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19 pages, 30826 KB  
Article
Weak Cloaking in Water Waves via Spatial-Transformation Metamaterials
by Chenxu Zhang, Zhigang Zhang, Peipei Zhou, Guanghua He and Zhengxiao Luan
Water 2026, 18(17), 2159; https://doi.org/10.3390/w18172159 - 1 Sep 2026
Viewed by 327
Abstract
When water waves encounter marine structures, significant scattering is produced, which affects the stability and safety of marine equipment. The cloaking of marine structures in water waves, achieved by water-wave transformation metamaterials, provides a new approach to solving this problem. However, in the [...] Read more.
When water waves encounter marine structures, significant scattering is produced, which affects the stability and safety of marine equipment. The cloaking of marine structures in water waves, achieved by water-wave transformation metamaterials, provides a new approach to solving this problem. However, in the anisotropic water depth required for perfect cloaking, the radial water depth tends to infinity, and the circumferential water depth tends to zero at the edge of the structure, leading to a singularity problem. This results in extreme parameters of the metamaterial near the structure, making fabrication difficult. To address the above issue, a comb-type metamaterial for weak scattering of water waves is designed in this paper based on space-transformation metamaterials, by which optimized control over the scattering characteristics of water waves is achieved. First, a general nonlinear spatial transformation is designed for both weak scattering and perfect cloaking. Then, the anisotropic water depths and equivalent gravitational acceleration parameters for the two cases are calculated and analyzed. Subsequently, the Helmholtz equation is solved using the finite element method, and the distributions of wave fields under anisotropic water depths and metamaterials for weak scattering and perfect cloaking are compared and analyzed. The results show that for weak scattering, the radial and circumferential water depths tend to constant values at the edge of the structure, thus resolving the singularity problem in perfect cloaking, while the control performance over water waves is comparable. Compared with perfect-cloaking metamaterials, the designed weak-scattering metamaterial significantly reduces the water depth parameters near the structure while maintaining water-wave control performance, making it easier to fabricate. Full article
(This article belongs to the Special Issue Wave-Driven Coastal Dynamics: Theory, Modeling, and Applications)
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22 pages, 4344 KB  
Article
Water Entry Characteristics of a Truncated-Cone Object with the Effect of Compressibility
by Ping Liu, Mengcheng Zeng, Yi Shen, Jiahao Huang, Zhi Yan and Yongliang Xiong
Aerospace 2026, 13(9), 769; https://doi.org/10.3390/aerospace13090769 - 27 Aug 2026
Viewed by 252
Abstract
Trans-medium vehicles, including supercavitating torpedoes, submarine-launched projectiles, and high-speed hydroballistic bodies, demonstrate increasingly diverse applications in crossing the air–water interface. For such vehicles, the truncated-cone (flat-headed) configuration represents a geometry of significant engineering relevance, as it is widely adopted in the nose sections [...] Read more.
Trans-medium vehicles, including supercavitating torpedoes, submarine-launched projectiles, and high-speed hydroballistic bodies, demonstrate increasingly diverse applications in crossing the air–water interface. For such vehicles, the truncated-cone (flat-headed) configuration represents a geometry of significant engineering relevance, as it is widely adopted in the nose sections of supercavitating projectiles and certain underwater ballistic penetrators where the flat head promotes rapid vaporization and cavity generation during high-speed water entry. The air-to-water transition process typically generates extreme hydrodynamic impact loads due to complex multiphase flow and fluid–structure coupling interactions, with water compressibility playing a significant role under hydroballistic conditions. This study focuses on the water-entry regime at velocities ranging from 300 to 1100 m/s, corresponding to hydroballistic speeds relevant to supercavitating vehicles (e.g., the Shkval torpedo operates at approximately 370 m/s) and the initial impact phase of high-speed trans-medium projectiles. Parametric studies are conducted with varying entry velocities (Mach 0.20~0.73 in water), impact angles, and structural dimensions to systematically investigate their effects on the peak slamming overload, using a dynamic mesh technique coupled with a VOF multiphase model with compressibility effects for both air and water phases. The results demonstrate that compressibility effects induce a pronounced air cushion effect during water impact, wherein compression waves generated during high-speed entry dominate the load formation process. Velocity is identified as the most sensitive factor affecting peak overload, followed by structural size parameters. The findings provide valuable guidance for the protective design of high-speed water-entry structures operating in the hydroballistic regime. Full article
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18 pages, 3177 KB  
Article
Analysis on Thresholds of Safe Operating Zones for Offloading Hoses in FLNG Systems
by Zhicheng Liu, Ying Xie, Fanhao Meng, Chen An and Menglan Duan
J. Mar. Sci. Eng. 2026, 14(17), 1570; https://doi.org/10.3390/jmse14171570 - 25 Aug 2026
Viewed by 217
Abstract
Despite the growing use of FLNG in offshore gas development, LNG hose safety during tandem offloading remains a critical challenge. Existing studies often analyze mooring dynamics and hose mechanics separately, lacking a unified framework that integrates multiple failure modes. This fragmented approach leads [...] Read more.
