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23 pages, 2376 KB  
Article
Study on the Permanent Deformation Characteristics of Unsaturated Sand Subgrade Fill Under Cyclic Loading
by Hongfei Yin, Chuang Zhang and Jianzhong Li
Appl. Sci. 2026, 16(9), 4086; https://doi.org/10.3390/app16094086 - 22 Apr 2026
Abstract
Under long-term cyclic loading, the cumulative plastic deformation of unsaturated sandy subgrade is a key control factor for the pavement’s service performance. However, its evolution mechanism and quantitative characterization still lack a universal model. In this study, based on the GDS dynamic triaxial [...] Read more.
Under long-term cyclic loading, the cumulative plastic deformation of unsaturated sandy subgrade is a key control factor for the pavement’s service performance. However, its evolution mechanism and quantitative characterization still lack a universal model. In this study, based on the GDS dynamic triaxial system, a series of cyclic tests were conducted under different conditions: matric suction from 0 to 90 kPa, net confining pressure from 30 to 120 kPa, dynamic stress amplitude from 60 to 240 kPa, and compaction degrees of 87–96%, reaching a total of 10,000 cycles. The results reveal that the permanent deformation of unsaturated sandy subgrade material evolves through three stages: fast, slow, and stable. The deformation is exponentially negatively correlated with matric suction, net confining pressure, and compaction degree, and exponentially positively correlated with dynamic stress amplitude. A coupling prediction model was developed by embedding matric suction and compaction degree factors into the Karg model. This model incorporates net confining pressure, dynamic stress amplitude, matric suction, and compaction degree. By using a normalized master curve method, the permanent deformation curves under different working conditions were compressed into a unique dimensionless function. The parameters have clear physical significance and allow for a unified description across stress, suction, state, and soil types. Experimental data, along with data from the literature, were used to validate the model, showing prediction errors of less than 10% and R2 > 0.95. The model provides a simple, high-precision, and transferable theoretical tool for long-service-life subgrade deformation control. Full article
(This article belongs to the Special Issue Geotechnical Engineering and Infrastructure Construction, 2nd Edition)
28 pages, 4725 KB  
Article
The Seismic Response of Two Geotechnically Similar GRS-MB Walls During the Chi-Chi Earthquake: Insights from the Finite Displacement Method
by Ching-Chuan Huang
Geotechnics 2026, 6(2), 39; https://doi.org/10.3390/geotechnics6020039 - 21 Apr 2026
Abstract
This study re-examines two geologically and geotechnically similar geosynthetic-reinforced soil walls with modular block facings (GRS-MBs) that exhibited markedly different seismic performances during the 1999 Chi-Chi earthquake (ML = 7.3). Integrating a multi-wedge failure mechanism that captures soil–facing–reinforcement interactions with a nonlinear [...] Read more.
This study re-examines two geologically and geotechnically similar geosynthetic-reinforced soil walls with modular block facings (GRS-MBs) that exhibited markedly different seismic performances during the 1999 Chi-Chi earthquake (ML = 7.3). Integrating a multi-wedge failure mechanism that captures soil–facing–reinforcement interactions with a nonlinear hyperbolic soil model representing shear stress–displacement behavior along the slip surface, the Force–equilibrium-based Finite Displacement Method (FFDM) provides consistent and robust displacement evaluations over a wide range of input seismic inertial forces. A systematic sensitivity investigation confirms that the FFDM framework responds to parameter variations in a physically meaningful manner, and that displacement predictions remain stable with respect to reasonable uncertainties in soil, reinforcement, and facing properties. The analysis clarifies why two similar GRS-MBs responded so differently during strong shaking and demonstrates the broader applicability of FFDM for displacement-based seismic assessment, including under shaking levels (e.g., kh ≈ 0.3) that would drive conventional limit–equilibrium calculations to Fs < 1.0, a physically impossible state requiring shear resistance greater than the soil’s ultimate strength. A comparative evaluation of seismic displacement predictions using the Newmark method and FFDM shows that FFDM successfully generates displacement-based seismic resisting curves and reproduces field-observed displacements. In contrast, the Newmark method yields order-of-magnitude variability in predicted movements and may be unsuitable for displacement-sensitive engineered slopes where deformations on the order of several 10−3–10−2 m are practically significant. For interaction-rich GRS-MBs with high values of khc, beyond the predictive capability of Newmark’s equation, FFDM offers a practical and physically grounded tool for seismic displacement assessment of reinforced soil structures. Full article
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24 pages, 5567 KB  
Article
The Bending Impact of the Failure Investigation of the Polymer-Reinforced Composite Protection Bars
by Ibrahim Kutay Yilmazcoban
Polymers 2026, 18(8), 1001; https://doi.org/10.3390/polym18081001 - 21 Apr 2026
Abstract
It is well established that an anti-intrusion beam is a passive safety system that serves an essential role for passengers during collisions. In this study, the influence of internal reinforcements on the bending failure of a cylindrical aluminum tube was systematically investigated through [...] Read more.
