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Search Results (973)

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Keywords = liquid–liquid equilibrium

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27 pages, 2419 KB  
Article
Portfolio Optimization Based on Transformer-GAN Enhanced Black–Litterman Framework for Quantitative Analysis
by Yongsheng Qiao, Risheng Qiao and Yongmei Qiao
Mathematics 2026, 14(16), 2939; https://doi.org/10.3390/math14162939 - 13 Aug 2026
Abstract
Portfolio optimization remains a challenging problem due to the dynamic, nonlinear, and uncertain characteristics of financial markets. Traditional portfolio construction approaches, including mean variance optimization and conventional Black–Litterman models, often suffer from inaccurate estimation of expected returns and unstable allocation caused by parameter [...] Read more.
Portfolio optimization remains a challenging problem due to the dynamic, nonlinear, and uncertain characteristics of financial markets. Traditional portfolio construction approaches, including mean variance optimization and conventional Black–Litterman models, often suffer from inaccurate estimation of expected returns and unstable allocation caused by parameter uncertainty. These limitations become more significant under structural breaks, regime transitions, volatility clustering, and extreme market events. This study proposes a Transformer-GAN enhanced Black–Litterman framework (TG-BL) that integrates temporal representation learning, uncertainty-aware scenario generation, and Bayesian portfolio optimization. The proposed framework consists of three complementary components. First, a Transformer-based encoder is employed to extract long- range temporal dependencies and latent market representations from historical financial sequences. Second, a conditional Generative Adversarial Network (GAN) is introduced to generate diverse future return scenarios conditioned on Transformer- derived market representations, enabling probabilistic modeling of future uncertainty rather than deterministic prediction. Third, the generated return distributions are incorporated into the Black–Litterman framework through dynamically calibrated views and confidence estimation. Unlike conventional approaches that directly replace equilibrium returns with machine-generated predictions, the proposed method preserves the Bayesian structure of Black–Litterman by adjusting the influence of model- generated views according to predictive uncertainty. This mechanism allows AI- based forecasts to complement rather than dominate market equilibrium information. Extensive experiments are conducted using historical financial data under multiple market conditions. The evaluation framework includes portfolio performance comparison, GAN-generated scenario validation, robustness analysis under volatility and liquidity stress, and component- wise ablation experiments. The results demonstrate that the proposed TG-BL framework improves risk-adjusted portfolio performance while maintaining robustness against market uncertainty. The findings indicate that the integration of temporal feature extraction, uncertainty modeling, and Bayesian portfolio allocation provides an effective decision-support framework for quantitative investment management. Full article
(This article belongs to the Special Issue AI, Machine Learning and Optimization)
37 pages, 1494 KB  
Article
A Non-Equilibrium Thermodynamic Framework for Sequential Symmetry Breaking in Driven Complex Fluids
by Antonio F. Miguel, Vinicius R. Pepe and Luiz A. O. Rocha
Entropy 2026, 28(8), 910; https://doi.org/10.3390/e28080910 - 13 Aug 2026
Abstract
The spontaneous emergence of macroscopic order in driven, far-from-equilibrium complex fluids lacks a generalized framework capable of bridging continuous and discrete symmetry-breaking transitions. In this study, we propose a non-equilibrium phenomenological framework that synthesizes irreversible thermodynamics, coupled Landau–de Gennes potential expansions, and active [...] Read more.
The spontaneous emergence of macroscopic order in driven, far-from-equilibrium complex fluids lacks a generalized framework capable of bridging continuous and discrete symmetry-breaking transitions. In this study, we propose a non-equilibrium phenomenological framework that synthesizes irreversible thermodynamics, coupled Landau–de Gennes potential expansions, and active hydrodynamics. The formulation employs a single tensorial order parameter, a nonlinear state-dependent jamming mobility closure, and a generalized set of dimensionless groups to map the non-equilibrium phase space. The model predicts a sequential symmetry-breaking cascade and reproduces the emergence of polar heliconical smectic and antiferroelectric phases in driven liquid crystals, as well as the transition from isotropic active gases to macroscopic fluid flocks and active Wigner crystals in purely repulsive Janus colloids. Across these systems, a dimensionless active torque number acts as the principal bifurcation parameter, suggesting that their macroscopic structural transitions are governed by a common balance between thermodynamic and kinematic effects rather than by the details of their microscopic interactions. Full article
16 pages, 5564 KB  
Article
Effect of Slag Chemistry on the Smelting Reduction Behavior of Chromite Ore
by Yijian Zhang, Jianliang Zhang, Ping Du, Yu Lu, Xun Zhou, Miao Luo and Jianyang Yin
Metals 2026, 16(8), 891; https://doi.org/10.3390/met16080891 - 10 Aug 2026
Viewed by 139
Abstract
This study aims to investigate the effects of slag chemical composition on the smelting reduction behavior and microstructural evolution of chromite at 1525–1550 °C, thereby providing theoretical guidance for optimizing the smelting reduction process. Through high-temperature melting experiments combined with Scanning Electron Microscope [...] Read more.
