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18 pages, 6757 KB  
Article
Integrated Construction Process Monitoring and Stability Assessment of a Geometrically Complex Large-Span Spatial Tubular Truss System
by Ruiheng Hou, Henghui Li, Hao Zhang, Haoliang Wang, Lei Chen and Qingjun Xian
Buildings 2025, 15(21), 4000; https://doi.org/10.3390/buildings15214000 (registering DOI) - 6 Nov 2025
Abstract
This study presents a comprehensive construction monitoring program for a geometrically complex, large-span spatial tubular truss system within a typical center steel exhibition hall. To ensure construction quality and structural integrity throughout the entire process, the monitoring strategy was rigorously aligned with the [...] Read more.
This study presents a comprehensive construction monitoring program for a geometrically complex, large-span spatial tubular truss system within a typical center steel exhibition hall. To ensure construction quality and structural integrity throughout the entire process, the monitoring strategy was rigorously aligned with the actual construction sequence. Real-time vertical displacement measurements were acquired at critical structural members and joints. A detailed finite element model of the entire structure was developed to systematically analyze the structural behavior of herringbone columns, primary and secondary trusses, and temporary supports during both installation and removal phases. Displacement patterns at key locations were investigated, and a global stability assessment was performed. Results demonstrate close agreement between finite element predictions and field measurements, confirming the rationality and reliability of the construction scheme. The structural system exhibited excellent stability across all construction stages, satisfying both architectural aesthetics and structural safety requirements. This study provides practical insights for construction control of similar large-span steel structures. Full article
(This article belongs to the Section Building Structures)
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22 pages, 6316 KB  
Article
Research on the Neutral Layer Deflection Phenomenon in Three-Dimensional Stretch Bending of Profiles
by Songyue Yang, Yu Wen, Hao Sun, Yi Li and Ce Liang
Metals 2025, 15(11), 1223; https://doi.org/10.3390/met15111223 - 5 Nov 2025
Abstract
This paper aims to study the deflection phenomenon of the neutral layer in the cross-section of profiles during the 3D stretch-bending process. By establishing the displacement field for both the stretching and bending processes of a profile with elastoplastic constitutive characteristics, and combining [...] Read more.
This paper aims to study the deflection phenomenon of the neutral layer in the cross-section of profiles during the 3D stretch-bending process. By establishing the displacement field for both the stretching and bending processes of a profile with elastoplastic constitutive characteristics, and combining the deformation processes, the geometric description of the profile deformation is constructed, and then linearized. Subsequently, by integrating the material’s constitutive properties and model boundary conditions, the analytical model parameters for profiles with regular cross-sections are solved. The analytical model effectively captures the behavior of the neutral layer and its deflection phenomenon. To further investigate, the finite element model was developed to simulate the deformation process. The distribution of the neutral layer in the simulation results matched the analytical predictions. To generalize the analytical results to profiles with arbitrary cross-sections, an L-shaped profile was analyzed, and a roller-based 3D flexible stretch-bending device with roller dies was used. By measuring the springback direction, the neutral layer deflection observed in both the analytical and finite element model results was validated. The results demonstrate that, under small deformation conditions, the neutral layer deflection during the 3D stretch-bending process was successfully predicted. Full article
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29 pages, 3863 KB  
Article
Stochastic Finite Element-Based Reliability Analysis of Construction Disturbance Induced by Boom-Type Roadheaders in Karst Tunnels
by Wenyun Ding, Yude Shen, Wenqi Ding, Yongfa Guo, Yafei Qiao and Jixiang Tang
Appl. Sci. 2025, 15(21), 11789; https://doi.org/10.3390/app152111789 - 5 Nov 2025
Abstract
Tunnel construction in karst formations faces significant geological uncertainties, which pose challenges for quantifying construction risks using traditional deterministic methods. This paper proposes a probabilistic reliability analysis framework that integrates the Stochastic Finite Element Method (SFEM), a Radial Basis Function Neural Network (RBFNN) [...] Read more.
