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31 pages, 6235 KB  
Article
A Spatiotemporal Cluster Analysis and Dynamic Evaluation Model for the Rock Mass Instability Risk During Deep Mining of Metal Mine
by Yuting Bian, Wei Zhu, Fang Yan and Xiaofeng Huang
Mathematics 2026, 14(8), 1261; https://doi.org/10.3390/math14081261 - 10 Apr 2026
Abstract
With the increasing depth of mining operations, accurate identification and assessment of rock mass instability risks are crucial for ensuring mine safety. This study proposes an integrated framework combining the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN), fuzzy comprehensive evaluation (FCE) [...] Read more.
With the increasing depth of mining operations, accurate identification and assessment of rock mass instability risks are crucial for ensuring mine safety. This study proposes an integrated framework combining the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN), fuzzy comprehensive evaluation (FCE) and kernel density estimation (KDE) for the identification and dynamic assessment of high-risk zones in deep mining. Using microseismic monitoring data from a lead–zinc mine in Northwest China (January–June 2023), the HDBSCAN algorithm adaptively identified 86 high-density clusters from 11,638 events. The weights of five evaluation indicators (moment magnitude, apparent stress, stress drop, peak ground acceleration, and ringing count) were determined objectively using the Euclidean distance method. FCE was then applied to classify cluster risk levels, revealing that 70.9% of the clusters were rated as high-risk (Level IV). KDE further illustrated the spatiotemporal migration of high-risk zones, showing a systematic shift from northeast to southwest along stopes and roadways, driven by mining unloading and geological structures. The integrated HDBSCAN-FCE-KDE framework demonstrates strong applicability and reliability in identifying and predicting rock mass instability risks, providing a scientific basis for proactive risk management in deep mining environments. Full article
(This article belongs to the Section D2: Operations Research and Fuzzy Decision Making)
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18 pages, 1861 KB  
Article
Ice Crystal Sedimentation Errors Arising from Weighted Fall Velocity in Three-Moment Bulk Cloud Microphysics Scheme
by Xiangjun Shi, Gongqi Jin and Jiarui Ma
Atmosphere 2026, 17(4), 357; https://doi.org/10.3390/atmos17040357 - 31 Mar 2026
Viewed by 238
Abstract
This study investigates ice crystal sedimentation calculation errors arising from three-moment bulk cloud scheme. Both offline tests and one-dimensional cloud model simulations indicate that sedimentation calculation errors are most pronounced at both the cloud bottom and cloud top. At the cloud bottom, the [...] Read more.
This study investigates ice crystal sedimentation calculation errors arising from three-moment bulk cloud scheme. Both offline tests and one-dimensional cloud model simulations indicate that sedimentation calculation errors are most pronounced at both the cloud bottom and cloud top. At the cloud bottom, the error stems from how the bulk method treats ice crystal sedimentation. Specifically, the method uses three weighted fall velocities (corresponding to the three moments) to represent instantaneous fluxes through a fixed altitude, which inherently assumes that falling ice crystals can only affect the adjacent model layer below. This assumption artificially constrains the falling distance of larger ice crystals. At the cloud top, the differences among these three weighted fall velocities can give rise to physical inconsistencies. This issue is handled by artificial adjustment, which leads to a spurious narrow size distribution shape of ice crystals, especially under model configurations with coarse temporal resolution (large dT) and fine vertical resolution (small dH). If only the sedimentation process is considered, the above calculation errors can be effectively minimized by lowering the dT/dH ratio. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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13 pages, 280 KB  
Article
Surface Diffusion at Finite Coverage: The Characteristic Function Method
by Elena E. Torres-Miyares and Salvador Miret-Artés
Surfaces 2026, 9(2), 32; https://doi.org/10.3390/surfaces9020032 - 28 Mar 2026
Viewed by 190
Abstract
In this work, the so-called characteristic function method is proposed as a new approach to describe and interpret the diffusion process with interacting adsorbates in terms of surface coverage. In this context, the intermediate scattering function is identified as a characteristic function that [...] Read more.