It is well established that an anti-intrusion beam is a passive safety system that serves an essential role for passengers during collisions. In this study, the influence of internal reinforcements on the bending failure of a cylindrical aluminum tube was systematically investigated through a series of composite beam tests. Polymeric materials, including cast polyamide (PA6) and polypropylene (PP), with varying wall thicknesses, were deemed suitable for use as the inner reinforcement of the Al 6063-T6 tube. The test setup, which simulates impact conditions experienced by structural components in full-scale crash tests, is a powerful tool for the bending impacts in the study. To describe the connection between bending impact and quasi-static loading of composite beams, each method is compared to clarify the composite’s failure behavior. An explicit Finite Element Analysis (FEA) of impact scenarios has been performed to understand the deformation behavior of polymer-reinforced composites and to determine the absorbed impact energy, thereby clarifying which specimen is better able to absorb bending impact energy. Primarily, three polymer-reinforced specimens were accepted with a hollow Al tube. After initial tests and simulations, the expected parametric study could not be achieved except for one. Then, three more combinations were offered. For one of the three specimens, the thickness of the central reinforcement PP was increased until a fully developed shaft was produced, resulting in better-than-expected bending impact-absorbing performance. The results indicate that the energy level of the inner reinforcements with polymeric materials increased 8.8 times, to about 750 J, compared to the plain Al tube (85 J) under bending impact loads. The numerical simulations are relevant and reliable for the details of the specimens’ impact process and show good agreement with the experimental results. Finally, depending on the content, this research, rather than focusing on the fundamental concept of polymer-reinforced aluminum crash tubes, focuses on the specific dynamic bending impact evaluation of the Al, PA6, and PP configuration and the design insight that hollow PP reinforcement can accelerate fracture. In contrast, a fully filled PP core inside a PA6 sleeve can suppress splitting and substantially improve impact energy absorption. Full article
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14 pages, 2940 KB  
Article
Some Approaches to Quantitative Classification of Plastic Deformation Processes Based on the Parameters of Their Stress–Strain State Determined by Simulation Modeling
by Valentin Kamburov and Rayna Dimitrova
Metals 2026, 16(4), 445; https://doi.org/10.3390/met16040445 - 20 Apr 2026
Viewed by 4
Abstract
The article discusses the methods for classifying processes for testing and processing metals by plastic deformation, based on the characteristics of their stress–strain state. The basic methods for determining the stress and strain states using fundamental scalar quantities representing the stress and strain [...] Read more.
The article discusses the methods for classifying processes for testing and processing metals by plastic deformation, based on the characteristics of their stress–strain state. The basic methods for determining the stress and strain states using fundamental scalar quantities representing the stress and strain tensors are discussed. Equations have been derived for the quantitative determination of the type of stress–strain state through a combination of principal stresses, represented as the strain rigidity of the deformation mode. A deformable work-hardening alloy, AA7075, from the database Quantor Form 8.2.4 software product, is used, which is deformed at room temperature with an analysis of elastic–plastic deformations. A classification of deformation processes for testing and processing metals by plastic deformation is proposed, using the stress triaxiality parameter and the strain rigidity coefficient. Some 2D and 3D diagrams have been created based on simulation modeling of plastic deformation processes using virtual tools, allowing the grouping of processes according to the measured principal stresses and their combinations, which represent the stress triaxiality and strain rigidity of the deformation mode. By determining the type of grouping in these diagrams and the change in the stress–strain state with increasing strain levels, the characteristic features of the deformation processes used in materials testing and in the processing metals by plastic deformation of metals/alloys have been confirmed. Full article
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15 pages, 3786 KB  
Article
A Flexible Copper Electrode Array for High-Density Surface Electromyography
by Chaoxin Li, Chenghong Lu, Jiuqiang Li and Kai Guo
Bioengineering 2026, 13(4), 467; https://doi.org/10.3390/bioengineering13040467 - 16 Apr 2026
Viewed by 201
Abstract
Precise monitoring of forearm muscle groups is crucial for decoding motor intentions in human–machine interfaces (HMIs) and rehabilitation. However, traditional surface electromyography (sEMG) electrodes face significant challenges in densely packed muscle regions with large skin deformations, leading to severe signal crosstalk and unstable [...] Read more.
