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14 pages, 1433 KB  
Article
From Friction Control to Dynamic Ratcheting and Actuation by Combined Normal and Tangential Oscillations
by Ibrohim Madatov, Qiang Li and Valentin L. Popov
Lubricants 2026, 14(8), 286; https://doi.org/10.3390/lubricants14080286 (registering DOI) - 25 Jul 2026
Abstract
The superposition of normal and tangential oscillations in frictional contacts can fundamentally alter the macroscopic friction law and generate directed motion and force. In this work, we investigate the transition between friction reduction, dynamic ratcheting, and vibrational actuation within a unified numerical framework [...] Read more.
The superposition of normal and tangential oscillations in frictional contacts can fundamentally alter the macroscopic friction law and generate directed motion and force. In this work, we investigate the transition between friction reduction, dynamic ratcheting, and vibrational actuation within a unified numerical framework based on a compliant Coulomb friction contact. The system is subjected to simultaneous harmonic oscillations in the normal and tangential directions with an arbitrary phase shift. First, the limiting cases of purely normal and purely tangential oscillations are revisited, demonstrating that both produce equivalent friction–reduction behavior when expressed in terms of appropriate dimensionless parameters. For sufficiently large tangential oscillation amplitudes, a transition to a bidirectional stick-slip regime is identified, characterized by alternating forward and backward motion within a single oscillation cycle. The general case of dual-mode excitation is then analyzed over a broad parameter range. Numerical simulations show that the macroscopic friction coefficient is governed by four dimensionless parameters: the normalized sliding velocity, the normal oscillation ratio, the tangential oscillation parameter, and the phase shift between the oscillation modes. The combined oscillations break the symmetry of the friction law with respect to the direction of motion, resulting in different critical velocities and friction coefficients for positive and negative sliding directions. Depending on the parameter combination, the system exhibits three distinct operational regimes: active friction control, dynamic ratcheting, and vibrational actuation. In the latter regime, the effective friction coefficient becomes negative, indicating a conversion of oscillatory energy into directed mechanical work. The results provide a unified physical interpretation of oscillation-induced transport and force generation in frictional contacts and establish general design principles for vibration-assisted friction-control systems, dynamic ratchets, and oscillatory actuators. Full article
24 pages, 3902 KB  
Article
SonarReg-GS SLAM: Sparse Sonar-Guided Depth Regularization for Underwater Gaussian Splatting SLAM
by Wen Yang, Xiaolong Qian, Xulin Liu and Jianxing Leng
Sensors 2026, 26(15), 4713; https://doi.org/10.3390/s26154713 (registering DOI) - 24 Jul 2026
Abstract
3D Gaussian Splatting (3DGS) SLAM provides an explicit scene representation for dense tracking and mapping, which is useful for underwater robotic perception. However, underwater monocular 3DGS SLAM lacks reliable metric depth cues: monocular depth estimation can provide dense structural priors, but its scale [...] Read more.
