Supercritical carbon dioxide (SC-CO2) power cycles offer a promising solution for offshore platforms' gas turbine waste heat recovery due to their compact design and high thermal efficiency. This study proposes a novel parallel-preheating recuperated Brayton cycle (PBC) using SC-CO2 for waste heat recovery on offshore gas turbines. An integrated energy, exergy, and economic (3E) model was developed and showed good predictive accuracy (deviations < 3%). The comparative analysis indicates that the PBC significantly outperforms the simple recuperated Brayton cycle (SBC). Under 100% load conditions, the PBC achieves a net power output of 4.55 MW, while the SBC reaches 3.28 MW, representing a power output increase of approximately 27.9%. In terms of thermal efficiency, the PBC reaches 36.7%, compared to 21.5% for the SBC, marking an improvement of about 41.4%. Additionally, the electricity generation cost of the PBC is 0.391 CNY/kWh, whereas that of the SBC is 0.43 CNY/kWh, corresponding to a cost reduction of approximately 21.23%. Even at 30% gas turbine load, the PBC maintains high thermoelectric and exergy efficiencies of 30.54% and 35.43%, respectively, despite a 50.8% reduction in net power from full load. The results demonstrate that the integrated preheater effectively recovers residual flue gas heat, enhancing overall performance. To meet the spatial constraints of offshore platforms, we maintained a pinch-point temperature difference of approximately 20 K in both the preheater and heater by adjusting the flow split ratio. This approach ensures a compact system layout while balancing cycle thermal efficiency with economic viability. This study offers valuable insights into the PBC's variable-load performance and provides theoretical guidance for its practical optimization in engineering applications.
{"title":"A Novel Parallel-Preheating Supercritical CO<sub>2</sub> Brayton Cycle for Waste Heat Recovery from Offshore Gas Turbines: Energy, Exergy, and Economic Analysis Under Variable Loads.","authors":"Dianli Qu, Jia Yan, Xiang Xu, Zhan Liu","doi":"10.3390/e28010106","DOIUrl":"10.3390/e28010106","url":null,"abstract":"<p><p>Supercritical carbon dioxide (SC-CO<sub>2</sub>) power cycles offer a promising solution for offshore platforms' gas turbine waste heat recovery due to their compact design and high thermal efficiency. This study proposes a novel parallel-preheating recuperated Brayton cycle (PBC) using SC-CO<sub>2</sub> for waste heat recovery on offshore gas turbines. An integrated energy, exergy, and economic (3E) model was developed and showed good predictive accuracy (deviations < 3%). The comparative analysis indicates that the PBC significantly outperforms the simple recuperated Brayton cycle (SBC). Under 100% load conditions, the PBC achieves a net power output of 4.55 MW, while the SBC reaches 3.28 MW, representing a power output increase of approximately 27.9%. In terms of thermal efficiency, the PBC reaches 36.7%, compared to 21.5% for the SBC, marking an improvement of about 41.4%. Additionally, the electricity generation cost of the PBC is 0.391 CNY/kWh, whereas that of the SBC is 0.43 CNY/kWh, corresponding to a cost reduction of approximately 21.23%. Even at 30% gas turbine load, the PBC maintains high thermoelectric and exergy efficiencies of 30.54% and 35.43%, respectively, despite a 50.8% reduction in net power from full load. The results demonstrate that the integrated preheater effectively recovers residual flue gas heat, enhancing overall performance. To meet the spatial constraints of offshore platforms, we maintained a pinch-point temperature difference of approximately 20 K in both the preheater and heater by adjusting the flow split ratio. This approach ensures a compact system layout while balancing cycle thermal efficiency with economic viability. This study offers valuable insights into the PBC's variable-load performance and provides theoretical guidance for its practical optimization in engineering applications.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840434/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that mixtures comprising multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.