Precise monitoring of forearm muscle groups is crucial for decoding motor intentions in human–machine interfaces (HMIs) and rehabilitation. However, traditional surface electromyography (sEMG) electrodes face significant challenges in densely packed muscle regions with large skin deformations, leading to severe signal crosstalk and unstable contact. Here, we report a flexible, low-cost 16-channel copper electrode array system designed for the high-density monitoring of multiple forearm muscle activities. Through a facile fabrication process, rigid copper is transformed into a conformable sensing interface. The optimized serpentine interconnects endow the array with excellent stretchability and effectively isolate motion-induced stress, ensuring high-quality signal acquisition under complex deformations. The high-density 2 × 8 array enables the spatiotemporal mapping of distributed flexor and extensor muscle groups. Integrated with a customized wireless data acquisition system, the array successfully demonstrates real-time, multi-channel sEMG monitoring of various hand movements (e.g., fist clenching, wrist flexion/extension), clearly revealing specific muscle activation patterns. This low-cost, high-performance flexible sensor array provides a highly promising tool for complex gesture decoding, electromyographic imaging, and next-generation wearable HMIs. Full article
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18 pages, 3036 KB  
Article
Analytical Development of Impact Response of Stiffened Composite Panel with Optimum Structural Behaviour
by José Juan Cruz Reyes and Hessam Ghasemnejad
J. Compos. Sci. 2026, 10(4), 213; https://doi.org/10.3390/jcs10040213 - 16 Apr 2026
Viewed by 181
Abstract
This paper presents an analytical framework for the preliminary design of stringer-stiffened composite panels subjected to low-velocity impact. The formulation combines First-Order Shear Deformation Theory with a two-degree-of-freedom spring–mass model, while the super-stringer is represented as a Euler–Bernoulli beam whose bending contribution is [...] Read more.
This paper presents an analytical framework for the preliminary design of stringer-stiffened composite panels subjected to low-velocity impact. The formulation combines First-Order Shear Deformation Theory with a two-degree-of-freedom spring–mass model, while the super-stringer is represented as a Euler–Bernoulli beam whose bending contribution is transferred to the skin mid-surface through the parallel axis theorem. This provides a computationally efficient tool for rapid parametric assessment of stiffened configurations at the early design stage. To support laminate selection, a Specific Impact Energy Index (SIEI) is introduced to rank configurations according to their elastic energy storage efficiency relative to the product of skin and stringer thicknesses. The tool is validated against both published experimental results and a finite element dynamic explicit model, demonstrating a good approximation of the impact response. It is then applied to identify the optimum laminate configuration for a super-stringer case study within the design space considered. Full article
(This article belongs to the Special Issue Characterization and Modeling of Composites, 4th Edition)
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30 pages, 3212 KB  
Article
Application of PSInSAR Monitoring for Large-Scale Landslide with Persistent Scatterers from Deep Learning Classification
by Yu-Heng Tai, Chi-Chuan Lo, Fuan Tsai and Chung-Pai Chang
Remote Sens. 2026, 18(8), 1181; https://doi.org/10.3390/rs18081181 - 15 Apr 2026
Viewed by 155
Abstract
The Persistent Scatterers InSAR (PSInSAR) technology, which utilizes pixels with stable phases to extract ground deformation, is an effective tool for large-scale, long-period surface monitoring applications. It has been widely applied to land subsidence monitoring, earthquake research, and infrastructure risk management. Furthermore, some [...] Read more.
