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19 pages, 2725 KB  
Article
A Multi-Task Strategy Integrating Multi-Scale Fusion for Bearing Temperature Prediction in High-Speed Trains Under Variable Operating Conditions
by Ruizhi Ding, Yan Shu, Chao Xi and Huixin Tian
Symmetry 2025, 17(9), 1397; https://doi.org/10.3390/sym17091397 - 27 Aug 2025
Abstract
In this paper, the concept of symmetry is utilized to inform the structural design of our multi-sensor fusion framework—that is, the hierarchical feature extraction and spatial–temporal correlation modeling exhibit symmetrical properties across sensor nodes and temporal scales. Monitoring bearing temperature in high-speed train [...] Read more.
In this paper, the concept of symmetry is utilized to inform the structural design of our multi-sensor fusion framework—that is, the hierarchical feature extraction and spatial–temporal correlation modeling exhibit symmetrical properties across sensor nodes and temporal scales. Monitoring bearing temperature in high-speed train bogies is crucial for assessing system health and ensuring operational safety. Accurate temperature prediction facilitates proactive maintenance. However, existing models struggle to capture multi-scale temporal patterns, long-term dependencies, and spatial correlations among bearings, and they often overlook varying operating conditions. To address these challenges and enhance prediction accuracy in real-world operations, this study proposes MSC-Ada-MTL, a novel framework that integrates multi-scale feature extraction and operating condition recognition through adaptive multi-task learning. The approach employs multi-scale hierarchical temporal networks (MSHNets) to capture temporal features across different scales from multiple bogie sensors. A speed-based recognition strategy classifies operating conditions to enhance model reliability and simplify prediction tasks. By leveraging multi-task learning, the framework simultaneously models temporal dynamics and spatial correlations, creating a comprehensive prediction model. Validation and ablation experiments demonstrate significant improvements in prediction accuracy and robustness across diverse operating scenarios. The proposed method effectively addresses the limitations of existing approaches by synergistically combining temporal multi-scale analysis, operational condition awareness, and spatial–temporal relationship modeling, providing enhanced adaptability for real-world railway maintenance applications. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Machine Learning)
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17 pages, 4213 KB  
Article
Physical Mechanisms of Linear and Nonlinear Optical Responses in Ferrocene-Embedded Cycloparaphenylenes
by Gang Zhang, Qianqian Wang, Yi Zou, Ying Jin and Jingang Wang
Chemistry 2025, 7(5), 136; https://doi.org/10.3390/chemistry7050136 - 25 Aug 2025
Abstract
This study employs molecular orbital (MO) analysis, density of states (DOS) analysis, and advanced techniques such as charge density difference (CDD), transition density matrix (TDM), transition electric dipole moment density (TEDM), and transition magnetic dipole moment density (TMDM) to systematically investigate the electronic [...] Read more.
This study employs molecular orbital (MO) analysis, density of states (DOS) analysis, and advanced techniques such as charge density difference (CDD), transition density matrix (TDM), transition electric dipole moment density (TEDM), and transition magnetic dipole moment density (TMDM) to systematically investigate the electronic structure characteristics of Fc-[8]CPP and Fc-[11]CPP. Using density functional theory (DFT) and time-dependent DFT (TD-DFT), the π-electron delocalization properties and optical behaviors of these molecules were analyzed. Furthermore, their responses to external electromagnetic fields were explored through electronic circular dichroism (ECD) and Raman spectroscopy, comparing chiral optical responses and electron–vibration coupling effects to elucidate their photophysical properties. The results reveal that the HOMO-LUMO energy gaps of Fc-[8]CPP and Fc-[11]CPP are 5.81 eV and 5.95 eV, respectively, with a slight increase as ring size grows; Fc-[8]CPP exhibits a stronger chiral response, while Fc-[11]CPP shows reduced chirality due to enhanced symmetry. Finally, TD-DFT calculations demonstrate that their optical absorption is dominated by localized excitations with partial charge transfer contributions. These findings provide a theoretical foundation for designing conjugated macrocyclic materials with superior optoelectronic performance. Full article
(This article belongs to the Section Theoretical and Computational Chemistry)
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17 pages, 5917 KB  
Article
Finite Element Simulation and Parametric Analysis of Load–Displacement Characteristics of Diaphragm Springs in Commercial Vehicle Clutches
by Ming Cheng, Zhen Shi, Jianhui Zhang and Pingxiang Ming
Symmetry 2025, 17(9), 1378; https://doi.org/10.3390/sym17091378 - 23 Aug 2025
Viewed by 184
Abstract
Diaphragm springs, as critical components in commercial vehicle clutch assemblies, directly determine the clutch’s working performance. The design of diaphragm springs, which possess a distinct symmetrical structure that underpins their mechanical behavior, centers on obtaining the large-end nonlinear load–displacement curve—a typical large deformation-induced [...] Read more.
