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30 pages, 7246 KiB  
Article
Linear Dependence of Sublimation Enthalpy on Young’s Elastic Modulus: Implications for Thermodynamics of Solids
by Anne M. Hofmeister
Materials 2025, 18(15), 3535; https://doi.org/10.3390/ma18153535 - 28 Jul 2025
Viewed by 289
Abstract
Classical thermodynamics omits rigidity, which property distinguishes solids from gases and liquids. By accounting for rigidity (i.e., Young’s elastic modulus, ϒ), we recently amended historical formulae and moreover linked heat capacity, thermal expansivity, and ϒ. Further exploration is motivation by the importance of [...] Read more.
Classical thermodynamics omits rigidity, which property distinguishes solids from gases and liquids. By accounting for rigidity (i.e., Young’s elastic modulus, ϒ), we recently amended historical formulae and moreover linked heat capacity, thermal expansivity, and ϒ. Further exploration is motivation by the importance of classical thermodynamics to various applied sciences. Based on heat performing work, we show here, theoretically, that density times sublimation enthalpy divided by the molar mass (ρΔHsub/M, energy per volume), depends linearly on ϒ (1 GPa = 109 J m−3). Data on diverse metals, non-metallic elements, chalcogenides, simple oxides, alkali halides, and fluorides with cubic structures validate this relationship at ambient conditions. Furthermore, data on hcp metals and molecular solids show that ρΔHsub/M is proportional to ϒ for anisotropic materials. Proportionality constants vary only from 0.1 to 0.7 among these different material types (>100 substances), which shows that the elastic energy reservoir of solids is large. Proportionality constants depend on whether molecules or atoms are sublimated and are somewhat affected by structure. We show that ductility of refractory, high-ϒ metals affect high-temperature determinations of their ΔHsub. Our results provide information on sublimation processes and subsequent gas phase reactions, while showing that elasticity of solids is the key parameter needed to assessing their energetics. Implications are highlighted. Full article
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24 pages, 2152 KiB  
Review
A Concise Overview of the Use of Low-Dimensional Molybdenum Disulfide as an Electrode Material for Li-Ion Batteries and Beyond
by Mattia Bartoli, Meltem Babayiğit Cinali, Özlem Duyar Coşkun, Silvia Porporato, Diego Pugliese, Erik Piatti, Francesco Geobaldo, Giuseppe A. Elia, Claudio Gerbaldi, Giuseppina Meligrana and Alessandro Piovano
Batteries 2025, 11(7), 269; https://doi.org/10.3390/batteries11070269 - 16 Jul 2025
Viewed by 438
Abstract
The urgent demand for sustainable energy solutions in the face of climate change and resource depletion has catalyzed a global shift toward cleaner energy production and more efficient storage technologies. Lithium-ion batteries (LIBs), as the cornerstone of modern portable electronics, electric vehicles, and [...] Read more.
The urgent demand for sustainable energy solutions in the face of climate change and resource depletion has catalyzed a global shift toward cleaner energy production and more efficient storage technologies. Lithium-ion batteries (LIBs), as the cornerstone of modern portable electronics, electric vehicles, and grid-scale storage systems, are continually evolving to meet the growing performance requirements. In this dynamic context, two-dimensional (2D) materials have emerged as highly promising candidates for use in electrodes due to their layered structure, tunable electronic properties, and high theoretical capacity. Among 2D materials, molybdenum disulfide (MoS2) has gained increasing attention as a promising low-dimensional candidate for LIB anode applications. This review provides a comprehensive yet concise overview of recent advances in the application of MoS2 in LIB electrodes, with particular attention to its unique electrochemical behavior at the nanoscale. We critically examine the interplay between structural features, charge-storage mechanisms, and performance metrics—chiefly the specific capacity, rate capability, and cycling stability. Furthermore, we discuss current challenges, primarily poor intrinsic conductivity and volume fluctuations, and highlight innovative strategies aimed at overcoming these limitations, such as through nanostructuring, composite formation, and surface engineering. By shedding light on the opportunities and hurdles in this rapidly progressing field, this work offers a forward-looking perspective on the role of MoS2 in the next generation of high-performance LIBs. Full article
(This article belongs to the Section Battery Mechanisms and Fundamental Electrochemistry Aspects)
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26 pages, 2868 KiB  
Article
Resonant Oscillations of Ion-Stabilized Nanobubbles in Water as a Possible Source of Electromagnetic Radiation in the Gigahertz Range
by Nikolai F. Bunkin, Yulia V. Novakovskaya, Rostislav Y. Gerasimov, Barry W. Ninham, Sergey A. Tarasov, Natalia N. Rodionova and German O. Stepanov
Int. J. Mol. Sci. 2025, 26(14), 6811; https://doi.org/10.3390/ijms26146811 - 16 Jul 2025
Viewed by 211
Abstract
It is well known that aqueous solutions can emit electromagnetic waves in the radio frequency range. However, the physical nature of this process is not yet fully understood. In this work, the possible role of gas nanobubbles formed in the bulk liquid is [...] Read more.