The Persistent Scatterers InSAR (PSInSAR) technology, which utilizes pixels with stable phases to extract ground deformation, is an effective tool for large-scale, long-period surface monitoring applications. It has been widely applied to land subsidence monitoring, earthquake research, and infrastructure risk management. Furthermore, some studies have successfully employed this method to monitor the progressive motion of creeping in landslide areas. However, these regions containing active landslides are usually covered by canopy layers, which cause low coherence in InSAR processing and reduce the number of stable pixels, thereby preventing long-term period monitoring in those areas. In this study, the supervised deep learning model, U-Net, based on a convolutional neural network, is applied to the differential InSAR dataset acquired from Sentinel-1 to improve persistent scatterer selection. A well-processed PSInSAR result, utilizing 55 Sentinel-1 images acquired from 5 November 2014 to 19 December 2017, is introduced as a dataset for model training. The pixel-based Persistent Scatterer (PS) labels used for model training are identified using the StaMPS software. The model is designed to identify the distributed scatterer (iDS) index using a single pair of SAR images. As a result, more iDS pixels can be obtained from a single interferogram, indicating a significant improvement over the StaMPS algorithm. The line-of-sight velocity and time series of PS pixels from the model prediction show a long-term uplift on the upper slope, which represents downslope sliding in the target area. Furthermore, some iDS pixels exhibit a seasonal deformation on the lower part of the slope. The capability for these additional deformation analyses underscores the potential of this new deep-learning-based approach. Full article
(This article belongs to the Special Issue Artificial Intelligence and Remote Sensing for Geohazards)
37 pages, 10729 KB  
Article
Surface Microstructural Characteristics of Textured Multicomponent TiN-Based Coated Cemented Carbides
by Xin Tong, Xiaolong Cao, Shucai Yang and Dongqi Yu
Coatings 2026, 16(4), 470; https://doi.org/10.3390/coatings16040470 - 14 Apr 2026
Viewed by 216
Abstract
To address the issues of high cutting temperatures and severe tool wear during titanium alloy machining, this study proposes a hybrid surface modification strategy combining micro-textures and multicomponent titanium nitride (TiN)-based coatings on cemented carbide tools. Using YG8 cemented carbide as the substrate, [...] Read more.
To address the issues of high cutting temperatures and severe tool wear during titanium alloy machining, this study proposes a hybrid surface modification strategy combining micro-textures and multicomponent titanium nitride (TiN)-based coatings on cemented carbide tools. Using YG8 cemented carbide as the substrate, micro-dimple textures were fabricated by fiber laser, and three coatings with different architectures (TiAlSiN, TiSiN/TiAlN, and TiSiN/TiAlSiN/TiAlN) were deposited via multi-arc ion plating technology. Based on a two-factor (texture diameter and texture spacing) and three-level orthogonal experiment, the evolution behaviors of surface morphology, phase composition, and mechanical properties of the textured multicomponent TiN-based coatings were systematically characterized and comparatively analyzed. The results reveal that: compared to the monolithic-structured TiAlSiN coating, the TiSiN/TiAlSiN/TiAlN and TiSiN/TiAlN composite coatings with multilayered composite structures can effectively relieve the residual stress inside the film–substrate system, and significantly suppress the phenomena of coating cracking and localized spallation caused by irregular protrusions of the recast layer at the micro-texture edges. X-ray diffraction (XRD) and crystallite size analyses indicate that the amorphous Si3N4 phase promoted by the Si element in the composite coatings effectively impedes the growth of TiN columnar crystals, achieving significant grain refinement. Mechanical property tests confirm that the existence of multicomponent composite interfaces effectively hinders dislocation movement. Among them, the textured TiSiN/TiAlSiN/TiAlN composite coating exhibits the optimal comprehensive performance; its microhardness, nanohardness, and H/E ratio (characterizing the resistance to plastic deformation) are increased by 17.94%, 8%, and approximately 45%, respectively, compared to those of the textured TiAlSiN coating. This study deeply elucidates the synergistic strengthening and toughening mechanisms between micro-texture parameters and the internal structures of the coatings, providing important theoretical guidance and experimental data support for the surface design of long-lifespan tools oriented towards the high-efficiency machining of titanium alloys. Full article
(This article belongs to the Special Issue Cutting Performance of Coated Tools)
23 pages, 3790 KB  
Article
CrystalCells: An Open-Source Modular Bioprinting Platform with Automated Tool Exchange, High-Performance Extruding, Thermal Control, and Microscopic Imaging
by Shuang Liang, Silas Habimana and Feiyang Zheng
Appl. Sci. 2026, 16(8), 3727; https://doi.org/10.3390/app16083727 - 10 Apr 2026
Viewed by 331
Abstract
Open-source bioprinting can broaden access to biofabrication, enabling existing systems to perform high-resolution tissue manufacturing. However, most of these focus on low cost, easy assembly, or specific biomaterial ink rather than making a robust standardized and modularized multifunction platform. In this study, we [...] Read more.