3D Gaussian Splatting (3DGS) SLAM provides an explicit scene representation for dense tracking and mapping, which is useful for underwater robotic perception. However, underwater monocular 3DGS SLAM lacks reliable metric depth cues: monocular depth estimation can provide dense structural priors, but its scale and reliability often degrade under underwater appearance changes. Forward-looking sonar (FLS) provides range–azimuth acoustic measurements whose range coordinate is related to physical distance, but raw sonar observations are sparse, noisy, and ambiguous. Our key insight is that FLS returns can serve as sparse metric depth anchors when they are associated with visually detected object regions. Based on this insight, we propose SonarReg-GS SLAM, an underwater visual–acoustic 3DGS SLAM framework with sparse sonar-guided depth regularization. Given synchronized RGB and sonar inputs, SonarReg-GS SLAM uses object masks to constrain the search space for acoustic range association. Filtered sonar responses are selected as sparse metric anchors through object-aware sampling, bearing-to-beam gating, and valid-pair checking. These anchors regularize the scale of monocular depth and generate metric depth priors for Gaussian initialization and tracking. An object-aware RGB mask loss further increases supervision on detected object regions while preserving full-scene mapping. Experiments on two public RGB–sonar underwater datasets show that SonarReg-GS SLAM improves tracking accuracy and mapping quality compared with representative classical SLAM and Gaussian Splatting SLAM baselines. Compared with Splat-SLAM, our method reduces the average ATE RMSE from 0.1296 m to 0.1015 m on UXO and from 0.5687 m to 0.4640 m on OPTI, corresponding to relative reductions of 21.7% and 18.4%, respectively. For rendering-based mapping, it increases the average PSNR from 28.05 dB to 29.61 dB on UXO and from 20.91 dB to 28.63 dB on OPTI while reducing the average LPIPS from 0.345 to 0.173 and from 0.450 to 0.303, respectively. Full article
(This article belongs to the Section Sensors and Robotics)
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14 pages, 393 KB  
Article
Missed Opportunities: Restitution and Relational Ethics
by Reilly Clark
Arts 2026, 15(7), 167; https://doi.org/10.3390/arts15070167 - 21 Jul 2026
Viewed by 424
Abstract
The return of African cultural objects represents an opportunity to practice what Felwine Sarr and Bénédicte Savoy call “a new relational ethics.” Oftentimes, repatriation begins and ends with the literal return of physical objects. This does little to address legacies of colonial theft, [...] Read more.
The return of African cultural objects represents an opportunity to practice what Felwine Sarr and Bénédicte Savoy call “a new relational ethics.” Oftentimes, repatriation begins and ends with the literal return of physical objects. This does little to address legacies of colonial theft, value extraction, and epistemicide. It can also reinscribe the power of Western interpretive frameworks and reproduce Western patterns of state power by returning objects to Western-style institutions within postcolonial nation-states. This essay considers the return of the Benin bronzes as a case study for these missed opportunities and alternative paths forward. It follows the various and sometimes competing means by which Benin bronzes came “home:” whether to the postcolonial nation of Nigeria, to the Oba of Benin himself, or to the controversial public-private partnership known as the Museum of West African Art (MOWAA). This essay considers how these various means of return, and these various meanings of “home,” can work against one another and can be co-opted as neoliberal and neocolonial forms of control. The essay also explores alternative paths forward through the framework of relational ethics. Sarr and Savoy first applied the phrase to the return of African cultural objects in their 2018 report. This essay expands on Sarr and Savoy’s report and builds from Native American and Indigenous scholars like Margaret Kovach and Linda Tuhiwai Smith, who identify opportunities to remake relations as a means of restitution. This includes remaking relations between indigenous communities, Western institutions, and postcolonial nation-states. It also includes remaking relations between human beings and the more-than-human world, including spirits of the ancestors, outside the systems of Western knowledge and value production. Full article
20 pages, 3730 KB  
Article
Physics-Verified Spectral Dreaming Enables Interpretable and Manufacturable Inverse Design of Multilayer Radiative Coolers
by Jiajun Wang and Xiuye Liu
Photonics 2026, 13(7), 687; https://doi.org/10.3390/photonics13070687 - 21 Jul 2026
Viewed by 208
Abstract
Optical inverse design faces a dilemma: neural surrogates enable fast, differentiable search but can yield physically unreliable pseudo-optima, whereas solver-in-the-loop optimization is reliable yet costly. Most surrogate methods also trust the surrogate throughout the search, train separate models for performance prediction and structure [...] Read more.