{"title":"Way More than the Sum of Their Parts: From Statistical to Structural Mixtures.","authors":"James P Crutchfield","doi":"10.3390/e28010111","DOIUrl":"10.3390/e28010111","url":null,"abstract":"<p><p>We show that mixtures comprising multicomponent systems typically are much more structurally complex than the sum of their parts; sometimes, infinitely more complex. We contrast this with the more familiar notion of statistical mixtures, demonstrating how statistical mixtures miss key aspects of emergent hierarchical organization. This leads us to identify a new kind of structural complexity inherent in multicomponent systems and to draw out broad consequences for system ergodicity.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12839733/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146060998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study presents an improved Nishenko-Buland (NB) model to address systematic biases in estimating the coefficient of variation for earthquake recurrence intervals based on a normalizing function TTave. Through Monte Carlo simulations, we demonstrate that traditional NB methods significantly underestimate the coefficient of variation when applied to limited paleoseismic datasets, with deviations reaching between 30 and 40% for small sample sizes. We developed a linear transformation and iterative optimization approach that corrects these statistical biases by standardizing recurrence interval data from different sample sizes to conform to a common standardized distribution. Application to 26 fault segments across 15 major active faults in the Hetao graben system yields a corrected coefficient of variation of α = 0.381, representing a 24% increase over the traditional method (α0 = 0.307). This correction demonstrates that conventional approaches systematically underestimate earthquake recurrence variability, potentially compromising seismic hazard assessments. The improved model successfully eliminates sampling bias through iterative convergence, providing more reliable parameters for probability distributions in renewal-based earthquake forecasting.
{"title":"Improved NB Model Analysis of Earthquake Recurrence Interval Coefficient of Variation for Major Active Faults in the Hetao Graben and Northern Marginal Region.","authors":"Jinchen Li, Xing Guo","doi":"10.3390/e28010107","DOIUrl":"10.3390/e28010107","url":null,"abstract":"<p><p>This study presents an improved Nishenko-Buland (NB) model to address systematic biases in estimating the coefficient of variation for earthquake recurrence intervals based on a normalizing function TTave. Through Monte Carlo simulations, we demonstrate that traditional NB methods significantly underestimate the coefficient of variation when applied to limited paleoseismic datasets, with deviations reaching between 30 and 40% for small sample sizes. We developed a linear transformation and iterative optimization approach that corrects these statistical biases by standardizing recurrence interval data from different sample sizes to conform to a common standardized distribution. Application to 26 fault segments across 15 major active faults in the Hetao graben system yields a corrected coefficient of variation of α = 0.381, representing a 24% increase over the traditional method (α<sub>0</sub> = 0.307). This correction demonstrates that conventional approaches systematically underestimate earthquake recurrence variability, potentially compromising seismic hazard assessments. The improved model successfully eliminates sampling bias through iterative convergence, providing more reliable parameters for probability distributions in renewal-based earthquake forecasting.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840126/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper examines whether information-theoretic complexity measures enhance industry-group return forecasting and portfolio construction within a machine-learning framework. Using daily data for 25 U.S. GICS industry groups spanning more than three decades, we augment gradient-boosted decision tree models with Shannon entropy and fuzzy entropy computed from recent return dynamics. Models are estimated at weekly, monthly, and quarterly horizons using a strictly causal rolling-window design and translated into two economically interpretable allocation rules, a maximum-profit strategy and a minimum-risk strategy. Results show that the top performing strategy, the weekly maximum-profit model augmented with Shannon entropy, achieves an accumulated return exceeding 30,000%, substantially outperforming both the baseline model and the fuzzy-entropy variant. On monthly and quarterly horizons, entropy and fuzzy entropy generate smaller but robust improvements by maintaining lower volatility and better downside protection. Industry allocations display stable and economically interpretable patterns, profit-oriented strategies concentrate primarily in cyclical and growth-sensitive industries such as semiconductors, automobiles, technology hardware, banks, and energy, while minimum-risk strategies consistently favor defensive industries including utilities, food, beverage and tobacco, real estate, and consumer staples. Overall, the results demonstrate that entropy-based complexity measures improve both economic performance and interpretability, yielding industry-rotation strategies that are simultaneously more profitable, more stable, and more transparent.