Open-source bioprinting can broaden access to biofabrication, enabling existing systems to perform high-resolution tissue manufacturing. However, most of these focus on low cost, easy assembly, or specific biomaterial ink rather than making a robust standardized and modularized multifunction platform. In this study, we present CrystalCells, a user-friendly modular open-source bioprinting system centered on the TridentExtruder, a high-performance syringe extruder with extrusion/retraction capability and tool-free automated syringe coupling. The system enables the automated exchange of syringe, temperature-controlling, microscope, and pipette modules. Repeated syringe return-and-pickup cycles showed repositioning errors within ±20 μm, while the extruder generated pressures above 950 kPa and exhibited lower elastic deformation than the Replistruder 4 under the same pressure conditions. CrystalCells supported the extrusion of pre-crosslinked alginate, FRESH printing, and dual-biomaterial inks printing with automated exchange. A microscope module resolved stained HeLa cells and enabled layer-by-layer imaging for defect detection during printing. A thermoelectric module maintained the syringe barrel below 6 °C during the printing of an alginate–collagen biomaterial ink at 23 °C (room temperature), and a pipette module transferred 2–10 μL volumes with errors within ±0.5 μL. These results show that CrystalCells is an open-source modular biofabrication platform integrating printing, imaging, temperature control, and liquid handling within a single workflow. Full article
(This article belongs to the Section Applied Biosciences and Bioengineering)
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49 pages, 675 KB  
Review
Automated Assembly of Large-Scale Aerospace Components: A Structured Narrative Survey of Emerging Technologies
by Kuai Zhou, Wenmin Chu, Peng Zhao, Xiaoxu Ji and Lulu Huang
Sensors 2026, 26(8), 2294; https://doi.org/10.3390/s26082294 - 8 Apr 2026
Viewed by 476
Abstract
Large-scale aerospace components (e.g., wings, fuselage sections, wing boxes, and rocket segments) feature large dimensions, low stiffness, complex interfaces, and strict assembly tolerances. Traditional rigid tooling and manual alignment struggle to meet the demands of high precision, efficiency, and flexibility in modern aerospace [...] Read more.
Large-scale aerospace components (e.g., wings, fuselage sections, wing boxes, and rocket segments) feature large dimensions, low stiffness, complex interfaces, and strict assembly tolerances. Traditional rigid tooling and manual alignment struggle to meet the demands of high precision, efficiency, and flexibility in modern aerospace manufacturing. This paper presents a structured literature review on the automated assembly of large-scale aerospace components, summarizing advances in three core domains: pose adjustment and positioning mechanisms, digital measurement technologies, and trajectory planning and control. Particular emphasis is placed on two cross-cutting themes: measurement uncertainty analysis and flexible assembly, which are critical for high-quality docking. The review classifies pose adjustment mechanisms into four categories (NC positioners, parallel kinematic machines, industrial robots, and novel mechanisms) and digital measurement into five branches (vision metrology, large-scale metrology, measurement field construction, uncertainty analysis, and auxiliary techniques). It also outlines five trajectory planning and control routes, covering traditional methods, multi-sensor fusion, digital twins, flexible assembly, and emerging intelligent approaches. The analysis reveals that current research suffers from fragmentation among mechanism design, metrology, and control, with insufficient integration of uncertainty propagation and flexible deformation modeling. Future systems will rely on heterogeneous equipment collaboration, uncertainty-aware closed-loop control, high-fidelity flexible modeling, and digital twin-driven decision-making. This review provides a unified framework and a technical reference for developing reliable, flexible, and scalable automated assembly systems for next-generation aerospace structures. Full article
(This article belongs to the Section Sensors and Robotics)
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25 pages, 3472 KB  
Article
Optimization of Punch Shaft Design for Reduced Punching Force and Enhanced Tool Life in S500MC Steel Sheet Forming
by Abdelwaheb Zeidi, Khaled Elleuch, Şaban Hakan Atapek, Jarosław Konieczny, Krzysztof Labisz and Janusz Ćwiek
Materials 2026, 19(7), 1470; https://doi.org/10.3390/ma19071470 - 7 Apr 2026
Viewed by 439
Abstract
This study presents a comprehensive numerical and experimental investigation into the influence of punch shaft geometry on punching force and tool durability in the cold forming of S500MC steel sheets using an AISI D2 punch. Finite element analyses were conducted to evaluate the [...] Read more.
