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12 pages, 396 KB  
Article
A Phenomenological Boundary Layer Approach to Interpret the Structure of the Heat Transfer Correlations for Laminar Forced Convection over Isothermal Flat Plates
by Massimo Corcione, Giovanni Di Bono and Alessandro Quintino
Appl. Sci. 2026, 16(1), 407; https://doi.org/10.3390/app16010407 (registering DOI) - 30 Dec 2025
Abstract
Forced convection heat transfer is commonly described by a correlation of the type Nu=AReγPrλ, where λ<γ for moderate-to-high-Pr fluids, whereas λ=γ for low-Pr fluids. Yet, the phenomenological basis of [...] Read more.
Forced convection heat transfer is commonly described by a correlation of the type Nu=AReγPrλ, where λ<γ for moderate-to-high-Pr fluids, whereas λ=γ for low-Pr fluids. Yet, the phenomenological basis of this structure is seldom examined. This work shows that such a correlation can be interpreted from purely physical intuition, without employing scaling arguments or solving the governing equations. Focusing on laminar flow over an isothermal flat plate, we introduce a new phenomenological boundary layer approach in which, by assessing how each independent variable qualitatively affects the thickness of the boundary layer, we construct the proportionality of Nu on Re and Pr. The approach provides a physical interpretation of why the exponents of established forced convection correlations fall within certain ranges. This perspective may help both educators seeking intuition-based explanations and researchers exploring alternative formulations of forced convection heat transfer. Full article
(This article belongs to the Section Applied Thermal Engineering)
11 pages, 949 KB  
Article
Using Step Trackers Among Older People Receiving Aged Care Services Is Feasible and Acceptable: A Mixed-Methods Study
by Rik Dawson, Judy Kay, Lauren Cameron, Bernard Bucalon, Catherine Sherrington and Abby Haynes
Healthcare 2026, 14(1), 86; https://doi.org/10.3390/healthcare14010086 (registering DOI) - 30 Dec 2025
Abstract
Background: Maintaining physical activity (PA) is vital for older people, particularly those with frailty and mobility limitations. Wearable activity trackers and digital feedback tools show promise for encouraging PA, but their feasibility and acceptability in aged care remain underexplored. This study evaluated the [...] Read more.
Background: Maintaining physical activity (PA) is vital for older people, particularly those with frailty and mobility limitations. Wearable activity trackers and digital feedback tools show promise for encouraging PA, but their feasibility and acceptability in aged care remain underexplored. This study evaluated the feasibility and acceptability of using wearable and mobile devices for step tracking and examined the usability of three interfaces (Fitbit, mobile app, and website) for reviewing PA progress in aged care. Methods: This is a user experience and feasibility study that does not involve objective physical activity quantification or device performance analysis. It is a mixed-methods feasibility study conducted with 14 participants aged ≥65 years from residential and community aged care services in metropolitan and regional New South Wales, Australia. Participants used a Fitbit Inspire 3 linked to a study website and a mobile phone step-counting app to monitor their steps across the three interfaces for four weeks. Feasibility was evaluated through enrolment and retention, and acceptability through a facilitator-led survey. Quantitative items on usability, comfort, motivation and device preference were summarised descriptively; open-ended responses were analysed thematically to identify user experiences, benefits, and barriers. Results: Step tracking was feasible, with 82% enrolment and 93% retention. Participants preferred the Fitbit over the mobile phone or website due to its ease of use, visibility and more enjoyable experience. Step tracking increased awareness of PA and supported confidence to move more. Participants valued reminders, rewards and opportunities for social sharing. Reported barriers included illness, usability challenges and occasional technical issues. Conclusions: Wearable step trackers show promise for supporting PA among older people receiving aged care. Despite the small sample and short follow-up, strong acceptability signals suggest that simple digital tools could enhance the reach and sustainability of mobility-promoting interventions into aged care systems. Future studies should examine long-term adherence, usability across diverse mobility and cognitive needs, and conditions for successful scale-up. Full article
(This article belongs to the Special Issue Health Promotion and Long-Term Care for Older Adults)
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19 pages, 3249 KB  
Article
Numerical Simulation of the Mineralization Process of the Axi Low-Sulfidation Epithermal Gold Deposit, Western Tianshan, China: Implications for Mineral Exploration
by Wenfa Shan, Xiancheng Mao, Zhankun Liu, Hao Deng, Qiao Yuan and Zhaohui Fu
Minerals 2026, 16(1), 41; https://doi.org/10.3390/min16010041 (registering DOI) - 29 Dec 2025
Abstract
The Axi gold deposit, a low-sulfidation epithermal deposit in the Western Tianshan, China, hosts over 50 t of gold resources and is widely regarded as the result of coupled processes of rock deformation, heat transfer, pore fluid flow, and chemical reactions. However, research [...] Read more.