This study aims to investigate the effects of slag chemical composition on the smelting reduction behavior and microstructural evolution of chromite at 1525–1550 °C, thereby providing theoretical guidance for optimizing the smelting reduction process. Through high-temperature melting experiments combined with Scanning Electron Microscope - Energy Dispersive Spectrometer(SEM-EDS) microstructural characterization and thermodynamic calculations, the influences of basicity, MgO content, and Al2O3 content on chromium reduction behavior, slag physicochemical properties, and spinel evolution mechanisms were systematically analyzed. The results indicate that a basicity of 1.2 effectively promotes the dissolution and reduction of chromium spinel, whereas excessively high basicity hinders the reduction process when using graphite as the reducing agent. Although increasing MgO content initially improves slag fluidity and reaction rates, it promotes the formation of a Mg-Al-rich solid product layer during the later stages of the reaction; this restricts the intra-phase diffusion of Cr3+ and causes the reduction process to stall. High Al2O3 content significantly increases system viscosity and impairs mass transfer, thereby reducing the degree of reduction. Under optimized conditions, specifically an Al2O3 content of 14 wt% and a temperature of 1550°C, the degree of reduction approaches 93%. Thermodynamic calculations further reveal that the efficiency of chromite smelting reduction is synergistically controlled by factors such as slag viscosity, liquid-phase behavior, and spinel equilibrium phase mass. The favorable slag composition identified in this study, basicity of 1.2, MgO content of 10 wt%, and Al2O3 content of 14 wt%, provides favorable physicochemical conditions for the efficient smelting reduction of chromite. Full article
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15 pages, 7100 KB  
Article
Physically Crosslinked Conductive Organic Gel with Excellent Elasticity and Environmental Stability
by Haiquan Zhang, Zhinan Zhao, Shishen Lan, Qiadong Yao, Minglei Lv and Ning Wang
Gels 2026, 12(8), 707; https://doi.org/10.3390/gels12080707 - 8 Aug 2026
Viewed by 149
Abstract
Liquid water in hydrogels exhibits an adsorption-desorption dynamic equilibrium with the surrounding environment, which leads to the instability of mechanical properties. To address this limitation, we propose an innovative design of conductive composite organogels by incorporating compatible linear lauryl alcohol (LA) and multi-walled [...] Read more.
Liquid water in hydrogels exhibits an adsorption-desorption dynamic equilibrium with the surrounding environment, which leads to the instability of mechanical properties. To address this limitation, we propose an innovative design of conductive composite organogels by incorporating compatible linear lauryl alcohol (LA) and multi-walled carbon nanotubes (CNTs) into a poly(butyl methacrylate) (PBMA) network. Carbon chains of LAform physical crosslinks with PBMA side chains, effectively replacing inherent polymer chain entanglements. This structural innovation facilitates rapid chain rotation and sliding during stretching, so that the gel has a super stretching property of up to 2460%. At elevated temperatures, weakened interactions between LA–PBMA and PBMA–PBMA chains reduce physical confinement of CNTs within the PBMA network. Simultaneously applying a directional electric field, CNTs undergo rotation and translation to reconstruct an optimized conductive pathway, granting the composite distinctive temperature-sensitive electrical conductivity. Critically, all components in the PBMA/LA/CNTs (PLCs) exhibit low volatility and hydrophobicity. These characteristics enable the organogel to retain excellent flexibility and stable electrical performance after prolonged immersion in deionized water, exposure to vacuum, and even under extreme conditions at 120 °C. Such comprehensive stability suggests promising applications in deep-sea exploration and aerospace engineering. Full article
(This article belongs to the Section Gel Chemistry and Physics)
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25 pages, 21697 KB  
Article
A Systematic Evaluation of SAFT-Type Equations of State for CO2–Polar Aprotic Solvent Systems: Model Selection and Optimization Strategies
by Meiting Wang, Xiangbo Wang, Jinghuo Wei, Junhui Yang, Lixi Liu and Zhi Yang
Processes 2026, 14(16), 2548; https://doi.org/10.3390/pr14162548 - 8 Aug 2026
Viewed by 352
Abstract
Accurate vapor–liquid equilibrium (VLE) modeling of CO2 in polar aprotic solvents (PASs) is critical for solvent screening and the design of carbon-capture processes. This study systematically evaluates three SAFT-type equations of state (EoSs), namely CPA, PC-SAFT, and SAFT-VR Mie, under a unified [...] Read more.