Tunnel construction in karst formations faces significant geological uncertainties, which pose challenges for quantifying construction risks using traditional deterministic methods. This paper proposes a probabilistic reliability analysis framework that integrates the Stochastic Finite Element Method (SFEM), a Radial Basis Function Neural Network (RBFNN) surrogate model, and Monte Carlo Simulation (MCS) method. The probability distributions of rock mass mechanical parameters and karst geometric parameters were established based on field investigation and geophysical prospecting data. The accuracy of the finite element model was verified through existing physical model tests, with the lateral karst condition identified as the most unfavorable scenario. Limit state functions with control indices, including tunnel crown settlement, invert uplift, ground surface settlement and convergence, were defined. A high-precision surrogate model was constructed using RBFNN (average R2 > 0.98), and the failure probabilities of displacement indices were quantitatively evaluated via MCS (10,000 samples). Results demonstrate that the overall failure probability of tunnel construction is 3.31%, with the highest failure probability observed for crown settlement (3.26%). Sensitivity analysis indicates that the elastic modulus of the disturbed rock mass and the clear distance between the karst cavity and the tunnel are the key parameters influencing deformation. This study provides a probabilistic risk assessment tool and a quantitative decision-making basis for tunnel construction in karst areas. Full article
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19 pages, 2680 KB  
Article
ESSTformer: A CNN-Transformer Hybrid with Decoupled Spatial Spectral Transformers for Hyperspectral Image Super-Resolution
by Hehuan Li, Chen Yi, Jiming Liu, Zhen Zhang and Yu Dong
Appl. Sci. 2025, 15(21), 11738; https://doi.org/10.3390/app152111738 - 4 Nov 2025
Abstract
Hyperspectral images (HSIs) are crucial for ground object classification, target detection, and related applications due to their rich spatial spectral information. However, hardware limitations in imaging systems make it challenging to directly acquire HSIs with a high spatial resolution. While deep learning-based single [...] Read more.
Hyperspectral images (HSIs) are crucial for ground object classification, target detection, and related applications due to their rich spatial spectral information. However, hardware limitations in imaging systems make it challenging to directly acquire HSIs with a high spatial resolution. While deep learning-based single hyperspectral image super-resolution (SHSR) methods have made significant progress, existing approaches primarily rely on convolutional neural networks (CNNs) with fixed geometric kernels, which struggle to model global spatial spectral dependencies effectively. To address this, we propose ESSTformer, a novel SHSR framework that synergistically integrates CNNs’ local feature extraction and Transformers’ global modeling capabilities. Specifically, we design a multi-scale spectral attention module (MSAM) based on dilated convolutions to capture local multi-scale spatial spectral features. Considering the inherent differences between spatial and spectral information, we adopt a decoupled processing strategy by constructing separate spatial and Spectral Transformers. The Spatial Transformer employs window attention mechanisms and an improved convolutional multi-layer perceptron (CMLP) to model long-range spatial dependencies, while the Spectral Transformer utilizes self-attention mechanisms combined with a spectral enhancement module to focus on discriminative spectral features. Extensive experiments on three hyperspectral datasets demonstrate that the proposed ESSTformer achieves a superior performance in super-resolution reconstruction compared to state-of-the-art methods. Full article
(This article belongs to the Special Issue Advances in Optical Imaging and Deep Learning)
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18 pages, 2861 KB  
Article
A Geometric Attribute Collaborative Method in Multi-Scale Polygonal Entity Matching Scenario: Integrating Sentence-BERT and Three-Branch Attention Network
by Zhuang Sun, Po Liu, Liang Zhai and Zutao Zhang
ISPRS Int. J. Geo-Inf. 2025, 14(11), 435; https://doi.org/10.3390/ijgi14110435 - 3 Nov 2025
Abstract
The cross-scale fusion and consistent representation of cross-source heterogeneous vector polygon data are fundamental tasks in the field of GIS, and they play an important role in areas such as the refined management of natural resources, territorial spatial planning, and the urban emergency [...] Read more.