The Axi gold deposit, a low-sulfidation epithermal deposit in the Western Tianshan, China, hosts over 50 t of gold resources and is widely regarded as the result of coupled processes of rock deformation, heat transfer, pore fluid flow, and chemical reactions. However, research on the ore-forming processes of this gold deposit from a coupled perspective remains limited, resulting in its ore-forming mechanisms being incompletely understood. In this paper, we use the concept of mineralization rate based on computational modeling to indicate the 3D spatial distribution of mineralization. The simulation results reveal the following: (1) temperature gradients play a key role in influencing mineral precipitation, whereas the effect of pore fluid pressure gradients is relatively negligible; (2) gold precipitation, characterized by a negative mineralization rate, predominantly took place along fault zones that exhibit vertical transitions from steep to gentle slopes or lateral bends, which are further distinguished by the accumulation of fluids and the presence of significant temperature gradients. Notably, this particular distribution pattern of gold precipitation closely mirrors the spatial arrangement of known gold orebodies. These findings suggest that the coupling of multiple physical and chemical processes at specific fault sites plays a critical role in ore formation, providing new insights into the mechanisms governing the development of the Axi gold deposit. Furthermore, based on these observations, it can be inferred that the deeper regions of the Axi gold deposit hold considerable mineralization potential. Full article
(This article belongs to the Special Issue 3D Mineral Prospectivity Modeling Applied to Mineral Deposits)
21 pages, 12653 KB  
Article
Decline Trends of Chlorophyll-a in the Yellow and Bohai Seas over 2005–2024 from Remote Sensing Reconstruction
by Yuhe Tian, Jun Song, Junru Guo, Yanzhao Fu and Yu Cai
J. Mar. Sci. Eng. 2026, 14(1), 61; https://doi.org/10.3390/jmse14010061 (registering DOI) - 29 Dec 2025
Abstract
Chlorophyll-a (Chl-a) concentration is a key indicator of coastal ecosystem health, reflecting both primary productivity and the ecosystem’s response to climate change and human activities. This study quantifies long-term Chl-a trends in the Yellow and Bohai Seas using a multi-source remote sensing reconstruction [...] Read more.