It is well known that aqueous solutions can emit electromagnetic waves in the radio frequency range. However, the physical nature of this process is not yet fully understood. In this work, the possible role of gas nanobubbles formed in the bulk liquid is considered. We develop a theoretical model based on the concept of gas bubbles stabilized by ions, or “bubstons”. The role of bicarbonate and hydronium ions in the formation and stabilization of bubstons is explained through the use of quantum chemical simulations. A new model of oscillating bubstons, which takes into account the double electric layer formed around their gas core, is proposed. Theoretical estimates of the frequencies and intensities of oscillations of such compound species are obtained. It was determined that oscillations of negatively charged bubstons can occur in the GHz frequency range, and should be accompanied by the emission of electromagnetic waves. To validate the theoretical assumptions, we used dynamic light scattering (DLS) and showed that, after subjecting aqueous solutions to vigorous shaking with a force of 4 or 8 N (kg·m/s2) and a frequency of 4–5 Hz, the volume number density of bubstons increased by about two orders of magnitude. Radiometric measurements in the frequency range of 50 MHz to 3.5 GHz revealed an increase in the intensity of radiation emitted by water samples upon the vibrational treatment. It is argued that, according to our new theoretical model, this radiation can be caused by oscillating bubstons. Full article
(This article belongs to the Section Physical Chemistry and Chemical Physics)
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25 pages, 5935 KiB  
Article
Point-Kernel Code Development for Gamma-Ray Shielding Applications
by Mario Matijević, Krešimir Trontl, Siniša Šadek and Paulina Družijanić
Appl. Sci. 2025, 15(14), 7795; https://doi.org/10.3390/app15147795 - 11 Jul 2025
Viewed by 220
Abstract
The point-kernel (PK) technique has a long history in applied radiation shielding, originating from the early days of digital computers. The PK technique applied to gamma-ray attenuation is one of many successful applications, based on the linear superposition principle applied to distributed radiation [...] Read more.
The point-kernel (PK) technique has a long history in applied radiation shielding, originating from the early days of digital computers. The PK technique applied to gamma-ray attenuation is one of many successful applications, based on the linear superposition principle applied to distributed radiation sources. Mathematically speaking, the distributed source will produce a detector response equivalent to the numerical integration of the radiation received from an equivalent number of point sources. In this treatment, there is no interference between individual point sources, while inherent limitations of the PK method are its inability to simulate gamma scattering in shields and the usage of simple boundary conditions. The PK method generally works for gamma-ray shielding with corrective B-factor for scattering and only specifically for fast neutron attenuation in a hydrogenous medium with the definition of cross section removal. This paper presents theoretical and programming aspects of the PK program developed for a distributed source of photons (line, disc, plane, sphere, slab volume, etc.) and slab shields. The derived flux solutions go beyond classical textbooks as they include the analytical integration of Taylor B-factor, obtaining a closed form readily suitable for programming. The specific computational modules are unified with a graphical user interface (GUI), assisting users with input/output data and visualization, developed for the fast radiological characterization of simple shielding problems. Numerical results of the selected PK test cases are presented and verified with the CADIS hybrid shielding methodology of the MAVRIC/SCALE6.1.3 code package from the ORNL. Full article
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19 pages, 1252 KiB  
Article
Analogy Analysis of Height Exergy and Temperature Exergy in Energy Storage System
by Yan Cui, Tong Jiang and Mulin Liu
Energies 2025, 18(14), 3675; https://doi.org/10.3390/en18143675 - 11 Jul 2025
Viewed by 242
Abstract
As a pivotal technology and infrastructure component for modern power systems, energy storage has experienced significant advancement in recent years. A fundamental prerequisite for designing future energy storage facilities lies in the systematic evaluation of energy conversion capabilities across diverse storage technologies. This [...] Read more.
