Search Results (528)

The appearance of a negative mass term in the classical, non-relativistic Klein–Gordon equation deduced from mechanical interactions describes a repulsive interaction. In the case of a traveling wave, this results in an increase in amplitude and a decrease in the wave propagation velocity. Since this leads to dissipation, it is a symmetry-breaking phenomenon. After the repulsive interaction is eliminated, the system evolves towards the original state. Given that the interactions within the system are conservative, it would be assumed that even the original state is restored. The analysis to be presented shows that a wave with a lower angular frequency than the original one is transformed back to a slightly larger amplitude. This description is a suitable model of the axion effect, during which an electromagnetic wave interacts with a repulsive field and becomes of a continuously lower frequency. Full article

Background: Despite the high prevalence of anterior cruciate ligament (ACL) surgeries, standardized, evidence-based rehabilitation protocols remain lacking. Digital medical devices (DMDs) like the “Orthelligent” system have gained relevance as adjuncts to traditional physiotherapy, offering continuous, objective monitoring of functional recovery. Methods: A retrospective cohort analysis included 335 patients who underwent ACL reconstruction and used the “Orthelligent home” system between August 2022 and December 2024. In total, 5675 recorded test and exercise events were analyzed. Functional recovery was assessed using the Limb Symmetry Index (LSI) across five defined rehabilitation phases (0–4). All patients followed a structured rehabilitation program aligned with current clinical practice guidelines, supplemented by Orthelligent as a home-based digital tool for daily monitoring. Results: Significant functional improvement was observed during early rehabilitation phases, with the LSI increasing from 0.64 ± 0.02 in phase 0 to 0.81 ± 0.01 in phase 2 (p < 0.001). Time since surgery was a significant positive predictor (p = 0.034), while pain showed a strong negative impact on performance (p < 0.001). Anthropometric factors had no significant effect. Exercises associated with high rates of drop-out, pain, or difficulty were identified and linked to specific rehab phases. Conclusions: This study demonstrates that digital rehabilitation monitoring can reliably reflect patient progress after ACL reconstruction. The early postoperative period (first 3 months) is critical for functional gains, highlighting the need for individualized, pain-sensitive rehabilitation strategies. Full article

The classification of exact solutions of Maxwell vacuum equations for pseudo-Riemannian spaces with spatial symmetry (homogeneous non-null spaces in Petrov) in the presence of electromagnetic fields invariant with respect to the action of the group of space motions is summarized. A new classification method is used, common to all homogeneous zero spaces of Petrov. The method is based on the use of canonical reper vectors and on the use of a new approach to the systematization of solutions. The classification results are presented in a form more convenient for further use. Using the previously made refinement of the classification of Petrov spaces, the classification of exact solutions of Maxwell vacuum equations for spaces with the group of motions $G_3\left(VIII\right)$ is completed. Full article

This work presents new results concerning weighted Hardy-type inequalities within the framework of delta conformable fractional integrals on arbitrary time scales. The proposed approach unifies the treatment of inequalities across continuous and discrete domains, enabling the derivation of original forms in both settings. The obtained results exhibit symmetry with classical inequalities, and several integral and discrete inequalities arise as special cases. These findings extend and generalize known results and enrich the theory of integral inequalities in fractional and dynamic calculus, providing a versatile platform for further developments in symmetric and weighted inequality analysis. Full article

The optimization of submerged entry nozzle (SEN) designs plays a pivotal role in achieving stable flow conditions and high-quality steel production during continuous casting. This study presents a comparative analysis of two SEN geometries under identical operational parameters using a combined approach of numerical simulation and physical modeling. A full-scale water model and a validated CFD framework based on the realizable k-$\epsilon$ and VOF models were employed to evaluate velocity distribution, turbulence intensity, free surface behavior, and flow symmetry. Results reveal that the SEN-2 design enhances flow stability near the meniscus region, promotes a consistent double-roll flow pattern (DRF), and reduces surface oscillations and sub-meniscus velocities, thereby minimizing the risk of mold flux entrapment. The proposed dimensionless KE number effectively quantifies the energy dissipation behavior of both designs, highlighting SEN-2’s superior hydraulic performance. This integrated methodology offers a robust evaluation framework for future nozzle development aimed at improving product quality without compromising productivity. Full article