Chlorophyll-a (Chl-a) concentration is a key indicator of coastal ecosystem health, reflecting both primary productivity and the ecosystem’s response to climate change and human activities. This study quantifies long-term Chl-a trends in the Yellow and Bohai Seas using a multi-source remote sensing reconstruction dataset generated with deep learning algorithms. Quantile regression was applied to assess changes across the 75th, 50th, and 25th percentiles, and environmental drivers—including sea surface temperature, mixed layer depth, wind speed, and sea surface height anomalies—were evaluated in representative regions such as estuaries, aquaculture zones, and offshore waters. From 2005 to 2024, Chl-a concentrations declined across the 75th, 50th, and 25th percentiles, with rates of −4.82 × 10−3, −4.50 × 10−3, and −4.09 × 10−3 mg·m−3·a−1, respectively (where “a” denotes year). The decline also showed strong seasonal differences, with summer decreases (−0.0638 mg·m−3·a−1) substantially greater than winter (−0.04 mg·m−3·a−1). Spatially, the decline was more pronounced in high-concentration nearshore waters, with rates of −0.0283 mg·m−3·a−1 in the Qinhuangdao region, compared to −0.0137 mg·m−3·a−1 in deeper offshore waters. Mixed-layer depth and wind speed emerged as the primary physical controls, with nearshore declines driven by enhanced vertical mixing and offshore changes dominated by mesoscale oceanic processes. These findings provide new insights for modeling and managing coastal ecosystems under combined climate and anthropogenic pressures. Full article
(This article belongs to the Section Physical Oceanography)
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15 pages, 7616 KB  
Article
Topology Design of Reconfigurable Intelligent Metasurfaces Based on Equivalent Circuit Model
by Juntao Xu, Chenyu Zhu, Yan Pan, Han Zhang, Chao Wu and Hongqiang Li
Micromachines 2026, 17(1), 41; https://doi.org/10.3390/mi17010041 (registering DOI) - 29 Dec 2025
Abstract
Previous studies on reconfigurable intelligent metasurface (RIS) design have primarily relied on full-wave electromagnetic simulation software, which often incurs high computational costs and lacks clear design direction. The design of multi-bit RIS remains challenging and there is currently no suitable systematic method for [...] Read more.
Previous studies on reconfigurable intelligent metasurface (RIS) design have primarily relied on full-wave electromagnetic simulation software, which often incurs high computational costs and lacks clear design direction. The design of multi-bit RIS remains challenging and there is currently no suitable systematic method for selecting the corresponding tuning devices. To overcome these limitations, this article proposes a novel equivalent circuit-based approach to RIS design. In contrast to the conventional approach, where the equivalent circuit model is derived from post-design evaluation of the scattering properties of RIS, our work is entirely driven by the equivalent circuit model from the outset to accomplish the unit cell design. A complete workflow as well as details of each constituent step are presented for the topology design of RIS based on equivalent circuit topology. Building on this circuit topology, a 3-bit reflective phase reconfigurable unit cell is developed based on a tunable band-stop filter circuit. We conducted adjustable phase verification experiments and beam deflection experiments. The consistency between the experimental results and circuit theory demonstrates the feasibility and practicality of the equivalent circuit method of RIS design. This circuit-to-structure methodology provides a physically interpretable and systematic framework for designing RIS with arbitrary electromagnetic responses, offering new insights into RIS design. Full article
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31 pages, 39539 KB  
Article
Thermovibrationally Driven Ring-Shaped Particle Accumulations in Corner-Heated Cavities with the D2h Symmetry
by Balagopal Manayil Santhosh and Marcello Lappa
Micromachines 2026, 17(1), 39; https://doi.org/10.3390/mi17010039 (registering DOI) - 29 Dec 2025
Abstract
Over the last decade, numerical simulations and experiments have confirmed the existence of a novel class of vibrationally excited solid-particle attractors in cubic cavities containing a fluid in non-isothermal conditions. The diversity of emerging particle structures, in both morphology and multiplicity, depends strongly [...] Read more.