{"title":"Entropy-Augmented Forecasting and Portfolio Construction at the Industry-Group Level: A Causal Machine-Learning Approach Using Gradient-Boosted Decision Trees.","authors":"Gil Cohen, Avishay Aiche, Ron Eichel","doi":"10.3390/e28010108","DOIUrl":"10.3390/e28010108","url":null,"abstract":"<p><p>This paper examines whether information-theoretic complexity measures enhance industry-group return forecasting and portfolio construction within a machine-learning framework. Using daily data for 25 U.S. GICS industry groups spanning more than three decades, we augment gradient-boosted decision tree models with Shannon entropy and fuzzy entropy computed from recent return dynamics. Models are estimated at weekly, monthly, and quarterly horizons using a strictly causal rolling-window design and translated into two economically interpretable allocation rules, a maximum-profit strategy and a minimum-risk strategy. Results show that the top performing strategy, the weekly maximum-profit model augmented with Shannon entropy, achieves an accumulated return exceeding 30,000%, substantially outperforming both the baseline model and the fuzzy-entropy variant. On monthly and quarterly horizons, entropy and fuzzy entropy generate smaller but robust improvements by maintaining lower volatility and better downside protection. Industry allocations display stable and economically interpretable patterns, profit-oriented strategies concentrate primarily in cyclical and growth-sensitive industries such as semiconductors, automobiles, technology hardware, banks, and energy, while minimum-risk strategies consistently favor defensive industries including utilities, food, beverage and tobacco, real estate, and consumer staples. Overall, the results demonstrate that entropy-based complexity measures improve both economic performance and interpretability, yielding industry-rotation strategies that are simultaneously more profitable, more stable, and more transparent.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840230/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146060949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ions in liquid helium exist in their simplest form in two configurations, as negatively charged "electron bubbles" (electrons in a void of about 35 Å in diameter) and as positive "snowballs" (He+ ions surrounded by a sphere of solid helium, about 14 Å in diameter). Here, we give an overview of studies with these ions when they are trapped at interfaces between different helium phases, i.e., the "free" surface between liquid and vapor, but also the interfaces between liquid and solid helium at high pressure and between phase-separated 3He-4He mixtures below the tricritical point. Three cases are discussed: (i) if the energy barrier provided by the interface is of the order of the thermal energy kBT, the ions can pass from one phase to the other with characteristic trapping times at the interface, which are in qualitative agreement with the existing theories; (ii) if the energy barrier is sufficiently high, the ions are trapped at the interface for extended periods of time, forming 2D Coulomb systems with intriguing properties; and (iii) at high electric fields and high ion densities, an electrohydrodynamic instability takes place, which is a model for critical phenomena.
{"title":"Ions at Helium Interfaces: A Review.","authors":"Paul Leiderer","doi":"10.3390/e28010109","DOIUrl":"10.3390/e28010109","url":null,"abstract":"<p><p>Ions in liquid helium exist in their simplest form in two configurations, as negatively charged \"electron bubbles\" (electrons in a void of about 35 Å in diameter) and as positive \"snowballs\" (He<sup>+</sup> ions surrounded by a sphere of solid helium, about 14 Å in diameter). Here, we give an overview of studies with these ions when they are trapped at interfaces between different helium phases, i.e., the \"free\" surface between liquid and vapor, but also the interfaces between liquid and solid helium at high pressure and between phase-separated <sup>3</sup>He-<sup>4</sup>He mixtures below the tricritical point. Three cases are discussed: (i) if the energy barrier provided by the interface is of the order of the thermal energy k<sub>B</sub><i>T</i>, the ions can pass from one phase to the other with characteristic trapping times at the interface, which are in qualitative agreement with the existing theories; (ii) if the energy barrier is sufficiently high, the ions are trapped at the interface for extended periods of time, forming 2D Coulomb systems with intriguing properties; and (iii) at high electric fields and high ion densities, an electrohydrodynamic instability takes place, which is a model for critical phenomena.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840215/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to meet the ever-growing demand in modern power electronics, the advanced soft magnetic materials (SMMs) are required to exhibit both excellent soft magnetic performance and mechanical properties. In this work, the effects of an annealing treatment on the soft magnetic properties, mechanical properties and microstructure of the Fe24.94Co24.94Ni24.94Al24.94Si0.24 high-entropy alloy (HEA) are investigated. The as-cast HEA consists of a body-centered cubic (BCC) matrix phase and spherical B2 nanoprecipitates with a diameter of approximately 5 nm, where a coherent relationship is established between the B2 phase and the BCC matrix. After annealing at 873 K, the alloy retains both the BCC and B2 phases, with their coherent relationship preserved; besides the spherical B2 nanoprecipitates, rod-shaped B2 nanoprecipitates are also observed. After the annealing treatment, the saturation magnetization (Ms) of the alloy varies slightly within the range of 103-113 Am2/kg, which may be induced by the precipitation of this rod-shaped nanoprecipitate phase in the alloy. The increase in the coercivity (Hc) of annealed HEA is due to the inhomogeneous grain distribution, increased lattice misfit and high dislocation density induced by the annealing. The nanoindentation result reveals that the hardness after annealing at 873 K exhibits a 25% improvement compared with the hardness of as-cast HEA, which is mainly due to dislocation strengthening and precipitation strengthening. This research finding can provide guidance for the development of novel ferromagnetic HEAs, so as to meet the demands for materials with excellent soft magnetic properties and superior mechanical properties in the field of sustainable electrical energy.