As a pivotal technology and infrastructure component for modern power systems, energy storage has experienced significant advancement in recent years. A fundamental prerequisite for designing future energy storage facilities lies in the systematic evaluation of energy conversion capabilities across diverse storage technologies. This study conducted a comparative analysis between pumped hydroelectric storage (PHS) and compressed air energy storage (CAES), defining the concepts of height exergy and temperature exergy. Height exergy is the maximum work capacity of a liquid due to height differences, while temperature exergy is the maximum work capacity of a gas due to temperature differences. The temperature exergy represents innovation in thermodynamic analysis; it is derived from internal exergy and proven through the Maxwell relation and the decoupling method of internal exergy, offering a more efficient method for calculating energy storage capacity in CAES systems. Mathematical models of height exergy and temperature exergy were established based on their respective forms. A unified calculation formula was derived, and their respective characteristics were analyzed. In order to show the meaning of temperature exergy more clearly and intuitively, a height exergy model of temperature exergy was established through analogy analysis, and it was concluded that the shape of the reservoir was a cone when comparing water volume to heat quantity, intuitively showing that the cold source had a higher energy storage density than the heat source. Finally, a typical hybrid PHS–CAES system was proposed, and a mathematical model was established and verified in specific cases based on height exergy and temperature exergy. It was demonstrated that when the polytropic exponent n = 1.2, the theoretical loss accounted for the largest proportion, which was 2.06%. Full article
(This article belongs to the Section D: Energy Storage and Application)
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21 pages, 3369 KiB  
Article
Thermal Runaway Critical Threshold and Gas Release Safety Boundary of 18,650 Lithium-Ion Battery in State of Charge
by Jingyu Zhao, Kexin Xing, Xinrong Jiang, Chi-Min Shu and Xiangrong Sun
Processes 2025, 13(7), 2175; https://doi.org/10.3390/pr13072175 - 8 Jul 2025
Viewed by 657
Abstract
In this study, we systematically investigated the characteristic parameter evolution laws of thermal runaway with respect to 18,650 lithium-ion batteries (LIBs) under thermal abuse conditions at five state-of-charge (SOC) levels: 0%, 25%, 50%, 75%, and 100%. In our experiments, we combined infrared thermography, [...] Read more.