Optical inverse design faces a dilemma: neural surrogates enable fast, differentiable search but can yield physically unreliable pseudo-optima, whereas solver-in-the-loop optimization is reliable yet costly. Most surrogate methods also trust the surrogate throughout the search, train separate models for performance prediction and structure optimization, and remain largely black-box. We propose Physics-Verified Spectral Dreaming (PVSD), a unified framework for forward prediction, inverse design, and physical interpretability: a frozen differentiable spectral surrogate “dreams” structural mutations by input-gradient ascent to explore the design space, while a physical solver adjudicates every accepted update—the surrogate proposes, physics decides. We instantiate it as PVSD-TMM for one-dimensional multilayer radiative coolers. The forward predictor attains R2=0.9936/0.9964/0.9828 for net cooling power, solar reflectance, and primary-window emissivity; neural dreaming lifts the population-mean net cooling power of 1000 random seeds from 466.7 to 65.8 W m−2 (91.4% reaching net cooling), and continuous-thickness refinement with 5 nm rounding yields a 14-layer manufacturable final design. Independent COMSOL finite-element and analytic TMM cross-validation converge to Pcool172 W m−2, Rsolar0.970, and εwin=0.9252. This is a full-spectrum radiative-balance result for an idealized radiative-only case (hconv=0), not a window-emittance-only metric; PVSD thus achieves high simulated broadband radiative-cooling performance under the stated assumptions, without claiming global optimality. Full article
(This article belongs to the Section Data-Science Based Techniques in Photonics)
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15 pages, 3952 KB  
Article
Physics-Informed Neural Network Simulation of Proppant Transport in Low-Viscosity Fracturing Fluid
by Yuyang Liu, Kai Shen, Guanglong Sheng and Hui Zhao
Processes 2026, 14(14), 2352; https://doi.org/10.3390/pr14142352 - 21 Jul 2026
Viewed by 186
Abstract
Proppant transport and deposition directly control fracture conductivity during hydraulic fracturing, especially under low-viscosity fracturing fluid conditions where strong convection, settling, deposition, and erosion coexist. To improve the computational efficiency of proppant transport simulation, this study develops a dual-network physics-informed neural network (dual-PINN) [...] Read more.
Proppant transport and deposition directly control fracture conductivity during hydraulic fracturing, especially under low-viscosity fracturing fluid conditions where strong convection, settling, deposition, and erosion coexist. To improve the computational efficiency of proppant transport simulation, this study develops a dual-network physics-informed neural network (dual-PINN) framework based on a previously developed fifth-order WENO proppant transport model. In the proposed framework, PINNc is used to predict the proppant concentration field, while PINNhp is used to predict the deposited proppant bed height. The governing physical constraints, including convection, effective diffusion, settling, deposition, and erosion, are embedded into the loss function to achieve coupled concentration–deposition prediction. The model is validated using a benchmark case with a fracture length of 100 m, fracture height of 30 m, fracture width of 0.002 m, injection rate of 0.015 m3/s, and inlet proppant concentration of 0.1. Compared with the fifth-order WENO reference solution, the RMSE values of the predicted proppant concentration at 100 s, 400 s, and 1500 s are 6.36 × 10−3, 7.38 × 10−3, and 8.28 × 10−3, respectively. The offline training time of the dual-PINN model is approximately 15 min, and the trained model requires only about 3 ms for one forward prediction. In comparison, the fifth-order WENO method requires 0.43–22.3 s for a single simulation under the tested mesh resolutions, corresponding to an online speed-up of approximately 143 to 7430. Sensitivity analyses further show that the proposed model maintains stable and physically consistent responses for inlet proppant concentrations of 0.01–0.25 and injection rates of 0.01–0.06 m3/s. These results demonstrate that the proposed dual-PINN framework can provide an efficient mesh-free surrogate for rapid proppant transport prediction and fracturing parameter optimization. Full article
(This article belongs to the Special Issue Application of Machine Learning in Geo-Energy Exploration Processes)
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30 pages, 35911 KB  
Article
Discontinuous Galerkin Forward Modeling of Wave Propagation with Split-Field Absorbing Boundary Conditions and Gradient-Based Adaptive Meshes
by Meng Li, Guoning Wu, Jinqiu Li and Chunyong Wu
Mathematics 2026, 14(14), 2641; https://doi.org/10.3390/math14142641 - 20 Jul 2026
Viewed by 126
Abstract
Wave propagation modeling in heterogeneous media requires numerical methods that can simultaneously handle complex geometries, artificial boundary reflections, and spatially varying resolution demands. In this study, we present a Discontinuous Galerkin (DG) forward modeling method for wave propagation with split-field absorbing boundary conditions [...] Read more.