Diaphragm springs, as critical components in commercial vehicle clutch assemblies, directly determine the clutch’s working performance. The design of diaphragm springs, which possess a distinct symmetrical structure that underpins their mechanical behavior, centers on obtaining the large-end nonlinear load–displacement curve—a typical large deformation-induced nonlinear problem. Traditional design relies on the A-L formula, but studies show finite element analysis (FEA) yields results closer to actual measurements. This study established an FEA model of the diaphragm spring’s disc spring (excluding separation fingers) and validated its correctness by comparing it with the A-L formula. Then, using FEA on models with separation fingers, it analyzed factors influencing the large-end load–displacement characteristics. Leveraging the inherent symmetry of the diaphragm spring structure, particularly the symmetrical distribution of separation fingers, the analysis process efficiently captures uniform mechanical responses during deformation, while this symmetric arrangement also ensures balanced load distribution during clutch operation, a critical factor for stabilizing the load–displacement curve. Results indicate the separation finger root is a key factor, with larger root holes, square holes (compared to circular ones), and more separation fingers reducing stiffness to effectively adjust the curve; in contrast, the tip and length of separation fingers have little impact, making the latter unsuitable for design adjustments. Full article
(This article belongs to the Section Engineering and Materials)
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20 pages, 4906 KB  
Article
Evaluation of Smile Aesthetics in Dental Students: Perceptions of Tooth Colour Changes Due to Incisor Inclination and Micro- and Mini-Aesthetic Characteristics Assessed by Professionals and Laypersons
by Eugen Bud, Alexandru Vlasa, Anamaria Bud, Mariana Pacurar, Sorana Maria Bucur, Daniela Esian, Elena Stepco, Olga Cheptanaru, Bianca Gabriela Nenec and Andrei Cosmin Nenec
Dent. J. 2025, 13(8), 380; https://doi.org/10.3390/dj13080380 - 20 Aug 2025
Viewed by 240
Abstract
Background: The present study investigated the relation between dental inclination, colorimetric variation, and aesthetic perception according to the modification of incisor inclination. Smile aesthetics, shaped by morphological factors and patient perception, are vital for social attractiveness and treatment success. This study aimed to [...] Read more.
Background: The present study investigated the relation between dental inclination, colorimetric variation, and aesthetic perception according to the modification of incisor inclination. Smile aesthetics, shaped by morphological factors and patient perception, are vital for social attractiveness and treatment success. This study aimed to assess the effect of varying head tilt on the perceived colour of upper central incisors by simulating changes in torque of the tooth, as well as evaluate factors influencing the perception of an aesthetic smile, including morphological characteristics and gingival aesthetic parameters. Methods: The study was comprised of three stages: colour analysis, evaluation of micro- and mini-aesthetic smile features, and an image-based assessment to determine evaluator perceptions and overall smile attractiveness. A sample of 50 students with complete, lesion-free anterior dentition was analysed. To simulate the effect of orthodontic torque changes during colour analysis, subjects tilted their heads downward and upward, representing palatal and buccal crown torque, respectively. Standardized macro-intraoral photographs were captured under controlled lighting conditions using a DSLR camera stabilized on a tripod in the different positions: the neutral head position (p0), 15° upward (p + 15), and 15° downward (p − 15). Digital colour analysis was conducted in the CIELAB colour space (L*, a*, b*). In the next stage, focusing on micro- and mini-aesthetic evaluation, an additional 50 smiles were generated using artificial intelligence via the SmileCloud program—one digitally enhanced smile per subject—complementing the initial set of 50 spontaneous smiles. These 100 smile images were evaluated by 50 laypersons and 50 dentists using a visual analogue scale via an online questionnaire, in order to assess perceptions, determine smile attractiveness, and quantify gingival aesthetic parameters. Results: The statistically significant regression results are as follows: those for the L* values in all three head inclinations: downward (−15 degrees), upward (+15 degrees), and total tilting (−15 to +15 degrees), as well as for the a* values for downward tilting and the b* values for total tilting. When