In this study, we systematically investigated the characteristic parameter evolution laws of thermal runaway with respect to 18,650 lithium-ion batteries (LIBs) under thermal abuse conditions at five state-of-charge (SOC) levels: 0%, 25%, 50%, 75%, and 100%. In our experiments, we combined infrared thermography, mass loss analysis, temperature monitoring, and gas composition detection to reveal the mechanisms by which SOC affects the trigger time, critical temperature, maximum temperature, mass loss, and gas release characteristics of thermal runaway. The results showed that as the SOC increases, the critical and maximum temperatures of thermal runaway increase notably. At a 100% SOC, the highest temperature on the positive electrode side reached 1082.1 °C, and the mass loss increased from 6.90 g at 0% SOC to 25.75 g at 100% SOC, demonstrating a salient positive correlation. Gas analysis indicated that under high-SOC conditions (75% and 100%), the proportion of flammable gases such as CO and CH4 produced during thermal runaway significantly increases, with the CO/CO2 ratio exceeding 1, indicating intensified incomplete combustion and a significant increase in fire risk. In addition, flammability limit analysis revealed that the lower explosive limit for gases is lower (17–21%) at a low SOC (0%) and a high SOC (100%), indicating greater explosion risks. We also found that the composition of gases released during thermal runaway varies substantially at different SOC levels, with CO, CO2, and CH4 accounting for over 90% of the total gas volume, while toxic gases, such as HF, although present in smaller proportions, pose noteworthy hazards. Unlike prior studies that relied on post hoc analysis, this work integrates real-time multi-parameter monitoring (temperature, gas composition, and mass loss) and quantitative explosion risk modeling (flammability limits via the L-C formula). This approach reveals the unique dynamic SOC-dependent mechanisms of thermal runaway initiation and gas hazards. This study provides theoretical support for the source tracing of thermal runaway fires and the development of preventive LIB safety technology and emphasizes the critical influence of the charge state on the thermal safety of batteries. Full article
(This article belongs to the Special Issue Machine Learning Optimization of Chemical Processes)
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20 pages, 20541 KiB  
Article
Influence of Stent Structure on Mechanical and Degradation Properties of Poly (Lactic Acid) Vascular Stent
by Shicheng He, Qiang Chen and Zhiyong Li
J. Funct. Biomater. 2025, 16(7), 248; https://doi.org/10.3390/jfb16070248 - 6 Jul 2025
Viewed by 615
Abstract
Biodegradable vascular stents (BVSs) face challenges related to inadequate mechanical strength, which can lead to adverse clinical outcomes. Improving the mechanical behavior of biodegradable vascular stents through structural design has been extensively explored. However, the corresponding effects of these mechanical enhancements on degradation [...] Read more.
Biodegradable vascular stents (BVSs) face challenges related to inadequate mechanical strength, which can lead to adverse clinical outcomes. Improving the mechanical behavior of biodegradable vascular stents through structural design has been extensively explored. However, the corresponding effects of these mechanical enhancements on degradation characteristics remain under-investigated. The present work focuses on examining how different stent design strategies affect the mechanical behavior and degradation characteristics of poly (lactic acid) (PLA) stents. The commercial PLA stent DESolve was adopted, and nine modified stents were constructed based on the geometrical configuration of the DESolve stent. The mechanical properties of the modified stents during radial crimping and three-point bending simulations were thoroughly studied. The degradation dynamics of the stents were characterized by four indices (i.e., mean number average molecular weight, residual volume fraction, mean von Mises stress, and stent diameter). The results indicated that both the widening ratio and direction affected the mechanical performance of the stents by increasing the radial stiffness and radial strength, minimizing recoil%, and decreasing the bending flexibility. Although the widening direction had a relatively minor influence on stent degradation, the associated increase in material volume contributed to an improved volumetric integrity and enhanced lumen preservation. This study established a theoretical basis for evaluating both the mechanical and degradation behaviors of PLA stents, offering valuable insights for future structural design optimization. Full article
(This article belongs to the Special Issue Bio-Additive Manufacturing in Materials Science)
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15 pages, 5152 KiB  
Article
Hydraulic Performance and Flow Characteristics of a High-Speed Centrifugal Pump Based on Multi-Objective Optimization
by Yifu Hou and Rong Xue
Fluids 2025, 10(7), 174; https://doi.org/10.3390/fluids10070174 - 2 Jul 2025
Viewed by 278
Abstract
Pump-driven liquid cooling systems are widely utilized in unmanned aerial vehicle (UAV) electronic thermal management. As a critical power component, the miniaturization and lightweight design of the pump are essential. Increasing the operating speed of the pump allows for a reduction in impeller [...] Read more.
