Search Results (708)

Ultra-high voltage (UHV) power transmission has become a prerequisite for the development of clean energy. However, arcs generated by UHV circuit breakers can easily lead to safety incidents, and developing arc-extinguishing gases with low global warming potential (GWP) presents certain challenges. It is a fact that fluorolefins, as a class of fluorinated compounds with low GWP, show high application potential in replacing traditional arc-extinguishing agents. In this study, all six conjugated perfluorinated compounds, including C₆F₆ and C₆F_8, were calculated within the density functional theory (DFT) framework at the B3LYP/6-311+G(d,p) level. The dipole moments, HOMO/LUMO energy gaps, and the inherent aromaticity of annular molecules under external electric fields of these fluorinated molecules are investigated accordingly. By analyzing these results, it is found that the influence of the conjugated structure on the stability of arc-extinguishing gases under high-voltage conditions was partially elucidated, providing useful insights for the subsequent development of environmentally friendly and high-performance arc-extinguishing gases. Full article

This article introduces a new flexible distribution, called the alpha power Topp–Leone Dagum (APTLDa) distribution, which extends the classical Dagum model by combining the Topp–Leone generator with the alpha power transformation (APT). The proposed distribution is capable of modeling data with symmetrical and asymmetrical shapes for the probability density and hazard rate functions. This makes it suitable for lifetime and reliability data analysis. Several important statistical properties of the new distribution are derived, including the quantile function, moments, entropy measures, order statistics, and reliability-related functions. Parameter estimation is carried out using the maximum likelihood method, and the performance of the estimators is examined through an extensive simulation study under different sample sizes and parameter settings. The simulation results demonstrate the consistency and good finite-sample behavior of the estimators. The practical usefulness of the proposed distribution is illustrated through applications to two real datasets, where its performance is compared with several competing models. The results show that the APTLDa distribution provides a flexible and effective alternative for modeling lifetime data. Full article

Most insects secrete special fluids from their tarsal pads which are essential for the function of their attachment systems. Previous studies investigated several physical and chemical characteristics of this pad fluid in different insect species. However, there is not much known about the mechanical properties of fluid from smooth adhesive pads. In this study, we used the stress–relaxation nanoindentation method to examine the viscoelastic properties of pad fluid from Sungaya aeta. Force–displacement and stress–relaxation curves on single fluid droplets were recorded with an atomic force microscope (AFM) and analyzed using Johnson–Kendall–Roberts (JKR) and generalized Maxwell models for determination of effective elastic modulus (E), work of adhesion (Δγ) and dynamic viscosity (η). In addition, we used white light interferometry (WLI) to measure the maximal height of freshly acquired droplets. Our results revealed three different categories of droplets, which we named “almost inviscid”, “viscous” and “rigid”. They are presumably determined at the moment of secretion and retain their characteristics even for several days. The observed mechanical properties suggest a non-uniform composition of different droplets. These findings provide a basis for advancing our understanding about the requirements for adaptive adhesion-mediating fluids and, hence, aid in advancing technical solutions for soft or liquid temporal adhesives and gripping devices. Full article

This essay explores how sanctity at Helfta was defined not by the perfection of song but by its interruption. The Book of Special Grace and the Herald of Divine Love praise Mechthild of Hackeborn and Gertrude the Great as singers of surpassing sweetness yet linger on the migraines, collapses, and illnesses that silenced their voices in the choir. These moments of suspension disclose muteness as more than absence: they reveal it as the paradoxical condition through which divine presence most fully resounds. Bringing sound studies into dialogue with disability studies, I argue that faltering breath, broken chant, and enforced silence function as theological and literary form. At Helfta, impairment itself becomes a hermeneutic structure, the hinge through which sanctity is revealed and narrative meaning is generated. In this framework, muteness operates as a form of narrative prosthesis—an interruption that both structures the hagiographical imagination and unsettles it by refusing cure or closure. By highlighting the fragility of voice as the very medium of divine disclosure, these texts testify that the sweetest music of Helfta lies not in unbroken chant but in silence transfigured into revelation. Full article