In this work, the so-called characteristic function method is proposed as a new approach to describe and interpret the diffusion process with interacting adsorbates in terms of surface coverage. In this context, the intermediate scattering function is identified as a characteristic function that is very well defined in probability theory. From this function, the generating functions of the moments and cumulants of the jump probability distribution are straightforwardly obtained at any order. This analysis is carried out in two stages. First, the dilute limit, corresponding to non-interacting adsorbates or very low surface coverage, is briefly reviewed. Second, the method is extended to low and intermediate coverages, where adsorbate-adsorbate interactions become relevant. A further consequence of the present analysis is that the static structure factor is also a characteristic function of the adsorbate separation distance distribution. This method thus provides a compact and physically transparent route for connecting scattering observables, diffusion coefficients, and coverage-dependent structural correlations. Full article
(This article belongs to the Collection Featured Articles for Surfaces)
12 pages, 2445 KB  
Article
Design and Implementation of an Underwater Cleaning System for Ship Maintenance via a Robotic Arm
by Chenghao Cao, Wenyong Guo, Jingzhou Fu, Jianggui Han and Xiaofeng Li
Appl. Sci. 2026, 16(7), 3222; https://doi.org/10.3390/app16073222 - 26 Mar 2026
Viewed by 205
Abstract
To better address the operational requirements for emergency underwater ship maintenance, this study proposes the use of an underwater robotic arm instead of divers for cleaning submerged hull sections. Experimental analyses are conducted to validate the stability and feasibility of the constructed underwater [...] Read more.
To better address the operational requirements for emergency underwater ship maintenance, this study proposes the use of an underwater robotic arm instead of divers for cleaning submerged hull sections. Experimental analyses are conducted to validate the stability and feasibility of the constructed underwater robotic arm cleaning system. Initially, hydrodynamic analysis of the robotic arm was performed using the Morison equation. Through fluent dynamic simulations, the hydrodynamic moments on each robotic arm during cleaning operations were obtained, confirming that stress under typical seawater flow velocities remained within the rated limits. Subsequently, dynamic simulations were carried out to determine the joint driving torques in a fluid environment, quantify the influence of the hydrodynamic resistance on the joint torque, and verify the accuracy of the fluid dynamics model. Finally, motion control and underwater cleaning experiments were implemented on the system. Experimental results further corroborated the correctness of the fluid model and operational environment analysis, demonstrating the expected cleaning performance and providing both data and experimental support for practical underwater maintenance during long-distance ship voyages. Full article
(This article belongs to the Section Robotics and Automation)
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13 pages, 2515 KB  
Article
Under Pressure: The Dividing Widom Zone and Possible Consequences on Dry scCO2–Rock Interaction Due to Varying Dipole Moment
by Massimo Calcara
Geosciences 2026, 16(4), 137; https://doi.org/10.3390/geosciences16040137 - 26 Mar 2026
Viewed by 279
Abstract
Recent years have witnessed growing interest in CO2 and in the possibility of injecting it into the Earth’s crust for multiple purposes. In addition to the fact that pure CO2 is already present in some geological formations, the most debated is [...] Read more.