Accurate vapor–liquid equilibrium (VLE) modeling of CO2 in polar aprotic solvents (PASs) is critical for solvent screening and the design of carbon-capture processes. This study systematically evaluates three SAFT-type equations of state (EoSs), namely CPA, PC-SAFT, and SAFT-VR Mie, under a unified parameter optimization framework. For pure-component saturation properties, SAFT-VR Mie yielded the lowest mean deviations across all investigated substances, with average AARD values of 0.066% for Psat and 0.127% for ρsat. However, the most accurate EoS for an individual substance depended on the property evaluated, and PC-SAFT produced lower deviations for several substance–property combinations. For binary CO2 + PAS systems, all three EoSs exhibited substantial pressure deviations when the binary interaction parameter (kij) was set to zero. Optimizing kij reduced the pressure AARD for every model–solvent combination, indicating that the default combining rules did not adequately represent the CO2–solvent cross-interactions. Notably, the specific improvement in pressure AARD% after introducing kij for each model revealed CPA’s superior sensitivity (e.g., for the CO2 + MEK system, pressure AARD% decreased from 14.43% to 4.07%, a reduction of over 70%). Furthermore, a comparative analysis of single-temperature (ST) and multi-temperature (MT) optimization strategies reveals that the ST optimization reduces the average pressure AARD% from 4.34% (MT) to 3.05%, whereas the MT-optimized kij values offer superior transferability across a broader temperature range. These findings elucidate the different applicable scenarios of model architecture and kij optimization strategies, providing actionable guidance for selecting appropriate thermodynamic models to support the simulation and optimization of carbon-capture systems. Full article
(This article belongs to the Section Chemical Processes and Systems)
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18 pages, 2786 KB  
Article
Enabling Rapid pH Equilibration Through Acoustic Microstreaming for Efficient pH Regulation in Microliter-Scale Samples with Screen-Printed Electrodes
by Ziyi Xiao, Ruyi Deng, Xin Liu, Jiahuan Zheng and Kaisong Yuan
Biosensors 2026, 16(8), 424; https://doi.org/10.3390/bios16080424 - 6 Aug 2026
Viewed by 228
Abstract
Real-time pH measurement and regulation of microliter-scale liquid samples are critical for microfluidic biochemical applications. However, traditional magnetic stirring for macroscopic systems is not applicable under such microscale conditions. This work develops an ultrasound-assisted screen-printed electrode (SPE) pH sensor integrated with a 3D-printed [...] Read more.
Real-time pH measurement and regulation of microliter-scale liquid samples are critical for microfluidic biochemical applications. However, traditional magnetic stirring for macroscopic systems is not applicable under such microscale conditions. This work develops an ultrasound-assisted screen-printed electrode (SPE) pH sensor integrated with a 3D-printed ultrasonic reflection cell and piezoelectric excitation unit. Ultrasound-induced acoustic streaming accelerates mass transfer inside microliter-scale samples. Upon acid addition, the ultrasonic-assisted system reaches potentiometric equilibrium far more rapidly than the static non-ultrasonic control. Optimized parameters are 30 s ultrasonic duration and 5 Vpp input amplitude. The sensor shows linearity from pH 3.04 to 4.15 with R2 = 0.9919. Phenolphthalein visualization directly confirms ultrasound-enhanced molecular diffusion. Its mass transfer efficiency matches traditional magnetic stirring, and stable fast equilibrium is realized in complex cell culture medium. This acoustofluidic micromixing strategy offers a simple integrated route for pH monitoring and the regulation of micro-volume biological samples. Full article
(This article belongs to the Special Issue Flexible Electronics for Biosensors)
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27 pages, 3164 KB  
Article
Study on the Promotion of Methane Hydrate Formation by Surface Modification of Quartz Sand
by Du Wang, Yuru Chen, Chang Chen, Xiaosen Li, Yu Zhang and Zhaoyang Chen
Energies 2026, 19(15), 3673; https://doi.org/10.3390/en19153673 - 5 Aug 2026
Viewed by 145
Abstract
Natural gas hydrates, with their vast reserves and high gas storage density, have emerged as a highly promising alternative energy source and technology for gas storage and transportation. Wettability, as a core surface property of porous media, directly influences hydrate nucleation, growth, occurrence [...] Read more.