This study presents a comprehensive numerical and experimental investigation into the influence of punch shaft geometry on punching force and tool durability in the cold forming of S500MC steel sheets using an AISI D2 punch. Finite element analyses were conducted to evaluate the effects of varying punch shaft diameters on stress distribution, deformation behavior, and resultant punching forces. Experimental validation was performed through controlled punching tests, measuring force responses and assessing tool wear. The results demonstrate that optimizing the punch shaft diameter reduces the maximum punching force and minimizes stress concentrations, thereby enhancing tool life. Specifically, larger punch shaft diameters contribute to more uniform stress distribution and decreased risk of premature tool failure. These findings provide valuable insights for tooling design in high-strength steel sheet forming processes, enabling improved efficiency and cost-effectiveness in manufacturing operations. Full article
(This article belongs to the Special Issue Modeling and Optimization of Material Properties and Characteristics)
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21 pages, 6200 KB  
Article
Prediction and Regulation of SCC’s Shrinkage Using the PSO-BPNN Model
by Tongyuan Ni, Lihua Shen, Shenghao Shen, Zaoyang Cai, Wen Chu, Chengshun Hu, Chenhui Jiang and Kai Jing
Materials 2026, 19(7), 1468; https://doi.org/10.3390/ma19071468 - 7 Apr 2026
Viewed by 352
Abstract
The shrinkage deformation is a significant risk to self-compacting concrete (SCC)-filled steel tube structures. It was essential to understand the concrete autogenous shrinkage strain before being regulated in order to determine compensation shrinkage measures. In this study, A PSO-BPNN model was constructed, which [...] Read more.
The shrinkage deformation is a significant risk to self-compacting concrete (SCC)-filled steel tube structures. It was essential to understand the concrete autogenous shrinkage strain before being regulated in order to determine compensation shrinkage measures. In this study, A PSO-BPNN model was constructed, which is based on the Particle Swarm Optimization-Back Propagation Neural Networks (PSO-BPNN), and the autogenous shrinkage strain of SCC was predicted based on PSO-BPNN before being regulated. Moreover, some experiments about compensating for shrinkage by expansion and by a combination of expansion and contraction were investigated. Based on this prediction, a series of experiments was conducted on the regulation of the shrinkage deformation of SCC for an actual bridge project. The results indicated that a good consistency of PSO-BPNN between predicted and measured values, demonstrating that PSO-BPNN is a model with high accuracy in predicting concrete autogenous shrinkage strain before regulation, and as a guidance for regulation to compensate for shrinkage. The prediction error was less than 10% for 28-day self-shrinkage, and the experimental workload was reduced. The PSO-BPNN is a convenient tool for predicting the shrinkage of SCC, enabling the determination of dosages of expansion agent and reducing shrinkage agent to achieve SCC’s shrinkage regulation. Full article
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23 pages, 399 KB  
Article
Curvature–Cohomology Criterion for Projectivity: A Synthesis of Classical Results in Hodge Theory
by Ghaliah Alhamzi, Mona Bin-Asfour, Emad Solouma, Abdullah Alahmari, Mansoor Alsulami and Sayed Saber
Axioms 2026, 15(4), 265; https://doi.org/10.3390/axioms15040265 - 6 Apr 2026
Viewed by 231
Abstract
This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, [...] Read more.