Pump-driven liquid cooling systems are widely utilized in unmanned aerial vehicle (UAV) electronic thermal management. As a critical power component, the miniaturization and lightweight design of the pump are essential. Increasing the operating speed of the pump allows for a reduction in impeller size while maintaining hydraulic performance, thereby significantly decreasing the overall volume and mass. However, high-speed operation introduces considerable internal flow losses, placing stricter demands on the geometric design and flow-field compatibility of the impeller. In this study, a miniature high-speed centrifugal pump (MHCP) was investigated, and a multi-objective optimization of the impeller was carried out using response surface methodology (RSM) to improve internal flow characteristics and overall hydraulic performance. Numerical simulations demonstrated strong predictive capability, and experimental results validated the model’s accuracy. At the design condition (10,000 rpm, 4.8 m3/h), the pump achieved a head of 46.1 m and an efficiency of 49.7%, corresponding to its best efficiency point (BEP). Sensitivity analysis revealed that impeller outlet diameter and blade outlet angle were the most influential parameters affecting pump performance. Following the optimization, the pump head increased by 3.7 m, and the hydraulic efficiency improved by 4.8%. In addition, the pressure distribution and streamlines within the impeller exhibited better uniformity, while the turbulent kinetic energy near the blade suction surface and at the impeller outlet was markedly decreased. This work provides theoretical support and design guidance for the efficient application of MHCPs in UAV thermal management systems. Full article
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20 pages, 3746 KiB  
Article
Agricultural Electrostatic Spraying Electrode Corrosion Degradation Mechanisms: A Multi-Parameter Coupling Model
by Yufei Li, Anni Zou, Jun Hu, Changxi Liu, Shengxue Zhao, Qingda Li, Wei Zhang and Yafei Wang
Agriculture 2025, 15(13), 1348; https://doi.org/10.3390/agriculture15131348 - 23 Jun 2025
Viewed by 463
Abstract
As an innovative plant protection method in precision agriculture, electrostatic spray technology can increase the droplet coverage area by over 30% coMpared to conventional spraying. This technology not only achieves higher droplet deposition density and coverage but also enables water and pesticide savings [...] Read more.
As an innovative plant protection method in precision agriculture, electrostatic spray technology can increase the droplet coverage area by over 30% coMpared to conventional spraying. This technology not only achieves higher droplet deposition density and coverage but also enables water and pesticide savings while reducing environmental pollution. This study, combining theoretical analysis with experimental validation, reveals the critical role of electrode material selection in induction-based electrostatic spray systems. Theoretical analysis indicates that the Fermi level and work function of electrode materials fundamentally determine charge transfer efficiency, while corrosion resistance emerges as a key parameter affecting system durability. To elucidate the effects of different electrode materials on droplet charging, a coMparative study was conducted on nickel, copper, and brass electrodes in both pristine and moderately corroded states based on the corrosion classification standard, using a targeted mesh-based charge-to-mass measurement device. The results demonstrated that the nickel electrode achieved a peak charge-to-mass ratio of 1.92 mC/kg at 10 kV, which was 8.5% and 11.6% higher than copper (1.77 mC/kg) and brass (1.72 mC/kg), respectively. After corrosion, nickel exhibited the smallest reduction in the charge-to-mass ratio (19.2%), significantly outperforming copper (40.2%) and brass (21.6%). Droplet size analysis using a Malvern Panalytical Spraytec spray particle analyzer (measurement range: 0.1–2000 µm) further confirmed the atomization advantages of nickel electrodes. The volume median diameter (Dv50) of droplets produced by nickel was 4.2–8 μm and 6.8–12.3 um smaller than those from copper and brass electrodes, respectively. After corrosion, nickel showed a smaller increase in droplet size spectrum inhomogeneity (24.5%), which was lower than copper (30.4%) and brass (25.8%), indicating superior droplet uniformity. By establishing a multi-factor predictive model for spray droplet size after electrode corrosion, this study quantifies the correlation between electrode characteristics and spray performance metrics. It provides a theoretical basis for designing weather-resistant electrostatic spray systems suitable for agricultural pesticide application scenarios involving prolonged exposure to corrosive chemicals. This work offers significant technical support for sustainable crop protection strategies. Full article
(This article belongs to the Section Agricultural Technology)
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16 pages, 1557 KiB  
Technical Note
Growth of a Single Bubble Due to Super-Saturation: Comparison of Correlation-Based Modelling with CFD Simulation
by Johannes Manthey, Wei Ding, Hossein Mehdipour, Montadhar Guesmi, Simon Unz, Uwe Hampel and Michael Beckmann
ChemEngineering 2025, 9(3), 63; https://doi.org/10.3390/chemengineering9030063 - 17 Jun 2025
Viewed by 404
Abstract
This paper investigates and assesses the potential applicability of global mass transfer coefficients derived from large-scale experiments to the bubble growth of a single bubble in a super-saturated flow (σ=9). Therefore, it presents, for a specific flow velocity [...] Read more.