Natural gas hydrates, with their vast reserves and high gas storage density, have emerged as a highly promising alternative energy source and technology for gas storage and transportation. Wettability, as a core surface property of porous media, directly influences hydrate nucleation, growth, occurrence morphology, and flow behavior. In this study, quartz sand with varying surface properties was prepared with the octyltrimethoxysilane (OTMS) silane coupling agent via surface chemical reactions. The methane hydrate (MH) equilibrium conditions as well as the formation kinetics in silica sand were measured, and the mechanism and potential of the surface modification for enhancing methane hydrate storage capacity were analyzed. The experimental results indicate that surface modification of quartz sand has no significant effect on the MH equilibrium condition. Hydrophobic modification of quartz sand provides more gas–liquid interfaces, increases the contact area, and thereby significantly enhances mass transfer under high-water-saturation conditions and accelerates the MH formation rate. However, excessively high surface hydrophobicity may reduce the effective gas–liquid interfacial area and limit the overall hydrate formation rate. Due to the influences of the hydrate distribution and aggregation, as well as gas diffusion on hydrate formation, the effect of the initial formation pressure on MH formation is only observed during the early stages of MH formation, while the temperature effect is less pronounced than that of formation pressure. It is suggested to further consider combining stirring with continuous gas injection to enhance gas–liquid flow and improve gas–liquid contact, thereby increasing the formation rate of hydrates. Full article
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27 pages, 1687 KB  
Article
Research on Early Warning Threshold Setting for Inventory Pledge Financing Under Supervisory Credit Restructuring
by Lili Xu, Chan He and Yubin Yang
Mathematics 2026, 14(15), 2721; https://doi.org/10.3390/math14152721 - 1 Aug 2026
Viewed by 170
Abstract
From the perspective of supervisory credit reconstruction, this study proposes the setting of early warning points. It employs a combined approach of evolutionary game theory and the stochastic cusp model to calculate the replenishment point and liquidation point, and simulates the impact of [...] Read more.
From the perspective of supervisory credit reconstruction, this study proposes the setting of early warning points. It employs a combined approach of evolutionary game theory and the stochastic cusp model to calculate the replenishment point and liquidation point, and simulates the impact of disruptive factors on these two points. The study reveals that: (1) The optimal equilibrium in the game between the two parties is reached when the 3PL enterprise chooses to positive supervise, the financial institution opts not to provide incentives, and instead relies on penalty deterrence, market discipline, and reputation mechanisms to ensure the 3PL enterprise implements active supervision activities; (2) During the evolutionary process of supervision, whether a sudden change in supervisory behavior occurs is determined by the bifurcation point of the stochastic cusp catastrophe model, which in turn dictates the settings of the replenishment and liquidation points; (3) The 3PL enterprise’s negative supervision penalty and the 3PL enterprise’s reputational loss are positively correlated with the replenishment point and negatively correlated with the liquidation point. This study provides theoretical and methodological support for supervisory credit reconstruction and quantitative implementation, which bolsters financial institutions’ confidence in inventory pledge financing and promotes the development of inclusive finance. Full article
(This article belongs to the Section E: Applied Mathematics)
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24 pages, 5562 KB  
Article
Synthesis, Performance, and Mechanism of Upcycled Lithium Slag-Based Geopolymers for High-Capacity Pb(II) Elimination
by Yang Tang, Zhouyueyang Cheng, Qilun Jin, Xiaojun Yang, Chuan Guan, Miao Deng, Binbin Tang, Huan Gao, Wenjie Jiang, Yang Xian, Ping Jiang, Peiyuan Peng and Zhenhua Feng
Processes 2026, 14(15), 2461; https://doi.org/10.3390/pr14152461 - 30 Jul 2026
Viewed by 261
Abstract
The concurrent disposal of industrial lithium slag (LS) and the remediation of heavy-metal-contaminated water remain critical environmental imperatives. Herein, industrial lithium slag was successfully upcycled into a high-capacity geopolymer via alkali activation to systematically evaluate its Pb(II) removal mechanisms. Synthesized under optimal conditions [...] Read more.