Over the last decade, numerical simulations and experiments have confirmed the existence of a novel class of vibrationally excited solid-particle attractors in cubic cavities containing a fluid in non-isothermal conditions. The diversity of emerging particle structures, in both morphology and multiplicity, depends strongly on the uni- or multi-directional nature of the imposed temperature gradients. The present study seeks to broaden this theoretical framework by further increasing the complexity of the thermal “information” coded along the external boundary of the fluid container. In particular, in place of the thermal inhomogeneities located in the center of otherwise uniformly cooled or heated walls, here, a cubic cavity with temperature boundary conditions satisfying the D2h (in Schoenflies notation) or “mmm” (in Hermann–Mauguin notation) symmetry is considered. This configuration, equivalent to a bipartite vertex coloring of a cube leading to a total of 24 thermally controlled planar surfaces, possesses three mutually perpendicular twofold rotation axes and inversion symmetry through the cube’s center. To reduce the problem complexity by suppressing potential asymmetries due to fluid-dynamic instabilities of inertial nature, the numerical analysis is carried out under the assumption of dilute particle suspension and one-way solid–liquid phase coupling. The results show that a kaleidoscope of new particle structures is enabled, whose main distinguishing mark is the essentially one-dimensional (filamentary) nature. These show up as physically disjoint or intertwined particle circuits in striking contrast to the single-curvature or double-curvature spatially extended accumulation surfaces reported in earlier investigations. Full article
(This article belongs to the Special Issue Microfluidic Systems for Sustainable Energy)
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43 pages, 820 KB  
Article
Research Frontiers in Machine Learning & Knowledge Extraction
by Andreas Holzinger, Luca Longo, Angelo Cangelosi and Javier Del Ser
Mach. Learn. Knowl. Extr. 2026, 8(1), 6; https://doi.org/10.3390/make8010006 (registering DOI) - 29 Dec 2025
Abstract
Machine Learning and Knowledge Extraction have evolved from algorithmic tools for pattern recognition into a unifying foundational scientific framework underpinning virtually all of today’s groundbreaking advances, enabling systematic discovery, interpretation and understanding across domains. This paper introduces a comprehensive research agenda that defines [...] Read more.
Machine Learning and Knowledge Extraction have evolved from algorithmic tools for pattern recognition into a unifying foundational scientific framework underpinning virtually all of today’s groundbreaking advances, enabling systematic discovery, interpretation and understanding across domains. This paper introduces a comprehensive research agenda that defines currently the future of innovation in Artificial Intelligence. We identify ten interrelated research frontiers that collectively map the transition from data-driven learning to knowledge-centric, trustworthy, and sustainable intelligence. These frontiers span the full spectrum of future AI research: from physics-informed and hybrid architectures that embed causality and domain knowledge, to multimodal and embedded intelligence that ground AI in real-world contexts; from interpretable and responsible design principles that ensure transparency and fairness, to safe and sustainable deployment in open-world environments. Together, these directions delineate a coherent roadmap toward AI systems that not only predict but also explain, reason, and collaborate. Future AI can be seen as a new member of your research lab, an active participant in knowledge creation, driven by interdisciplinary integration, global cooperation, ethical responsibility, and human oversight. By embedding principles of transparency, sustainability, and societal alignment from the outset, we envision AI as both a catalyst for scientific discovery and a cornerstone of responsible technological progress. Full article
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17 pages, 1203 KB  
Article
A Score-Fusion Method Based on the Sine Cosine Algorithm for Enhanced Multimodal Biometric Authentication
by Eslam Hamouda, Alaa S. Alaerjan, Ayman Mohamed Mostafa and Mayada Tarek
Sensors 2026, 26(1), 208; https://doi.org/10.3390/s26010208 - 28 Dec 2025
Viewed by 38
Abstract
Score fusion is a technique that combines the matching scores from multiple biometric modalities for an authentication system. Biometric modalities are unique physical or behavioral characteristics that can be used to identify individuals. Biometric authentication systems use these modalities to verify or identify [...] Read more.