The cross-scale fusion and consistent representation of cross-source heterogeneous vector polygon data are fundamental tasks in the field of GIS, and they play an important role in areas such as the refined management of natural resources, territorial spatial planning, and the urban emergency response. However, the existing methods suffer from two key limitations: the insufficient utilization of semantic information, especially non-standardized attributes, and the lack of differentiated modeling for 1:1, 1:M, and M:N matching relationships. To address these issues, this study proposes a geometric–attribute collaborative matching method for multi-scale polygonal entities. First, matching relationships are classified into 1:1, 1:M, and M:N based on the intersection of polygons. Second, geometric similarities including spatial overlap, size, shape, and orientation are computed for each relationship type. Third, semantic similarity is enhanced by fine-tuning the pre-trained Sentence-BERT model, which effectively captures the complex semantic information from non-standardized descriptions. Finally, a three-branch attention network is constructed to specifically handle the three matching relationships, with adaptive feature weighting via attention mechanisms. The experimental results on datasets from Tunxi District, Huangshan City, China show that the proposed method outperforms the existing approaches including geometry–attribute fusion and BPNNs in precision, recall, and F1-score, with improvements of 3.38%, 1.32%, and 2.41% compared to the geometry–attribute method, and 2.91%, 0.27%, and 1.66% compared to BPNNs, respectively. A generalization experiment on Hefei City data further validates its robustness. This method effectively enhances the accuracy and adaptability of multi-scale polygonal entity matching, providing a valuable tool for multi-source GIS database integration. Full article
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23 pages, 9802 KB  
Article
Influence of the Semicircular Cycle in a Labyrinth Weir on the Discharge Coefficient
by Erick Dante Mattos-Villarroel, Waldo Ojeda-Bustamante, Carlos Díaz-Delgado, Humberto Salinas-Tapia, Carlos Francisco Bautista-Capetillo, Jorge Flores-Velázquez and Cruz Ernesto Aguilar-Rodríguez
Water 2025, 17(21), 3151; https://doi.org/10.3390/w17213151 - 3 Nov 2025
Abstract
The labyrinth weir is an effective hydraulic structure, offering high discharge efficiency and economic advantages, making it a suitable option for dam construction or rehabilitation projects. Owing to its complex geometry, significant research efforts have been dedicated to enhancing its hydraulic performance. Since [...] Read more.
The labyrinth weir is an effective hydraulic structure, offering high discharge efficiency and economic advantages, making it a suitable option for dam construction or rehabilitation projects. Owing to its complex geometry, significant research efforts have been dedicated to enhancing its hydraulic performance. Since the beginning of this century, Computational Fluid Dynamics (CFD) has emerged as a vital approach, complementing traditional methods in the design of hydraulic structures. This study employs CFD ANSYS FLUENT to examine the discharge coefficient of a semicircular labyrinth weir, featuring a cyclic arrangement and a half-round crest profile. The numerical models and simulations address two-phase flow (air and water) under incompressible and free-surface conditions. The CFD ANSYS FLUENT approach used is multiphase flow modeling using the Volume of Fluid method to track the free water surface. For turbulence effects, it is complemented with the standard k-ε model and the Semi-Implicit Method for Pressure Linked Equations algorithm for pressure–velocity coupling. In addition, for boundary conditions, the flow velocity was defined as the inlet to the channel and atmospheric pressure as the outlet, and the walls of the channel and weir are considered solid, stationary, and non-sliding walls. The model was validated with experimental data reported in the literature. The results indicate that the semicircular labyrinth weir achieves greater discharge capacity when the headwater ratio HT/P increases for HT/P ≤ 0.25. A regression analysis mathematical model was also developed, using the HT/P ratio, to predict