The concurrent disposal of industrial lithium slag (LS) and the remediation of heavy-metal-contaminated water remain critical environmental imperatives. Herein, industrial lithium slag was successfully upcycled into a high-capacity geopolymer via alkali activation to systematically evaluate its Pb(II) removal mechanisms. Synthesized under optimal conditions (11 mol/L alkali concentration, 0.616 solid-to-liquid ratio), the geopolymer showed exceptional Pb(II) capture, achieving ~99% removal efficiency within 120 min for a 100 mg/L Pb(II) solution at pH 6.0. The adsorption kinetics obeyed the pseudo-first-order model, yielding a remarkable theoretical equilibrium capacity of 284 mg/g. Thermodynamic results reveal a spontaneous (ΔG < 0), endothermic (ΔH = 17.66 kJ/mol) process with increased interfacial randomness (ΔS > 0). Integrating macroscopic performance with characterizations and density functional theory (DFT) computations elucidated a site-specific chemisorption mechanism and the precipitation of PbSO4 caused by Pb(II) and SO42− in LS. Ultimately, this work provides a sustainable paradigm for the value-added upcycling of industrial solid waste. Full article
(This article belongs to the Section Materials Processes)
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21 pages, 2497 KB  
Article
Sequential Pyruvic Acid Pretreatment and Alkaline Extraction of Bamboo Leaf Phenolics: Two-Stage Mass Transfer Kinetics
by Yongkang Mo, Xiaoying Liu, Jingpeng Zhou, Jianquan Ren, Baojie Liu, Chengrong Qin, Chen Liang and Shuangquan Yao
Foods 2026, 15(15), 2655; https://doi.org/10.3390/foods15152655 - 28 Jul 2026
Viewed by 283
Abstract
This study examined total phenolic release and mass transfer during sequential pyruvic acid (PA) pretreatment and sodium hydroxide (NaOH) extraction of bamboo leaves. A 4 × 4 design comprised PA concentrations of 7.0, 8.0, 9.0, and 10.0% and NaOH concentrations of 3.0, 4.0, [...] Read more.
This study examined total phenolic release and mass transfer during sequential pyruvic acid (PA) pretreatment and sodium hydroxide (NaOH) extraction of bamboo leaves. A 4 × 4 design comprised PA concentrations of 7.0, 8.0, 9.0, and 10.0% and NaOH concentrations of 3.0, 4.0, 5.0, and 6.0%. Kinetic curves from 40 to 120 min showed rapid release followed by a gradual approach to equilibrium. Normalized conversion F(t) was used to evaluate release progression, and two consistent fitting windows were applied for parameter estimation. The LDF model described the 40, 60, and 80 min data and provided kf, while the Crank spherical diffusion model described the 80, 100, and 120 min data and provided Deff. These overlapping windows represent different portions of the same continuous extraction process rather than physically separate stages. Model comparison and predictive validation supported the framework. The characteristic time ratio τm/τd exceeded 2 under all tested conditions, indicating that external liquid film transfer contributed the greater relative resistance. The condition of 8.0% PA and 5.0% NaOH provided the most balanced performance, yielding 18.55 ± 0.26 mg GAE/g, equivalent to 94.4% of the maximum. These results provide a practical basis for rate control analysis and condition selection. Full article
(This article belongs to the Section Food Physics and (Bio)Chemistry)
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16 pages, 17763 KB  
Article
An Investigation into How Seed Slurry Preparation Affects the Final Crystal Size Distribution
by Alexander Riddell, Qi Feng Chan, Yu Ng Chen and Xiongwei Ni
AppliedChem 2026, 6(3), 49; https://doi.org/10.3390/appliedchem6030049 - 28 Jul 2026
Viewed by 217
Abstract
For continuous crystallization of pharmaceutical and organic chemical compounds in a plug flow crystallizer, seed slurry, prepared in advance, is continuously fed into the crystallizer for controlled secondary nucleation and subsequently desired crystal properties. It is well known that the preparation of macro [...] Read more.