{"title":"Influences of Annealing Treatment on Soft Magnetic Properties, Mechanical Properties and Microstructure of Fe<sub>24.94</sub>Co<sub>24.94</sub>Ni<sub>24.94</sub>Al<sub>24.94</sub>Si<sub>0.24</sub> High-Entropy Alloy.","authors":"Shiqi Zhang, Pin Jiang, Xuanbo Shi, Xiaohua Tan, Hui Xu","doi":"10.3390/e28010110","DOIUrl":"10.3390/e28010110","url":null,"abstract":"<p><p>In order to meet the ever-growing demand in modern power electronics, the advanced soft magnetic materials (SMMs) are required to exhibit both excellent soft magnetic performance and mechanical properties. In this work, the effects of an annealing treatment on the soft magnetic properties, mechanical properties and microstructure of the Fe<sub>24.94</sub>Co<sub>24.94</sub>Ni<sub>24.94</sub>Al<sub>24.94</sub>Si<sub>0.24</sub> high-entropy alloy (HEA) are investigated. The as-cast HEA consists of a body-centered cubic (BCC) matrix phase and spherical B2 nanoprecipitates with a diameter of approximately 5 nm, where a coherent relationship is established between the B2 phase and the BCC matrix. After annealing at 873 K, the alloy retains both the BCC and B2 phases, with their coherent relationship preserved; besides the spherical B2 nanoprecipitates, rod-shaped B2 nanoprecipitates are also observed. After the annealing treatment, the saturation magnetization (M<sub>s</sub>) of the alloy varies slightly within the range of 103-113 Am<sup>2</sup>/kg, which may be induced by the precipitation of this rod-shaped nanoprecipitate phase in the alloy. The increase in the coercivity (H<sub>c</sub>) of annealed HEA is due to the inhomogeneous grain distribution, increased lattice misfit and high dislocation density induced by the annealing. The nanoindentation result reveals that the hardness after annealing at 873 K exhibits a 25% improvement compared with the hardness of as-cast HEA, which is mainly due to dislocation strengthening and precipitation strengthening. This research finding can provide guidance for the development of novel ferromagnetic HEAs, so as to meet the demands for materials with excellent soft magnetic properties and superior mechanical properties in the field of sustainable electrical energy.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840540/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigated the diffusive dynamics of a Lévy walk subject to stochastic resetting through combined numerical and theoretical approaches. Under exponential resetting, the process mean squared displacement (MSD) undergoes a sharp transition from free superdiffusive behavior with exponent γ0 to a steady-state saturation regime. In contrast, power-law resetting with exponent β exhibits three asymptotic MSD regimes: free superdiffusion for β<1, superdiffusive scaling with a linearly β-decreasing exponent for 1<β<γ0+1, and localization characterized by finite steady-state plateaus for β>γ0+1. MSD scaling laws derived via renewal theory-based analysis demonstrate excellent agreement with numerical simulations. These findings offer new insights for optimizing search strategies and controlling transport processes in non-equilibrium environments.
{"title":"Lévy Diffusion Under Power-Law Stochastic Resetting.","authors":"Jianli Liu, Yunyun Li, Fabio Marchesoni","doi":"10.3390/e28010104","DOIUrl":"10.3390/e28010104","url":null,"abstract":"<p><p>We investigated the diffusive dynamics of a Lévy walk subject to stochastic resetting through combined numerical and theoretical approaches. Under exponential resetting, the process mean squared displacement (MSD) undergoes a sharp transition from free superdiffusive behavior with exponent γ0 to a steady-state saturation regime. In contrast, power-law resetting with exponent β exhibits three asymptotic MSD regimes: free superdiffusion for β<1, superdiffusive scaling with a linearly β-decreasing exponent for 1<β<γ0+1, and localization characterized by finite steady-state plateaus for β>γ0+1. MSD scaling laws derived via renewal theory-based analysis demonstrate excellent agreement with numerical simulations. These findings offer new insights for optimizing search strategies and controlling transport processes in non-equilibrium environments.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12839795/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multi-object tracking (MOT) has attracted increasing attention and achieved remarkable progress. However, accurately tracking objects with homogeneous appearance, heterogeneous motion, and heavy occlusion remains a challenge because of two problems: (1) missing association due to recognizing an object as background and (2) false prediction caused by the predominant utilization of linear motion models and the insufficient discriminability of object appearance representations. To address these challenges, this paper proposes a lightweight, generic, and appearance-independent MOT method with an unscented Kalman filter (UKF) on a Lie group called LUKF-Track. The method utilizes detection boxes across the entire range of scores in data association and matches objects across frames by employing a motion model, where the propagation and prediction of object states are formulated using a UKF on the Lie group. LUKF-Track achieves state-of-the-art results on three public benchmarks, MOT17, MOT20, and DanceTrack, which are characterized by highly nonlinear object motion and severe occlusions.