This paper investigates and assesses the potential applicability of global mass transfer coefficients derived from large-scale experiments to the bubble growth of a single bubble in a super-saturated flow (σ=9). Therefore, it presents, for a specific flow velocity (u=1ms, Re=10,678), a comparison between correlation-based modelling and 3D Large Eddy Simulation–Volume of Fluid (LES-VOF) Computational Fluid Dynamics (CFD) simulations (minimum cell size of 10 µm, Δt = 10 µs). After the verification of the CFD with pool nucleation bubbles, two cases are regarded: (1) the bubble flowing in the bulk and (2) a bubble on a wall with a crossflow. The correlation-based modelling results in a nearly linear relationship between bubble radius and time; meanwhile, theoretically, the self-similarity rule offers r~Bt0.5. The Avdeev correlation gives the best agreement with the CFD simulation for a bubble in the flow bulk (case 1), while the laminar approach for calculation of the exposure time of the penetration theory shows good agreement with the CFD simulation for the bubble growth at the wall (case 2). This preliminary study provides the first quantitative validation of global mass transfer coefficient correlations at the single-bubble scale, suggesting that computationally intensive CFD simulations may be omitted for rapid estimations. Future work will extend the analysis to a wider range of flow velocities and bubble diameters to further validate these findings. Full article
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16 pages, 1508 KiB  
Review
Current Trends in Facelift and Necklift Procedures
by Carter J. Boyd and Daniel J. Ceradini
J. Clin. Med. 2025, 14(12), 4273; https://doi.org/10.3390/jcm14124273 - 16 Jun 2025
Viewed by 938
Abstract
Many surgical and nonsurgical options are available to patients seeking facial rejuvenation. In this review, we aim to provide an overview of the current trends in facelift and necklift procedures while simultaneously highlighting the utility of nonsurgical treatments. A comprehensive literature review was [...] Read more.
Many surgical and nonsurgical options are available to patients seeking facial rejuvenation. In this review, we aim to provide an overview of the current trends in facelift and necklift procedures while simultaneously highlighting the utility of nonsurgical treatments. A comprehensive literature review was performed using the PubMed, Google Scholar, and Cochrane Library databases, with the objective of including recent literature published on facelift and necklift procedures from 2015 to 2025. Articles were selected based on relevance, with a specific focus on including a wide breadth of techniques. A considerable body of literature has been published to further classify the soft-tissue anatomy of the face and neck. In particular, these studies focus on the characterization of the three-dimensional anatomy of the facial nerve with emphasis on safe planes of dissection to avoid inadvertent facial nerve injury. The current literature continues to debate both the theoretical and practical advantages and disadvantages of various facelift techniques. Broadly speaking, facelift techniques can be divided into those that manipulate the superficial musculoaponeurotic system (SMAS) layer on its superficial surface and those that undermine the SMAS to varying extents. Numerous approaches are available to improve the contour of the neck and jawline, including manipulation of the platysma muscle and subplatysmal volume reduction. Other surgical procedures and nonsurgical treatments should be considered to optimize and enhance facelift and necklift results. Advancements in patient safety include a focus on minimizing complications while reducing the length of recovery. Facelift and necklift procedures remain the foundational pillars for facial rejuvenation. With attention to patient-specific anatomy, surgeons can work collaboratively with patients to provide global facial optimization by choosing appropriate facelift and necklift techniques in combination with other ancillary procedures. Doing so will deliver enduring, elegant results. Full article
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14 pages, 6740 KiB  
Article
High-Entropy Sulfide Nanoarchitectures with Triple-Shelled Hollow Design for Durable Sodium–Ion Batteries
by Mingyang Chen, Yan Liu, Zhenchun Fang, Yinan Wang, Shaonan Gu and Guowei Zhou
Nanomaterials 2025, 15(12), 881; https://doi.org/10.3390/nano15120881 - 7 Jun 2025
Viewed by 520
Abstract
Metal sulfides are promising anode candidates for sodium–ion batteries (SIBs) due to their high theoretical capacities. However, their practical application is limited by significant volume extension and sluggish Na+ diffusion during cycling, which lead to rapid capacity degradation and poor long-term stability. [...] Read more.