the head is tilted downwards, the central incisors are positioned retrusively, and the L* b* values reveal a darker and more yellowish appearance, whereas, with the head tilted upwards, the central incisors protrude, and L* a* values indicate a brighter and more greenish appear. In the evaluation stage of the smile aesthetics study, no significant differences were observed in the judgments between laypersons and dentists or between males and females. Smiles with a high or average anterior line, parallel arc, upward lip curvature, visible first/second premolars, a smile index of 5.08–5.87, and symmetry score of 1.04 were rated as more attractive. Significant asymmetries were observed between upper dental hemi-quadrants in gingival contour and interdental papilla height, highlighting subtle morphological variations relevant to smile aesthetics. Conclusions: Aesthetic assessment revealed that the findings suggest a measurable impact of head position on dental colour perception and aesthetic evaluation. Evaluator variables including profession and gender exerted negligible effects on aesthetic perception, whereas smile attractiveness features and gingival aesthetic parameters demonstrate significant clinical applicability in patient management. Full article
(This article belongs to the Special Issue Advances in Esthetic Dentistry)
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16 pages, 2789 KB  
Article
A Numerical Study on Lightning Damages and Residual Strength of CFRP Laminates Considering Delamination Induced by Thermal Stress
by Qian-Zhi Yin, Jiapeng Bian and Yin Fan
Polymers 2025, 17(16), 2245; https://doi.org/10.3390/polym17162245 - 19 Aug 2025
Viewed by 348
Abstract
Most numerical studies on carbon fiber-reinforced polymer (CFRP) lightning damages fail to account for delamination, a factor that plays a significant role in the subsequent analysis of residual strength. This study establishes an electro-thermo-mechanical coupled numerical model incorporating delamination effects to predict lightning-induced [...] Read more.
Most numerical studies on carbon fiber-reinforced polymer (CFRP) lightning damages fail to account for delamination, a factor that plays a significant role in the subsequent analysis of residual strength. This study establishes an electro-thermo-mechanical coupled numerical model incorporating delamination effects to predict lightning-induced damage in carbon fiber-reinforced plastic (CFRP) composites. Subsequently, parametric investigations evaluate the influence of varying input loads and stacking sequences on interlaminar pyrolysis and delamination damage, with damage assessment quantitatively conducted based on simulated post-strike uniaxial ultimate compressive loads. Post-strike uniaxial compressive strength reduction with cohesive elements is 28.91%, demonstrating closer alignment with experimental reduction (36.72%) than the 21.12% reduction predicted by the interlaminar-effect-neglecting model. Under combined thermal expansion and shockwave overpressure, the 28.91% compressive strength reduction demonstrates closer alignment with the experimental 36.72% reduction than the 25.13% reduction observed under isolated shockwave overpressure. The results highlight the critical role of thermal delamination in compressive strength reduction, with distinct waveform-dependent mechanisms: under C-waveform lightning currents, arc thermal effects cannot be neglected; D-waveform strikes exhibit predominant contributions from impact loading to delamination damage, with thermally driven delamination likewise pronounced. Increased current amplitude correlates with amplified mechanical damage severity, while premature symmetry in ply stacking sequences exacerbates compressive performance degradation. This work enhances multi-physics modeling fidelity by bridging thermal delamination and mechanical degradation pathways, offering foundational insights for optimizing lightning strike resistance in advanced aerospace composite systems. Full article
(This article belongs to the Special Issue Fibre-Reinforced Polymer Laminates: Structure and Properties)
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23 pages, 4588 KB  
Article
Discrete Memristor-Based Hyperchaotic Map and Its Analog Circuit Implementation
by Haiwei Sang, Zongyun Yang, Xianzhou Liu, Qiao Wang and Xiong Yu
Symmetry 2025, 17(8), 1358; https://doi.org/10.3390/sym17081358 - 19 Aug 2025
Viewed by 276
Abstract
In this paper, control parameters are incorporated into the absolute discrete memristor (A-DM) map proposed by Bao, and its dynamic characteristics are analyzed. Subsequently, the A-DM is introduced into the traditional sine map via parallel coupling to construct a new sine A-DM hyperchaotic [...] Read more.
