Search Results (85)

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

Background/Objectives: This research presents a novel analytical method for breast tumor characterization and tissue classification by leveraging intravoxel incoherent motion diffusion-weighted imaging (IVIM-DWI) combined with hyperspectral imaging techniques and deep learning. Traditionally, dynamic contrast-enhanced MRI (DCE-MRI) is employed for breast tumor diagnosis, but it involves gadolinium-based contrast agents, which carry potential health risks. IVIM imaging extends conventional diffusion-weighted imaging (DWI) by explicitly separating the signal decay into components representing true molecular diffusion ($D$) and microcirculation of capillary blood (pseudo-diffusion or $D*$). This separation allows for a more comprehensive, non-invasive assessment of tissue characteristics without the need for contrast agents, thereby offering a safer alternative for breast cancer diagnosis. The primary purpose of this study was to evaluate different methods for breast tumor characterization using IVIM-DWI data treated as hyperspectral image stacks. Dice similarity coefficients and Jaccard indices were specifically used to evaluate the spatial segmentation accuracy of tumor boundaries, confirmed by experienced physicians on dynamic contrast-enhanced MRI (DCE-MRI), emphasizing detailed tumor characterization rather than binary diagnosis of cancer. Methods: The data source for this study consisted of breast MRI scans obtained from 22 patients diagnosed with mass-type breast cancer, resulting in 22 distinct mass tumor cases analyzed. MR images were acquired using a 3T MRI system (Discovery MR750 3.0 Tesla, GE Healthcare, Chicago, IL, USA) with axial IVIM sequences and a bipolar pulsed gradient spin echo sequence. Multiple b-values ranging from 0 to 2500 s/mm² were utilized, specifically thirteen original b-values (0, 15, 30, 45, 60, 100, 200, 400, 600, 1000, 1500, 2000, and 2500 s/mm²), with the last four b-value images replicated once for a total of 17 bands used in the analysis. The methodology involved several steps: acquisition of multi-b-value IVIM-DWI images, image pre-processing, including correction for motion and intensity inhomogeneity, treating the multi-b-value data as hyperspectral image stacks, applying hyperspectral techniques like band expansion, and evaluating three tumor detection methods: kernel-based constrained energy minimization (KCEM), iterative KCEM (I-KCEM), and deep neural networks (DNNs). The comparisons were assessed by evaluating the similarity of the detection results from each method to ground truth tumor areas, which were manually drawn on DCE-MRI images and confirmed by experienced physicians. Similarity was quantitatively measured using the Dice similarity coefficient and the Jaccard index. Additionally, the performance of the detectors was evaluated using 3D-ROC analysis and its derived criteria (AUC_OD, AUC_TD, AUC_BS, AUC_TD−BS, AUC_ODP, AUC_SNPR). Results: The findings objectively demonstrated that the DNN method achieved superior performance in breast tumor detection compared to KCEM and I-KCEM. Specifically, the DNN yielded a Dice similarity coefficient of 86.56% and a Jaccard index of 76.30%, whereas KCEM achieved 78.49% (Dice) and 64.60% (Jaccard), and I-KCEM achieved 78.55% (Dice) and 61.37% (Jaccard). Evaluation using 3D-ROC analysis also indicated that the DNN was the best detector based on metrics like target detection rate and overall effectiveness. The DNN model further exhibited the capability to identify tumor heterogeneity, differentiating high- and low-cellularity regions. Quantitative parameters, including apparent diffusion coefficient ($ADC$), pure diffusion coefficient ($D$), pseudo-diffusion coefficient ($D*$), and perfusion fraction ($PF$), were calculated and analyzed, providing insights into the diffusion characteristics of different breast tissues. Analysis of signal intensity decay curves generated from these parameters further illustrated distinct diffusion patterns and confirmed that high cellularity tumor regions showed greater water molecule confinement compared to low cellularity regions. Conclusions: This study highlights the potential of combining IVIM-DWI, hyperspectral imaging techniques, and deep learning as a robust, safe, and effective non-invasive diagnostic tool for breast cancer, offering a valuable alternative to contrast-enhanced methods by providing detailed information about tissue microstructure and heterogeneity without the need for contrast agents. Full article