the discharge coefficient for 0.05 ≤ HT/P ≤ 1. Relative to other geometrical configurations, the semicircular labyrinth weir demonstrated a discharge capacity that was up to 88% higher than that of the trapezoidal labyrinth weir. Both weir and cycle efficiency were assessed, and maximum weir efficiency was observed when HT/P ≤ 0.1, while cycle efficiency peaked at HT/P ≤ 0.25. The geometric configuration under analysis demonstrated greater economic efficiency by providing a reduced total length and enhanced discharge capacity relative to trapezoidal designs, especially when the sidewall angle α is considered as α ≤ 12°. The study concludes by presenting a design sequence detailing the required concrete volume for construction, which is subsequently compared to the specifications of a trapezoidal labyrinth weir. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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27 pages, 4791 KB  
Article
Methodological Approach for Determining the Aerodynamic Resistance Using 3D Scanning: Application in Mine Ventilation Modeling
by Andrzej Szmuk, Klaudia Zwolińska-Glądys, Zbigniew Kuczera and Marek Borowski
Appl. Sci. 2025, 15(21), 11723; https://doi.org/10.3390/app152111723 - 3 Nov 2025
Viewed by 38
Abstract
Accurate assessment of aerodynamic resistance in mine ventilation networks is essential for ensuring operational safety and energy efficiency, yet traditional measurement approaches remain time-consuming and prone to uncertainty. This study presents a novel methodology for constructing digital ventilation models of underground mine workings [...] Read more.
Accurate assessment of aerodynamic resistance in mine ventilation networks is essential for ensuring operational safety and energy efficiency, yet traditional measurement approaches remain time-consuming and prone to uncertainty. This study presents a novel methodology for constructing digital ventilation models of underground mine workings using markerless LiDAR scanning combined with automated data processing. The proposed procedure includes segmentation of point clouds into sections, calculation of geometric parameters, and direct determination of resistance coefficients, which are subsequently exported to VentSim software. The approach was validated through a case study conducted in a Polish coal mine, where a 369 m ventilation siding was scanned and analyzed. The comparison between numerical simulations and in situ measurements demonstrated strong agreement, with differences not exceeding ±5% for airflow velocity, pressure drop, and total flow rate, while larger deviations were observed for cross-sectional area (+5.1%). The method is limited by potential inaccuracies in determining excavation geometry, which can lead to errors in calculating resistance coefficients, particularly at excavation intersections and at the beginning and end of scanning sections. Point cloud analysis, determination of resistance coefficients for individual sections (segments), spatial transformation, and point cloud reduction, along with integration with VentSim, are based on Python scripts. Calculation results can be easily exported to other computational programs. The proposed approach enables integration with various sensors and allows for assigning this value directly to a given section (segment of the excavation). The method can support the construction of digital twins for mines or underground tunnels. The implementation codes of the developed algorithms have also been made available for educational and scientific purposes under the Modified GNU General Public License v3 (GPLv3). Full article
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27 pages, 5041 KB  
Article
Transformative Art History, Empowering Geometry: STEAM-H Education and Critical–Visual Maker Culture Towards Sustainable Futures
by Elisa-Isabel Chaves-Guerrero and Silvia-Natividad Moral-Sánchez
Educ. Sci. 2025, 15(11), 1458; https://doi.org/10.3390/educsci15111458 - 2 Nov 2025
Viewed by 182
Abstract
What if future teachers could learn to read the world like art historians, reason about it like mathematicians, and engage with it as sustainable change-makers? Through the lens of STEAM-H, this study examines their potential to become transformative educators fostering critical thinking and [...] Read more.
