessEditor’s ChoiceArticle

A New Class of Trigonometric B-Spline Curves

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

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

Cited by 3 | Viewed by 2982

Abstract

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

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

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

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15 pages, 3759 KB

Open AccessEditor’s ChoiceArticle

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

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

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

Cited by 23 | Viewed by 2684

Abstract

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

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

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

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17 pages, 3560 KB

Open AccessFeature PaperEditor’s ChoiceArticle

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

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

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

Cited by 4 | Viewed by 3642

Abstract

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

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

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

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