Hydrogen is critical for achieving carbon neutrality as a clean energy source. However, its low ambient energy density poses challenges for storage, making efficient and safe hydrogen storage a bottleneck. Metal hydride-based solid-state hydrogen storage has emerged as a promising solution due to its high energy density, low operating pressure, and safety. In this work, the thermodynamic and kinetic characteristics of the hydrogenation and dehydrogenation processes are investigated and analyzed in detail, and the effects of initial conditions on the thermochemical hydrogen storage reactor are discussed. Multiphysics field modeling of the magnesium-based hydrogen storage tank was conducted to analyze the reaction processes. Distributions of temperature and reaction rate in the reactor and temperature and pressure during the hydrogen loading process were discussed. Radially, wall-adjacent regions rapidly dissipate heat with short reaction times, while the central area warms into a thermal plateau. Inward cooling propagation shortens the plateau, homogenizing temperatures—reflecting inward-to-outward thermal diffusion and exothermic attenuation, alongside a reaction rate peak migrating from edge to center. Axially, initial uniformity transitions to bottom-up thermal expansion after 60 min, with sustained high top temperatures showing nonlinear decay under $∆$t = 20 min intervals, where cooling rates monotonically accelerate. The greater the hydrogen pressure, the shorter the period of the temperature rise and the steeper the curve, while lower initial temperatures preserve local maxima but shorten plateaus and cooling time via enhanced thermal gradients. Full article

La-doped Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ cathode materials were successfully synthesized by the sol-gel method. The structure, morphology, element valence states, cyclic voltammetry, and cyclic properties were characterized to investigate the properties of the synthesized materials. The as-prepared La-doped Li_1.2Ni_0.13Mn_0.54Co_0.13O₂ materials exhibit well the crystalline hexagonal layered structures with lamellar-like particles featuring a rough surface. The optimal sample, designated as LLRMO-2 with 1/100 La³⁺ doping, delivers an impressive discharge capacity of 271.2 mAh g⁻¹ with a capacity retention of 87.8% after 100 cycles at the current density of 100 mA g⁻¹ compared with that of 203.5 mAh g⁻¹ with only 110.6 mAh g⁻¹ after 100 cycles for the pristine sample. Furthermore, the LLRMO-2 cathode exhibits a superior rate capability compared to the pristine sample and shows excellent cyclic performances with the capacity retention of 48.1% after 400 cycles. The voltage decay per cycle is only 1.60 mV, which is less than 3.70 mV of the pristine one. The enhanced capacity, rate capability, and cyclic performance observed in the La-doped Li-rich layered cathode can be attributed to the improved structural stability as well as the higher diffusion coefficient of lithium ions. These results suggest that the strategy of introducing La³⁺ into the transition metal slabs is an efficient approach for boosting electrochemical performances of Li-rich Mn-based cathode materials via enhancing structural stability. Full article

Sodium-ion batteries present an economical energy storage solution, yet their anode kinetics remain slow, impeding rate performance and cyclability. Layered FeSe anodes, characterized by metallic conductivity, hold potential, but structural decay and insufficient active sites during cycling continue to pose challenges. Herein, these challenges are addressed through the implementation of dual Ni doping and Se vacancy engineering in FeSe@C to synergistically regulate cationic/anionic configurations. The ionic substitution of larger Fe²⁺ ions (0.78 Å ionic radius) with smaller Ni²⁺ ions (0.69 Å) induces lattice distortion and generates abundant Se vacancies, enhancing electron transport, active site accessibility, and Na⁺ adsorption. These synergistic modifications effectively boost Na⁺ diffusion kinetics and electrolyte compatibility, creating a favorable electrochemical environment for fast sodium storage. Consequently, the optimized 2%Ni-FeSe@C electrode retains an exceptional discharge specific capacity of 307.67mAh g⁻¹ after 1000 cycles at an ultrahigh current density of 5 Ag⁻¹, showcasing superior rate capability and long-term cycling stability, paving the way for practical high-power SIBs. Full article