{"title":"A Multi-Object Tracking Method with an Unscented Kalman Filter on a Lie Group Manifold.","authors":"Xinyu Wang, Li Liu, Fanzhang Li","doi":"10.3390/e28010103","DOIUrl":"10.3390/e28010103","url":null,"abstract":"<p><p>Multi-object tracking (MOT) has attracted increasing attention and achieved remarkable progress. However, accurately tracking objects with homogeneous appearance, heterogeneous motion, and heavy occlusion remains a challenge because of two problems: (1) missing association due to recognizing an object as background and (2) false prediction caused by the predominant utilization of linear motion models and the insufficient discriminability of object appearance representations. To address these challenges, this paper proposes a lightweight, generic, and appearance-independent MOT method with an unscented Kalman filter (UKF) on a Lie group called LUKF-Track. The method utilizes detection boxes across the entire range of scores in data association and matches objects across frames by employing a motion model, where the propagation and prediction of object states are formulated using a UKF on the Lie group. LUKF-Track achieves state-of-the-art results on three public benchmarks, MOT17, MOT20, and DanceTrack, which are characterized by highly nonlinear object motion and severe occlusions.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12840057/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146060843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Among corrosive environments, Cl- is one of the most aggressive anions which can cause electrochemical corrosion and the resultant failures of alloys, and the increase in Cl- concentration will further deteriorate the passive film in many conventional alloys. Here, we report single-phase Nb25Mo25Ta25Ti20W5Cx (x = 0.1, 0.3, 0.8 at.%) refractory high-entropy alloys (RHEAs) with excellent corrosion resistance in high-concentration NaCl solutions. According to potentiodynamic polarization, electrochemical impedance spectroscopy, corroded morphology and the current-time results, the RHEAs demonstrate even better corrosion resistance with the increase in NaCl concentration to 23.5 wt.%, significantly superior to 304 L stainless steel. Typically, the corrosion current density (icorr) and over-passivation potential (Et) reached the lowest and highest value, respectively, in the 23.5 wt.% NaCl solution, and the icorr (2.36 × 10-7 A/cm2) of Nb25Mo25Ta25Ti20W5C0.1 alloy is nearly two orders lower than that of 304 L stainless steel (1.75 × 10-5 A/cm2). The excellent corrosion resistance results from the formation of passive films with fewer defects and more stable oxides. Moreover, with the addition of the appropriate C element, the RHEAs also demonstrated improved strength and plasticity simultaneously, for example, the Nb25Mo25Ta25Ti20W5C0.3 alloy exhibited an average yield strength of 1368 MPa and a plastic strain of 19.7%. The present findings provide useful guidance to address the conflict between the excellent corrosion resistance and high strength of advanced alloys.
