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23 pages, 5265 KB  
Review
Research Progress on the Microstructure, Mechanical Properties, and Corrosion Behavior of TC4 Alloy Fabricated by Selective Laser Melting
by Huiling Zhou, Ji Li, Shugang Zhang, Bin Yang, Yuanbin Gui, Xiangbo Li, Huixia Zhang, Xiaoru Zhuo, Sheng Lu and Yanxin Qiao
Metals 2026, 16(3), 284; https://doi.org/10.3390/met16030284 - 3 Mar 2026
Abstract
Selective laser melting (SLM), a pivotal additive manufacturing (AM) technology for titanium alloys, enables near-net-shape forming of complex structures with relative densities of up to 99.9%, making it indispensable in aerospace, biomedical, and marine engineering. This review comprehensively updates the state of the [...] Read more.
Selective laser melting (SLM), a pivotal additive manufacturing (AM) technology for titanium alloys, enables near-net-shape forming of complex structures with relative densities of up to 99.9%, making it indispensable in aerospace, biomedical, and marine engineering. This review comprehensively updates the state of the art on SLM-fabricated TC4 (Ti-6Al-4V) alloy, addressing critical gaps in previous studies by integrating novel research progress, in-depth mechanistic analyses, and multi-dimensional comparisons. The core focus is on the unique thermal cycle (106–108 °C/s heating/cooling rates) of SLM, which induces a predominant needle-like martensitic α′ phase (99.7%) and minimal β phase (0.3%), leading to intrinsic anisotropy and low ductility. Room-temperature tensile strength reaches 1315.32 MPa with 9.6% elongation, and high-cycle fatigue limits the range from 417 to 829 MPa, strongly dependent on process parameters and post-treatment. Corrosion anisotropy is systematically analyzed: the XY plane (parallel to scanning direction) exhibits superior corrosion resistance in 1 M HCl (fewer pits and lower corrosion current density) and 3.5% NaCl (more stable passive film) compared to the XZ plane (deposition direction). Novel insights include: (1) synergistic effects of SLM process parameters (laser power–scanning speed–hatch spacing) on defect evolution and microstructure uniformity; (2) atomistic mechanisms of α′→α + β phase transformation during post-heat treatment; and (3) corrosion–mechanical coupling behavior in harsh environments (e.g., marine and biomedical). Post-treatment strategies are refined: annealing at 800 °C for 2 h achieves 1099 MPa tensile strength and 17.4% elongation, while hot isostatic pressing (HIP) reduces porosity from 0.08% to 0.01% and weakens fatigue anisotropy. This review also identifies unresolved challenges (e.g., in situ defect monitoring and multi-field regulated performance) and proposes future directions (e.g., AI-driven process optimization and functional gradient structures). Full article
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25 pages, 9144 KB  
Article
Sustainable Metal Recovery from Untreated Mining Tailings by Direct Electrodeposition Under Different Current Densities
by Joaquin Aburto-Hole, Pablo I. R. Pincheira, Pablo Acuna, Lina Uribe, Diego Contreras Bilbao and Diógenes Hernández
Environments 2026, 13(3), 135; https://doi.org/10.3390/environments13030135 - 1 Mar 2026
Viewed by 133
Abstract
Mining tailings are waste generated continuously in large quantities and have accumulated over time, posing significant environmental challenges. This study evaluates the influence of low (MinPC) and high (MaxPC) current densities on the recovery of elements from untreated mining tailings obtained from SCM [...] Read more.