This study presents a morphing Non-Uniform Rational B-Spline (NURBS) optimization method for enhancing sports car aerodynamics, with performance evaluation conducted in the vehicle’s symmetry plane. The morphing approach enables precise, smooth deformations of rear-end and spoiler geometries while preserving shape continuity, allowing controlled aerodynamic modifications suitable for comparative analysis. Flow simulations were carried out in ANSYS Fluent 2022 using the Reynolds-Averaged Navier–Stokes (RANS) equations with the standard k-ε turbulence model, selected for its stability and accuracy in predicting boundary-layer evolution, wake behavior, and flow separation in external automotive flows. Three configurations were assessed: the baseline model, a spoiler-equipped version, and two NURBS-morphed designs. The symmetry-plane evaluation ensured bilateral balance across all variants, enabling direct comparison of drag and lift performance. The results show that the proposed morphing strategy achieved notable lift reduction and favorable drag-to-lift ratios while maintaining manufacturability. The findings demonstrate that combining NURBS-based morphing with symmetry-plane aerodynamic assessment offers an efficient, reliable framework for vehicle aerodynamic optimization, bridging geometric flexibility with robust computational evaluation. Full article

Collective intelligence systems have demonstrated considerable potential in dynamic adversarial environments due to their distributed, self-organizing, and highly robust characteristics. The crux of an efficacious defense lies in establishing a dynamically adjustable, non-uniform defense structure through the differentiation of internal member roles. The proposed model is a heterogeneous-swarm adaptive-defense model based on symmetry breaking and skin effect. The model draws from symmetry theory, incorporating the skin effect of conductor currents and the hierarchical structural characteristics of biological groups, such as starlings. The construction of a radially symmetric dynamic hierarchical swarm structure is achieved by assigning different types of individuals with distinct safety radius preferences. Secondly, the principle of symmetry breaking is employed to establish a phase transition mechanism from radial symmetry to directed defense, thereby achieving an adaptive barrier formation algorithm. This algorithm enables the defensive group to assess threat characteristics and dynamically adjust defense resource deployment. The simulation results obtained from this study validate the phase transition process from continuous rotational symmetry to directed defense. This process demonstrates the barrier formation mechanism and ensures the safety and integrity of the core units within the group. Full article

The Cramér–von Mises (CM) statistic can assess the goodness-of-fit when the null distribution is independent of the underlying distribution, provided it is continuous, resulting in a universality that supports symmetry in its application and interpretation. Along with other order statistics, it serves in a battery of tests. A key element in its use is availability of the cumulative distribution function inverse for calculating the p-value. CM does not have an explicit formula for the cumulative distribution function. Here, a Monte–Carlo experiment was deployed to generate a large amount of data resembling CM. Furthermore, regression analysis was deployed, in order to obtain the dependence of the p-value as function of the statistic and of the sample size. For two cases, one assuming Beta distribution and the other assuming Cauchy distribution, an analysis using the CM statistic was conducted. Full article

This paper presents a comprehensive review and theoretical analysis of integrating Cyclic Solvent Injection (CSI) with multilateral well (MLW) technologies to enhance heavy oil recovery. Given that many MLW configurations inherently exhibit symmetrical geometries, CSI–MLW integration offers structural advantages for fluid distribution. CSI offers a non-thermal mechanism for oil production through viscosity reduction, oil swelling, and foamy oil behaviour, but its application is often limited by poor sweep efficiency and non-uniform solvent distribution in conventional single-well configurations. In contrast, MLW configurations are effective in increasing reservoir contact and improving flow control but lack solvent-based enhancement mechanisms. In particular, symmetrical MLW configurations, such as dual-opposing laterals and evenly spaced fishbone laterals, can facilitate balanced solvent distribution and pressure profiles, thereby improving sweep efficiency and mitigating early breakthrough. By synthesizing experimental findings and theoretical insights from the existing literature, laboratory studies have reported that post-CHOPS CSI using a 28% C₃H₈–72% CO₂ mixture can recover about 50% of the original oil in place after six cycles, while continuous-propagation CSI (CPCSI) has achieved up to ~85% OOIP in 1D physical models. These representative values illustrate the performance spectrum observed across different CSI operational modes, underscoring the importance of operational parameters in governing recovery outcomes. Building on this foundation, this paper synthesizes key operational parameters, including solvent composition, pressure decline rate, and well configuration, that influence CSI performance. While previous studies have extensively reviewed CSI and MLW as separate technologies, systematic analyses of their integration remain limited. This review addresses that gap by providing a structured synthesis of CSI–MLW interactions, supported by representative quantitative evidence from the literature. The potential synergy between CSI and MLW is highlighted as a promising direction to overcome current limitations. By leveraging geometric symmetry in well architecture, the integrated CSI–MLW approach offers unique opportunities for optimizing solvent utilization, enhancing recovery efficiency, and guiding future experimental and field-scale developments. Such symmetry-oriented designs are also central to the experimental framework proposed in this study, in which potential methods, such as the microfluidic visualization of different MLW configurations, spanning small-scale visualization studies, bench-scale experiments on fluid and chemical interactions, and mock field setups with pipe networks, are proposed as future avenues to further explore and validate this integrated strategy. Full article