In this paper, control parameters are incorporated into the absolute discrete memristor (A-DM) map proposed by Bao, and its dynamic characteristics are analyzed. Subsequently, the A-DM is introduced into the traditional sine map via parallel coupling to construct a new sine A-DM hyperchaotic map (SAHM). The dynamics of SAHM are investigated using Lyapunov exponent spectra and bifurcation diagrams, with additional analysis on its multi-stability and symmetry properties. Circuit simulations successfully realize the attractors corresponding to SAHM under typical parameters. Evaluations of SAHM’s complexity, performance comparisons, and its application to pseudorandom number generators (PRNG) demonstrate that SAHM is well-suited for secure encryption scenarios. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Chaos Theory and Application)
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28 pages, 2049 KB  
Article
Joint Optimization of Delivery Time, Quality, and Cost for Complex Product Supply Chain Networks Based on Symmetry Analysis
by Peng Dong, Weibing Chen, Kewen Wang and Enze Gong
Symmetry 2025, 17(8), 1354; https://doi.org/10.3390/sym17081354 - 19 Aug 2025
Viewed by 246
Abstract
Products with complex structures are structurally intricate and involve multiple professional fields and engineering construction elements, making it difficult for a single contractor to independently develop and manufacture such complex structural products. Therefore, during the research, development, and production of complex products, collaboration [...] Read more.
Products with complex structures are structurally intricate and involve multiple professional fields and engineering construction elements, making it difficult for a single contractor to independently develop and manufacture such complex structural products. Therefore, during the research, development, and production of complex products, collaboration between manufacturers and suppliers is essential to ensure the smooth completion of projects. In this process, a complex supply chain network is often formed to achieve collaborative cooperation among all project participants. Within such a complex supply chain network, issues such as delayed delivery, poor product quality, or low resource utilization by any participant may trigger the bullwhip effect. This, in turn, can negatively impact the delivery cycle, product cost, and quality of the entire complex product, causing it to lose favorable competitive positions such as quality advantages and delivery advantages in fierce market competition. Therefore, this paper firstly explores the mechanism of complex product manufacturing and the supply network of complex product manufacturing, in order to grasp the inherent structure of complex product manufacturing with a focus on identifying symmetrical properties among supply chain nodes. Secondly, a complex product supply chain network model is constructed with the Graphical Evaluation and Review Technique (GERT), incorporating symmetry constraints to reflect balanced resource allocation and mutual dependencies among symmetrical nodes. Then, from the perspective of supply chain, we focus on identifying the shortcomings of supply chain suppliers and optimizing the management cost of the whole supply chain in order to improve the quality of complex products, delivery level, and cost saving level. This study constructs a Restricted Grey GERT (RG-GERT) network model with constrained outputs, integrates moment-generating functions and Mason’s Formula to derive transfer functions, and employs a hybrid algorithm (genetic algorithm combined with non-linear programming) to solve the multi-objective optimization problem (MOOP) for joint optimization of delivery time, quality, and cost. Empirical analysis is conducted using simulated data from Y Company’s aerospace equipment supply chain, covering interval parameters such as delivery time [5–30 days], cost [40,000–640,000 CNY], and quality [0.85–1.0], validated with industry-specific constraints. Empirical analysis using Y Company’s aerospace supply chain data shows that the model achieves a maximum customer satisfaction of 0.96, with resource utilization efficiency of inefficient suppliers improved by 15–20% (p < 0.05) after secondary optimization. Key contributions include (1) integrating symmetry analysis to simplify network modeling; (2) extending GERT with grey parameters for non-probabilistic uncertainty; (3) developing a two-stage optimization framework linking customer satisfaction and resource efficiency. Full article
(This article belongs to the Section Computer)
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28 pages, 2339 KB  
Article
Biomechanical Effects of Lower Limb Asymmetry During Running: An OpenSim Computational Study
by Andreea Maria Mănescu, Carmen Grigoroiu, Neluța Smîdu, Corina Claudia Dinciu, Iulius Radulian Mărgărit, Adrian Iacobini and Dan Cristian Mănescu
Symmetry 2025, 17(8), 1348; https://doi.org/10.3390/sym17081348 - 18 Aug 2025
Viewed by 404
Abstract
Symmetry and asymmetry significantly influence running biomechanics, performance, and injury risk. Given the practical, ethical, and methodological constraints inherent in human-subject studies, computational modeling emerges as a valuable alternative for exploring biomechanical asymmetries in detail. This study systematically evaluated the mechanical effects of [...] Read more.