Wave propagation modeling in heterogeneous media requires numerical methods that can simultaneously handle complex geometries, artificial boundary reflections, and spatially varying resolution demands. In this study, we present a Discontinuous Galerkin (DG) forward modeling method for wave propagation with split-field absorbing boundary conditions and gradient-based adaptive meshes. The wave equation is formulated as a first-order hyperbolic system and discretized by the DG method, which preserves local conservation and is well suited for explicit Runge–Kutta time integration on unstructured meshes. To reduce spurious reflections from truncated computational boundaries, a split-field absorbing boundary treatment is introduced in the absorbing layer through directional damping terms, maintaining the first-order structure and local update form of the DG scheme. In addition, a physics-based mesh metric is constructed from the local velocity-gradient length scale, allowing the mesh to be automatically coarsened in smooth regions and refined near strong velocity contrasts, interfaces, and discontinuities. Numerical convergence tests show that the quadratic DG scheme achieves the expected third-order accuracy in the L2 norm. Quantitative PML evaluation gives a reflection coefficient of approximately 1.65×105, indicating effective suppression of artificial boundary reflections. For the three-dimensional Marmousi model, the proposed adaptive mesh reduces the number of tetrahedral elements from 158,492 to 88,681, decreases the CPU time from 241.4453 s to 139.1328 s, and reduces memory consumption from 3788.67 MB to 2109.55 MB compared with the uniform mesh. These results demonstrate that the proposed method can improve the balance between computational efficiency and solution accuracy while maintaining stable and physically interpretable wavefield modeling in heterogeneous media. Full article
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20 pages, 2360 KB  
Article
The Dual Role of Artificial Intelligence in Sustainability Governance: Time–Frequency Evidence from Climate Response and Infectious Disease Attention in China
by Ruiqian Zhang, Jiayi Lyu, Yan Chen and Zhengzheng Li
Sustainability 2026, 18(14), 7419; https://doi.org/10.3390/su18147419 - 20 Jul 2026
Viewed by 338
Abstract
Artificial intelligence (AI) is increasingly regarded as a key instrument for sustainability governance, but its role may differ across risk domains. Rather than functioning solely as an anticipatory tool, AI may also develop reactively in response to risk shocks. Using monthly Chinese data [...] Read more.
Artificial intelligence (AI) is increasingly regarded as a key instrument for sustainability governance, but its role may differ across risk domains. Rather than functioning solely as an anticipatory tool, AI may also develop reactively in response to risk shocks. Using monthly Chinese data from January 2013 to December 2023, this study examines the dual role of AI in sustainability governance by analyzing its time–frequency relationships with climate-related government response and infectious disease-related market attention. The continuous wavelet transform and partial wavelet coherence are employed, with the World Uncertainty Index controlled. The results show that AI-sector development is positively associated with both risk-related signals, but the lead–lag patterns differ substantially. In the climate-response domain, the relationship shifts from risk-signal precedence in 2015–2016 to AI-sector precedence in short-term bands after 2020, suggesting that AI-related capacity may have become increasingly embedded in anticipatory climate governance. In contrast, infectious disease-related attention mainly precedes AI-sector movements, especially during 2017–2018 and the COVID-19 period, indicating a more reactive role of AI in public health risk contexts. These findings do not provide causal evidence that AI directly reduces physical climate risks or epidemiological burdens. Instead, they reveal the dual role of AI as both a response to sustainability-related risk shocks and a potential contributor to forward-looking governance capacity. This study contributes to AI and sustainability governance research by clarifying the conditions and boundaries under which AI shifts from reactive crisis response toward anticipatory risk preparedness. Full article
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35 pages, 6767 KB  
Article
Study on Longitudinal Dynamic Stability of a Swift-Inspired Idealized Model Considering Body Periodic Vibrations
by Yating Gao and Dong Xue
Aerospace 2026, 13(7), 650; https://doi.org/10.3390/aerospace13070650 - 17 Jul 2026
Viewed by 225
Abstract
This study focuses on the longitudinal dynamic stability of swifts in cruising forward flight, which is critical for their high maneuverability but remains insufficiently investigated. Understanding longitudinal dynamic stability is the essential prerequisite for revealing the physical mechanism underlying their maneuverability: it is [...] Read more.