Metal sulfides are promising anode candidates for sodium–ion batteries (SIBs) due to their high theoretical capacities. However, their practical application is limited by significant volume extension and sluggish Na+ diffusion during cycling, which lead to rapid capacity degradation and poor long-term stability. In this work, we report the rational design of a hollow triple-shelled high-entropy sulfide (NaFeZnCoNiMn)9S8, synthesized through sequential templating method under hydrothermal conditions. Transmission electron microscopy confirms its well-defined three-shelled architecture. The inter-shell voids effectively buffer Na+ insertion/desertion-induced volume extension, while the tailored high-entropy matrix enhances electronic conductivity and accelerates Na+ transport. This synergistic design yields outstanding performance, including a high initial Coulombic efficiency (ICE) of 94.1% at 0.1 A g−1, low charge-transfer resistance (0.32~2.54 Ω), fast Na+ diffusion efficiency (10−8.5–10−10.5 cm2 s−1), and reversible capacity of 582.6 mAh g−1 after 1600 cycles at 1 A g−1 with 91.2% capacity retention. These results demonstrate the potential of high-entropy, multi-shelled architectures as a robust platform for next-generation durable SIB anodes. Full article
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20 pages, 645 KiB  
Article
Variable Dose-Constraints Method Based on Multiplicative Dynamical Systems for High-Precision Intensity-Modulated Radiation Therapy Planning
by Omar M. Abou Al-Ola, Takeshi Kojima, Ryosei Nakada, Norihisa Obata, Kohei Hayashi and Tetsuya Yoshinaga
Mathematics 2025, 13(11), 1852; https://doi.org/10.3390/math13111852 - 2 Jun 2025
Viewed by 354
Abstract
An optimization framework that effectively balances dose–volume constraints and treatment objectives is required in intensity-modulated radiation therapy (IMRT) planning. In our previous work, we proposed a dynamical systems-based approach in which dose constraints, along with beam coefficients, are treated as state variables and [...] Read more.
An optimization framework that effectively balances dose–volume constraints and treatment objectives is required in intensity-modulated radiation therapy (IMRT) planning. In our previous work, we proposed a dynamical systems-based approach in which dose constraints, along with beam coefficients, are treated as state variables and dynamically evolve within a continuous-time system. This method improved the accuracy of the solution by dynamically adjusting the dose constraints, but it had a significant drawback. Specifically, because it is as an iterative process derived from discretization of a linear differential equation system using the additive Euler method, a lower-bound clipping procedure is required to prevent the state variables for both beam coefficients and dose constraints from taking negative values. This issue could prevent constrained optimization from functioning properly and undermine the feasibility of the treatment plan. To address this problem, we propose two types of multiplicative continuous-time dynamical system that inherently preserve the nonnegativity of the state variables. We theoretically prove that the initial value problem for these systems converges to a solution that satisfies the constraints of consistent IMRT planning. Furthermore, to ensure computational practicality, we derive discretized iterative schemes from the continuous-time systems and confirm that their iterations maintain nonnegativity. This framework eliminates the need for artificial clipping procedures and leads to the multiplicative variable dose-constraints method, which dynamically adjusts dose constraints during the optimization process. Finally, numerical experiments are conducted to support and illustrate the theoretical results, showing how the proposed method achieves high-precision IMRT planning while ensuring physically meaningful solutions. Full article
(This article belongs to the Special Issue Research on Dynamical Systems and Differential Equations)
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13 pages, 441 KiB  
Article
Some New and Sharp Inequalities of Composite Simpson’s Formula for Differentiable Functions with Applications
by Wei Liu, Yu Wang, Ifra Bashir Sial and Loredana Ciurdariu
Mathematics 2025, 13(11), 1814; https://doi.org/10.3390/math13111814 - 29 May 2025
Viewed by 340
Abstract
Composite integral formulas offer greater accuracy by dividing the interval into smaller subintervals, which better capture the local behavior of function. In the finite volume method for solving differential equations, composite formulas are mostly used on control volumes to achieve high-accuracy solutions. In [...] Read more.