Symmetry and asymmetry significantly influence running biomechanics, performance, and injury risk. Given the practical, ethical, and methodological constraints inherent in human-subject studies, computational modeling emerges as a valuable alternative for exploring biomechanical asymmetries in detail. This study systematically evaluated the mechanical effects of lower limb imbalance during running using a simulation-based musculoskeletal framework in OpenSim. A total of 130 simulations were performed, incorporating controlled asymmetries in limb strength, stride length, and ground reaction forces (±5% and ±10%), to quantify alterations in joint moments, ground reaction forces (GRF), and muscular activation patterns. Results demonstrated clear biomechanical deviations under asymmetric conditions. Vertical ground reaction forces (GRF) decreased on the weaker limb and increased on the stronger limb, with peak knee joint moments rising by up to 20% under pronounced asymmetry. Muscle activation in major lower limb muscles, including the gastrocnemius and quadriceps, increased substantially on the stronger side, reflecting compensatory mechanical loading. These findings highlight the negative consequences of uneven limb loading and support the use of computational modeling to guide personalized training, rehabilitation, and injury prevention strategies. Full article
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16 pages, 1879 KB  
Article
Parameter-Gain Accelerated ZNN Model for Solving Time-Variant Nonlinear Inequality-Equation Systems and Application on Tracking Symmetrical Trajectory
by Yihui Lei, Longyi Xu and Jialiang Chen
Symmetry 2025, 17(8), 1342; https://doi.org/10.3390/sym17081342 - 17 Aug 2025
Viewed by 265
Abstract
Time-variant nonlinear problems have always been a kind of complex research object in the field of control. The accuracy and efficiency of settling time-variant nonlinear inequality-equation (NIE) systems are often affected by the nonlinearity degree of the systems, and there are currently no [...] Read more.
Time-variant nonlinear problems have always been a kind of complex research object in the field of control. The accuracy and efficiency of settling time-variant nonlinear inequality-equation (NIE) systems are often affected by the nonlinearity degree of the systems, and there are currently no complete algorithms to settle the time-variant NIE systems effectively. To settle this class of complex systems effectively, time-variant NIE systems are first equivalently transformed into a time-variant equation by introducing a nonnegative variable. Then, through the idea of zeroing neural network (ZNN) and the role of time-variant parameter-gain functions, a parameter-gain accelerated ZNN (PGAZNN) model is proposed to solve time-variant NIE systems. Theoretically, the stability of the proposed PGAZNN model is proved by strict mathematical analysis. In addition, the PGAZNN model can achieve fixed-time convergence, and the upper-bound of convergence time is estimated. Finally, numerical simulation example and symmetry trajectory tracking are given to verify the validity and correctness of the proposed PGAZNN model. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Intelligent Control and Computing)
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24 pages, 1377 KB  
Review
Statistical Analysis and Mechanisms of Aircraft Electrical Power System Failures Under Redundant Symmetric Architecture: A Review
by Zhaoyang Zeng, Jinkai Wang, Qingyu Zhu, Changqi Qu and Xiaochun Fang
Symmetry 2025, 17(8), 1341; https://doi.org/10.3390/sym17081341 - 17 Aug 2025
Viewed by 387
Abstract
The aircraft power supply system plays a crucial role in maintaining the stability and safety of airborne avionics. With the evolution toward more electric and all-electric aircraft, its architecture increasingly adopts symmetrical configurations, such as dual-redundant paths and three-phase balanced outputs. However, these [...] Read more.
The aircraft power supply system plays a crucial role in maintaining the stability and safety of airborne avionics. With the evolution toward more electric and all-electric aircraft, its architecture increasingly adopts symmetrical configurations, such as dual-redundant paths and three-phase balanced outputs. However, these symmetry-based designs are often disrupted by diverse fault mechanisms encountered in complex operational environments. This review contributes a comprehensive and structured analysis of how such fault events lead to symmetry-breaking phenomena across different subsystems, including generators, converters, controllers, and distribution networks. Unlike previous reviews that treat faults in isolation, this study emphasizes the underlying physical mechanisms and hierarchical fault propagation characteristics, revealing how structural coupling and multi-physics interactions give rise to failure modes. The paper concludes by outlining future research directions in symmetry-aware fault modeling and intelligent maintenance strategies, aiming to address the growing complexity and reliability demands of next-generation aircraft. Full article
(This article belongs to the Special Issue Symmetry in Fault Detection and Diagnosis for Dynamic Systems)
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12 pages, 2131 KB  
Article
Harnessing Excited-State Iminium Form in 1,5-Diaminonaphthalene for Rapid Water Detection in Organic Solvents
by Erika Kopcsik, Péter Kun and Miklós Nagy
Photochem 2025, 5(3), 22; https://doi.org/10.3390/photochem5030022 - 15 Aug 2025
Viewed by 226
Abstract
Accurate detection of water in organic solvents is essential for various industrial and analytical applications. In this study, we present a simple, rapid, and sensitive fluorescence-based method for water quantification using 1,5-diaminonaphthalene (1,5-DAN) as a solvatochromic probe. This method exploits the excited-state intramolecular [...] Read more.