The contact process is a nonequilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the effects of particle mobility and diffusion on criticality have been preliminarily explored, they remain poorly understood in many aspects. In this work, we examine how the critical rate of the model varies with the probability of particle mobility. By analyzing different stochastic evolutions of the system, we employ two modern approaches: (1) Random Matrix Theory (RMT): By building on the success of RMT, particularly Wishart-like matrices, in studying statistical physics of systems with up-down symmetry via magnetization dynamics [R. da Silva, IJMPC 2022], we demonstrate its applicability to models with an absorbing state; (2) Optimized Temporal Power Laws: By using short-time dynamics, we optimize power laws derived from ensemble-averaged evolutions of the system. Both methods consistently reveal that the critical rate decays with mobility according to a simple Belehradek function. Additionally, a straightforward mean-field analysis supports the decay of the critical parameter with mobility, although it predicts a simpler linear dependence. We also demonstrate that the more sophisticated pair approximation mean-field model developed by ben-Avraham and Köhler aligns closely with the Belehradek function, precisely matching our lattice simulation results. Full article

In this study, the γ → α phase transition and decomposition of AlH₃ were probed using integrated hot-stage polarized microscopy, in situ XRD, DSC, and fluorescence analysis. Phase coexistence at 100 °C and complete transition at 140 °C were demonstrated by in situ XRD. Meanwhile, synchronized fluorescence decay (ImageJ-quantified) and XRD evolution analysis confirmed the temperature-dependent kinetics, with the isothermal γ → α durations decreasing from 225 min (100 °C) to 5 min (180 °C). The transition involved competing surface nucleation and bulk diffusion, which was accelerated by the reduced diffusion resistance at elevated temperatures. Above 160 °C, α → Al decomposition dominated via interfacial reactions and H₂ release, accompanied by gas-induced crystalline fracturing. DSC analysis revealed heating-rate-dependent core–shell thermal gradients, which caused hysteresis. At the same time, the experiment also shows that the surface oxidation of γ-AlH₃ may have hindered transitions through passivation layer formation. This work validates Gao et al.’s core–shell model, demonstrating that combined fluorescence and conventional techniques elucidate kinetic laws in metastable systems. Full article

Transition metal selenides are considered one of the most promising materials for sodium-ion battery anodes due to their excellent theoretical capacity. However, it remains challenging to suppress the volume variation and the resulted capacity decay during the charge–discharge process. Herein, hollow-structured CoNiSe₂ dual transition metal selenides wrapped in a carbon shell (HS-Co_xNi_ySe₂@C) were deliberately designed and prepared through sequential coating of polyacrylonitrile (PAN), ion exchange of ZIF-67 with Ni²⁺ metal ions, and carbonization/selenization. The hollow structure was evidenced by transmission electron microscopy, and the crystalline structure was confirmed by X-ray diffraction. The ample internal space of HS-Co_xNi_ySe₂@C effectively accommodated volume expansion during the charge and discharge processes, and the large surface area enabled sufficient contact between the electrode and electrolyte and shortened the diffusion path of sodium ions for a feasible electrochemical reaction. The surface area and ionic conductivity of HS-Co_xNi_ySe₂@C were strongly dependent on the ratio of Co to Ni. The synergistic effect between Co and Ni enhanced the conductivity and electron mobility of HS-Co_xNi_ySe₂@C, thereby improving charge transfer efficiency. By taking into account the structural advantages and rational metal selenide ratios, significant improvements can be achieved in the cycling performance, rate performance, and overall electrochemical stability of sodium-ion batteries. The optimized HS-Co_xNi_ySe₂@C demonstrated excellent performance, and the reversible capacity remained at 334 mAh g⁻¹ after 1000 cycles at a high current of 5.0 A g⁻¹. Full article