Despite the growing use of FLNG in offshore gas development, LNG hose safety during tandem offloading remains a critical challenge. Existing studies often analyze mooring dynamics and hose mechanics separately, lacking a unified framework that integrates multiple failure modes. This fragmented approach leads to unclear safety boundaries and inadequate risk control. Therefore, this study proposes a multi-parameter safe operating zone threshold method based on coupled dynamic analysis. First, a three-dimensional time-domain dynamic analysis model is developed using OrcaFlex, which integrates the floating bodies, hoses, and mooring system into a unified coupling framework based on hydrodynamic theory, simulating the dynamic response of the offloading system under combined wind, wave, and current actions. Second, tension, bending moment, and curvature are selected as safety evaluation parameters. These three parameters correspond to the core criteria of typical failure modes, namely axial overload failure, ultimate bending failure, and local joint failure, respectively. By comparing them with their allowable values, the safety status of the hose under various operating conditions is determined. Finally, a coupled safety threshold analysis method incorporating both “sea state return period” and “operational vessel distance” is proposed. The results indicate that, at a fixed vessel distance, the dynamic response of the hose increases significantly with worsening sea states. Tension satisfies the safety factor requirements under most sea conditions. However, the bending moment first exceeds the limit starting from the 5-year return period, making it the primary failure control indicator. Curvature exceeds the limit notably under the 50-year return period and beyond, becoming the main risk source under extreme sea states. The safe operational vessel distances under different sea states are also calculated, systematically revealing the response patterns and failure sequences of tension, curvature, and bending moment of the LNG hose under combined wind, wave, and current actions. Furthermore, by integrating safety margin calculations, an operational classification standard comprising a safe zone, a warning zone, and a danger zone is proposed, along with the upper limits of safe vessel distance and operational windows for each sea state. The threshold determination method established in this paper can provide effective engineering support for FLNG offloading operation planning, hose selection, and operational risk management. Full article
(This article belongs to the Section Ocean Engineering)
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21 pages, 4966 KB  
Article
Optimizing Machine Learning Models for Predicting Rock Cohesion and Angle of Internal Friction: A Comparative Study of Lithological Analysis, Robustness Assessment, and SHAP Explanations
by Jianjun Xie and Xuebin Xie
Appl. Sci. 2026, 16(17), 8360; https://doi.org/10.3390/app16178360 - 22 Aug 2026
Viewed by 173
Abstract
Rock cohesion (c) and angle of internal friction (φ) are core parameters for rock mass stability analysis and engineering design; however, traditional triaxial tests are costly and time-consuming, limiting their availability in preliminary engineering assessments. To address this limitation, [...] Read more.