Mining tailings are waste generated continuously in large quantities and have accumulated over time, posing significant environmental challenges. This study evaluates the influence of low (MinPC) and high (MaxPC) current densities on the recovery of elements from untreated mining tailings obtained from SCM Paicaví by electrodeposition. To define both conditions, tailings were placed in containers with electrodes spaced 3–18 cm apart, and controlled currents of 1–100 mA were applied. Although MaxPC electrodes recovered a greater mass of material (1.51 g) than MinPC (0.22 g), the latter achieved higher enrichment of elements such as Ni and Mn. Under MinPC conditions, Ni exhibited the highest recovery, enrichment (19.3), and selectivity (4.8), whereas under MaxPC, the enrichment and selectivity decreased to 9.6 and 2.0, respectively. Elemental analyses (XRF, AAS, ICP-MS), together with mineralogical characterization (XRD, FT-IR, and SEM-EDS), identified quartz, pyrite, and chlorite as the main phases associated with the recovered elements. Overall, the results demonstrate that direct electrodeposition enables selective metal recovery from untreated tailings without pretreatment, chemical reagents, or additional water consumption, providing a novel and environmentally sustainable route for tailings valorization. Full article
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21 pages, 4561 KB  
Article
Study of the Microstructure and Properties of CoCrFeNiMnx High-Entropy Alloys
by Zhengpeng Zhang, Shichen Yan, Jiankang Huang, Tianxiang Zhao, Chen Dong, Abdul Bari, Jiaojiao Xie, Xiaoquan Yu and Yingwei Chen
Metals 2026, 16(3), 250; https://doi.org/10.3390/met16030250 - 25 Feb 2026
Viewed by 155
Abstract
High-entropy alloys (HEAs) provide a broad compositional space for tuning phase stability and surface durability. CoCrFeNiMnx (x = 0.5, 1.0, 1.5, and 2.0) alloys were fabricated by vacuum arc melting and characterized by X-ray diffraction (XRD), optical microscopy (OM), scanning electron microscopy [...] Read more.
High-entropy alloys (HEAs) provide a broad compositional space for tuning phase stability and surface durability. CoCrFeNiMnx (x = 0.5, 1.0, 1.5, and 2.0) alloys were fabricated by vacuum arc melting and characterized by X-ray diffraction (XRD), optical microscopy (OM), scanning electron microscopy with energy-dispersive spectroscopy (SEM/EDS), microhardness testing, electrochemical testing in 3.5 wt.% NaCl, and X-ray photoelectron spectroscopy (XPS). Density functional theory (DFT) calculations and first-principles molecular dynamics were further employed to analyze the Mn-dependent electronic structure and oxygen–metal bonding. The XRD results indicate a transition from a single FCC solid solution at x ≤ 1.0 to an FCC + BCC constitution at x ≥ 1.5. With increasing Mn, microstructures evolve from coarse dendrites toward higher fractions of equiaxed grains. Hardness decreases from 163.6 HV (x = 0.5) to 125.1 HV (x = 1.0) and then increases to 162.6 HV (x = 2.0), indicating competing solid-solution and phase/segregation effects. Electrochemical measurements show enhanced corrosion resistance with Mn addition; the x = 2.0 alloy exhibits the lowest fitted corrosion current density (icorr = 0.3482 × 10−6 μA·cm−2) and the most stable passivation response. XPS reveals passive films dominated by Fe2O3 together with Mn3+ oxides, whose synergistic formation promotes a denser barrier layer. DFT predicts a monotonic decrease in Fermi level and a narrowed conduction band range as Mn increases, consistent with reduced electron transfer activity during anodic dissolution. Interfacial simulations show that O preferentially bonds with Cr and Mn, while Ni–O bonds have the lowest estimated rupture barrier, rationalizing a tendency toward localized corrosion at Ni-associated sites. Full article
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18 pages, 4871 KB  
Article
From Quantum to Classical Within the Framework of Integral Quantization
by Ligia M. C. S. Rodrigues, Evaldo M. F. Curado, Diego Noguera and Alan C. Maioli
Symmetry 2026, 18(3), 403; https://doi.org/10.3390/sym18030403 - 25 Feb 2026
Viewed by 243
Abstract
Integral quantization is a powerful framework for mapping classical phase-space functions—defined on a symplectic manifold—onto quantum operators in a Hilbert space. It encompasses several quantization methods, such as coherent-state quantization, and inherently incorporates operator symmetrization. The formalism relies on a choice of weight [...] Read more.