This study focuses on the longitudinal dynamic stability of swifts in cruising forward flight, which is critical for their high maneuverability but remains insufficiently investigated. Understanding longitudinal dynamic stability is the essential prerequisite for revealing the physical mechanism underlying their maneuverability: it is the dynamic stability characteristics that determine how the flight state responds to disturbances and control inputs, thereby laying a foundation for subsequent flight control during agile maneuvers. Conventional studies mostly adopt steady or quasi-steady assumptions, which cannot accurately reflect the influence of periodic body vibration. This study combines CFD numerical simulation and dynamic modeling to systematically analyze the unsteady dynamic stability of swifts. A bio-inspired dynamic model is established using the BE3357B airfoil with a 5° sweep angle, and the flapping-wing motion is decomposed into three degrees of freedom: sweeping, pitching, and flapping. Numerical reliability is assessed through grid independence and time-step independence verification. Aerodynamic force and moment trimming are performed on fixed-DOF and free-DOF models, where the latter considers coupled heaving–pitching motion and adjusted trim parameters. Stability analysis is conducted using three aerodynamic derivative methods: fixed velocity, forced oscillation, and Floquet. By solving small perturbation equations, eigenvalues and eigenmodes are obtained. All three methods identify two stable modes: a short-period mode with damping coefficient 0.1236–0.1870 and oscillation period 0.1121 s–0.1380 s, and a long-period mode with damping coefficient 0.2456–0.6203 and damping half-life 3.5803 s–4.8890 s, verifying stability under periodic vibration and unsteady aerodynamic coupling. Flow field results show clear distinct dynamic pressure and drag fluctuation characteristics between the downstroke and the upstroke. The unsteady stability framework provides a theoretical reference for analyzing the longitudinal stability of biomimetic flapping-wing aircraft and offers useful insight for future bird-inspired flight dynamics studies. Full article
(This article belongs to the Section Aeronautics)
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23 pages, 3332 KB  
Article
Towards Early-Stage Corrosion Prediction Using UHF RFID Measurements: A Machine Learning Feasibility Study
by Ali Imam Sunny, Mehadi Hasan Bijoy, Shahriar Uddin Saikat, Mohammed Dahiru Buhari, Adi Mahmud Jaya Marindra, Moontasir Bin Salim, Jun Zhang and Guiyun Tian
NDT 2026, 4(3), 20; https://doi.org/10.3390/ndt4030020 - 16 Jul 2026
Viewed by 220
Abstract
Conventional corrosion monitoring techniques often require costly instrumentation and direct access to structures, limiting their suitability for long-term monitoring. This study presents a machine learning feasibility study for early-stage corrosion detection using Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) measurements. Machine learning algorithms [...] Read more.
Conventional corrosion monitoring techniques often require costly instrumentation and direct access to structures, limiting their suitability for long-term monitoring. This study presents a machine learning feasibility study for early-stage corrosion detection using Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) measurements. Machine learning algorithms were applied to a previously published RFID corrosion dataset obtained from steel specimens exposed to marine atmospheric corrosion for 0, 1, 3, and 6 months. RFID-derived features, including Analogue Identifier (AID), forward power, frequency, phase, and backscattered power, were analysed using unsupervised and supervised learning methods. For corrosion-stage discrimination, Density-Based Spatial Clustering of Applications with Noise (DBSCAN) achieved an Adjusted Rand Index (ARI) of 1.00, a Normalised Mutual Information (NMI) score of 1.00, and a Silhouette score of 0.790. For nominal corrosion-thickness state estimation, a Random Forest regressor achieved an R2 of 1.00, RMSE of 1.34 µm, and MAE of 0.21 µm under 15-fold cross-validation. Additional Leave-One-Sample-Out (LOSO) validation using readcount-based measurement-event groupings yielded an RMSE of 0.12 µm and an R2 of 1.00. These results reflect nominal corrosion-thickness state estimation from repeated measurements on a single physical specimen per corrosion stage. SHAP analysis identified forward power and AID as the dominant predictive features. The results demonstrate the potential of RFID-enabled machine learning for early-stage corrosion assessment and provide a foundation for future experimental validation. Full article
(This article belongs to the Topic Nondestructive Testing and Evaluation)
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13 pages, 2200 KB  
Review
Liquid Metal Biomimicry: Bridging Fluidity and Biological Adaptability
by Sen Chen
Biomimetics 2026, 11(7), 499; https://doi.org/10.3390/biomimetics11070499 - 16 Jul 2026
Viewed by 271
Abstract
Liquid metals, particularly gallium-based alloys, uniquely combine fluidic compliance with metallic conductivity, which makes them ideal candidates for biomimetic design. Rather than treating biomimicry as the mere imitation of biological forms, we argue that liquid metal biomimicry should be understood as the realization [...] Read more.