Rock cohesion (c) and angle of internal friction (φ) are core parameters for rock mass stability analysis and engineering design; however, traditional triaxial tests are costly and time-consuming, limiting their availability in preliminary engineering assessments. To address this limitation, this study develops a machine learning framework that predicts these parameters from easily measurable physical properties, enabling rapid and cost-effective estimation without the need for complex laboratory testing. Based on a total of 199 sets of measured data from four rock types (shale, limestone, quartzite, and quartz-mica schist) in the Himalayan region, this study uses P-wave velocity (Vp), density (ρ), uniaxial compressive strength (UCS), and tensile strength (TS) as input variables. It employs four models: Support Vector Regression (SVR), Random Forest (RF), Multi-Layer Perceptron (MLP), and extreme gradient boosting (XGBoost) to predict c and φ. Hyperparameters were tuned using grid search and Bayesian optimization. We compared unified modeling with rock-type-specific modeling, performed interpretability analysis using SHapley Additive exPlanations (SHAP), and tested robustness by introducing Gaussian noise. The results show that XGBoost produced the best predictions at c (test set R2 = 0.9901, RMSE = 0.512 MPa), while the Bayesian-optimized SVR model yielded the best results at φ (R2 = 0.9776, RMSE = 0.744°). Rock-type-specific modeling improved the R2 for limestone at φ by 0.3541; the SHAP contribution for UCS and TS exceeded 70%; Random Forest demonstrated the best noise resistance, with a decrease in R2 of less than 0.04 under 10% noise. In summary, the strategy proposed in this paper allows for the selection of prediction schemes based on data quality and lithological differences, providing a feasible approach for rapidly obtaining rock strength parameters. Full article
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20 pages, 12303 KB  
Article
Sensitivity Analysis and Calibration of the SWAN Model for Simulating Typhoon Doksuri Waves Along the Fujian Coast: Implications for Economic Decision Costs
by Tong Li, Hongkun Lin and Cheng Chen
Water 2026, 18(16), 2053; https://doi.org/10.3390/w18162053 - 21 Aug 2026
Viewed by 329
Abstract
This paper evaluates the sensitivity and calibration of the third-generation shallow-water wave model SWAN for Typhoon Doksuri (No. 202305) along the Fujian coast. Sensitivity analyses were conducted for model initialization, wind forcing, and key physical parameters. The results show that a 1-day spin-up [...] Read more.
This paper evaluates the sensitivity and calibration of the third-generation shallow-water wave model SWAN for Typhoon Doksuri (No. 202305) along the Fujian coast. Sensitivity analyses were conducted for model initialization, wind forcing, and key physical parameters. The results show that a 1-day spin-up period is sufficient to largely reduce the initial error caused by a cold start. A locally refined unstructured triangular grid was adopted, and ERA5 reanalysis winds were blended with the Holland empirical typhoon wind field to better represent extreme winds near the typhoon core. Further tests indicate that the combination of the Janssen wind input scheme, cds1 = 3.5, LTA triad wave interaction scheme, JONSWAP bottom friction scheme, and a wave-breaking parameter of 0.73 can effectively reproduce the typhoon wave process along the Fujian coast. The optimized simulations agree well with buoy observations and provide a reference for typhoon wave forecasting and coastal disaster risk assessment. Full article
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31 pages, 19938 KB  
Article
Dynamic Analysis of Jacket-Type Offshore Wind Turbine Considering Equivalent Scour Effect and Wind-Wave Directionality
by Bin Wang, Jiawei Yu, Chao Luo, Yujia Tang, Yongqing Lai and Jingxian Fan
J. Mar. Sci. Eng. 2026, 14(16), 1452; https://doi.org/10.3390/jmse14161452 - 7 Aug 2026
Viewed by 359
Abstract
Jacket foundations, with their excellent adaptability and economic efficiency, have been increasingly widely applied in medium-deep water areas. However, the scouring and erosion effects in the marine environment, coupled with complex wind-wave loads, have severely restricted the long-term safe service of jacket foundations. [...] Read more.