Integral quantization is a powerful framework for mapping classical phase-space functions—defined on a symplectic manifold—onto quantum operators in a Hilbert space. It encompasses several quantization methods, such as coherent-state quantization, and inherently incorporates operator symmetrization. The formalism relies on a choice of weight function, whose flexibility allows for a family of possible quantizations. In this work, we address the inverse problem: given a quantum operator, how can one determine a classical phase-space function whose integral quantization reproduces exactly that operator? We propose a systematic method, within the integral quantization framework, to construct such a classical function, which depends on the chosen weight. We demonstrate that quantizing the resulting function recovers the original operator, thereby establishing a consistent two-way mapping between classical and quantum descriptions. The method is applied to several physically relevant operators: the projector, a mixed-state density operator, the annihilation operator, and an entangled state. We also analyze how quantum entanglement manifests in the structure of the corresponding classical phase-space function. Full article
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24 pages, 3016 KB  
Article
Data-Driven Computation Scheme for Duncan–Chang EB Model
by Chaojun Han, Qianhui Liu, Xiaohang Li and Hezuo Zhang
Mathematics 2026, 14(5), 751; https://doi.org/10.3390/math14050751 - 24 Feb 2026
Viewed by 147
Abstract
This paper extends the data-driven computational mechanics paradigm to nonlinear materials characterized by the Duncan–Chang Elastic-Bulk (E-B) constitutive model. Unlike in linear elastic systems, geotechnical media exhibit stress-dependent tangent moduli and non-convex constitutive manifolds. We propose a recursive nested data-driven solver that dynamically [...] Read more.
This paper extends the data-driven computational mechanics paradigm to nonlinear materials characterized by the Duncan–Chang Elastic-Bulk (E-B) constitutive model. Unlike in linear elastic systems, geotechnical media exhibit stress-dependent tangent moduli and non-convex constitutive manifolds. We propose a recursive nested data-driven solver that dynamically adapts the phase-space distance metric to account for pressure-dependent hardening. A rigorous mathematical analysis of convergence is provided, demonstrating that the solver’s performance is governed by the local transversality between the conservation law constraint set and the nonlinear material manifold. We derive explicit error bounds that couple spatial discretization resolution with material data density. Numerical experiments using triaxial test data from a high-altitude region validate the theoretical predictions, showing that the proposed scheme demonstrates convergence in single-element tests. Full article
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14 pages, 3034 KB  
Article
Transport Dynamics and Multiscale Turbulence Analysis of Vegetation Canopies Based on Wind Tunnel Experiments
by Guoliang Chen, Fei Li, Ruiqi Wang, Chun-Ho Liu and Ziwei Mo
Atmosphere 2026, 17(2), 226; https://doi.org/10.3390/atmos17020226 - 23 Feb 2026
Viewed by 273
Abstract
The momentum transport and scale-dependent motion characteristics within vegetation canopies play a crucial role in shaping near-surface turbulent structures and exchange processes, yet the interactions among different turbulent scales and their statistical representations remain insufficiently understood. Based on a series of controlled wind [...] Read more.
The momentum transport and scale-dependent motion characteristics within vegetation canopies play a crucial role in shaping near-surface turbulent structures and exchange processes, yet the interactions among different turbulent scales and their statistical representations remain insufficiently understood. Based on a series of controlled wind tunnel experiments, this study identifies coherent turbulent structures using a phase-space algorithm constructed from streamwise velocity fluctuation u′, acceleration a, and jerk j, and compares transport efficiency (exuberance η). This study uses scale-wise (cut-off frequency) momentum flux contribution analysis, natural visibility graph (NVG), and large–small-scale amplitude modulation to examine transport and multiscale behaviors across different canopy densities, array layouts, and inflow conditions. Results show that canopy density (different Cd drag coefficient) is a primary factor governing transport efficiency. Under low-wind staggered configurations, increasing canopy density strengthens the contribution of low-frequency large-scale motions to total momentum flux. In contrast, high-wind aligned configurations intensify canopy-top shear, enhancing small-scale motions and thereby reducing the relative contribution of large-scale motions. NVG analysis further reveals that in high-density canopies, large-scale acceleration and deceleration events tend toward equilibrium, whereas deceleration events dominate consistently in low- and medium-density cases. Amplitude modulation results indicate that high-density cases exhibit highly consistent modulation behavior, followed by low-density cases, while medium-density cases display a pronounced height-dependent variation, characterized by a distinct modulation critical point. This study proposes a unified analytical framework integrating coherent structure detection, graph-theoretic analysis, multiscale transport characterization, and large–small-scale modulation, providing a comprehensive description of momentum transport and scale motions within canopy flows, and it offers new insight into the mechanisms governing complex vegetation canopy turbulence. Full article
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17 pages, 4964 KB  
Article
A Study on the Mitigation of Back-EMF Imbalance in Axial Flux Motors with PCB Stators
by Min-Su Youn, Min-Ki Hong, Seung-Hoon Ko, Dong-Woo Nam and Won-Ho Kim
Energies 2026, 19(4), 1060; https://doi.org/10.3390/en19041060 - 18 Feb 2026
Viewed by 181
Abstract
As the electrification of the automotive industry accelerates, the importance of small-scale motors used in applications such as HVAC systems and water pumps is growing. To design small motors that exhibit high efficiency and high output within limited spaces, applying axial flux motors [...] Read more.