Nonlinear transport of tracer particles immersed in a sheared dilute gas with inelastic collisions is analyzed within the framework of the Boltzmann kinetic equation. Two different yet complementary approaches are employed to obtain exact results. First, we maintain the structure of the inelastic Boltzmann collision operator but consider inelastic Maxwell models (IMMs) instead of the realistic model of inelastic hard spheres (IHS). Using IMMs enables us to compute the collisional moments of the inelastic Boltzmann operator for mixtures without explicitly knowing the velocity distribution functions of the mixture. Second, we consider a kinetic model of the Boltzmann equation for IHS. This kinetic model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle velocity and a gas of IHS. We solve the Boltzmann–Lorentz kinetic equation for tracer particles using a generalized Chapman–Enskog-like expansion around the shear flow distribution. This reference distribution retains all hydrodynamic orders in the shear rate. The mass flux is obtained to first order in the deviations of the concentration, pressure, and temperature from their values in the reference state. Due to the anisotropy induced in the velocity space by shear flow, the mass flux is expressed in terms of tensorial quantities rather than conventional scalar diffusion coefficients. Unlike the previous results obtained for IHS using different approximations, the results derived in this paper are exact. Generally, the comparison between the IHS results and those found here shows reasonable quantitative agreement, especially for IMM results. This good agreement shows again evidence of the reliability of IMMs for studying rapid granular flows. Finally, we analyze segregation by thermal diffusion as an application of the theory. Phase diagrams illustrating segregation are presented and compared with previous IHS results, demonstrating qualitative agreement. Full article

This study presents a frequency-domain analysis of a finite-element (FEM)-based rotor–nacelle model for wind turbines, validated against the open-source time-domain tool OpenFAST. The analysis was carried out using METHOD, an in-house computational framework implemented in Python. While time-domain models remain standard for nonlinear aeroelastic simulations, frequency-domain approaches offer advantages in early-stage design, control development, and system identification due to their efficiency, transparency, and suitability for parametric studies. The FEM model includes flexible blades, hub, and nacelle dynamics and includes tower and fixed or floating platform components with rotor–tower frequency interactions. In this work, a fixed tower is considered to isolate rotor behaviour. Beam-element formulation enables the computation of natural frequencies, mode shapes, and frequency response functions, and an equivalent rotor model is implemented in OpenFAST for consistent benchmarking. Validation results show close correspondence between the two modelling approaches. Key operational parameters agree within 3%, while structural responses, including flap-wise deflection, bending moments, and resultant quantities, typically fall within an overall accuracy range of 5–15%, consistent with expected differences arising from reference-frame conventions and modelling assumptions. Discrepancies are discussed in terms of numerical damping, model assumptions (differences in the axis system), and the influence of structural simplifications. Overall, the FEM model captures the dominant dynamic behaviour with satisfactory accuracy and a consistent orientation of global response. Computational efficiency results further highlight the advantages of the METHOD framework. Wind-field generation is completed roughly an order of magnitude faster, and long-duration aeroelastic simulations achieve substantial speed-ups, reaching more than one order of magnitude for multi-hour cases, demonstrating strong scalability relative to OpenFAST. Overall, the results confirm that a well-constructed yet still simplified frequency-domain FEM rotor model can provide a robust and computationally efficient alternative to conventional time-domain solvers. Moreover, the computational performance presented here represents a lower bound, as further improvements are readily achievable through parallelisation and solver-level optimisation. Future papers will present the full-system aero-hydro-elastic coupling for fixed and floating offshore wind turbine applications. Full article

This paper investigates the concomitants of order statistics from the bivariate generalized linear exponential (BGLE) distribution. We obtain the probability density function of a single concomitant and the joint probability density function of two concomitants of order statistics from the BGLE distribution. In addition, expressions for the single and product moments of concomitants of order statistics are derived. Furthermore, we find the best linear unbiased estimator of a scale parameter related to a study variable using various ranked set sampling techniques. Finally, we apply the findings to a real-life dataset. Full article

We establish precise exponential tail estimates for lacunary trigonometric sums of the form $f_N\left(x\right)={\sum }_{k=1}^N{c}_k\cos \left(2\pi n_{k}x\right)$, under the Hadamard gap condition. Using cumulant expansions and moment-generating function techniques, we obtain non-asymptotic upper bounds for the tail probabilities, including third-order corrections that refine the classical central limit theorem estimates. Furthermore, several examples illustrate these bounds for various choices of coefficients, highlighting the transition from subgaussian to stretched-exponential tail behavior. Full article

A biomechanical evaluation of knee loading during squatting is essential for understanding functional capacity after total knee arthroplasty (TKA). This study compares knee joint kinetics in healthy native knees and in posterior-stabilized TKA (PS-TKA) across BMI categories using 3D motion capture and inverse dynamics. Sixty-two knees (31 healthy, 31 PS-TKA) were analyzed. Native knees demonstrated greater flexion capacity and higher joint loading than PS-TKA knees. Peak resultant joint forces reached 3.50 ± 1.00 BW in healthy knees compared with 2.90 ± 1.20 BW in PS-TKA knees. Healthy knees also generated higher joint moments, with maximum adduction and rotation moments of 5.07% BW × height and 1.29% BW × height, respectively. Body mass index (BMI) significantly influenced loading patterns in native knees, increasing anterior–posterior forces, quadriceps demand, and resultant moments, whereas loading in PS-TKA knees showed minimal BMI dependence. These findings highlight fundamental biomechanical differences between native and prosthetic knees and provide population-specific insights relevant to rehabilitation and high-flexion activities common in Asian populations. Full article