Jacket foundations, with their excellent adaptability and economic efficiency, have been increasingly widely applied in medium-deep water areas. However, the scouring and erosion effects in the marine environment, coupled with complex wind-wave loads, have severely restricted the long-term safe service of jacket foundations. In this study, a structure-pile-soil coupled dynamic response model considering the effects of scour depth and changes in wind and wave directions for the jacket-type offshore wind turbine is developed by integrating the wind and wave load generation capability of OpenFAST and the nonlinear pile-soil interaction analysis function of OpenSees. By quantitatively analyzing key response parameters such as tower top displacement, nacelle acceleration, and internal forces of the foundation tower and pile shaft, this study reveals the significant influence of soil stiffness degradation induced by scour on structural dynamic characteristics, and verifies the effective suppression mechanism of the feathering shutdown strategy on structural responses under extreme loads. The research results indicate that scour has a negligible impact on the fundamental frequency of the jacket-type offshore wind turbine structure, while it significantly reduces the high-order frequencies and leads to a substantial increase in pile shaft internal forces; the effect of wind-wave angle intensifies the spatially coupled vibration response of the structure. The study provides important theoretical and technical support for the anti-scour design, multi-directional load assessment, and formulation of safety control strategies for jacket foundations in complex deep-sea environments. Full article
(This article belongs to the Special Issue Offshore Renewable Energy: Waves, Tides, and Wind)
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15 pages, 4549 KB  
Article
A Comparative Study of Machine Learning Algorithms for Measuring Thin-Film Thickness Using Terahertz Time-Domain Waves Simulated by the Finite Difference Time Domain Method
by Pingan Liu, Xiangjun Li, Yibing Liu and Liguo Zhu
Coatings 2026, 16(8), 931; https://doi.org/10.3390/coatings16080931 - 4 Aug 2026
Viewed by 341
Abstract
Terahertz (THz) waves offer unique advantages, including non-contact operation, high penetration capability, and high resolution, making them particularly well-suited for the non-destructive thickness measurement of film-structured materials. In reflective terahertz time-domain spectroscopy (THz-TDS), thickness measurement approaches are generally classified into three categories: optimization-based [...] Read more.
Terahertz (THz) waves offer unique advantages, including non-contact operation, high penetration capability, and high resolution, making them particularly well-suited for the non-destructive thickness measurement of film-structured materials. In reflective terahertz time-domain spectroscopy (THz-TDS), thickness measurement approaches are generally classified into three categories: optimization-based methods that rely on theoretical models, time-of-flight (ToF), and machine learning. Model-based optimization techniques require precise knowledge of the optical parameters and structural configuration of each layer; however, they often suffer from slow convergence and are prone to becoming trapped in local optima. In contrast, ToF-based methods determine thickness by calculating the time delay between echo pulses reflected from different interfaces, yet their applicability is limited when the film thickness is extremely small. Machine learning, especially deep learning, enables the establishment of a direct, data-driven mapping between THz waveforms (or their extracted features) and the target thickness. Such approaches offer rapid inference, strong robustness to noise, and good adaptability to thin or structurally complex films, although their accuracy remains dependent on the quality of training data and the generalization capability of the model. In this study, high-fidelity THz waveform data generated via finite-difference time-domain (FDTD) simulations are utilized to conduct a comparative investigation into the film thickness prediction performance of several representative machine learning algorithms, including Back Propagation (BP) neural networks, Support Vector Machines (SVM), Random Forests (RF), Extreme Learning Machines (ELM), K-Nearest Neighbors (KNN), and Partial Least Squares (PLS) regression. The results indicate that, in terms of prediction error, the overall ranking of algorithmic performance from best to worst is: PLS > RF > SVM > BP > ELM > KNN. These findings provide valuable guidance for the future application of machine learning-assisted THz-TDS in precise film thickness measurement. Full article
(This article belongs to the Section Thin Films)
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28 pages, 7290 KB  
Article
Linking Meteo-Marine Forcing and Spatial Damage Patterns in Calabria After Cyclone Harry (Southern Italy)
by Carmela Vennari, Graziella Emanuela Scarcella, Loredana Antronico, Deborah Biondino, Francesco Chiaravalloti and Roberto Coscarelli
Earth 2026, 7(4), 129; https://doi.org/10.3390/earth7040129 - 3 Aug 2026
Viewed by 767
Abstract
Mediterranean coastal regions are increasingly affected by hydrometeorological hazards associated with high-impact weather events, including cyclones. Between 18 and 21 January 2026, the intense extratropical cyclone Harry affected Sicily, Sardinia, and Calabria, producing severe weather conditions including heavy precipitation, strong winds, and extreme [...] Read more.