As the electrification of the automotive industry accelerates, the importance of small-scale motors used in applications such as HVAC systems and water pumps is growing. To design small motors that exhibit high efficiency and high output within limited spaces, applying axial flux motors (AFMs) instead of conventional radial flux motors (RFMs) can maximize the power density within the same volume, offering advantages in both weight reduction and miniaturization. This study proposes an optimized end-turn layout design to mitigate back-EMF imbalance in AFMs utilizing PCB stators. Optimization results demonstrated that the structure employing a non-adjacent end-turn layout with equalized average end-turn heights (BCAACB type) exhibited the best performance in terms of average resistance and phase resistance variance, effectively mitigating back-EMF imbalance. The validity of the optimized end-turn structure was verified through finite element analysis (FEA). The analysis confirmed that the motor’s back-EMF balance was improved, and the magnitude of phase resistance was reduced. This reduction led to lower copper loss, thereby increasing overall efficiency. Furthermore, the variance in resistance for each phase was minimized, resulting in enhanced electrical balance. The results of this study are expected to contribute to enhancing the applicability of PCB stators in small motor design. Full article
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21 pages, 2975 KB  
Article
Functional and Morphological Outcomes of Duration-Dependent Electrical Stimulation in Silicone Conduit-Mediated Peripheral Nerve Repair in Rats
by Ching-Feng Su, Ming-Hsuan Lu, Joanna Pi-Jung Lee, Chung-Chia Chen, Yung-Hsiang Chen and Yueh-Sheng Chen
Bioengineering 2026, 13(2), 218; https://doi.org/10.3390/bioengineering13020218 - 13 Feb 2026
Viewed by 375
Abstract
Peripheral nerve regeneration is most rapid during the early post-injury period but gradually slows over time, often limiting functional recovery. Electrical stimulation (ES) delivered via percutaneous needle electrodes has been shown to modulate the local neural microenvironment and promote axonal regeneration; however, the [...] Read more.
Peripheral nerve regeneration is most rapid during the early post-injury period but gradually slows over time, often limiting functional recovery. Electrical stimulation (ES) delivered via percutaneous needle electrodes has been shown to modulate the local neural microenvironment and promote axonal regeneration; however, the optimal temporal window and duration of stimulation remain unclear. This study aimed to evaluate the time-dependent effects of needle-based ES on peripheral nerve regeneration in a rat model of sciatic nerve transection, using a well-established silicone nerve conduit as a stable and reproducible non-biodegradable repair model. Female Sprague–Dawley rats underwent sciatic nerve transection and repair. Postoperatively (PO), animals were randomly assigned to control (C) needle insertion or needle-based ES groups, receiving stimulation for either 3 weeks (C-3W-PO and ES-3W-PO, respectively) or 7 weeks (C-7W-PO and ES-7W-PO, respectively). Functional recovery was evaluated using cold plate latency and rotarod performance tests. Electrophysiological assessments included measurements of nerve conduction velocity (NCV), compound muscle action potential amplitude, and muscle action potential (MAP) area. Histomorphometric analysis of regenerated nerve tissue quantified total nerve cross-sectional area, endoneurial space, axon number, and axon density. Retrograde labeling with fluoro-gold (FG) was used to quantify reinnervated motor neurons. Immunohistochemical analyses of calcitonin gene-related peptide (CGRP) and macrophage-associated markers were conducted to assess sensory neuropeptide expression and immune cell infiltration within the regenerated nerve. ES significantly improved both sensory and motor recovery in a duration-dependent manner. Behavioral data showed increased cold pain thresholds and improved motor coordination in ES groups, with the most pronounced functional gains observed in the ES-7W-PO group. Electrophysiological measures revealed higher NCV, amplitude, and MAP area in ES-treated animals, with the most pronounced improvements at 7 weeks. Morphologically, ES enhanced nerve regeneration, as evidenced by increased total and endoneurial areas, axonal counts, and axon density. FG-labeled neuron counts were significantly elevated in ES groups, indicating enhanced motor reinnervation. At 3 weeks, ES induced higher CGRP expression and macrophage density, suggesting transient activation of sensory-associated and pro-regenerative immune responses during the early post-injury phase. These findings demonstrate that ES accelerates peripheral nerve repair in rats and that sustained stimulation across the early regenerative window yields superior structural and functional outcomes. Full article