What if future teachers could learn to read the world like art historians, reason about it like mathematicians, and engage with it as sustainable change-makers? Through the lens of STEAM-H, this study examines their potential to become transformative educators fostering critical thinking and spatial–geometric competencies. The aim is to analyse how future teachers demonstrate Critical Spatial Literacy (CSL) skills—such as spatial literacy, critical thinking, and onto-semiotic dimensions—when carrying out hermeneutic readings of works of art and constructing models from AI-generated images within the framework of Critical–Visual Maker (CVM) Culture. This qualitative-descriptive study examines evidence from students’ analyses of pairs of classical and contemporary artworks, as well as models linked to the Sustainable Development Goals (SDGs), applying CSL categories in both cases. The findings reveal a transition from formal descriptions in mathematics and art history to more complex critical interpretations. Furthermore, the interrelationship among the three groups of categories proposed in the theoretical framework becomes evident. The study concludes that, by engaging in reflective and critical questioning, the interaction between STEAM-H, CSL, and CVM Culture can constitute an effective educational ecosystem for fostering geometric creativity, critical spatial literacy, and interdisciplinarity, thereby contributing to the development of a critical and egalitarian citizenship committed to global challenges and sustainable futures. Full article
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17 pages, 307 KB  
Article
Generalization of the Rafid Operator and Its Symmetric Role in Meromorphic Function Theory with Electrostatic Applications
by Aya F. Elkhatib, Atef F. Hashem, Adela O. Mostafa and Mohammed M. Tharwat
Symmetry 2025, 17(11), 1837; https://doi.org/10.3390/sym17111837 - 2 Nov 2025
Viewed by 84
Abstract
This study introduces a new integral operator Ip,μδ that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses: Σp+δ,μ,α, consisting [...] Read more.
This study introduces a new integral operator Ip,μδ that extends the traditional Rafid operator to meromorphic p-valent functions. Using this operator, we define and investigate two new subclasses: Σp+δ,μ,α, consisting of functions with nonnegative coefficients, and Σp+δ,μ,α,c, which further fixes the second positive coefficient. For these classes, we establish a necessary and sufficient coefficient condition, which serves as the foundation for deriving a set of sharp results. These include accurate coefficient bounds, distortion theorems for functions and derivatives, and radii of starlikeness and convexity of a specific order. Furthermore, we demonstrate the closure property of the class Σp+δ,μ,α,c, identify its extreme points, and then construct a neighborhood theorem. All the findings presented in this paper are sharp. To demonstrate the practical utility of our symmetric operator paradigm, we apply it to a canonical fractional electrodynamics problem. We demonstrate how sharp distortion theorems establish rigorous, time-invariant upper bounds for a solitary electrostatic potential and its accompanying electric field, resulting in a mathematically guaranteed safety buffer against dielectric breakdown. This study develops a symmetric and consistent approach to investigating the geometric characteristics of meromorphic multivalent functions and their applications in physical models. Full article
(This article belongs to the Special Issue Symmetry in Complex Analysis Operators Theory)
22 pages, 6748 KB  
Article
Automated 3D Reconstruction of Interior Structures from Unstructured Point Clouds
by Youssef Hany, Wael Ahmed, Adel Elshazly, Ahmad M. Senousi and Walid Darwish
ISPRS Int. J. Geo-Inf. 2025, 14(11), 428; https://doi.org/10.3390/ijgi14110428 - 31 Oct 2025
Viewed by 286
Abstract
The automatic reconstruction of existing buildings has gained momentum through the integration of Building Information Modeling (BIM) into architecture, engineering, and construction (AEC) workflows. This study presents a hybrid methodology that combines deep learning with surface-based techniques to automate the generation of 3D [...] Read more.