Score fusion is a technique that combines the matching scores from multiple biometric modalities for an authentication system. Biometric modalities are unique physical or behavioral characteristics that can be used to identify individuals. Biometric authentication systems use these modalities to verify or identify individuals. Score fusion can improve the performance of biometric authentication systems by exploiting the complementary strengths of different modalities and reducing the impact of noise and outliers from individual modalities. This paper proposes a new score fusion method based on the Sine Cosine Algorithm (SCA). SCA is a meta-heuristic optimization algorithm used in various optimization problems. The proposed method extracts features from multiple biometric sources and then computes intra/inter scores for each modality. The proposed method then normalizes the scores for a given user using different biometric modalities. Then, the mean, maximum, minimum, median, summation, and Tanh are used to aggregate the scores from different biometric modalities. The role of the SCA is to find the optimal parameters to fuse the normalized scores. We evaluated our methods on the CASIA-V3-Internal iris dataset and the AT&T (ORL) face database. The proposed method outperforms existing optimization-based methods under identical experimental conditions and achieves an Equal Error Rate (EER) of 1.003% when fusing left iris, right iris, and face. This represents an improvement of up to 85.89% over unimodal baselines. These findings validate SCA’s effectiveness for adaptive score fusion in multimodal biometric systems. Full article
(This article belongs to the Section Biosensors)
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34 pages, 6240 KB  
Article
Mechanistic Prediction of Machining-Induced Deformation in Metallic Alloys Using Property-Based Regression and Principal Component Analysis
by Mohammad S. Alsoufi and Saleh A. Bawazeer
Machines 2026, 14(1), 37; https://doi.org/10.3390/machines14010037 - 28 Dec 2025
Viewed by 102
Abstract
Accurately predicting machining-induced deformation is crucial for high-precision CNC turning, particularly when working with dissimilar metallic alloys. This study presents a novel, data-driven framework that integrates empirical deformation analysis, multivariate regression, and principal component analysis (PCA) to predict axial deformation as a function [...] Read more.
Accurately predicting machining-induced deformation is crucial for high-precision CNC turning, particularly when working with dissimilar metallic alloys. This study presents a novel, data-driven framework that integrates empirical deformation analysis, multivariate regression, and principal component analysis (PCA) to predict axial deformation as a function of intrinsic material properties, including Brinell hardness, thermal conductivity, and Young’s modulus. The approach begins with second-order polynomial modeling of experimentally observed force–deformation behavior, from which three physically interpretable coefficients, nonlinear (a), load-sensitive (b), and intercept (c), are extracted. Each coefficient is then modeled using log-linear power-law regression, revealing strong statistical relationships with material properties. Specifically, the nonlinear coefficient correlates predominantly with thermal conductivity, while both the linear and offset terms are governed mainly by hardness, with average R2 values exceeding 0.999 across all materials. To improve physical insight and reduce dimensionality, three non-dimensional ratios (H/E, k/E, H/k) are also introduced, enhancing correlation and interpretability. PCA further confirms that over 93% of the total variance in deformation behavior can be captured using just two principal components, with clear separation of materials based on thermomechanical signature and deformation coefficients. This is the first comprehensive study to unify empirical modeling, property-driven regression, and PCA for deformation prediction in CNC-machined alloys. The resulting framework offers a scalable, interpretable, and physically grounded alternative to black-box models, providing rapid screening of new materials, reduced experimental demand, and support for smart manufacturing applications, such as digital twins and material-informed process optimization. Full article
(This article belongs to the Section Advanced Manufacturing)
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22 pages, 2990 KB  
Article
A New Semi-Empirical Model to Predict Vehicle Instability in Urban Flooding
by Omayma Amellah
Water 2026, 18(1), 80; https://doi.org/10.3390/w18010080 - 28 Dec 2025
Viewed by 126
Abstract
Urban floods frequently destabilize most objects they encounter, including vehicles, which potentially worsens flood impacts, leading to significant casualties and material losses. Improving the prediction of vehicle instability under flood conditions is therefore essential for effective risk assessment and emergency management. This work [...] Read more.