(This article belongs to the Special Issue Nerve Regeneration)
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21 pages, 9298 KB  
Article
Peculiar Storm-Time Dynamics of the Summer Solstice Ionosphere over the Indian Region During the June 2025 Geomagnetic Storm
by Prajakta Chougule, Sugumar Iswariya, Siva Sai Kumar Rajana, Dadaso Shetti, Susmita Chougule, Chiranjeevi G. Vivek, J. R. K. Kumar Dabbakuti, Ajeet K. Maurya, Sudipta Sasmal and Sampad Kumar Panda
Atmosphere 2026, 17(2), 189; https://doi.org/10.3390/atmos17020189 - 11 Feb 2026
Viewed by 421
Abstract
This study investigates the temporal and latitudinal variability of the ionosphere over the Indian longitude region during the intense geomagnetic storm from 1 to 3 June 2025, using GNSS receiver observations and magnetometer recordings, along with space-based measurements from in situ Swarm satellite, [...] Read more.
This study investigates the temporal and latitudinal variability of the ionosphere over the Indian longitude region during the intense geomagnetic storm from 1 to 3 June 2025, using GNSS receiver observations and magnetometer recordings, along with space-based measurements from in situ Swarm satellite, COSMIC-2 radio occultation, GUVI/TIMED-derived O/N2 ratios, and model-derived electric fields. This particular event is relatively new and is characterized by the bifurcated variation with two distinct main phases separated by a short-lived recovery phase. The results revealed distinct features associated with the geomagnetic storm, including positive and negative ionospheric phases, thermospheric compositional changes, and the latitudinal propagation of disturbances. On 1 June, the observed strong positive ionospheric storm was driven by Prompt Penetration Electric Fields (PPEFs) and equatorward neutral winds, which triggered the upliftment of F-region plasma to higher altitudes through the enhanced equatorial fountain effect, leading to an unusually long-lasting Total Electron Content (TEC) enhancement from day to night. The analysis also revealed the distinct latitudinal behaviour, exhibiting the clear poleward extension of the Equatorial Ionization Anomaly (EIA) crest and significant TEC enhancements (~150–200% of the quiet day values) from low to mid latitudes as compared to the equatorial location through an efficient plasma redistribution. Conversely, pronounced negative ionospheric storm effect at almost all latitudinal locations on 2 June confirms complex and unusual storm-time dynamics, with inhibited upward plasma drifts due to the presence of Disturbance Dynamo Electric Fields (DDEFs), while the thermospheric O/N2 ratio caused an extensive decrease in electron density over the Indian region. Minor negative storm noticed on 3 June coincides with the storm recovery period, reflecting prolonged disturbance dynamo effects and gradual recovery in thermospheric conditions. Overall, the current study highlights the strong sensitivity of the regional ionosphere to prevailing coupled electrodynamic-thermospheric forcing during the June 2025 geomagnetic storm that has not yet been reported for this event over the Indian longitude sector. Moreover, the findings from this study underscore peculiar storm-time behaviour of summer solstice ionosphere over the Indian longitude sector, driven by complex coupled processes which could be incorporated into ionospheric models and forecasting frameworks. Full article
(This article belongs to the Section Upper Atmosphere)
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19 pages, 2683 KB  
Article
First Major Eruption of Solar Cycle 25: Impacts of the 3 July 2021 X1.59 Solar Flare on the Ionosphere and Primary Cosmic Rays
by Vladimir A. Srećković, Nikola Veselinović, Aleksandra Kolarski, Mihailo Savić, Žarko Medić, Milica Langović and Filip Arnaut
Atmosphere 2026, 17(2), 180; https://doi.org/10.3390/atmos17020180 - 10 Feb 2026
Viewed by 250
Abstract
The X1.59 solar flare on 3 July 2021, was the first X-class flare of Solar Cycle 25 and the first since the X-class flare on 10 September 2017. This event was notable for producing a rare geomagnetic crochet, a temporary and localized perturbation [...] Read more.