Recent years have witnessed growing interest in CO2 and in the possibility of injecting it into the Earth’s crust for multiple purposes. In addition to the fact that pure CO2 is already present in some geological formations, the most debated is Carbon Capture and Storage (CCS), which aims to capture and trap CO2 through water-assisted reactions that promote its precipitation; moreover, proposed technological improvements to geothermal plants foresee the use of pure CO2 as a working fluid and energy carrier for electricity generation in terms of MWh. These applications require detailed knowledge and a deep understanding of CO2 behaviour under non-standard conditions. Upon entering the Earth’s crust, CO2 is subjected to progressively increasing temperature and pressure. The resulting effects are not limited to a reduction in intermolecular distance; they also include changes in molecular geometry, as well as in chemical and thermodynamic behaviour. For instance, a dipole moment may arise even in the gaseous phase as intermolecular distances decrease. Moreover, CO2 typically reaches supercritical conditions at depths of approximately 700 m. It is therefore necessary to account for both phase transitions and variations in molecular structure, as these can significantly influence the surrounding environment and the stoichiometric relationships with other substances. In this work, a steady-state column was simulated, representing CO2 injection down to a depth of 5 km, assuming an average geothermal gradient of 30 °C/km and nine different initial pressures, so nine different steady state columns. The results highlight the presence of a wedge-shaped region acting as a barrier for stepwise-equilibrated CO2: the computed CO2 column profiles avoid this region. This wedge includes part of the liquid–gas boundary under subcritical conditions, as well as the Widom lines above the critical point. It effectively separates two supercritical regimes, namely gas-like and liquid-like domains. In this context, the present work provides insights into the Widom region—possibly extending into subcritical conditions—and into these two distinct regimes. This may have implications for the solvent capacity of CO2 for ionic species. Ultimately, the initial pressure appears to determine the behaviour of CO2 at depth. Full article
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45 pages, 7117 KB  
Article
Topology-Based Machine Learning and Regime Identification in Stochastic, Heavy-Tailed Financial Time Series
by Prosper Lamothe-Fernández, Eduardo Rojas and Andriy Bayuk
Mathematics 2026, 14(7), 1098; https://doi.org/10.3390/math14071098 - 24 Mar 2026
Viewed by 216
Abstract
Classic machine learning and regime identification methods applied to financial time series lack theoretical guarantees and exhibit systematic failure modes: heavy-tails invalidate moment-based geometry, rendering distances and centroids dominated by extremes or unstable; jumps violate smoothness, destabilizing local regressions, kernel methods, and gradient-based [...] Read more.
Classic machine learning and regime identification methods applied to financial time series lack theoretical guarantees and exhibit systematic failure modes: heavy-tails invalidate moment-based geometry, rendering distances and centroids dominated by extremes or unstable; jumps violate smoothness, destabilizing local regressions, kernel methods, and gradient-based learning; and non-stationarity disrupts neighborhood relations, so distances in classical feature spaces no longer reflect meaningful proximity. To address these challenges, we propose a topology-based machine-learning framework grounded on probabilistic reconstruction of state-space geometry, which replaces moment- and smoothness-dependent representations with deformation-stable summaries of state-space geometry, preserving neighborhoods, adjacency, and topology. The finite-sample validity of homeomorphic state-space reconstruction, required for topology-based machine learning, is assessed through numerical studies on synthetic data with heavy tails, jumps, and known ground-truth regimes. Further diagnostics of local invertibility and bounded geometric distortion quantify when embedding windows are consistent with local diffeomorphic behavior, enabling metric-sensitive, geometry-aware learning. Clustering of Hilbert-space summaries accurately recovers underlying market tail-risk regimes with robust results across selected filtrations. Temporal, feature-space, and cluster-label null tests confirm that topology-based clustering captures genuine topological structure rather than noise or artifacts, and encodes temporal dependencies at local, mesoscopic, and network levels associated with market regimes. Full article
(This article belongs to the Section E: Applied Mathematics)
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19 pages, 3052 KB  
Article
Quantifying Spatial Effects in Row-Pile Support Systems for Loess Deep Excavations: Model Test, Numerical, and Theoretical Study
by Yuan Yuan, Hui-Mei Zhang and Long Sui
Buildings 2026, 16(7), 1275; https://doi.org/10.3390/buildings16071275 - 24 Mar 2026
Viewed by 179
Abstract
Three-dimensional spatial effects in deep excavations critically govern the mechanical response of retaining structures and adjacent soils, yet their quantitative characterization remains a challenge. This study systematically investigates the spatial behavior of row-pile-supported foundation pits through an integrated approach combining model tests, theoretical [...] Read more.