Mediterranean coastal regions are increasingly affected by hydrometeorological hazards associated with high-impact weather events, including cyclones. Between 18 and 21 January 2026, the intense extratropical cyclone Harry affected Sicily, Sardinia, and Calabria, producing severe weather conditions including heavy precipitation, strong winds, and extreme wave activity. This study investigates both the meteo-marine characteristics of the event and its associated damage in Calabria, where the cyclone triggered multiple hazards (wave storms, landslides, flooding, and strong winds). Meteo-marine forcing was characterized using integrated rainfall data, wave parameters, and wind data. In situ observations, radar-derived precipitation estimates, satellite measurements, and model-based reanalysis products were combined to provide a comprehensive evaluation of the event. A georeferenced database of 195 damage records was compiled and classified according to the EU Floods Directive (2007/60/EC), allowing spatial analyses within a GIS framework. Although the cyclone produced exceptional rainfall totals, locally exceeding 580 mm in 90 h, the distribution of impacts reveals the predominance of coastal processes. Wave storm-related damage accounted for 68% of all recorded impacts, mainly affecting transportation and communication infrastructures, tourism facilities, and population. The prevalence of coastal damage appears to be linked not only to the intensity of marine forcing but also to its persistence which locally exceeded the maximum climatological persistence, suggesting that event duration plays a critical role in determining impact severity. Geomorphological analyses indicate that short-term coastal vulnerability is influenced not only by long-term shoreline evolution but also by local topographic characteristics and exposure to marine forcing. These findings contribute to improving risk assessment and mitigation strategies for Mediterranean coastal regions under a changing climate. Full article
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16 pages, 9568 KB  
Article
Equivalent Circuit Extraction of SAW Resonator with Spurious Modes Interference over a −55 °C to 85 °C Temperature Range
by Xianli Tang, Yonghao Jia and Yuandong Gu
Micromachines 2026, 17(8), 893; https://doi.org/10.3390/mi17080893 - 25 Jul 2026
Viewed by 983
Abstract
Surface acoustic wave (SAW) resonators are widely employed to design radio-frequency (RF) filters in wireless communication. To adapt to various application scenarios, the article proposes an equivalent circuit model based on the Butterworth–Van Dyke (BVD) model for SAW devices operating with spurious modes [...] Read more.
Surface acoustic wave (SAW) resonators are widely employed to design radio-frequency (RF) filters in wireless communication. To adapt to various application scenarios, the article proposes an equivalent circuit model based on the Butterworth–Van Dyke (BVD) model for SAW devices operating with spurious modes and at extreme ambient temperatures. In cases where the resonance frequencies of the spurious modes are close to those of the main mode, isolation capacitances (IC) are proposed in the modeling process. With the IC, the different resonance frequencies produced by the proposed equivalent circuit model can be flexibly adjusted. The extreme temperature influence on the SAW resonators is investigated using the proposed model. In the temperature-dependent test environment, the performance of the SAW devices changes, and these changes are captured by the proposed model. Especially for the resonators’ spurious-mode frequencies, which are less influenced by temperature near room temperature unless extreme temperatures are applied. The parameters motional resistance Rm and motional inductance Lm are considered temperature-dependent and are used to describe the influence of the ambient temperature. The RF characteristics of the SAW devices are modeled with the proposed model and verified with measurement data. The consistent results between the measured data and simulated data indicate that the proposed model is accurate and the modeling work is effective. Full article
(This article belongs to the Special Issue MEMS/NEMS Devices and Applications, 4th Edition)
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24 pages, 9507 KB  
Article
WaveUAV-YOLO: A Lightweight Architecture for UAV Object Detection with Frequency-Domain Edge Preservation and Stable Gradient Fusion
by Qi Wang, Shengqi Xu and Yongji Chen
Remote Sens. 2026, 18(14), 2404; https://doi.org/10.3390/rs18142404 - 20 Jul 2026
Viewed by 529
Abstract
Unmanned Aerial Vehicle (UAV) object detection is a core technology for cross-modal, wide-area surveillance. However, operating at high altitudes under complex flight conditions imposes extreme physical constraints, generating massive sub-pixel targets, elongated morphologies, and dense object clustering. These challenges are critically important because [...] Read more.