For continuous crystallization of pharmaceutical and organic chemical compounds in a plug flow crystallizer, seed slurry, prepared in advance, is continuously fed into the crystallizer for controlled secondary nucleation and subsequently desired crystal properties. It is well known that the preparation of macro seed crystals using either the dry or wet method is a highly time-, energy- and material-intensive process, often taking many hours to prepare a 1 L seed slurry. The focus of this work is to examine whether how the seed slurry is made up could have any effect on the final crystal properties. We divide the seed slurry into two parts: the “saturation part” corresponds to the amount of solute required to establish solid–liquid equilibrium and is fully dissolved, and the “supersaturation part” involves a small amount of solid seed crystals in excess of the equilibrium saturation condition. The hypothesis states that if dissolved seed crystals have lost their surface properties (such as size, morphology, interfacial effects), the final crystal size distributions would then inherit that of the solid seed crystals. If this is true, this would provide a great and efficient shortcut for the lengthy and energy-intensive process of making up seed slurries, as product crystals from a previous batch of any size distribution could be used for the make-up of the saturation part of the seed slurry. Using adipic acid and L-glutamic acid with high and low solubilities, the hypothesis has been validated experimentally under batch conditions. Full article
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17 pages, 3000 KB  
Review
Thermal-Temporal Treatment Preparation of the Melt Before Amorphization to Obtain Nanocrystalline Magnetic Cores with Unique Magnetic Characteristics
by Vladimir S. Tsepelev, Kaiming Wu and Nadezhda P. Tsepeleva
Nanomaterials 2026, 16(15), 922; https://doi.org/10.3390/nano16150922 - 27 Jul 2026
Viewed by 520
Abstract
This review presents a current understanding of the relationship between the structure of multicomponent metallic melts and the processes of amorphization and nanocrystallization. Particular attention is paid to the thermal-temporal treatment (TTT) of melts as a precision method for monitoring the nonequilibrium state [...] Read more.
This review presents a current understanding of the relationship between the structure of multicomponent metallic melts and the processes of amorphization and nanocrystallization. Particular attention is paid to the thermal-temporal treatment (TTT) of melts as a precision method for monitoring the nonequilibrium state of the liquid phase, the relaxation kinetics of cluster associations, and liquid–liquid transitions (LLT). The mechanisms by which precrystallization melt treatment affects the homogeneity of the amorphous precursor, the size of nanograins (7–15 nm), the phase composition (Fe3Si, Fe2B), and the resulting magnetic characteristics of toroidal cores (μmax > 600,000, Hc < 0.5 A/m) are investigated. Based on an analysis of structural models of metallic melts (cybotactic, quasicrystalline, and quasichemical), it is shown that critical temperatures, viscosity hysteresis, and oscillatory relaxation serve as indicators of melt equilibrium. It is noted that the optimized TTT protocols combined with controlled annealing at 542–572 °C enable the formation of Fe3Si nanograins with exceptional magnetic softness. The results open the possibility of discussing the prospects for integrating TTT with in situ diagnostics, CALPHAD modeling, and the potential of machine learning for the design of next-generation soft magnetic nanomaterials with tailored frequency characteristics for high-frequency power electronics and their use in electromagnetic shielding. Full article
(This article belongs to the Topic New Research on Thin Films and Nanostructures)
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20 pages, 13092 KB  
Article
Thermodynamic Assessment of CaO-Al2O3-Fe2O3 System
by Wenqing Zhao, Lideng Ye, Junfeng Wu, Hong Chen, Ligang Zhang and Libin Liu
Materials 2026, 19(14), 3136; https://doi.org/10.3390/ma19143136 - 21 Jul 2026
Viewed by 293
Abstract
The CaO-Al2O3-Fe2O3 system is widely encountered in cement production, iron ore sintering, metallurgical slags, and refractory materials. A thermodynamic assessment of the CaO-Fe2O3 and CaO-Al2O3-Fe2O3 systems [...] Read more.