Niobium pentoxide (Nb₂O₅) is a promising anode candidate for lithium-ion batteries due to its high theoretical capacity, excellent rate capability, and safe working potential. However, its inherent low conductivity limits its practical application in fast-charging scenarios. In this work, we develop an ultrathin carbon-coated two-dimensional T-Nb₂O₅ nanosheet composite (T-Nb₂O₅@UTC) through a facile solvothermal reaction and subsequent CVD acetylene decomposition. This unique design integrates a two-dimensional nanosheet structure with an ultrathin carbon layer, significantly enhancing electronic conductivity, reducing ion diffusion pathways, and preserving structural integrity during cycling. The T-Nb₂O₅@UTC electrode demonstrates an impressive specific capacity of 214.7 mAh g⁻¹ at a current density of 0.1 A g⁻¹, maintaining 117.9 mAh g⁻¹ at 5 A g⁻¹, much outperforming the bare T-Nb₂O₅ (179.6 mAh g⁻¹ at 0.1 A g⁻¹ and 62.9 mAh g⁻¹ at 5 A g⁻¹). It exhibits outstanding cyclic stability, retaining a capacity of 87.9% after 200 cycles at 0.1 A g⁻¹ and 83.7% after 1000 cycles at 1 A g⁻¹. In a full-cell configuration, the assembled T-Nb₂O₅@UTC||LiFePO₄ battery exhibits a desirable specific capacity of 186.2 mAh g⁻¹ at 0.1 A g⁻¹ and only a 1.5% capacity decay after 120 cycles. This work underscores a nanostructure engineering strategy for enhancing the electrochemical performance of Nb₂O₅-based anodes toward high-energy-density and fast-charging applications. Full article

This study explores the escape dynamics of bistable systems influenced by multiplicative noise, extending the classical Kramers rate formula to scenarios involving state-dependent diffusion in asymmetric potentials. Using a generalized stochastic calculus framework, we derive an analytical expression for the escape rate and corroborate it with numerical simulations. The results highlight the critical role of the equilibrium potential $U_{\mathrm{eq}}\left(x\right)$, which incorporates noise intensity, stochastic prescription, and diffusion properties. We show how asymmetries and stochastic calculus prescriptions influence transition rates and equilibrium configurations. Using path integral techniques and weak noise approximations, we analyze the interplay between noise and potential asymmetry, uncovering phenomena such as barrier suppression and metastable state decay. The agreement between numerical and analytical results underscores the robustness of the proposed framework. This work provides a comprehensive foundation for studying noise-induced transitions in stochastic systems, offering insights into a broad range of applications in physics, chemistry, and biology. Full article

Niobium pentoxide (T-Nb₂O₅) is a promising anode material for dual-ion batteries due to its high lithium capacity and fast ion storage and release mechanism. However, T-Nb₂O₅ suffers from the disadvantages of poor electrical conductivity and fast cycling capacity decay. Herein, a nitrogen-doped three-dimensional porous carbon (RMF) was prepared for loading niobium pentoxide to construct a composite system with excellent electrochemical performance. The obtained T-Nb₂O₅/RMF composites have a well-developed pore structure and a high specific surface area of 1568.5 m² g⁻¹, which could effectively increase the contact area between the material and electrolyte, improving the electrode reaction and lithium-ion transfer diffusion. Nitrogen doping increased surface polarity, creating more active sites and accelerating the electrode reaction rate. The introduction of T-Nb₂O₅ imparted high power density and excellent cycling stability to the battery. The composites exhibited good electrochemical performance when used as dual-ion battery anode, with a stable cycle life of 207.2 mA h g⁻¹ at 1 A g⁻¹ current density after 650 cycles and great rate performance of 181.5 mA h g⁻¹ at 5A g⁻¹ was also obtained. This work provides the possibility for applying T-Nb₂O₅/RMF as an anode for a high-performance dual-ion battery. Full article

During the underwater movement of a submarine, cooling water at a specific temperature is discharged into the surrounding water through nuclear reactor secondary loop circulation, creating a thermal jet. Thermal jets are characterized by initial velocity and temperature properties that allow for complete mixing with the surrounding water through a combination of mixing and heat transfer processes. This paper aims to investigate the movement and diffusion of underwater thermal jets, specifically examining the temperature stratification of the ambient water, the initial velocity of the jet, and the effect of temperature on the velocity field and temperature field of the underwater thermal jet. This study utilizes particle velocity measurements and the laser-induced fluorescence method to measure the velocity field and temperature field of the thermal jet, as well as simulation methods to validate conclusions. The experimental and simulation conditions in this paper are mainly categorized into two types: uniform water body and thermally-stratified water body. Upon analysis and comparison of the experimental and simulation results, it has been observed that an increase in jet velocity will hinder the upward diffusion of jet temperature, decrease the floating height of the jet, and slow down the rate at which the jet temperature decays. Furthermore, as the difference between the jet temperature and the ambient water temperature increases, the upward diffusion of the jet temperature becomes predominant, resulting in a 40–50% increase in its floating rate. It is evident that the stratification conditions of the background environment have a significant impact on the jet temperature diffusion. When the jet temperature diffuses to the thermally-stratified interface of water in the tank, it ceases to float due to density differences; consequently, its temperature cannot diffuse further towards or reach the water surface. Full article