Urban floods frequently destabilize most objects they encounter, including vehicles, which potentially worsens flood impacts, leading to significant casualties and material losses. Improving the prediction of vehicle instability under flood conditions is therefore essential for effective risk assessment and emergency management. This work introduces a new physics-based, hazard assessment model for vehicle instability in urban floodwaters. The core of the model is the construction of a comprehensive parameter that integrates the main hydraulic mechanisms responsible for vehicle destabilization within a single and integrative formulation. An extensive set of experimental data covering multiple vehicle types was used and integrated into the modelling framework. Through calibration, model parameters were determined for three representative vehicle categories, allowing the derivation of distinct critical stability curves as functions of flow depth and velocity. Vehicle stability is evaluated using a physics-based force balance approach that explicitly accounts for the interaction between flood hydrodynamics and vehicle physical characteristics, enhancing model adaptability across different vehicle types and flood scenarios. The proposed model is validated through comparison with existing experimental data and stability criteria, including widely used guidelines. The results show good agreement while demonstrating improved accuracy in predicting critical stability thresholds for modern vehicles. Overall, the model provides a generalizable parameter for flood hazard assessment, with direct applications in urban flood risk mapping and decision support for emergency management. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
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21 pages, 6350 KB  
Article
An Experimental Investigation on the Barrier Performance of Complex-Modified Bentonite
by Jiangdong Xu, Hai Lin, Youshan Su and Shanke Tang
Appl. Sci. 2026, 16(1), 299; https://doi.org/10.3390/app16010299 - 27 Dec 2025
Viewed by 76
Abstract
The barrier performance of containment liners against heavy metals and other contaminants is a critical element in ensuring environmental safety. However, the high concentration of multivalent cations in landfill leachate raises concerns about the effectiveness of conventional barriers (e.g., sodium bentonite). To address [...] Read more.
The barrier performance of containment liners against heavy metals and other contaminants is a critical element in ensuring environmental safety. However, the high concentration of multivalent cations in landfill leachate raises concerns about the effectiveness of conventional barriers (e.g., sodium bentonite). To address concerns regarding the high permeability and elevated heavy metal concentrations in effluents from sodium bentonite (Na-B) barriers, this study proposes the use of new complex-modified sorbent bentonite—specifically treated with disodium ethylenediaminetetraacetate (EDTA-2Na) and sodium tripolyphosphate (STPP). Batch adsorption and flexible-wall permeability tests in extreme synthetic leachate demonstrate that the complex-modified sodium bentonite not only maintains low permeability but also enhances contaminant adsorption capacity of barriers. When modified with 2% EDTA-2Na and 4% STPP (by mass), the maximum Zn(II) adsorption capacity of bentonite was measured at 43.22 and 48.22 μg/g, respectively. These values correspond to enhancements by a factor of 1.99 and 2.32 compared to the unmodified Na-B. Simultaneously, the hydraulic conductivity met the permeability requirements for engineering barrier systems (k < 1 × 10−7 cm/s) throughout the tested range of confining pressures. Microscopic analyses confirmed the successful incorporation of functional groups into bentonite by both EDTA-2Na and STPP. STPP-induced electrostatic repulsion, promoting ordered particle stacking and dense structure formation. EDTA-2Na physically filled pores to block ion migration pathways while electrochemically counteracting double-layer compression under high ionic strength. This effective strategy resolves the long-standing trade-off between permeability and adsorption capacity in conventional bentonite, providing a theoretical basis for designing barrier materials in complex contaminated sites. Full article
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43 pages, 5707 KB  
Review
Graph Representation Learning for Battery Energy Systems in Few-Shot Scenarios: Methods, Challenges and Outlook
by Xinyue Zhang and Shunli Wang
Batteries 2026, 12(1), 11; https://doi.org/10.3390/batteries12010011 - 26 Dec 2025
Viewed by 100
Abstract
Graph representation learning (GRL) has emerged as a unifying paradigm for modeling the relational and heterogeneous nature of battery energy storage systems (BESS), yet a systematic synthesis focused on data-scarce (few-shot) battery scenarios is still lacking. Graph representation learning offers a natural way [...] Read more.