This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Yau’s solution of the Calabi conjecture, the Bochner–Kodaira–Nakano identity, and Kodaira’s embedding theorem—is well-known, their combination yields a transparent geometric criterion: if the first Chern class c1(M) admits a semi-positive real (1,1) representative that is strictly positive at some point (or equivalently has a maximal rank n somewhere), then M is projective. Beyond the maximal rank case, we refine Girbau’s classical vanishing theorem to obtain an optimal rank-sensitive bound: if 2πc1(M) has a semi-positive representative whose pointwise rank is k somewhere, then Hp,0(M)=0 for all p>nk. This sharpens the classical Girbau–Griffiths–Harris vanishing theorem and quantifies how partial positivity of a Ricci representative constrains Hodge cohomology. We situate these criteria alongside classical tests (Kodaira integrality and Moishezon) and numerical descriptions of the Kähler cone (Demailly–Paun), discuss deformation-invariance properties, and relate them to RC positivity and Campana–Peternell-type statements. Examples illustrate the sharpness of the hypotheses, and we survey the effective bounds—ranging from rigorous uniform high ampleness results to conjectural optimal constants—with clear distinction between proven theorems, refinements of classical results, and open problems. The contribution of this work lies not in new analytic techniques but in (1) isolating a sharp curvature condition at the level of c1(M); (2) organizing classical tools into a direct projectivity criterion; and (3) clarifying the rank-dependent vanishing behavior that follows from partial positivity. Full article
(This article belongs to the Special Issue Recent Advances in Complex Analysis and Applications, 2nd Edition)
22 pages, 1280 KB  
Article
Enhancing Early Skin Cancer Detection: A Deep Learning Approach with Multi-Scale Feature Refinement and Fusion
by Siyuan Wu, Pengfei Zhao, Huafu Xu and Zimin Wang
Symmetry 2026, 18(4), 612; https://doi.org/10.3390/sym18040612 - 5 Apr 2026
Viewed by 318
Abstract
The global incidence of skin cancer is rising, making it an increasingly critical public health issue. Malignant skin tumors such as melanoma originate from pathological alterations in skin cells, and their accurate early-stage segmentation is crucial for quantitative analysis, early diagnosis, and effective [...] Read more.
The global incidence of skin cancer is rising, making it an increasingly critical public health issue. Malignant skin tumors such as melanoma originate from pathological alterations in skin cells, and their accurate early-stage segmentation is crucial for quantitative analysis, early diagnosis, and effective treatment. However, achieving precise and efficient segmentation remains a major challenge, as existing methods often struggle to capture complex lesion characteristics. To address this challenge, we propose a novel deep learning framework that integrates the PVT v2 backbone with two key modules: the Spatial-Aware Feature Enhancement (SAFE) module and the Multiscale Dual Cross-attention Fusion (MDCF) module. The SAFE module enhances multi-scale encoder features through a dual-branch architecture, which adaptively extracts offset information to integrate fine-grained shallow details with deep semantic information, thereby bridging the feature gap across network depths. The MDCF module establishes bidirectional cross-attention between decoder and encoder features, followed by multi-scale deformable convolutions that capture lesion boundaries and small fragments across heterogeneous receptive fields, thereby enriching semantic details while suppressing background interference. The proposed model was evaluated on two public benchmark datasets (ISIC 2016 and ISIC 2018), achieving Intersection over Union (IoU) scores of 87.33% and 83.67%, respectively. These results demonstrate superior performance compared to current state-of-the-art methods and indicate that our framework significantly enhances skin lesion image analysis, offering a promising tool for improving early detection of skin cancer. Full article
(This article belongs to the Special Issue Symmetric/Asymmetric Study in Medical Imaging)
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30 pages, 3637 KB  
Article
A Hybrid-Dimensional Iterative Coupled Modeling of Lubrication Flow in Deformable Geological Media with Discrete Fracture Networks
by Yue Xu, Tao You and Qizhi Zhu
Materials 2026, 19(7), 1444; https://doi.org/10.3390/ma19071444 - 4 Apr 2026
Viewed by 387
Abstract
Fluid-driven fracture processes are central to the development of subsurface energy systems such as geothermal and hydrocarbon reservoirs. Although phase-field formulations have become a widely used tool for describing fracture initiation and growth, the diffuse representation of cracks makes it difficult to resolve [...] Read more.
Fluid-driven fracture processes are central to the development of subsurface energy systems such as geothermal and hydrocarbon reservoirs. Although phase-field formulations have become a widely used tool for describing fracture initiation and growth, the diffuse representation of cracks makes it difficult to resolve flow behavior accurately inside discrete fracture networks (DFNs) and to represent hydro-mechanical coupling in a sharp-interface sense. This study develops a hybrid-dimensional iterative framework for lubrication-flow simulation in deformable fractured geomaterials. By leveraging phase-field point clouds together with non-conforming discretization schemes for both the solid matrix and fracture domains, the proposed framework enables the dynamic reconstruction of evolving fracture networks. The theoretical formulation and numerical implementation of the coupling strategy are presented in detail. Hydraulic benchmark examples verify the performance of the fluid flow solver under various physical conditions. The classical Sneddon problem and Khristianovic–Geertsma–de Klerk (KGD) model are employed to validate the solid deformation solver, confirming accurate predictions of crack opening displacement and mesh independence in fracture width calculation. Additional simulations with complex pre-existing fracture patterns further demonstrate the applicability of the framework to coupled hydro-mechanical analysis in fractured media. Full article
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