Current mainstream remote sensing target detection algorithms mostly estimate the rotation angle of targets by designing different bounding box descriptions and loss functions. However, they fail to consider the symmetry–asymmetry duality anisotropy in the distribution of key features required for target localization. Moreover, the equivalent feature extraction mode of shared convolutional kernels may lead to difficulties in accurately predicting parameters with different attributes, thereby reducing the performance of the detector. In this paper, we propose the Feature Equalization and Hierarchical Decoupling Network (FEHD-Net), which comprises three core components: a Symmetry-Enhanced Parallel Interleaved Convolution Module (PICM), a Parameter Decoupling Module (PDM), and a Critical Feature Matching Loss Function (CFM-Loss). PICM captures diverse spatial features over long distances by integrating square convolution and multi-branch continuous orthogonal large kernel strip convolution sequences, thereby enhancing the network’s capability in processing long-distance spatial information. PDM decomposes feature maps with different properties and assigns them to different regression branches to estimate the parameters of the target’s rotating bounding box. Finally, to stabilize the training of anchors with different qualities that have captured the key features required for detection, CFM-Loss utilizes the intersection ratio between anchors and true value labels, as well as the uncertainty of convolutional regression during training, and designs an alignment criterion (symmetry-aware alignment) to evaluate the regression ability of different anchors. This enables the network to fine-tune the processing of templates with different qualities, achieving stable training of the network. A large number of experiments demonstrate that compared with existing methods, FEHD-Net can achieve state-of-the-art performance on DOTA, HRSC2016, and UCAS-AOD datasets. Full article

This paper investigates the pth moment exponential stability of random impulsive delayed nonlinear systems (RIDNS) with multiple periodic delayed impulses. Moreover, the continuous dynamics are described by random delay differential equations whose random disturbances are driven by second-order moment processes. Using the periodic impulsive intensity (PII), average delay time (ADT), average impulsive delay (AID), as well as the Lyapunov method, we present some pth exponential stability criteria for impulsive random delayed nonlinear systems with multiple delayed impulses. Furthermore, the criterion is unified, which is not only applicable to stable or unstable original systems but also takes into account the coexistence of stabilizing and destabilizing impulses. The periodic structure of impulses and their intensities introduces an intrinsic temporal symmetry, which plays a critical role in determining the stability behavior of the system. This symmetry-based perspective highlights the fundamental impact of regularly recurring impulsive actions on system dynamics. Several illustrated examples are given to verify the effectiveness of our results. Full article

During the continuous operation of trailing suction hopper dredger (TSHD), equipment workload exhibits significant time-varying characteristics. Maintaining dynamic symmetry between power generation and consumption is crucial for ensuring system stability and preventing power supply failures. Key challenges lie in dynamic perception, accurate prediction, and real-time power management to achieve this equilibrium. To address this issue, this paper proposes and constructs a “prediction-driven dynamic power management method.” Firstly, to model the complex temporal dependencies of the workload sequence, we introduce and improve a dilated convolutional long short-term memory network (Dilated-LSTM) to build a workload prediction model with strong long-term dependency awareness. This model significantly improves the accuracy of workload trend prediction. Based on the accurate prediction results, a dynamic power management strategy is developed: when the predicted total power consumption is about to exceed a preset margin threshold, the Power Management System (PMS) automatically triggers power reduction operations for adjusfigure loads, aiming to maintain grid balance without interrupting critical loads. If the power that the generator can produce is still less than the required power after the power is reduced, and there is still a risk of supply-demand imbalance, the system uses an Improved Grey Wolf Optimization (IGWO) algorithm to automatically disconnect some non-critical loads, achieving real-time dynamic symmetry matching of generation capacity and load demand. Experimental results show that this mechanism effectively prevents generator overloads or ship-wide power failures, significantly improving system stability and the reliability of power supply to critical loads. The research results provide effective technical support for intelligent energy efficiency management and safe operation of TSHDs and other vessels with complex working conditions. Full article