The X1.59 solar flare on 3 July 2021, was the first X-class flare of Solar Cycle 25 and the first since the X-class flare on 10 September 2017. This event was notable for producing a rare geomagnetic crochet, a temporary and localized perturbation in Earth’s magnetic field during the flare’s peak. To the best of our knowledge, this study represents the first VLF-based analysis of this event, as well as the first comprehensive multi-instrument investigation of it. VLF observations from the NAA and DHO transmitters were used to investigate the ionospheric response via amplitude and phase variations. Key low ionosphere parameters, including the effective reflection height, sharpness factor, time delay and electron density profiles were derived. The results reveal rapid ionospheric responses closely correlated with X-ray flux peaks, including sudden phase and amplitude perturbations indicative of increased low ionosphere ionization and the geomagnetic crochet effect. Simultaneously, cosmic-ray measurements from ground detectors showed negligible modulation and no significant Forbush decrease, consistent with the flare’s weak and partially Earth-directed CME. Also, the spectrum of energetic protons measured in-situ in near-Earth space shows little disturbance. This integrated study demonstrates the sensitivity of the lower ionosphere to intense solar radiation and highlights the limited short-term impact on cosmic-ray and solar energetic proton flux, providing a comprehensive assessment of flare-driven space-weather effects during the early phase of Solar Cycle 25. Full article
(This article belongs to the Special Issue Advances in Observation and Simulation Studies of Ionosphere)
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14 pages, 3859 KB  
Article
Compact Analytic Two-Gaussian Representation of Universal Short-Range Coulomb Correlations in Soft-Core Fluids
by Hiroshi Frusawa
Axioms 2026, 15(2), 123; https://doi.org/10.3390/axioms15020123 - 6 Feb 2026
Viewed by 311
Abstract
Soft-core Coulomb fluids, exemplified by the two-dimensional Gaussian-charge one-component plasma, serve as fundamental benchmarks for both mathematical theory and computational modeling of coarse-grained dynamics, including stochastic density functional theory, dynamical density functional theory, and dissipative particle dynamics. In these systems, the conventional mean-field [...] Read more.
Soft-core Coulomb fluids, exemplified by the two-dimensional Gaussian-charge one-component plasma, serve as fundamental benchmarks for both mathematical theory and computational modeling of coarse-grained dynamics, including stochastic density functional theory, dynamical density functional theory, and dissipative particle dynamics. In these systems, the conventional mean-field description, or the random phase approximation (RPA), is frequently employed due to its analytic simplicity; however, its validity is restricted to weak coupling regimes. Here we demonstrate that Coulomb correlations induce a structural crossover to a strongly correlated liquid where the nearest-neighbor distance saturates rather than decreasing monotonically, a behavior fundamentally incompatible with mean-field predictions. Central to our analysis is the emergence of a universal scaling law: when rescaled by the coupling constant, the short-range direct correlation function (DCF) collapses onto a single curve across the strong coupling regime. Exploiting this universality, we construct a closed-form analytic representation of the DCF using a two-Gaussian basis. This compact form accurately reproduces hypernetted-chain radial distribution functions and structure factors while ensuring exact compliance with thermodynamic sum rules. Beyond theoretical elegance, the proposed kernel offers a computationally efficient alternative to RPA-based approximations, enabling real-space dynamical methods to incorporate strong correlations without modifying long-range smoothed-charge electrostatics. Its analytic transparency bridges rigorous integral equation theory and practical dynamical kernels, additionally providing a physics-informed prior for emerging machine-learning models. Collectively, these results establish a mathematically rigorous testbed for advancing the modeling of strongly correlated soft matter systems. Full article
(This article belongs to the Section Mathematical Physics)
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13 pages, 7644 KB  
Article
Simulation Study of Influence of Nano-Confinement Effect on Shale Fluid Phase Characteristics: A Case Study of Gulong Shale Oil
by Zhenlong Song, Ke Zhang, Yu Zhang, Yaoze Cheng, Wenning Zhou, Jian Ma, Xiaolin Zhou and Maomao Hong
Processes 2026, 14(3), 548; https://doi.org/10.3390/pr14030548 - 4 Feb 2026
Viewed by 250
Abstract
Songliao Basin hosts abundant shale oil and gas resources, yet the phase behavior of the fluids is still unclear since the confinement effect of the shale reservoir alters the adsorption effect on the pore walls. In this study, molecular dynamics (MD) simulations were [...] Read more.