Unmanned Aerial Vehicle (UAV) object detection is a core technology for cross-modal, wide-area surveillance. However, operating at high altitudes under complex flight conditions imposes extreme physical constraints, generating massive sub-pixel targets, elongated morphologies, and dense object clustering. These challenges are critically important because conventional lightweight detectors deployed on edge devices often suffer from severe high-frequency edge loss during spatial downsampling, morphological distortion of anisotropic targets, and the mathematical suppression of weak feature gradients during cross-scale fusion, ultimately leading to severe missed detections. To overcome these inherent bottlenecks, this paper proposes WaveUAV-YOLO, a lightweight architecture prioritizing frequency-domain edge preservation and stable gradient propagation. First, a Wavelet High-Frequency Downsampling (WHFD) module augments standard convolutions by utilizing Haar wavelet decomposition to explicitly capture and compensate for the lost boundary cues of sub-pixel targets. Second, an Asymmetric Multi-scale Bottleneck without Dimensionality Compression (C2f_AMSB) cancels forced channel compression and introduces asymmetric convolutions to effectively adapt to elongated targets. Third, a Mean-Normalized Feature Aggregation (FFM_Concat) prevents deep background features from suppressing weak shallow signals during fusion. Extensive experiments on VisDrone2019, DIOR, NWPU, and HIT-UAV demonstrate that WaveUAV-YOLO (11.70 M parameters) achieves competitive or superior detection precision against recent lightweight UAV detectors. Furthermore, it achieves an end-to-end inference speed of ≈50 FPS on a standard desktop GPU, validating a favorable balance between sub-pixel detection reliability and computational efficiency for adverse UAV environments. Full article
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9 pages, 1804 KB  
Article
Effects of h-BN Doping on the Microstructure, Mechanical Properties, and Dielectric Properties of Silicon Nitride Ceramics
by Xia Liu, Ying Wang, Hongfei Shao, Xin Zhang and Jinyong Zhang
Materials 2026, 19(13), 2775; https://doi.org/10.3390/ma19132775 - 30 Jun 2026
Viewed by 327
Abstract
Silicon nitride ceramics exhibit excellent structural strength and electromagnetic wave transmission performance, yet demonstrate significant thermal shock instability under extreme conditions. Boron nitride (BN), on the other hand, possesses outstanding thermal shock resistance and electromagnetic wave transmission properties but exhibits relatively lower structural [...] Read more.
Silicon nitride ceramics exhibit excellent structural strength and electromagnetic wave transmission performance, yet demonstrate significant thermal shock instability under extreme conditions. Boron nitride (BN), on the other hand, possesses outstanding thermal shock resistance and electromagnetic wave transmission properties but exhibits relatively lower structural strength. Compositing these two materials holds promise for developing an integrated material that combines high-temperature load-bearing capacity with wave transmission capability. This study employed spark plasma sintering (SPS) technology to systematically investigate how varying BN content affects the sintering densification process and microstructural evolution of Si3N4/BN composite ceramics. Furthermore, we elucidated the mechanisms by which material composition and processing parameters influence key mechanical properties, dielectric characteristics, and other multifunctional attributes of the composites, providing a theoretical foundation for synergistic optimization design. The results indicate that BN incorporation suppresses both the phase transition from α-Si3N4 to β-Si3N4 during sintering and the growth of elongated β-Si3N4 crystals: the former hinders densification while the latter promotes it, resulting in a dual competitive mechanism that initially increases followed by decreases in sintered density. The effects of BN content on elastic modulus and fracture toughness align with trends in sintering density, whereas hardness, flexural strength, dielectric constant, and dielectric loss all show a monotonically decreasing trend with increasing BN content. Full article
(This article belongs to the Section Advanced and Functional Ceramics and Glasses)
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15 pages, 10257 KB  
Article
Experimental Demonstration of Geometric Tilt-to-Length Noise Model in Test Mass Interferometer
by Mengyang Zhao, Jia Shen, Shaoxin Wang, Keqi Qi, Heshan Liu, Peng Xu, Ruihong Gao and Ziren Luo
Sensors 2026, 26(13), 4111; https://doi.org/10.3390/s26134111 - 29 Jun 2026
Viewed by 520
Abstract
Space-based gravitational wave detection missions impose extremely stringent requirements on the measurement precision of the laser interferometer, where tilt-to-length coupling noise emerges as a critical factor degrading performance. This paper focuses on geometric tilt-to-length noise in the test mass interferometer, conducting both theoretical [...] Read more.