In ultrafast science, the strong-field approximation (SFA) provides a powerful framework to describe high-order harmonic generation (HHG) and related phenomena. Meanwhile, within the current ab initio theoretical framework, the use of nonlocal potentials in calculating multi-electron molecular wave functions is almost unavoidable. We find that when such wave functions are directly applied to compute transition dipole moments for correcting SFA, it introduces a fundamental gauge transformation problem. Specifically, the nonlocal potential contributes an additional gauge-dependent phase function to the dipole operator, which directly modifies the phase of the transition dipole. As a consequence, the saddle-point equations acquire an entirely different structure compared to the standard SFA, leading to a splitting of the conventional short and long classical trajectories in HHG into multiple distinct quantum trajectories. Here, “complex molecules” refers to multi-center molecular systems whose nonlocal electronic structure leads to gauge-dependent strong-field responses. Our analysis highlights that the validity of gauge in-variation cannot be assumed universally in SFA framework. Our approach combines the molecular strong-field approximation with gauge transformation analysis, incorporating nonlocal pseudopotentials, saddle-point equations, and multi-center recombination effects. Full article

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

In this work, we introduce a new four-parameter distribution, called the integrated linear–Weibull (ILW) model, constructed by embedding a dynamic linear component within the Weibull framework. The ILW distribution is capable of capturing a wide variety of symmetric and asymmetric density shapes and accommodates diverse failure-rate behaviors. We derive several of its key mathematical and statistical properties, including moments, extropy, cumulative residual entropy, order statistics, and their asymptotic forms. The mean residual life function and its reciprocal relationship with the failure rate are also obtained. An algorithm for generating random samples from the ILW distribution is provided, and model identifiability is examined numerically through the Kullback–Leibler divergence. Parameter estimation is carried out via maximum likelihood, and a simulation study is conducted to assess the accuracy of the estimators; the results show improvements in estimator performance as sample size increases. Finally, three real datasets involving failure-time observations and one describing hydrological and epidemiological data are analyzed to demonstrate the practical usefulness of the ILW model. In these applications, the proposed model exhibits competitive or superior performance relative to several existing lifetime distributions based on standard model selection criteria and goodness-of-fit measures. Full article

We introduce the Symmetric-$\mathbb{Z}$ (Sy-$\mathbb{Z}$) family, a unified class of symmetric discrete distributions on the integers obtained by multiplying a three-point symmetric sign variable by an independent non-negative integer-valued magnitude. This sign-magnitude construction yields interpretable, zero-centered models with tunable mass at zero and dispersion balanced across signs, making them suitable for outcomes, such as differences of counts or discretized return increments. We derive general distributional properties, including closed-form expressions for the probability mass and cumulative distribution functions, bilateral generating functions, and even moments, and show that the tail behavior is inherited from the magnitude component. A characterization by symmetry and sign–magnitude independence is established and a distinctive operational feature is proved: for independent members of the family, the sum and the difference have the same distribution. As a central example, we study the symmetric Poisson model, providing measures of skewness, kurtosis, and entropy, together with estimation via the method of moments and maximum likelihood. Simulation studies assess finite-sample performance of the estimators, and applications to datasets from finance and education show improved goodness-of-fit relative to established integer-valued competitors. Overall, the Sy-$\mathbb{Z}$ framework offers a mathematically tractable and interpretable basis for modeling symmetric integer-valued outcomes across diverse domains. Full article

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data. Full article

In this paper, we introduce and investigate a novel family of parameter-dependent operators incorporating multiple shape parameters ${\left\{{\lambda }_k\right\}}_{k=1}^n$, whose underlying basis functions include these parameters and exhibit a symmetry property. This parameter-dependent formulation provides a unified and flexible framework for constructing positive linear operators with enhanced approximation and shape-preserving capabilities. We establish fundamental properties of the proposed operators, including nonnegativity, linearity, end-point interpolation, monotonicity preservation and partition of unity; derive their central moments; and determine direct approximation theorems and Voronovskaja-type results. Finally, numerical experiments and graphical illustrations demonstrate the improved performance and adaptability of the proposed scheme compared with existing Bernstein-type variants. The presented framework unifies several classical and generalized operator families while providing additional shape control for practical applications in computer-aided geometric design and function approximation. Full article