Micro-expressions, characterized by brief and subtle facial muscle movements, are essential for conveying nuanced emotions in digital humans, yet existing rendering techniques often produce rigid or emotionally monotonous animations due to the inadequate modeling of temporal dynamics and action unit interdependencies. This paper proposes a graph-driven framework for micro-expression rendering that generates emotionally diverse and lifelike expressions. We employ a 3D-ResNet-18 backbone network to perform joint spatio-temporal feature extraction from facial video sequences, enhancing sensitivity to transient motion cues. Action units (AUs) are modeled as nodes in a symmetric graph, with edge weights derived from empirical co-occurrence probabilities and processed via a graph convolutional network to capture structural dependencies and symmetric interactions. This symmetry is justified by the inherent bilateral nature of human facial anatomy, where AU relationships are based on co-occurrence and facial anatomy analysis (as per the FACS), which are typically undirected and symmetric. Human faces are symmetric, and such relationships align with the design of classic spectral GCNs for undirected graphs, assuming that adjacency matrices are symmetric to model non-directional co-occurrences effectively. Predicted AU activations and timestamps are interpolated into continuous motion curves using B-spline functions and mapped to skeletal controls within a real-time animation pipeline (Unreal Engine). Experiments on the CASME II dataset demonstrate superior performance, achieving an F1-score of 77.93% and an accuracy of 84.80% (k-fold cross-validation, k = 5), outperforming baselines in temporal segmentation. Subjective evaluations confirm that the rendered digital human exhibits improvements in perceptual clarity, naturalness, and realism. This approach bridges micro-expression recognition and high-fidelity facial animation, enabling more expressive virtual interactions through curve extraction from AU values and timestamps. Full article

Under varying operating conditions, motor bearings undergo continuous changes, necessitating the development of deep learning models capable of robust fault diagnosis. While meta-learning can enhance generalization in low-data scenarios, it is often susceptible to overfitting. Domain adaptation mitigates this by aligning feature distributions across domains; however, most existing methods primarily focus on global alignment, overlooking intra-class subdomain variations. To address these limitations, we propose a novel Dynamic Balance Domain-Adaptation based Few-shot Diagnosis framework (DBDA-FD), which incorporates both global and subdomain alignment mechanisms along with a dynamic balancing factor that adaptively adjusts their relative contributions during training. Furthermore, the proposed framework implicitly leverages the concept of symmetry in feature distributions. By simultaneously aligning global and subdomain-level representations, DBDA-FD enforces a symmetric structure between source and target domains, which enhances generalization and stability under varying operational conditions. Extensive experiments on the CWRU and PU datasets demonstrate the effectiveness of DBDA-FD, achieving 97.6% and 97.3% accuracy on five-way five-shot and three-way five-shot tasks, respectively. Compared to state-of-the-art baselines such as PMML and ADMTL, our method achieves up to 1.4% improvement in accuracy while also exhibiting enhanced robustness against domain shifts and class imbalance. Full article

We theoretically investigate high-order harmonic generation from ethylbenzene (C₈H₁₀), toluene (C₇H₈), and benzene (C₆H₆) molecules driven by a circularly polarized laser field using time-dependent density functional theory. By comparing the harmonic spectra of these structurally related molecules, we find that ethylbenzene, which features a larger molecular size due to the ethyl group, exhibits a higher harmonic cutoff and stronger harmonic intensity than toluene and benzene. Time-resolved electron density distributions, together with the probability current density analysis, indicate that under long-wavelength conditions (e.g., 1200 nm), the ethyl group in ethylbenzene and the methyl group in toluene significantly enhance the probability of ionized electrons from neighboring nuclei colliding with nearby nuclei, thereby leading to stronger harmonic emission, with ethylbenzene > toluene > benzene. In contrast, under short-wavelength conditions (e.g., 200 nm), the harmonic intensities of the three molecules show little difference, and the effects of the ethyl and methyl groups on the harmonic yield can be neglected. The influence of laser intensity and wavelength on high-order harmonic generation is further analyzed, confirming the robustness of the structural enhancement effect. Additionally, we study the harmonic ellipticity of ethylbenzene under different carrier-envelope phases, and find that while circularly polarized harmonics can be obtained, their spectral continuity is insufficient for synthesizing isolated circularly polarized attosecond pulses. This limitation is attributed to the broken ring symmetry caused by the ethyl substitution. Our findings offer insight into the relationship between molecular structure and harmonic response in strong-field physics, and provide a pathway for designing efficient circularly polarized attosecond pulse sources. Full article