Space-based gravitational wave detection missions impose extremely stringent requirements on the measurement precision of the laser interferometer, where tilt-to-length coupling noise emerges as a critical factor degrading performance. This paper focuses on geometric tilt-to-length noise in the test mass interferometer, conducting both theoretical modeling and experimental validation. First, based on the principles of geometrical optics, an analytical expression is derived for the optical path length difference variation induced by test mass angular jitter, clarifying the coupling mechanisms of the various system parameters to the tilt-to-length coupling. Numerical simulations demonstrate an excellent agreement between the theoretical model and simulation results. To further validate the theoretical model, an experimental system combining laser heterodyne interferometry and differential wavefront sensing technique is designed and constructed, with a fast steering mirror employed to simulate test mass angular jitter, enabling precise measurement of both the optical path and angular variations. By varying the lateral displacement dlat of the fast steering mirror, the experimental data exhibit strong consistency with the theoretical prediction of the first-order tilt-to-length coupling coefficient, with a linear fitting error as low as 1.5%. Moreover, the independence of the second-order and zero-order terms relative to dlat also aligns with the theoretical expectation. Thus, the first experimental verification of the geometric tilt-to-length coupling model is presented in this paper. Full article
(This article belongs to the Section Optical Sensors)
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34 pages, 1678 KB  
Article
FFT-Free Neural Operators for Helmholtz Scattering via Adaptive Coefficient Modulation
by Ju O Kim and Deokwoo Lee
Appl. Sci. 2026, 16(12), 5997; https://doi.org/10.3390/app16125997 - 13 Jun 2026
Viewed by 404
Abstract
Fourier Neural Operators (FNOs) exhibit mode saturation on high-contrast inhomogeneous media, and recent multi-scale extensions (MscaleFNO) further worsen out-of-distribution (OOD) generalization. We introduce the Helmholtz Neural Operator (HNO), a physics-informed, FFT-free branch–trunk operator in the DeepONet family, with a hybrid SIREN+learnable-Fourier trunk and [...] Read more.
Fourier Neural Operators (FNOs) exhibit mode saturation on high-contrast inhomogeneous media, and recent multi-scale extensions (MscaleFNO) further worsen out-of-distribution (OOD) generalization. We introduce the Helmholtz Neural Operator (HNO), a physics-informed, FFT-free branch–trunk operator in the DeepONet family, with a hybrid SIREN+learnable-Fourier trunk and a dual-path rank-32 hypernetwork branch, with bounded multiplicative gating on per-mode coefficients. At a matched parameter count (∼1.05 M, five seeds), HNO achieves a 2.6× lower OOD generalization gap than FNO (19.6% vs. 50.6%, p=1.7×103, Cohen’s d=5.1), 5.1× lower than vanilla DeepONet (19.6% vs. 99.9%, p=8.2×103), and 6.0× lower than MscaleFNO (19.6% vs. 117.4%, p=2.4×106); MscaleFNO’s deficit grows at 4.2× more parameters, ruling out capacity starvation. HNO is 4.6×/16.4× faster than FNO/MscaleFNO and 64×–245× faster than multi-threaded FD-PML (MKL PARDISO, 12 cores; 183×–698× vs. single-thread scipy.spsolve), making it suitable as a forward surrogate inside many-query workflows. Absolute accuracy on extreme-contrast (15:1) OOD samples is limited (relative L21), so HNO is positioned as a many-query surrogate or warm start for refinement loops, not a stand-alone replacement for direct solvers. A scope limitation is that HNO underperforms FNO on elliptic Darcy Flow, confirming specialization for hyperbolic/wave equations rather than universal operator learning. Full article
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27 pages, 2594 KB  
Article
The Effect of Dark Matter Halo Annihilation on Gravitational Waves
by Yu Wang, Meilin Liu and Haiguang Xu
Universe 2026, 12(6), 162; https://doi.org/10.3390/universe12060162 - 30 May 2026
Cited by 1 | Viewed by 337
Abstract
We investigate the influence of dark matter halos surrounding supermassive black holes on the gravitational waves emitted by extreme mass ratio inspirals (EMRIs). Focusing on circular orbits, we model the orbital evolution by incorporating both gravitational-wave radiation reaction and dynamical friction induced by [...] Read more.