To improve the performance of valves in relation to the leakage rate, a comprehensive evaluation of the valve characteristics and behavior during pressure exposure is important. Often, these low gas flow rates below 0.1 cm³/min cannot be accurately measured with conventional flow sensors. This paper presents a small and low-cost test rig for measuring gas leakage rates accurately, even far below 0.1 cm³/min, with the pressure decay method. These leakage flows are substantiated with a flow model, where we demonstrate the feasibility of modeling those gas flows with an extended Navier–Stokes framework to obtain more accurate theoretical predictions. As expected, the comparison to the experimental results proves that the classical Navier–Stokes system is unsuitable for modeling Knudsen flows. Hence, self-diffusion of gas, a wall-slip boundary condition, and an effective mean free path model were introduced in a physically evident manner. In terms of the calculated mass flow, while self-diffusion and slip boundary conditions explain deviations from the classical Navier–Stokes equation for Knudsen numbers already smaller than 1, the effective mean free path model has an effect, especially when Kn > 1. For simplified conditions, an analytical solution was presented and compared to the results of an OpenFOAM CFD-solver for flow rates through more complex gap-flow geometries of the flap valve. Hereby, acceptable deviations between 10% and 20% were observed. A comparison with measurement results was carried out. The reproducibility of the measurement method was verified by comparing multiple measurements of one silicon microvalve sample to a state-of-the-art flow sensor. Three geometrically similar passive silicon microvalves were measured with air overpressure decreasing from 15 kPa relative to atmospheric pressure. Maximum gas volume flowing in a blocking direction of 1–26 µL/min with high reproducibility and marginal noise were observed. Full article

In this paper, we consider the Cauchy problem of a time-fractional nonlinear diffusion equation. According to Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time under some sufficient conditions. We next provide sufficient conditions for the existence of global solutions by using the results of Zhang and Sun. In conclusion, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity. Full article

In the process of promoting the commercialization of proton exchange membrane fuel cells, the long-term durability of the fuel cell has become a key consideration. While existing durability tests are critical for assessing cell performance, they are often time-consuming and do not quickly reflect the impact of actual operating conditions on the cell. In this study, improved testing protocols were utilized to solve this problem, which is designed to shorten the testing cycle and evaluate the degradation of the cell performance under real operating conditions more efficiently. Accelerated durability analysis for evaluating the MEA lifetime and performance decay process was carried out through two testing protocols—open circuit voltage (OCV)-based accelerated durability testing (ADT) and relative humidity (RH) cycling-based ADT. OCV-based ADT revealed that degradation owes to a combined mechanical and chemical process. RH cycling-based ADT shows that degradation comes from a mainly mechanical process. In situ fluoride release rate technology was employed to elucidate the degradation of the proton exchange membrane during the ADT. It was found that the proton exchange membrane suffered more serious damage under OCV-based ADT. The loss of F⁻ after the durability test was up to 3.50 × 10⁻⁴ mol/L, which was 4.3 times that of the RH cycling-based ADT. In addition, the RH cycling-based ADT had a significant effect on the catalyst layer, and the electrochemically active surface area decreased by 48.6% at the end of the ADT. Moreover, it was observed that the agglomeration of the catalysts was more obvious than that of OCV-based ADT by transmission electron microscopy. It is worth noting that both testing protocols have no obvious influence on the gas diffusion layer, and the contact angle of gas diffusion layers does not change significantly. These findings contribute to understanding the degradation behavior of proton exchange membrane fuel cells under different working conditions, and also provide a scientific basis for developing more effective testing protocols. Full article