Accurate detection of water in organic solvents is essential for various industrial and analytical applications. In this study, we present a simple, rapid, and sensitive fluorescence-based method for water quantification using 1,5-diaminonaphthalene (1,5-DAN) as a solvatochromic probe. This method exploits the excited-state intramolecular charge transfer (ICT) behavior of 1,5-DAN, which undergoes a symmetry-breaking transition in the presence of protic solvents such as water, leading to a distinct redshift in its emission spectrum and a change from a structured double-band to a single ICT band. We demonstrate that, in solvents like acetonitrile and tetrahydrofuran, the emission maxima of 1,5-DAN correlate linearly with water content up to 100%, while ratiometric analysis of peak intensities allows for sensitive detection in low concentration ranges. This method achieved limits of detection as low as 0.08% (v/v) in MeCN, with high reproducibility and minimal sample preparation. Application to a real MeCN–water azeotrope confirms the method’s accuracy, matching classical refractometric measurements. Our findings highlight the potential of 1,5-DAN as a low-cost, efficient, and non-destructive fluorescent sensor for monitoring moisture in organic solvents, offering a practical alternative to conventional methods such as Karl Fischer titration for both bulk and trace water analysis. Full article
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23 pages, 1445 KB  
Article
Inclined MHD Flow of Carreau Hybrid Nanofluid over a Stretching Sheet with Nonlinear Radiation and Arrhenius Activation Energy Under a Symmetry-Inspired Modeling Perspective
by Praveen Kumari, Hemant Poonia, Pardeep Kumar and Md Aquib
Symmetry 2025, 17(8), 1330; https://doi.org/10.3390/sym17081330 - 15 Aug 2025
Viewed by 322
Abstract
This work investigates the intricate dynamics of the Carreau hybrid nanofluid’s inclined magnetohydrodynamic (MHD) flow, exploring both active and passive control modes. The study incorporates critical factors, including Arrhenius activation energy across a stretched sheet, chemical interactions, and nonlinear thermal radiation. The formulation [...] Read more.
This work investigates the intricate dynamics of the Carreau hybrid nanofluid’s inclined magnetohydrodynamic (MHD) flow, exploring both active and passive control modes. The study incorporates critical factors, including Arrhenius activation energy across a stretched sheet, chemical interactions, and nonlinear thermal radiation. The formulation of the boundary conditions and governing equations is inherently influenced by symmetric considerations in the physical geometry and flow assumptions. Such symmetry-inspired modeling facilitates dimensional reduction and numerical tractability. The analysis employs realistic boundary conditions, including convective heat transfer and control of nanoparticle concentration, which are solved numerically using MATLAB’s bvp5c solver. Findings indicate that an increase in activation energy results in a steeper concentration boundary layer under active control, while it flattens in passive scenarios. An increase in the Biot number (Bi) and relaxation parameter (Γ) enhances heat transfer and thermal response, leading to a rise in temperature distribution in both cases. Additionally, the 3D surface plot illustrates elevation variations from the surface at low inclination angles, narrowing as the angle increases. The Nusselt number demonstrates a contrasting trend, with thermal boundary layer thickness increasing with higher radiation parameters. A graphical illustration of the average values of skin friction, Nusselt number, and Sherwood number for both active and passive scenarios highlights the impact of each case. Under active control, the Brownian motion’s effect diminishes, whereas it intensifies in passive control. Passive techniques, such as zero-flux conditions, offer effective and low-maintenance solutions for systems without external regulation, while active controls, like wall heating and setting a nanoparticle concentration, maximize heat and mass transfer in shear-thinning Carreau fluids. Full article
(This article belongs to the Special Issue Symmetrical Mathematical Computation in Fluid Dynamics)
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15 pages, 8766 KB  
Article
Strong-Field Interaction of Molecules with Linearly Polarized Light: Pathway to Circularly Polarized Harmonic Generation
by Shushan Zhou, Hao Wang, Nan Xu, Dan Wu and Muhong Hu
Symmetry 2025, 17(8), 1329; https://doi.org/10.3390/sym17081329 - 15 Aug 2025
Viewed by 272
Abstract
In recent years, the generation of circularly polarized attosecond pulses has garnered significant attention due to their potential applications in ultrafast spectroscopy and, notably, in chiral-sensitive molecular detection. The traditional methods for generating such pulses often involve complex laser configurations or specially engineered [...] Read more.