The automatic reconstruction of existing buildings has gained momentum through the integration of Building Information Modeling (BIM) into architecture, engineering, and construction (AEC) workflows. This study presents a hybrid methodology that combines deep learning with surface-based techniques to automate the generation of 3D models and 2D floor plans from unstructured indoor point clouds. The approach begins with point cloud preprocessing using voxel-based downsampling and robust statistical outlier removal. Room partitions are extracted via DBSCAN applied in the 2D space, followed by structural segmentation using the RandLA-Net deep learning model to classify key building components such as walls, floors, ceilings, columns, doors, and windows. To enhance segmentation fidelity, a density-based filtering technique is employed, and RANSAC is utilized to detect and fit planar primitives representing major surfaces. Wall-surface openings such as doors and windows are identified through local histogram analysis and interpolation in wall-aligned coordinate systems. The method supports complex indoor environments including Manhattan and non-Manhattan layouts, variable ceiling heights, and cluttered scenes with occlusions. The approach was validated using six datasets with varying architectural characteristics, and evaluated using completeness, correctness, and accuracy metrics. Results show a minimum completeness of 86.6%, correctness of 84.8%, and a maximum geometric error of 9.6 cm, demonstrating the robustness and generalizability of the proposed pipeline for automated as-built BIM reconstruction. Full article
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35 pages, 5223 KB  
Article
Physics-Based Machine Learning for Vibration Mitigation by Open Buried Trenches
by Luís Pereira, Luís Godinho, Fernando G. Branco, Paulo da Venda Oliveira, Pedro Alves Costa and Aires Colaço
Appl. Sci. 2025, 15(21), 11609; https://doi.org/10.3390/app152111609 - 30 Oct 2025
Viewed by 137
Abstract
Mitigating ground vibrations from sources like vehicles and construction operations poses significant challenges, often relying on computationally intensive numerical methods such as Finite Element Methods (FEM) or Boundary Element Methods (BEM) for analysis. This study addresses these limitations by developing and evaluating Machine [...] Read more.
Mitigating ground vibrations from sources like vehicles and construction operations poses significant challenges, often relying on computationally intensive numerical methods such as Finite Element Methods (FEM) or Boundary Element Methods (BEM) for analysis. This study addresses these limitations by developing and evaluating Machine Learning (ML) methodologies for the rapid and accurate prediction of Insertion Loss (IL), a critical parameter for assessing the effectiveness of open trenches as vibration barriers. A comprehensive database was systematically generated through high-fidelity numerical simulations, capturing a wide range of geometric, elastic, and physical configurations of a stratified geotechnical system. Three distinct ML strategies—Artificial Neural Networks (ANN), Support Vector Machines (SVM), and Random Forests (RF)—were initially assessed for their predictive capabilities. Subsequently, a Meta-RF stacking ensemble model was developed, integrating the predictions of these base methods. Model performance was rigorously evaluated using complementary statistical metrics (RMSE, MAE, NMAE, R), substantiated by in-depth statistical analyses (normality tests, Bootstrap confidence intervals, Wilcoxon tests) and an analysis of input parameter sensitivity. The results clearly demonstrate the high efficacy of Machine Learning (ML) in accurately predicting IL across diverse, realistic scenarios. While all models performed strongly, the RF and the Meta-RF stacking ensemble models consistently emerged as the most robust and accurate predictors. They exhibited superior generalization capabilities and effectively mitigated the inherent biases found in the ANN and SVM models. This work is intended to function as a proof-of-concept and offers promising avenues for overcoming the significant computational costs associated with traditional simulation methods, thereby enabling rapid design optimization and real-time assessment of vibration mitigation measures in geotechnical engineering. Full article
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20 pages, 8413 KB  
Article
An Analytical and Numerical Study of Wear Distribution on the Combine Harvester Header Platform: Model Development, Comparison, and Experimental Validation
by Honglei Zhang, Zhong Tang, Liquan Tian, Tiantian Jing and Biao Zhang
Lubricants 2025, 13(11), 482; https://doi.org/10.3390/lubricants13110482 - 30 Oct 2025
Viewed by 286
Abstract
The header platform of a combine harvester is subjected to severe abrasive and corrosive wear from rice stalks and environmental factors, which significantly limits its service life and operational efficiency. Accurately predicting the complex distribution of this wear over time and across the [...] Read more.