Three-dimensional spatial effects in deep excavations critically govern the mechanical response of retaining structures and adjacent soils, yet their quantitative characterization remains a challenge. This study systematically investigates the spatial behavior of row-pile-supported foundation pits through an integrated approach combining model tests, theoretical analysis, and numerical simulations. A novel formulation for the spatial effect influence coefficient K is derived from limit equilibrium principles and subsequently validated via ABAQUS-based finite element simulations. Model test results reveal pronounced spatial heterogeneity in earth pressure and bending moment distributions along the pit perimeter: lateral earth pressure at corner regions exceeds that at mid-side locations at equivalent depths, whereas bending moments in mid-side piles are substantially larger than those at corners. Displacement field measurements further demonstrate that corner zones, constrained bidirectionally, undergo minimal deformation, while maximum displacement occurs at the midpoints of the long sides. These observations collectively confirm the existence of a marked corner effect and a subdued side-midpoint effect under three-dimensional confinement. Complementary numerical analyses indicate that the coefficient K decreases monotonically with increasing half-angle corners and distance from the corner, thereby quantitatively capturing the decay of spatial constraint intensity. Together, these findings establish a theoretical framework for assessing excavation-induced spatial effects and provide actionable guidance for the rational design of deep foundation pit support systems. Full article
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20 pages, 1689 KB  
Article
Optimization-Driven Multimodal Brain Tumor Segmentation Using α-Expansion Graph Cuts
by Roaa Soloh, Bilal Nakhal and Abdallah El Chakik
Computation 2026, 14(3), 70; https://doi.org/10.3390/computation14030070 - 15 Mar 2026
Viewed by 331
Abstract
Precise segmentation of brain tumors from multimodal MRI scans is essential for accurate neuro-oncological diagnosis and treatment planning. To address this challenge, we propose a label-free optimization-driven segmentation framework based on the α-expansion graph cut algorithm, offering improved computational efficiency and interpretability [...] Read more.
Precise segmentation of brain tumors from multimodal MRI scans is essential for accurate neuro-oncological diagnosis and treatment planning. To address this challenge, we propose a label-free optimization-driven segmentation framework based on the α-expansion graph cut algorithm, offering improved computational efficiency and interpretability compared to deep learning alternatives. The method relies on structured optimization and handcrafted features, including local intensity patches, entropy-based texture descriptors, and statistical moments, to compute voxel-wise unary potentials via gradient-boosted decision trees (XGBoost). These are integrated with spatially adaptive pairwise terms within a graph model optimized through α-expansion. Evaluation on 146 BraTS validation volumes demonstrates reliable whole-tumor overlap, with a mean Dice score of 0.855 ± 0.184 and a 95% Hausdorff distance of 18.66 mm. Bootstrap analysis confirms the statistical stability of these results. The low computational overhead and modular design make the method particularly suitable for transparent and resource-constrained clinical deployment scenarios. Full article
(This article belongs to the Section Computational Biology)
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14 pages, 3656 KB  
Article
Quantitative Geometric Properties of Concrete Armour Unit Hexacone
by Yangwoo Lee, Hyoseob Kim and Hojun Yoo
J. Mar. Sci. Eng. 2026, 14(5), 506; https://doi.org/10.3390/jmse14050506 - 7 Mar 2026
Viewed by 312
Abstract
Physical properties are important for the selection of concrete armour units (CAUs) for a specific site. Geometric properties are closely linked to physical properties. Here, new concepts in geometric properties that may be related to structural stability are proposed. Void ratio, overall slenderness, [...] Read more.