We investigate the influence of dark matter halos surrounding supermassive black holes on the gravitational waves emitted by extreme mass ratio inspirals (EMRIs). Focusing on circular orbits, we model the orbital evolution by incorporating both gravitational-wave radiation reaction and dynamical friction induced by the dark matter distribution, including possible density spikes near the black hole. Using frequency-domain waveform analysis, we compute the phase evolution of gravitational waves and quantify the dephasing caused by different halo parameters, including slope, density, and mass ratio. We further explore the distinguishability of dark matter models with annihilation, non-annihilation, and p-wave velocity dependence, as well as the potential to differentiate between astrophysical and primordial black holes. Our results show that even small variations in the dark matter properties lead to observable phase differences over a four-year EMRI evolution, making space-based detectors such as LISA sensitive probes of central dark matter distributions. Finally, we employ the Fisher matrix formalism to estimate the precision with which key parameters, such as halo slope and density, can be constrained, demonstrating that EMRI observations provide a promising avenue to probe both the nature of dark matter and the formation history of supermassive black holes. Full article
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34 pages, 6141 KB  
Article
Optimization of Extreme Design Parameters for Swell-Dominated Waves Using a Gaussian Mixture Model
by Chao Li, Yudong Feng, Yuliang Zhao and Xin Ma
J. Mar. Sci. Eng. 2026, 14(11), 988; https://doi.org/10.3390/jmse14110988 - 27 May 2026
Viewed by 325
Abstract
Environmental condition assessment is essential for the design of floating wind turbines, particularly when determining design sea states that balance safety and economy. The environmental contour method, typically constructed through the Inverse First Order Reliability Method combined with parametric joint distributions, is widely [...] Read more.
Environmental condition assessment is essential for the design of floating wind turbines, particularly when determining design sea states that balance safety and economy. The environmental contour method, typically constructed through the Inverse First Order Reliability Method combined with parametric joint distributions, is widely adopted for this purpose. However, conventional models often struggle to adequately characterize complex sea states involving mixed wind and swell systems, which exhibit multimodality and irregular dependence structures. To address this limitation, this study applies the use of Gaussian mixture models (GMM) to construct environmental contours. The GMM-based approach models the joint distribution of environmental variables in a flexible and data-adaptive manner, with the number of mixture components determined by the Bayesian Information Criterion and model parameters estimated via the expectation-maximization algorithm. Compared with the conventional conditional Weibull–Lognormal model, the GMM significantly improves fitting accuracy: the RMSE decreases from approximately 0.06 to below 0.0013, and the R2 increases to nearly 1.000 across all three datasets. The KS and χ2 tests confirm that the GMM adequately fits the observed data at the 0.05 significance level, whereas the baseline model is rejected in several cases. For the 100-year return period, the GMM yields maximum significant wave heights of 4.19–4.55 m with associated peak periods of 18.8–20.3 s, while the baseline model gives 4.02–4.18 m and 14.3–14.6 s, respectively. These quantitative improvements demonstrate that the mixture-based contours capture the intricate characteristics of wind–swell coexisting sea conditions more accurately, leading to enhanced representativeness of extreme sea states. Consequently, the adopted method enables more refined and reliable design sea state assessments for tested datasets, contributing to the optimization of environmental parameter selection for floating wind turbines. Full article
(This article belongs to the Special Issue Breakthrough Research in Marine Structures)
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