The header platform of a combine harvester is subjected to severe abrasive and corrosive wear from rice stalks and environmental factors, which significantly limits its service life and operational efficiency. Accurately predicting the complex distribution of this wear over time and across the platform’s surface, however, remains a significant challenge. This paper, for the first time, systematically establishes a quantitative mapping relationship from “material motion trajectory” to “component wear profile” and introduces a novel method for time-sequence wear validation based on corrosion color gradients, providing a complete research paradigm to address this challenge. To this end, an analytical model based on rigid-body dynamics was first developed to predict the motion trajectory of a single rice stalk. Subsequently, a full-scale Discrete Element (DEM) model of the header platform–flexible rice stalk system was constructed. This model simulated the complex flow process of the rice population with high fidelity and was used to analyze the influence of key operating parameters (spiral auger rotational speed, cutting width) on wear distribution. Finally, real-world wear data were obtained through in situ mapping of a header platform after long-term service (1300 h) and multi-period (0–1600 h) image analysis. Through a three-way quantitative comparison among the theoretical trajectory, simulated trajectory, and the actual wear profile, the results indicate that the simulated and theoretical trajectories are in good agreement in terms of their macroscopic trends (Mean Squared Error, MSE, ranging from 0.4 to 6.2); the simulated and actual wear profiles exhibit an extremely high degree of geometric similarity, with the simulated wear area showing a 95.1% match to the actual measured area (Edit Distance: 0.14; Hamming Distance: 1). This research not only confirms that the flow trajectory of rice is the determining factor for the wear distribution on the header platform but, more importantly, the developed analytical and numerical methods offer a robust theoretical basis and effective predictive tools for optimizing the wear resistance and predicting the service life of the header platform, thereby demonstrating significant engineering value. Full article
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17 pages, 294 KB  
Article
Approximate Fiber Products of Schemes and Their Étale Homotopical Invariants
by Dongfang Zhao
Mathematics 2025, 13(21), 3448; https://doi.org/10.3390/math13213448 - 29 Oct 2025
Viewed by 212
Abstract
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, ϕ:XS and ψ:YS, coincide exactly. This condition of strict equality, however, is insufficient [...] Read more.
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, ϕ:XS and ψ:YS, coincide exactly. This condition of strict equality, however, is insufficient for describing many real-world applications, such as the geometric structure of semantic spaces in modern large language models whose foundational architecture is the Transformer neural network: The token spaces of these models are fundamentally approximate, and recent work has revealed complex geometric singularities, challenging the classical manifold hypothesis. This paper develops a new framework to study and quantify the nature of approximate alignment between morphisms in the context of arithmetic geometry, using the tools of étale homotopy theory. We introduce the central object of our work, the étale mismatch torsor, which is a sheaf of torsors over the product scheme X×SY. The structure of this sheaf serves as a rich, intrinsic, and purely algebraic object amenable to both qualitative classification and quantitative analysis of the global relationship between the two morphisms. Our main results are twofold. First, we provide a complete classification of these structures, establishing a bijection between their isomorphism classes and the first étale cohomology group Hét1(X×SY,π1ét(S)̲). Second, we construct a canonical filtration on this classifying cohomology group based on the theory of infinitesimal neighborhoods. This filtration induces a new invariant, which we term the order of mismatch, providing a hierarchical, algebraic measure for the degree of approximation between the morphisms. We apply this framework to the concrete case of generalized Howe curves over finite fields, demonstrating how both the characteristic class and its order reveal subtle arithmetic properties. Full article
(This article belongs to the Section B: Geometry and Topology)
17 pages, 5002 KB  
Article
Evaluating the Predictive Potential of Patient-Specific Biomechanical Models in Class III Protraction Therapy
by Joeri Meyns, Wout Vertenten, Sohaib Shujaat, Sofie Van Cauter, Constantinus Politis, Jos Vander Sloten and Reinhilde Jacobs
Bioengineering 2025, 12(11), 1173; https://doi.org/10.3390/bioengineering12111173 - 28 Oct 2025
Viewed by 253
Abstract
Predicting treatment outcomes in Class III protraction therapy remains challenging. Although finite element analysis (FEA) helps in the study of biomechanics and planning of orthodontic treatment, its use in Class III protraction has mainly been in evaluating appliance designs rather than patient-specific anatomy. [...] Read more.