Composite integral formulas offer greater accuracy by dividing the interval into smaller subintervals, which better capture the local behavior of function. In the finite volume method for solving differential equations, composite formulas are mostly used on control volumes to achieve high-accuracy solutions. In this work, error estimates of the composite Simpson’s formula for differentiable convex functions are established. These error estimates can be applied to general subdivisions of the integration interval, provided the integrand satisfies a first-order differentiability condition. To this end, a novel and general integral identity for differentiable functions is established by considering general subdivisions of the integration interval. The new integral identity is proved in a manner that allows it to be transformed into different identities for different subdivisions of the integration interval. Then, under the convexity assumption on the integrand, sharp error bounds for the composite Simpson’s formula are proved. Moreover, the well-known Hölder’s inequality is applied to obtain sharper error bounds for differentiable convex functions, which represents a significant finding of this study. Finally, to support the theoretical part of this work, some numerical examples are tested and demonstrate the efficiency of the new bounds for different partitions of the integration interval. Full article
(This article belongs to the Section C1: Difference and Differential Equations)
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13 pages, 3626 KiB  
Article
Lithiophilic Modification of Self-Supporting Carbon-Based Hosts and Lithium Metal Plating/Stripping Behaviors
by Zipeng Jiang, Shoudong Xie, Guijun Yang, Huiyuan Chen, Jiahang Lv, Ang Li, Chengwei Fan and Huaihe Song
Nanomaterials 2025, 15(10), 746; https://doi.org/10.3390/nano15100746 - 15 May 2025
Viewed by 406
Abstract
Metallic lithium anodes possess the lowest redox potential (−3.04 V vs. SHE) and an ultra-high theoretical capacity (3860 mAh g−1, 2061 mAh cm−3). However, during electrochemical cycling, lithium metal tends to plate unevenly, leading to the formation of lithium [...] Read more.
Metallic lithium anodes possess the lowest redox potential (−3.04 V vs. SHE) and an ultra-high theoretical capacity (3860 mAh g−1, 2061 mAh cm−3). However, during electrochemical cycling, lithium metal tends to plate unevenly, leading to the formation of lithium dendrites. Moreover, severe electrochemical corrosion occurs at the interface between metallic lithium and traditional copper foil current collectors. To address these issues, we selected corrosion-resistant carbon paper as a lithium metal host and modified a uniform distribution of silver nanoparticles and a F-doped amorphous carbon structure as a highly lithiophilic F-CP@Ag host to enhance lithium-ion transport kinetics and achieve improved affinity with lithium metal. The silver nanoparticles reduced the lithium nucleation energy barrier, while F doping resulted in a LiF-rich solid electrolyte interphase that better accommodated volume changes in lithium metal. These two strategies worked together to ensure uniform and stable lithium metal plating/stripping on the F-CP@Ag host. Consequently, under the conditions of 1 mA cm−2 and 1 mAh cm−2, the symmetric cell exhibited stable cycling with a polarization voltage of 8 mV for up to 1400 h. This work highlights the corrosion problem of lithium metal on traditional copper foil current collectors and provides guidance for the long-term cycling stability of lithium metal anodes. Full article
(This article belongs to the Section Energy and Catalysis)
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