{"title":"Sustainable High Corrosion Resistance in High-Concentration NaCl Solutions for Refractory High-Entropy Alloys with High Strength and Good Plasticity.","authors":"Shunhua Chen, Xinxin Liu, Chong Li, Wuji Wang, Xiaokang Yue","doi":"10.3390/e28010105","DOIUrl":"10.3390/e28010105","url":null,"abstract":"<p><p>Among corrosive environments, Cl<sup>-</sup> is one of the most aggressive anions which can cause electrochemical corrosion and the resultant failures of alloys, and the increase in Cl<sup>-</sup> concentration will further deteriorate the passive film in many conventional alloys. Here, we report single-phase Nb<sub>25</sub>Mo<sub>25</sub>Ta<sub>25</sub>Ti<sub>20</sub>W<sub>5</sub>C<i><sub>x</sub></i> (<i>x</i> = 0.1, 0.3, 0.8 at.%) refractory high-entropy alloys (RHEAs) with excellent corrosion resistance in high-concentration NaCl solutions. According to potentiodynamic polarization, electrochemical impedance spectroscopy, corroded morphology and the current-time results, the RHEAs demonstrate even better corrosion resistance with the increase in NaCl concentration to 23.5 wt.%, significantly superior to 304 L stainless steel. Typically, the corrosion current density (<i>i</i><sub>corr</sub>) and over-passivation potential (<i>E</i><sub>t</sub>) reached the lowest and highest value, respectively, in the 23.5 wt.% NaCl solution, and the <i>i</i><sub>corr</sub> (2.36 × 10<sup>-7</sup> A/cm<sup>2</sup>) of Nb<sub>25</sub>Mo<sub>25</sub>Ta<sub>25</sub>Ti<sub>20</sub>W<sub>5</sub>C<sub>0.1</sub> alloy is nearly two orders lower than that of 304 L stainless steel (1.75 × 10<sup>-5</sup> A/cm<sup>2</sup>). The excellent corrosion resistance results from the formation of passive films with fewer defects and more stable oxides. Moreover, with the addition of the appropriate C element, the RHEAs also demonstrated improved strength and plasticity simultaneously, for example, the Nb<sub>25</sub>Mo<sub>25</sub>Ta<sub>25</sub>Ti<sub>20</sub>W<sub>5</sub>C<sub>0.3</sub> alloy exhibited an average yield strength of 1368 MPa and a plastic strain of 19.7%. The present findings provide useful guidance to address the conflict between the excellent corrosion resistance and high strength of advanced alloys.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12839976/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146060959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xuwei Tan, Tian Xie, Xue Zheng, Aylin Yener, Myungjin Lee, Ali Payani, Hugo Latapie, Xueru Zhang
Federated learning (FL) is a distributed learning paradigm that facilitates training a global machine-learning model without collecting the raw data from distributed clients. Recent advances in FL have addressed several considerations that are likely to transpire in realistic settings, such as data distribution heterogeneity among clients. However, most of the existing works still consider clients' data distributions to be static or conforming to a simple dynamic, e.g., in participation rates of clients. In real FL applications, client data distributions change over time, and the dynamics, i.e., the evolving pattern, can be highly non-trivial. Furthermore, evolution may take place from training to testing. In this paper, we address dynamics in client data distributions and aim to train FL systems from time-evolving clients that can generalize to future target data. Specifically, we propose two algorithms, FedEvolve and FedEvp, which are able to capture the evolving patterns of the clients during training and are test-robust under evolving distribution shifts. FedEvolve explicitly models the temporal evolution by learning two distinct representation mappings that capture the transition between consecutive data domains for each client. In addition, FedEvp learns a single, evolving-domain-invariant representation by aligning current data with prototypes that are continuously updated from all previously seen domains. Through extensive experiments on both synthetic and real data, we show the proposed algorithms can significantly outperform the FL baselines across various network architectures.
{"title":"Federated Learning Under Evolving Distribution Shifts.","authors":"Xuwei Tan, Tian Xie, Xue Zheng, Aylin Yener, Myungjin Lee, Ali Payani, Hugo Latapie, Xueru Zhang","doi":"10.3390/e28010101","DOIUrl":"10.3390/e28010101","url":null,"abstract":"<p><p>Federated learning (FL) is a distributed learning paradigm that facilitates training a global machine-learning model without collecting the raw data from distributed clients. Recent advances in FL have addressed several considerations that are likely to transpire in realistic settings, such as data distribution heterogeneity among clients. However, most of the existing works still consider clients' data distributions to be static or conforming to a simple dynamic, e.g., in participation rates of clients. In real FL applications, client data distributions change over time, and the dynamics, i.e., the evolving pattern, can be highly non-trivial. Furthermore, evolution may take place from training to testing. In this paper, we address dynamics in client data distributions and aim to train FL systems from time-evolving clients that can generalize to future target data. Specifically, we propose two algorithms, <i>FedEvolve</i> and <i>FedEvp</i>, which are able to capture the evolving patterns of the clients during training and are test-robust under evolving distribution shifts. FedEvolve explicitly models the temporal evolution by learning two distinct representation mappings that capture the transition between consecutive data domains for each client. In addition, FedEvp learns a single, evolving-domain-invariant representation by aligning current data with prototypes that are continuously updated from all previously seen domains. Through extensive experiments on both synthetic and real data, we show the proposed algorithms can significantly outperform the FL baselines across various network architectures.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"28 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12839774/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146061127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}