Physical properties are important for the selection of concrete armour units (CAUs) for a specific site. Geometric properties are closely linked to physical properties. Here, new concepts in geometric properties that may be related to structural stability are proposed. Void ratio, overall slenderness, member slenderness, mass distribution with the distance from the gravity centre, and moment of inertia with respect to the gravity centre or pivot line are measurable, and we focus on geometric properties of several CAU structures. All CAUs have the same mass of 32 t. Hexacone has exceptionally high mass density near the leg tips, which helps to increase the moment of inertia. The moment of inertia of a Hexacone with respect to the horizontal pivot axis at the bottom line of the units is also the largest of the four tested. Hexacone is the most resistant to external torques when standing on its own. There is a possibility that a layer of Hexacones could be the most stable of the four types of units, especially when Hexacones are randomly placed or regularly placed with mixed vertical and horizontal columns. Future development of CAUs will aim to achieve a larger moment of inertia, raising the interlocking level and strengthening member endurance at the same time. Full article
(This article belongs to the Special Issue Analysis of Strength, Fatigue, and Vibration in Marine Structures)
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25 pages, 4798 KB  
Article
Mechanical Analysis and Verification Research on Asymmetric Four-Point Bending for the JCO Forming Process of LSAW Pipes
by Zhiyuan Zhang, Yi Liu, Zhiwen Lu, Junfang Shen, Yan Gao and Yize Chen
Materials 2026, 19(5), 914; https://doi.org/10.3390/ma19050914 - 27 Feb 2026
Viewed by 266
Abstract
Large-diameter longitudinal submerged arc welded (LSAW) pipes represent a critical component of long-distance oil and gas transmission pipelines. To enhance the forming efficiency of the JCO (J-shape to C-shape to O-shape) forming process for LSAW pipes, and to reduce residual straight segment in [...] Read more.
Large-diameter longitudinal submerged arc welded (LSAW) pipes represent a critical component of long-distance oil and gas transmission pipelines. To enhance the forming efficiency of the JCO (J-shape to C-shape to O-shape) forming process for LSAW pipes, and to reduce residual straight segment in order to minimize the ovality of the formed pipes, an asymmetric four-point air bending (AFB) process was proposed. In this process, one end of the sheet contacts the dies with a straight segment, while the other end contacts a circular arc segment. The distribution of bending moments and mechanical model under different bending stages were analyzed, and analytical formulas for the main forming indexes before and after springback were derived. Experimental and finite element simulation verification were conducted for the AFB process. The results indicated that the error between the experimental and simulation results and the theoretical results was small, and the variation trends were consistent. Furthermore, the ellipticity of the pipes formed by the AFB process was less than 0.66%, which is obviously lower than that of the pipe formed by the symmetric four-point air bending (SFB) process. The forming quality and production efficiency of the pipe is improved, thereby proving the feasibility and reliability of the AFB process and promoting the development of LSAW pipe JCO forming processes. Full article
(This article belongs to the Section Mechanics of Materials)
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24 pages, 4737 KB  
Article
Numerical Study of a Parabolically Deformed Beam for Solar Concentration Applications
by Rodolfo Y. Salas-Bernal, Pablo Sosa-Flores, Armando Piña-Ortiz, Carlos A. Pérez-Rábago, Agustín Brau-Ávila, Rafael E. Cabanillas-López and Ricardo A. Pérez-Enciso
Solar 2026, 6(1), 11; https://doi.org/10.3390/solar6010011 - 12 Feb 2026
Viewed by 437
Abstract
Recent advances in design, manufacturing and development techniques have been very relevant to making solar collectors feasible for production in a variety of applications. In the field of concentrated solar thermal technologies, several techniques have been developed to achieve high levels of radiation [...] Read more.
Recent advances in design, manufacturing and development techniques have been very relevant to making solar collectors feasible for production in a variety of applications. In the field of concentrated solar thermal technologies, several techniques have been developed to achieve high levels of radiation concentration. The generation of concave curvature geometry through the polishing of the reflective surface or through specialized machining is one of the most common methods. However, the way in which these bends are obtained can vary significantly, depending on the required quality of optical concentration for the application. This study presents a simple parametric technique to achieve a parabolic curvature for solar concentration applications. To do this, a controlled bending deformation was applied to a metal hollow profile beam supported by a pin and roller at each of the ends, and only two symmetric point loads were applied to generate a bending moment to induce a bending of a curved shape. It was found that, for a given load configuration, a parabolic geometry was generated along a partial center section of the beam. The analysis carried out showed that under the load configuration analyzed, up to 66% of the beam length adopted a fully parabolic geometry. The technique proposed in this work allows for the creation of parabolas with variable focal distances, offering versatility in the design of solar concentrating systems. It also allows corrective adjustments to be made during the assembly of the complete solar concentrator system. Full article
(This article belongs to the Topic Advances in Solar Technologies, 2nd Edition)
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32 pages, 2652 KB  
Article
Risk Factor Analysis of Single Motorcycle Accidents in Road Traffic
by Edward Kozłowski, Mateusz Traczyński, Przemysław Skoczyński, Piotr Jaskowski and Radovan Madlenak
Appl. Sci. 2026, 16(3), 1629; https://doi.org/10.3390/app16031629 - 5 Feb 2026
Viewed by 774
Abstract
This research examines the risk factors that influence injury severity in individual motorcycle accidents, utilising a dataset of 5253 incidents. Five machine learning algorithms—multinomial logistic regression, classification trees, random forests, XGBoost, and neural networks—were used to classify the results into three groups: Death [...] Read more.