Liquid metals, particularly gallium-based alloys, uniquely combine fluidic compliance with metallic conductivity, which makes them ideal candidates for biomimetic design. Rather than treating biomimicry as the mere imitation of biological forms, we argue that liquid metal biomimicry should be understood as the realization of biological strategies through the intrinsic physics of fluidity and interfacial dynamics. This review organizes existing research within a hierarchical framework that couples physical liquidity, interface biology analogy, and functional emergence to explain how adaptive behaviors naturally arise from dynamic liquid metal systems. We examine representative systems across morphological and functional dimensions and contend that their true significance lies not in replicating nature but in addressing problems that conventional rigid materials cannot solve. Looking forward, we identify several transformative directions that collectively chart a roadmap toward truly intelligent and autonomous bioinspired systems. By bridging the physics of fluidity with the principles of biological adaptability, liquid metal biomimicry holds transformative potential for soft robotics, wearable electronics, neuromorphic computing, and biomedical engineering. Full article
(This article belongs to the Special Issue Liquid Metal Biomimicry: Toward Bio-Inspired Smart Materials)
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10 pages, 404 KB  
Article
Running Demands in Sub-Elite Male Rugby Players: Do You Train Like You Play?
by Francesco Chiarello, Corrado Lupo, Damiano Li Volsi, Luca Beratto, Domenico Cherubini, Paolo Riccardo Brustio and Alexandru Nicolae Ungureanu
Sports 2026, 14(7), 302; https://doi.org/10.3390/sports14070302 - 16 Jul 2026
Viewed by 200
Abstract
This study investigated whether weekly training sessions replicate the running demands of match play in sub-elite rugby union athletes, examining the principle of training specificity across positional roles. A total of 30 male players from a sub-elite rugby union team participated, contributing 306 [...] Read more.
This study investigated whether weekly training sessions replicate the running demands of match play in sub-elite rugby union athletes, examining the principle of training specificity across positional roles. A total of 30 male players from a sub-elite rugby union team participated, contributing 306 training and match data points. External load variables were collected using 18 Hz GNSS devices and analyzed across ten time-motion KPIs, including distance per minute, maximal speed, distance distribution across speed zones, and acceleration–deceleration profiles. Linear mixed models assessed differences between training and match play within forwards, backs, and scrum-halves. Results revealed significant mismatches between training and match running demands, with positional roles exhibiting distinct profiles. Forwards performed substantially lower running volumes and intensities in training, particularly in moderate-speed zones. Backs showed similar total volumes but markedly reduced high-intensity actions, including maximal speed, high-speed running, and severe decelerations. Scrum-halves displayed the greatest alignment, with no major discrepancies across conditions. These findings indicate that game-based training alone does not sufficiently reproduce match play running intensity for any position. Integrating targeted closed-skill blocks and supplementary high-intensity conditioning within predominantly game-based frameworks may help balance representativeness, repetition, and physical overload, supporting more effective preparation for the running demands of competition. Full article
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12 pages, 318 KB  
Article
Photoproduction of the Quarkonia Pairs in the CGC Framework
by Marat Siddikov, Ivan Zemlyakov and Michael Roa
Particles 2026, 9(3), 74; https://doi.org/10.3390/particles9030074 - 15 Jul 2026
Viewed by 184
Abstract
In this manuscript, we present the results of our studies on the exclusive photoproduction of quarkonium-photon pairs with large invariant mass. In our analysis, we focus on the production of the ηcγ and χcJγ pairs in high energy [...] Read more.