In recent years, the generation of circularly polarized attosecond pulses has garnered significant attention due to their potential applications in ultrafast spectroscopy and, notably, in chiral-sensitive molecular detection. The traditional methods for generating such pulses often involve complex laser configurations or specially engineered targets, limiting their experimental feasibility. In this study, we present a streamlined and effective approach to producing circularly polarized attosecond pulses by employing a linearly polarized laser field in conjunction with a stereosymmetric linear molecule, 1-butyne (C4H6). The generation of high-order harmonics by this molecular system reveals a distinct plateau in the perpendicular polarization component, which facilitates the generation of isolated attosecond pulses with circular polarization. Through a detailed analysis of the time-dependent charge density dynamics across atomic sites, we identify the atoms primarily responsible for the emission of circularly polarized harmonics in the plane orthogonal to the driving field. Moreover, we explore the role of multi-orbital contributions in shaping the polarization properties of the harmonic spectra. Our findings underscore the importance of molecular symmetry and the electronic structure in tailoring the harmonic polarization, and they demonstrate a viable pathway for using circularly polarized attosecond pulses to probe molecular chirality. This method offers a balance between simplicity and performance, opening new avenues for practical applications in chiral recognition and ultrafast stereochemical analysis. Full article
(This article belongs to the Section Physics)
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2 pages, 123 KB  
Editorial
Applications Based on Symmetry/Asymmetry in Fluid Mechanics
by Xi Chen
Symmetry 2025, 17(8), 1323; https://doi.org/10.3390/sym17081323 - 14 Aug 2025
Viewed by 166
Abstract
This Special Issue of Symmetry is devoted to recent advances in the analysis and applications of fluid mechanics based on Symmetry/Asymmetry [...] Full article
(This article belongs to the Special Issue Applications Based on Symmetry/Asymmetry in Fluid Mechanics)
25 pages, 12363 KB  
Review
Clock Noise Suppression Techniques in Space-Borne Gravitational Wave Detection: A Review
by Yijun Xia, Aoting Fang, Mingyang Xu, Yujie Tan and Chenggang Shao
Symmetry 2025, 17(8), 1314; https://doi.org/10.3390/sym17081314 - 13 Aug 2025
Viewed by 283
Abstract
Space-borne gravitational wave (GW) detection is poised to significantly advance the frontiers of astrophysics, gravitation, and cosmology, which might make it possible to measure the fundamental symmetries of space-time. A critical component in GW detection is the employment of ultra-stable oscillators (USOs) on [...] Read more.
Space-borne gravitational wave (GW) detection is poised to significantly advance the frontiers of astrophysics, gravitation, and cosmology, which might make it possible to measure the fundamental symmetries of space-time. A critical component in GW detection is the employment of ultra-stable oscillators (USOs) on each satellite, serving as precision timing references to drive analog-to-digital converters (ADCs) for digital sampling of GW signals. Achieving the required sensitivity in GW detection hinges on highly accurate clock timing. However, the challenges posed by ADC aperture jitter and sampling clock jitter cannot be overlooked. They disrupt sampling timing, introduce clock noise, and distort the digitized signal, thus limiting the effectiveness of GW detection in space. To overcome this problem, researchers have developed pilot tone correction techniques and proposed innovative clock noise calibrated time-delay interferometry (TDI), optical comb TDI techniques, and sideband arm locking techniques that effectively suppress the effects of clock noise. This study provides an in-depth and comprehensive summary of the current status of clock noise and its suppression techniques in the space-borne GW detection. Through a systematic review and analysis, the aim is to provide theoretical and experimental technical support and optimization suggestions for the implementation of China’s space-borne GW detection mission. Full article
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