This research examines the risk factors that influence injury severity in individual motorcycle accidents, utilising a dataset of 5253 incidents. Five machine learning algorithms—multinomial logistic regression, classification trees, random forests, XGBoost, and neural networks—were used to classify the results into three groups: Death (13.48%), Injury (80.14%), and No injury (6.38%). In all models, passenger presence was the most important predictor of injury. Motorcycle accidents involving passengers do not always have more serious consequences for several overlapping reasons. On the one hand, a motorcycle with a passenger has a significantly higher mass, which increases the braking distance and kinetic energy at the moment of collision, hindering quick defensive manoeuvres, cornering, and reactions to sudden hazards. Often, the rider also refrains from sudden movements to prevent the passenger from losing their balance. In the case of single-rider motorcycle accidents on roadways, approximately 5% of those involved with a passenger were fatalities, while approximately 48% were uninjured; in the case of those without a passenger, no one was uninjured. It follows from the above that the presence of a passenger increases the rider’s sense of responsibility. Other factors that significantly increased risk were single-lane carriageways, vehicle overturning, contaminated road surfaces, and collisions with complex objects, e.g., like trees. The multinomial logistic regression model had an overall accuracy of 69.2% on the test set. The Recurrent Neural Network achieved the best overall accuracy of 79.56%. Balanced accuracy, as the average between sensitivity and specificity of the RNN model for the “death” class was 68.15%, for the “injury” class—72.6%, and for the “no injury” class—96.61%. The Area Under the ROC Curve of the Recurrent Neural Networks model for “no injury” was 0.97, indicating it was very good at distinguishing between this class and the other classes. Even though it was easy to tell which cases did not involve injuries, it was still hard to tell the difference between fatal and non-fatal injuries in all models. The results support interventions tailored to specific situations, such as improved road lighting and speed control in rural areas, as well as helmet enforcement and safety measures at intersections in cities. Full article
(This article belongs to the Special Issue New Challenges in Vehicle Dynamics and Road Traffic Safety)
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33 pages, 21513 KB  
Article
A No-Reference Multivariate Gaussian-Based Spectral Distortion Index for Pansharpened Images
by Bishr Omer Abdelrahman Adam, Xu Li, Jingying Wu and Xiankun Hao
Sensors 2026, 26(3), 1002; https://doi.org/10.3390/s26031002 - 3 Feb 2026
Viewed by 462
Abstract
Pansharpening is a fundamental image fusion technique used to enhance the spatial resolution of remote sensing imagery; however, it inevitably introduces spectral distortions that compromise the reliability of downstream analyses. Existing no-reference (NR) quality assessment methods often fail to exclusively isolate these spectral [...] Read more.