In this manuscript, we present the results of our studies on the exclusive photoproduction of quarkonium-photon pairs with large invariant mass. In our analysis, we focus on the production of the ηcγ and χcJγ pairs in high energy kinematics. We use the Color Glass Condensate (CGC) framework for analysis and demonstrate that at leading order in αs the cross-sections of these processes are determined by the forward dipole scattering amplitude. The kinematic distributions of the produced particles allow us to study the dipole amplitude in detail, making this process a very clean probe for studies of saturation physics. Using phenomenological parametrizations of the dipole amplitudes, we estimate numerically the differential production cross-sections for ηcγ and χcγ in the kinematics of ultraperipheral collisions at the LHC and the future Electron-Ion Collider (EIC). Furthermore, we assess the role of this process as a possible background to the exclusive photoproduction of C-even quarkonia, which is frequently considered as a tool for odderon searches. Full article
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22 pages, 1137 KB  
Article
OPERA: A Unified Framework for AI-Assisted Polymer Metamaterial Design Through Operator Learning, Physics Embedding, and Normalizing-Flow Inverse Architecture
by Koffi Enakoutsa and Ivan Giorgio
Polymers 2026, 18(14), 1733; https://doi.org/10.3390/polym18141733 - 15 Jul 2026
Viewed by 220
Abstract
Additive manufacturing has opened an extraordinary design space for polymer metamaterials, enabling microstructures whose macroscopic mechanical behavior is governed largely by geometry rather than by chemical composition. A principled design framework must solve two coupled problems: a forward problem (given a microstructure, predict [...] Read more.
Additive manufacturing has opened an extraordinary design space for polymer metamaterials, enabling microstructures whose macroscopic mechanical behavior is governed largely by geometry rather than by chemical composition. A principled design framework must solve two coupled problems: a forward problem (given a microstructure, predict effective properties) and an inverse problem (given target properties, generate a microstructure). Convolutional neural networks (CNNs) solve the forward problem accurately, but the inverse problem remains more challenging for three reasons reported in the literature: (i) many surrogates predict only a scalar proxy rather than the full second-order elastic tensor; (ii) fixed or randomly initialized inverse decoders create a distribution-shift gap between surrogate predictions and physical re-evaluation; and (iii) dataset bias toward near-solid configurations limits exploration of low-density and anisotropic designs. We present a unified framework, the Operator-Physics-Enhanced Reverse Architecture (OPERA), that addresses all three issues. First, the forward surrogate predicts the complete 3×3 plane-stress stiffness tensor Ceff in Voigt notation, with an analytical layer enforcing Cij=Cji and positive definiteness by construction, achieving R2>0.99 on the directional moduli and density and R2>0.88 on the off-diagonal coupling term C16 and the effective Poisson ratio. Second, a normalizing-flow decoder Fϕ, jointly trained with the forward surrogate, keeps inverse design on the training manifold and reduces the surrogate–PDE re-evaluation gap from more than 30% to below 6% on held-out targets. Third, a five-family dataset with uniform coverage of ρ[0.10,0.95] is augmented through an expected-improvement active-learning loop. We embed minimum-feature-size, connectivity, and print-direction constraints into the optimization through differentiable regularization and report agreement of R2=0.987 between predictions and tensile measurements on ten FDM-printed specimens. The framework is demonstrated on five problems (auxetic, extreme anisotropy, isotropic low-density, chiral, and hierarchical), with an average target error of 6.8%. The results are framed relative to a reproduced scalar-proxy baseline; we provide an explicit statistical uncertainty analysis, a baseline-reproduction protocol, and a discussion of the method’s assumptions and numerical enforcement. Full article
(This article belongs to the Special Issue 3D/4D Printing of Polymers: Recent Advances and Applications)
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21 pages, 16664 KB  
Article
Fatigue Life Mapping of Rubber Isolators Based on Maximum Strain Energy Density and Cyclic Energy Dissipation Criteria with Specimen Data
by Yupeng Du, Jinying Huang, Zhenfang Fan, Jiaolin Wei, Wenwen Zhang and Xiaolong Wang
Polymers 2026, 18(14), 1732; https://doi.org/10.3390/polym18141732 - 15 Jul 2026
Viewed by 273
Abstract
The ride stability and driving comfort of vehicles are highly dependent on the performance of the damping system. The fatigue life prediction of damping components using rubber as the core damping material has become a research hotspot in the field of vehicle vibration [...] Read more.