Songliao Basin hosts abundant shale oil and gas resources, yet the phase behavior of the fluids is still unclear since the confinement effect of the shale reservoir alters the adsorption effect on the pore walls. In this study, molecular dynamics (MD) simulations were employed to clarify this issue. A binary mixture was built to represent Gulong shale oil and the phase state properties under the confinement effect were evaluated. In addition, a series of pure alkane models were constructed to analyze the influence of hydrocarbon type, temperature, and mineral composition on phase behavior. The simulation results showed that the typical Gulong shale fluid remains liquid state in the nanopores. Owing to the confinement effect, both viscosity and density under nano space decrease sharply compared to those at bulk space. Therefore, field development should somewhat rely on high-pressure stimulation to create flow paths, followed by CO2 huff-and-puff technology to maintain production pressure. In addition, fluid composition, temperature, and mineral type are the primary factors governing the magnitude of the confinement effect. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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29 pages, 14000 KB  
Article
Direct Phasing of Protein Crystals with Hybrid Difference Map Algorithms
by Hongxing He, Yang Liu and Wu-Pei Su
Molecules 2026, 31(3), 472; https://doi.org/10.3390/molecules31030472 - 29 Jan 2026
Cited by 1 | Viewed by 227
Abstract
Direct methods for solving protein crystal structures from X-ray diffraction data provide an essential approach for validating predicted models while avoiding external model bias. Nevertheless, traditional iterative projection algorithms, including the widely used Difference Map (DiffMap), are often limited by modest phase retrieval [...] Read more.
Direct methods for solving protein crystal structures from X-ray diffraction data provide an essential approach for validating predicted models while avoiding external model bias. Nevertheless, traditional iterative projection algorithms, including the widely used Difference Map (DiffMap), are often limited by modest phase retrieval success rates. To address this limitation, we introduce a novel Hybrid Difference Map (HDM) algorithm that synergistically combines the strengths of DiffMap and the Hybrid Input–Output (HIO) method through six distinct iterative update rules. HDM retains an optimized DiffMap-style relaxation term for fine-grained density modulation in protein regions while adopting HIO’s efficient negative feedback mechanism for enforcing the solvent flatness constraint. Using the transmembrane photosynthetic reaction center 2uxj as a test case, the first HDM formula, HDM-f1, successfully recovered an atomic-resolution structure directly from random phases under a conventional full-resolution phasing scheme, demonstrating the robust phasing capability of the approach. Systematic evaluation across 22 protein crystal structures (resolution 1.5–3.0 Å, solvent content ≥ 60%) revealed that all six HDM variants outperformed DiffMap, achieving 1.8–3.5× higher success rates (average 2.8×), performing on par with or exceeding HIO under a conventional phasing scheme. Further performance gains were achieved by integrating HDM with advanced strategies: resolution weighting and a genetic algorithm-based evolutionary scheme. The genetic evolution strategy boosted the success rate to nearly 100%, halved the median number of iterations required for convergence, and reduced the final phase error to approximately 35° on average across test structures through averaging of multiple solutions. The resulting electron density maps were of high interpretability, enabling automated model building that produced structures with a backbone RMSD of less than 0.5 Å when compared to their PDB-deposited counterparts. Collectively, the HDM algorithm suite offers a robust, efficient, and adaptable framework for direct phasing, particularly for challenging cases where conventional methods struggle. Our implementation supports all space groups providing an accessible tool for the broader structural biology community. Full article
(This article belongs to the Special Issue Crystal and Molecular Structure: Theory and Application)
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17 pages, 5227 KB  
Article
Synergistic Regulation of Microstructure and Mechanical Property in TiAl Alloys via Rolling and Cyclic Heat Treatment
by Shiwei Tian, Zhiqian Liao, Dejun Song, Chong Li, Kuishan Sun, Lin Yuan and Haitao Jiang
Metals 2026, 16(1), 126; https://doi.org/10.3390/met16010126 - 22 Jan 2026
Viewed by 161
Abstract
The presence of the brittle β/B2 phase in TiAl alloys often deteriorates their mechanical properties, posing a significant challenge for manufacturing large-sized, high-performance sheets. To address this issue, this study systematically investigates the synergistic effect of pack rolling and subsequent heat treatment on [...] Read more.