The CaO-Al2O3-Fe2O3 system is widely encountered in cement production, iron ore sintering, metallurgical slags, and refractory materials. A thermodynamic assessment of the CaO-Fe2O3 and CaO-Al2O3-Fe2O3 systems was carried out in this study based on the CALculation of PHAse Diagrams (CALPHAD) method. The liquid was modeled using the ionic two-sublattice model, expressed as (Ca+2, Al+3, Fe+2) P (O−2, AlO1.5, FeO1.5, Va, O) Q. The Compound Energy Formalism (CEF) was adopted to describe compounds and solid solutions. A self-consistent thermodynamic assessment of the CaO-Fe2O3 and CaO-Al2O3-Fe2O3 systems was achieved, enabling accurate reproduction of phase equilibrium and thermodynamic data. The obtained thermodynamic description provides a useful foundation for the design, optimization, and processing of refractory materials. Full article
(This article belongs to the Section Metals and Alloys)
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14 pages, 875 KB  
Article
Melt–Vapor Phase Transition and Distillation Separation of Magnesium–Silver Alloys
by Valeriy Volodin, Sergey Trebukhov, Alina Nitsenko, Arailym Mukangaliyeva, Xeniya Linnik and Nurila Burabayeva
Metals 2026, 16(7), 810; https://doi.org/10.3390/met16070810 - 20 Jul 2026
Viewed by 330
Abstract
In this study, the partial pressure values of magnesium over Mg–Ag system alloys were determined by the boiling point method and are presented as a temperature–concentration dependence. A similar dependence for the partial vapor pressure of silver was obtained with the numerical integration [...] Read more.
In this study, the partial pressure values of magnesium over Mg–Ag system alloys were determined by the boiling point method and are presented as a temperature–concentration dependence. A similar dependence for the partial vapor pressure of silver was obtained with the numerical integration of the Gibbs–Duhem equation. The boundaries of the vapor–liquid equilibrium fields were calculated at atmospheric pressure (101.3 kPa) and under vacuum (1.33 kPa). A complete phase diagram was constructed, including the boundaries of the liquid–vapor phase transition at the specified pressures. It was shown that the composition of the equilibrium vapor phase is represented almost entirely by magnesium over nearly the entire range of component concentrations. Thus, when the melt contains 1 wt. % in the melt and exhibits a boiling temperature of 1187 °C (1460 K), the vapor phase contains 94.67 wt. % magnesium, with silver accounting for the remainder. Therefore, the separation of liquid magnesium–silver alloys presents no significant technological difficulties. Based on the thermodynamic activities of the components, the partial and integral mixing functions, namely, entropy and enthalpy, were determined. The thermodynamic functions of formation and evaporation of Mg–Ag system alloys may be used for energy calculations of distillation processes and will supplement the physicochemical database. Full article
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28 pages, 21898 KB  
Article
Investigation of Hydraulic Instability During the Transient Process from Synchronous Condenser Pumping Mode to Pumping Mode
by Lei Deng, Longxiang Chen, Haichao Feng, Xiaotong Yan, Ziwei Zhong, Lingkai Zhu, Huixiang Chen and Kan Kan
Appl. Sci. 2026, 16(14), 7199; https://doi.org/10.3390/app16147199 - 18 Jul 2026
Viewed by 317
Abstract
The transition process from synchronous condenser pump (SCP) mode to pumping mode determines the response rapidity of the startup procedure and operational stability of pump-turbines; however, the complex gas–liquid interaction and transient hydraulic characteristics during this process remain insufficiently understood. To address this, [...] Read more.
The transition process from synchronous condenser pump (SCP) mode to pumping mode determines the response rapidity of the startup procedure and operational stability of pump-turbines; however, the complex gas–liquid interaction and transient hydraulic characteristics during this process remain insufficiently understood. To address this, this study develops a numerical framework for the SCP-to-pumping transition process, incorporating the full-passage system, a multiscale mesh strategy for coupling mainstream and clearance flow regions, and a gas–liquid two-phase flow model based on the Volume of Fluid (VOF) method. The reliability of the numerical model is verified through comparison with model experiments, demonstrating good agreement between simulations and experimental data. Based on the validated model, the transient evolution of hydraulic forces, pressure pulsations, and internal flow structures is systematically analyzed. Axial force analysis reveals a significant internal equilibrium; the crown bears a maximum instantaneous fluctuation of approximately 2800 kN. Conversely, the radial force is primarily dominated by blade hydraulic thrust (1294 kN), showing distinct anisotropic behavior. The runner blade channels and the upper draft tube region are identified as critical areas with intense pressure fluctuations, with peak-to-peak pressure amplitudes reaching 45~48 m and 54 m head, respectively. Furthermore, reducing the duration of the exhaust process constitutes the main strategy for accelerating the transition and mitigating prolonged high-amplitude force and pressure fluctuations. The findings provide new insights into the transient hydraulic mechanisms of SCP-to-pumping transitions and offer guidance for optimizing transition control strategies in pumped-storage units. Full article
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