Pansharpening is a fundamental image fusion technique used to enhance the spatial resolution of remote sensing imagery; however, it inevitably introduces spectral distortions that compromise the reliability of downstream analyses. Existing no-reference (NR) quality assessment methods often fail to exclusively isolate these spectral errors from spatial artifacts or lack sensitivity to specific radiometric inconsistencies. To address this gap, this paper proposes a novel No-Reference Multivariate Gaussian-based Spectral Distortion Index (MVG-SDI) specifically designed for pansharpened images. The methodology extracts a hybrid feature set, combining First Digit Distribution (FDD) features derived from Benford’s Law in the hyperspherical color space (HCS) and Color Moment (CM) features. These features are then used to fit Multivariate Gaussian (MVG) models to both the original multispectral and fused images, with spectral distortion quantified via the Mahalanobis distance between their statistical parameters. Experiments on the NBU dataset showed that the MVG-SDI correlates more strongly with standard full-reference benchmarks (such as SAM and CC) than existing NR methods like QNR. Tests with simulated distortions confirmed that the proposed index remains stable and accurate even when facing specific spectral degradations like hue shifts or saturation changes. Full article
(This article belongs to the Special Issue Remote Sensing Image Fusion and Object Tracking)
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22 pages, 2932 KB  
Article
Theoretical Calculation of Caq+ (q = 0, 1, 2) Interacting with a Krypton Atom: Electronic Structure and Vibrational Spectra Association
by Wissem Zrafi, Mohamed Bejaoui, Hela Ladjimi, Jamila Dhiflaoui and Hamid Berriche
Atoms 2026, 14(1), 5; https://doi.org/10.3390/atoms14010005 - 12 Jan 2026
Viewed by 662
Abstract
The potential energy curves and spectroscopic constants of the ground and several low-lying excited states of the Caq+-Kr (q = 0, 1, 2) van der Waals complexes were investigated using one- and two-electron pseudopotential approaches. This treatment effectively reduces the number [...] Read more.
The potential energy curves and spectroscopic constants of the ground and several low-lying excited states of the Caq+-Kr (q = 0, 1, 2) van der Waals complexes were investigated using one- and two-electron pseudopotential approaches. This treatment effectively reduces the number of active electrons in Caq+-Kr to a single valence electron for q = 1 and two valence electrons for q = 0, allowing the use of large and flexible basis sets for both Ca and Kr atoms. Within this work, potential energy curves (PECs) were calculated at the SCF level for the Ca+-Kr system, while both SCF and full configuration interaction (FCI) calculations were performed for the neutral Ca-Kr. Spin–orbit coupling effects were explicitly included in all calculations to accurately describe the fine-structure splitting of the asymptotic atomic states. The short-range core–core interaction for Ca2+-Kr was obtained using high-level CCSD(T) calculations. Spectroscopic constants were derived from the computed PECs and compared with available theoretical and experimental results, showing consistent trends. Furthermore, the transition dipole moments (TDM) were evaluated as a function of internuclear distances, including spin–orbit effects, to provide a comprehensive description of the electronic structure and radiative properties of these weakly bound systems. Full article
(This article belongs to the Section Atomic, Molecular and Nuclear Spectroscopy and Collisions)
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20 pages, 10445 KB  
Article
Ab Initio Computational Investigations of Low-Lying Electronic States of Yttrium Lithide and Scandium Lithide
by Jean Tabet, Nancy Zgheib, Sylvie Magnier and Fadia Taher
Computation 2026, 14(1), 14; https://doi.org/10.3390/computation14010014 - 8 Jan 2026
Viewed by 391
Abstract
Ab initio studies using CASSCF/MRCI calculations have been performed to investigate the spectroscopic properties of YLi and ScLi molecules. Our calculations have computed 25 singlet and triplet states for YLi and 37 electronic states for ScLi. The lowest lying states, including the ground [...] Read more.
Ab initio studies using CASSCF/MRCI calculations have been performed to investigate the spectroscopic properties of YLi and ScLi molecules. Our calculations have computed 25 singlet and triplet states for YLi and 37 electronic states for ScLi. The lowest lying states, including the ground state 1+ of YLi, have been investigated for the first time. The spin–orbit coupling in YLi has also been assessed from the splitting between Ω components generated from the lowest triplet lying Λ–S states. Regarding ScLi, the ground state is found to be the (1)3Δ state. Spectroscopic constants, energy levels at equilibrium, permanent dipole moments, and transition dipole moments have also been calculated. The potential energy curves for all calculated states have been displayed to large bond internuclear distances. In both ScLi and YLi, the potential energy curves have shown a small dissociation energy for the lowest states (1) 1,3Δ, (1) 1,3Π and (1) 1,3+. Full article
(This article belongs to the Special Issue Feature Papers in Computational Chemistry)
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