Graph representation learning (GRL) has emerged as a unifying paradigm for modeling the relational and heterogeneous nature of battery energy storage systems (BESS), yet a systematic synthesis focused on data-scarce (few-shot) battery scenarios is still lacking. Graph representation learning offers a natural way to describe the structure and interaction of battery cells, modules and packs. At the same time, battery applications often suffer from very limited labeled data, especially for new chemistries, extreme operating conditions and second-life use. This review analyzes how graph representation learning can be combined with few-shot learning to support key battery management tasks under such data-scarce conditions. We first introduce the basic ideas of graph representation learning, including models based on neighborhood aggregation, contrastive learning, autoencoders and transfer learning, and discuss typical data, model and algorithm challenges in few-shot scenarios. We then connect these methods to battery state estimation problems, covering state of charge, state of health, remaining useful life and capacity. Particular attention is given to approaches that use graph neural models, meta-learning, semi-supervised and self-supervised learning, Bayesian deep networks, and federated learning to extract transferable features from early-cycle data, partial charge–discharge curves and large unlabeled field datasets. Reported studies show that, with only a small fraction of labeled samples or a few initial cycles, these methods can achieve state and life prediction errors that are comparable to or better than conventional models trained on full datasets, while also improving robustness and, in some cases, providing uncertainty estimates. Based on this evidence, we summarize the main technical routes for few-shot battery scenarios and identify open problems in data preparation, cross-domain generalization, uncertainty quantification and deployment on real battery management systems. The review concludes with a research outlook, highlighting the need for pack-level graph models, physics-guided and probabilistic learning, and unified benchmarks to advance reliable graph-based few-shot methods for next-generation intelligent battery management. Full article
(This article belongs to the Section Battery Modelling, Simulation, Management and Application)
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27 pages, 1371 KB  
Article
The Thermodynamic Cliff: Pricing the Climate Adaptation Gap in Digital Infrastructure
by Seyedarash Aghili and Mehmet Nurettin Uğural
Systems 2026, 14(1), 34; https://doi.org/10.3390/systems14010034 - 26 Dec 2025
Viewed by 129
Abstract
Conventional climate-risk frameworks, ranging from ESG ratings to Integrated Assessment Models (IAMs), systematically underestimate physical risks by overlooking the non-linear physics that govern infrastructure failure. These top-down models perceive climate change as a manageable operational expense, thereby obscuring the substantial capital requirements necessary [...] Read more.
Conventional climate-risk frameworks, ranging from ESG ratings to Integrated Assessment Models (IAMs), systematically underestimate physical risks by overlooking the non-linear physics that govern infrastructure failure. These top-down models perceive climate change as a manageable operational expense, thereby obscuring the substantial capital requirements necessary to sustain system reliability as global temperatures escalate. This study proposes a physics-first framework to quantify the “Adaptation Gap”—a measurable, unaccounted-for capital liability representing the additional cost needed to upgrade assets to maintain fault tolerance. Within this specific geographic and asset context, it has been determined that restoring fault tolerance for new equipment necessitates a 19.7% (95% CI: 16.5–22.9%) increase in capital expenditure, which increases the Adaptation Gap to 28.7% for typical in-service assets, potentially increasing the true cost for aging assets to between 25% and 30%. Although the quantitative findings are specific to the case study, the methodological framework—assessed as superior to traditional risk metrics—is designed for global application in pricing the Adaptation Gap across all infrastructure sectors with thermal constraints. Our methodology provides a blueprint for establishing a new standard of climate-adjusted valuation, transforming abstract physical risks into a tangible, auditable capital liability. Full article
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25 pages, 1421 KB  
Article
The Geometry of Modal Closure—Symmetry, Invariants, and Transform Boundaries
by Robert Castro
Symmetry 2026, 18(1), 48; https://doi.org/10.3390/sym18010048 - 26 Dec 2025
Viewed by 68
Abstract
Modal decomposition, introduced by Fourier, expresses complex functions, such as sums of symmetric basis modes. However, convergence alone does not ensure structural fidelity. Discontinuities, sharp gradients, and localized features often lie outside the chosen basis’s symmetry class, producing artifacts such as the Gibbs [...] Read more.