Predicting treatment outcomes in Class III protraction therapy remains challenging. Although finite element analysis (FEA) helps in the study of biomechanics and planning of orthodontic treatment, its use in Class III protraction has mainly been in evaluating appliance designs rather than patient-specific anatomy. The predictive accuracy of FEA has not been validated in Class III protration therapy. In this study, ten patients (5 female, 5 male, aged 7–11 years) with Class III malocclusion received either facemask or mentoplate treatment. CT scans from four patients were used to construct simplified finite element models, and predictions were compared with one-year treatment outcomes from six additional patients. While stress patterns differed between treatments, patient-specific geometrical factors had a more significant impact on deformation than treatment type. FEM-predicted maxillary changes (mean: 0.352 ± 0.12 mm) were approximately one-tenth of actual changes (mean: 1.612 ± 0.64 mm), with no significant correlation. Current FEM approaches, though useful for understanding force distribution, cannot reliably predict clinical outcomes in growing Class III patients. The findings suggest that successful prediction models must incorporate biological and growth factors beyond pure biomechanics. Accurate prediction of treatment outcomes requires comprehensive models that integrate multiple biological and developmental factors. Full article
(This article belongs to the Special Issue Orthodontic Biomechanics)
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32 pages, 3130 KB  
Review
Marine Hydrogen Pressure Reducing Valves: A Review on Multi-Physics Coupling, Flow Dynamics, and Structural Optimization for Ship-Borne Storage Systems
by Heng Xu, Hui-Na Yang, Rui Wang, Yi-Ming Dai, Zi-Lin Su, Ji-Chao Li and Ji-Qiang Li
J. Mar. Sci. Eng. 2025, 13(11), 2061; https://doi.org/10.3390/jmse13112061 - 28 Oct 2025
Viewed by 291
Abstract
As a zero-carbon energy carrier, hydrogen is playing an increasingly vital role in the decarbonization of maritime transportation. The hydrogen pressure reducing valve (PRV) is a core component of ship-borne hydrogen storage systems, directly influencing the safety, efficiency, and reliability of hydrogen-powered vessels. [...] Read more.
As a zero-carbon energy carrier, hydrogen is playing an increasingly vital role in the decarbonization of maritime transportation. The hydrogen pressure reducing valve (PRV) is a core component of ship-borne hydrogen storage systems, directly influencing the safety, efficiency, and reliability of hydrogen-powered vessels. However, the marine environment—characterized by persistent vibrations, salt spray corrosion, and temperature fluctuations—poses significant challenges to PRV performance, including material degradation, flow instability, and reduced operational lifespan. This review comprehensively summarizes and analyzes recent advances in the study of high-pressure hydrogen PRVs for marine applications, with a focus on transient flow dynamics, turbulence and compressible flow characteristics, multi-stage throttling strategies, and valve core geometric optimization. Through a systematic review of theoretical modeling, numerical simulations, and experimental studies, we identify key bottlenecks such as multi-physics coupling effects under extreme conditions and the lack of marine-adapted validation frameworks. Finally, we conducted a preliminary discussion on future research directions, covering aspects such as the construction of coupled multi-physics field models, the development of marine environment simulation experimental platforms, the research on new materials resistant to vibration and corrosion, and the establishment of a standardized testing system. This review aims to provide fundamental references and technical development ideas for the research and development of high-performance marine hydrogen pressure reducing valves, with the expectation of facilitating the safe and efficient application and promotion of hydrogen-powered shipping technology worldwide. Full article
(This article belongs to the Special Issue Dynamics and Control of Marine Mechatronics)
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