The ride stability and driving comfort of vehicles are highly dependent on the performance of the damping system. The fatigue life prediction of damping components using rubber as the core damping material has become a research hotspot in the field of vehicle vibration isolation. Taking an automotive engine rubber isolator as the research carrier, this paper jointly carries out finite element simulation analysis and structural component fatigue life tests. A dual-parameter mapping framework is proposed, which integrates maximum strain energy density and cyclic energy dissipation instead of using a single damage indicator. This approach comprehensively accounts for the coupling effect of energy storage and energy dissipation coexisting under actual service conditions. Through uniaxial tensile tests on rubber specimens, combined with finite element simulations and physical model parameters, a quantitative mapping relationship between laboratory specimens and full-scale engine rubber isolators is established. Based on this mapping, the fatigue life curve of the isolator is derived from the specimen-based failure characteristics. Validation tests under two randomly selected operating conditions yield prediction errors of 7.5% and 6.9%, demonstrating that the proposed model can accurately achieve equivalent fatigue life transformation from small specimens to actual components. Unlike conventional direct extrapolation methods, this approach does not require complex multiaxial fatigue tests on the component itself; it only needs simple specimen fatigue data, significantly reducing development costs, while providing a reliable theoretical basis for material selection, fatigue performance optimization, and forward structural design of rubber isolators. Full article
(This article belongs to the Section Polymer Processing and Engineering)
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19 pages, 3896 KB  
Article
Graph Neural Operator-Based Surrogate Modelling of Multi-Field CFD Results in Biomass Boiler
by Przemysław Motyl, Danuta Król and Sławomir Poskrobko
Energies 2026, 19(14), 3314; https://doi.org/10.3390/en19143314 - 14 Jul 2026
Viewed by 688
Abstract
Computational fluid dynamics provides detailed spatial distributions of physical fields in biomass boiler combustion, but the computational cost of each simulation limits its application in parametric studies and near-real-time workflows. This work investigates whether a Graph Neural Operator (GNO) can serve as a [...] Read more.
Computational fluid dynamics provides detailed spatial distributions of physical fields in biomass boiler combustion, but the computational cost of each simulation limits its application in parametric studies and near-real-time workflows. This work investigates whether a Graph Neural Operator (GNO) can serve as a fast surrogate model that maps boiler operating parameters to six coupled CFD field distributions simultaneously. The reference case is a 10 kW wood-pellet boiler with internal flue gas recirculation (FGR), described and experimentally validated in an earlier publication by the authors. CFD data were collected on the symmetry plane of the combustion chamber for 80 operating points defined by the thermal load ratio (P/P0) and the excess air ratio λ. A GNO surrogate was trained on 64 cases to predict temperature, velocity magnitude, static pressure, and mole fractions of CO, O2, and CO2 at each node of an unstructured spatial graph. On a held-out validation set of 16 operating cases, the model achieved R2 values of 0.988 for temperature, 0.919 for velocity magnitude, 0.982 for pressure, 0.999 for CO, 0.992 for O2, and 0.985 for CO2. After training, each prediction is generated in a single forward pass, providing a computationally efficient approximation compared to the full CFD solver. A dedicated generalisation study on independent off-grid CFD cases confirmed that the surrogate interpolates within the parameter domain with essentially no loss of accuracy and degrades only moderately when extrapolated towards a higher thermal load and leaner mixtures. The results demonstrate that a baseline GNO surrogate can capture the spatial structure of coupled thermo-fluid and species fields in a realistic combustion geometry within the investigated parameter range and suggest applicability to digital-twin-oriented workflows where repeated parametric queries of boiler operation are required. Full article
(This article belongs to the Special Issue AI-Driven Modeling and Optimization for Industrial Energy Systems)
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