Modal decomposition, introduced by Fourier, expresses complex functions, such as sums of symmetric basis modes. However, convergence alone does not ensure structural fidelity. Discontinuities, sharp gradients, and localized features often lie outside the chosen basis’s symmetry class, producing artifacts such as the Gibbs overshoot. This study introduces a unified geometric framework for assessing when modal representations remain faithful by defining three symbolic invariants—curvature (κ), strain (τ), and compressibility (σ)—and their diagnostic ratio Γ = κ/τ. Together, these quantities measure how closely the geometry of a function aligns with the symmetry of its modal basis. The condition Γ < σ identifies the domain of structural closure: this is the region in which expansion preserves both accuracy and symmetry. Analytical demonstrations for Fourier, polynomial, and wavelet systems show that overshoot and ringing arise precisely where this inequality fails. Numerical illustrations confirm the predictive value of the invariants across discontinuous and continuous test functions. The framework reframes modal analysis as a problem of geometric compatibility rather than convergence alone, establishing quantitative criteria for closure-preserving transforms in mathematics, physics, and applied computation. It provides a general diagnostic for detecting when symmetry, curvature, and representation fall out of alignment, offering a new foundation for adaptive and structure-aware transform design. In practical terms, the invariants (κ, τ, σ) offer a diagnostic for identifying where modal systems preserve geometric structure and where they fail. Their link to symmetry arises because curvature measures structural deviation, strain measures representational effort within a given symmetry class, and compressibility quantifies efficiency. This geometric viewpoint complements classical convergence theory and clarifies why adaptive spectral methods, edge-aware transforms, multiscale PDE solvers, and learned operators benefit from locally increasing strain to restore the closure condition Γ < σ. These applications highlight the broader analytical and computational relevance of the closure framework. Full article
(This article belongs to the Section Mathematics)
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23 pages, 4759 KB  
Article
Physics-Constrained Meta-Embedded Neural Network for Bottom-Hole Pressure Prediction in Radial Oil Flow Reservoirs
by Linhao Qiu, Yuxi Yang, Yunxiu Sai and Youyou Cheng
Processes 2026, 14(1), 89; https://doi.org/10.3390/pr14010089 - 26 Dec 2025
Viewed by 153
Abstract
With the advancement of petroleum engineering, the increasing complexity of formations and unpredictable conditions make wellbore pressure prediction more challenging. Accurate bottom-hole pressure (BHP) prediction is crucial for the safe and stable development of oil and gas reservoirs. Solving the partial differential equations [...] Read more.
With the advancement of petroleum engineering, the increasing complexity of formations and unpredictable conditions make wellbore pressure prediction more challenging. Accurate bottom-hole pressure (BHP) prediction is crucial for the safe and stable development of oil and gas reservoirs. Solving the partial differential equations (PDEs) governing fluid flow is key to this prediction. As deep learning becomes widespread in scientific and engineering applications, physics-informed neural networks (PINNs) have emerged as powerful tools for solving PDEs. However, traditional PINNs face challenges such as insufficient fitting accuracy, large errors, and gradient explosion. This study introduces MetaPress, a novel physics-informed neural network structure, to address inaccurate formation pressure prediction. MetaPress incorporates a meta-learning-based embedding function that integrates spatial information into the input and forget gates of Long Short-Term Memory networks. This enables the model to capture complex spatiotemporal features of flow problems, improving its generalization and nonlinear modeling capabilities. Using the MetaPress architecture, we predicted BHP under single-phase flow conditions, achieving an error of less than 2% for L2. This approach offers a novel method for solving seepage equations and predicting BHP, providing new insights for subsequent studies on reservoir fluid flow processes. Full article
(This article belongs to the Topic Exploitation and Underground Storage of Oil and Gas)
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