The presence of the brittle β/B2 phase in TiAl alloys often deteriorates their mechanical properties, posing a significant challenge for manufacturing large-sized, high-performance sheets. To address this issue, this study systematically investigates the synergistic effect of pack rolling and subsequent heat treatment on the microstructure evolution and mechanical properties of a Ti-44Al-4Nb-1.5Mo-0.1B-0.1Y alloy. Sheets with two different deformation levels (R7: 69.8% and R11: 83.0% reduction) were prepared via pack rolling. This was followed by a series of heat treatments at different temperatures (1150–1350 °C) and cyclic heat treatments at 1250 °C (3, 6, and 9 cycles). The results demonstrate that the higher deformation level (R11) promoted extensive dynamic recrystallization, resulting in a uniform microstructure of equiaxed γ, α2, and β phases, while the lower deformation (R7) retained a significant fraction of deformed γ/α2 lamellae. Heat treatment at 1250 °C was identified as optimal for transforming the microstructure into fine lamellar colonies while effectively reducing the β/B2 phase. Cyclic heat treatment at this temperature further decreased the β-phase content to 4.1% after 9 cycles. The elimination mechanism was determined to follow the β→ α → γ + α2 phase transformation sequence, driven by the combined effect of rolling-induced defects and cyclic thermal stress. Cyclic heat treatment at this temperature was particularly effective in generating a high density of nucleation sites within the lamellar colonies, leading to significant refinement of the lamellar structure. Consequently, the R11 sheet subjected to 9 cycles of heat treatment exhibited a 15.5% increase in tensile strength and an 8.3% improvement in elongation compared to the hot-isostatically pressed state. This enhancement is primarily attributed to the significant refinement of lamellar colonies and the reduction in interlamellar spacing. This work presents an effective integrated processing strategy for fabricating high-performance TiAl alloy sheets with superior strength and toughness. Full article
(This article belongs to the Special Issue Microstructure and Deformation Mechanisms of Alloys)
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45 pages, 1821 KB  
Review
Understanding Squeezed States of Light Through Wigner’s Phase-Space
by Sibel Başkal and Marilyn E. Noz
Mathematics 2026, 14(2), 335; https://doi.org/10.3390/math14020335 - 19 Jan 2026
Viewed by 287
Abstract
This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from [...] Read more.
This paper starts with the transition from classical physics to quantum mechanics which was greatly aided by the concept of phase space. The role of canonical transformations in quantum mechanics is addressed. The Wigner phase-space distribution function is then defined which arises from the formulation of the density matrix, followed by the harmonic oscillator in phase space. Coherent and one- and two-mode squeezed states of light as well as the squeezed vacuum are discussed in the phase-space picture. Attention is also drawn to the fact that squeezed states naturally generate entanglement between the two-modes. Coupled harmonic oscillators are also elucidated in connection with the Wigner phase space. Note that the phase-space picture of quantum mechanics has become an important scientific language for the rapidly expanding field of quantum optics. Here, we mainly focus on the simplest form of the Wigner function, which finds application in many branches of quantum mechanics. We make use of several symmetry groups such as Lorentz groups, the symplectic group in two and four dimensions, and the Euclidean group. The decoherence problem of an optical field is examined through a reformulation of the Poincaré sphere as a further illustration of the density matrix. Full article
(This article belongs to the Section E4: Mathematical Physics)
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