Search Results (40)

We propose a two-level theory that connects Lin-equation-based dynamical coarse-graining of the turbulence cascade with an information-theoretic selection principle in logarithmic wavenumber space. This framework places the dissipation-range spectral shape on a verifiable logical basis rather than on ad hoc fitting. At the first (dynamical) level, we formulate an autonomous conservative Fokker–Planck equation for the normalized density and probability current. Under sufficient boundary decay and a strictly positive effective diffusion, the sign-reversed Kullback–Leibler divergence is shown to be a Lyapunov functional, yielding a rigorous H-theorem and fixing the arrow of time in scale space. At the second (selection) level, the dissipation range is treated as a stationary boundary-value problem for an open system by introducing a killing term for an unnormalized scale density. A WKB (Liouville–Green) analysis restricts the admissible tail to a stretched-exponential form and links the tail exponent to the high-wavenumber scaling of the effective diffusion. The exponential prefactor is fixed by dissipation-rate consistency, and the remaining degree of freedom is determined by one-dimensional Kullback–Leibler minimization (Hyper-MaxEnt) against a globally constructed reference distribution. The resulting exponent range is validated against the high-resolution DNS spectra reported in the literature. Full article

In this paper we present a brief review of extended general relativity in four dimensions and solve versions of the extended equations for the case of static spherical symmetry in various contexts, for a previously studied Lagrangian. The exterior vacuum yields a Schwarzschild solution with an additional scalar field potential that falls off logarithmically, the latter essentially an inverse square force. That is probably not adequate as a dark matter force, but might contribute. When a constant density field of ions holds sway in the exterior, a solution identical to the cosmological constant extension of Schwarzschild occurs, together with a scalar field potential declining as $r^{-3/2}$, however it is not asymptotically flat. An inverse square declining distribution of ionic material, according to perturbation theory, results in an additional linear gravity potential that would provide further attraction in the gravity term. A limited exact solution in the same case yields a cubic equation with a Schwarzschild solution, corresponding to $A=0$, and two MOND-like possible potentials, one vanishing at infinity, but a better solution must be found. The approximate solution is complex (one of many) and the system requires further study. Ionic matter is ubiquitous in the universe and provides a source for the scalar field, which suggests that the extended Einstein equations could be of utility in the dark matter problem, provided such an electromagnetic scalar force could be found and differentiated from the usual, far stronger electromagnetic forces. Further, it’s possible that the strong photon flux outside stars might have an influence, and is under current investigation. These calculations show that extending the concept of curvature and working in four dimensions with larger operators may bring new tools to the study of physics and unified field theories. Full article

This paper introduces a new class of probability distributions, termed the generated log exponentiated polynomial (GLEP) family, designed to enhance flexibility in modeling complex real financial data. The proposed family is constructed through a novel cumulative distribution function that combines logarithmic and exponentiated polynomial structures, allowing for rich distributional shapes and tail behaviors. We present comprehensive mathematical properties, including useful series expansions for the density, cumulative, and quantile functions, which facilitate the derivation of moments, generating functions, and order statistics. Characterization results based on the reverse hazard function and conditional expectations are established. The model parameters are estimated using various frequentist methods, including Maximum Likelihood Estimation (MLE), Cramer–von Mises (CVM), Anderson–Darling (ADE), Right Tail Anderson–Darling (RTADE), and Left Tail Anderson–Darling (LEADE), with a comparative simulation study assessing their performance. Risk analysis is conducted using actuarial key risk indicators (KRIs) such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Tail Variance (TV), Tail Mean Variance (TMV), and excess function (EL), demonstrating the model’s applicability in financial and insurance contexts. The practical utility of the GLEP family is illustrated through applications to real and simulated datasets, including house price dynamics and insurance claim sizes. Peaks Over Random Threshold Value-at-Risk (PORT-VaR) analysis is applied to U.K. motor insurance claims and U.S. house prices datasets. Some recommendations are provided. Finally, a comparative study is presented to prove the superiority of the new family. Full article

Stochastic vibration control of uncertain structures under random loading is an important problem and its minimax optimal control strategy remains to be developed. In this paper, a stochastic optimal control strategy for uncertain structural systems under random excitations is proposed, based on the minimax stochastic dynamical programming principle and the Bayes optimal estimation method with the combination of stochastic dynamics and Bayes inference. The general description of the stochastic optimal control problem is presented including optimal parameter estimation and optimal state control. For the estimation, the posterior probability density conditional on observation states is expressed using the likelihood function conditional on system parameters according to Bayes’ theorem. The likelihood is replaced by the geometrically averaged likelihood, and the posterior is converted into its logarithmic expression to avoid numerical singularity. The expressions of state statistics are derived based on stochastic dynamics. The statistics are further transformed into those conditional on observation states based on optimal state estimation. Then, the obtained posterior will be more reliable and accurate, and the optimal estimation will greatly reduce uncertain parameter domains. For the control, the minimax strategy is designed by minimizing the performance index for the worst-parameter system, which is obtained by maximizing the performance index based on game theory. The dynamical programming equation for the uncertain system is derived according to the minimax stochastic dynamical programming principle. The worst parameters are determined by the maximization of the equation, and the optimal control is determined by the minimization of the resulting equation. The minimax optimal control by combining the Bayes optimal estimation and minimax stochastic dynamical programming will be more effective and robust. Finally, numerical results for a five-story frame structure under random excitations show the control effectiveness of the proposed strategy. Full article

Focusing on the three critical factors influencing laser communication systems operating in marine environments: atmospheric turbulence disturbances, atmospheric attenuation, and optical aberration effects, in this paper, we employ numerical simulation methods to systematically investigate the influence of four typical Zernike aberrations (defocus, y-coma, spherical aberration, and y-secondary quadrupole) on laser atmospheric transmission characteristics and system bit error rates. A comparison of their atmospheric transmission performance with that of the aberration-free state is also presented. The results show that reducing turbulence strength or increasing receiver aperture radius can effectively mitigate the scintillation effect of intensity fluctuations. Among the four typical aberrations, the fluctuation range of the relative change rate of the scintillation index for y-coma aberration relative to the aberration-free state is the largest. In weak turbulence and short-distance laser transmission over the sea, the beam drift caused by these four aberrations is not significant, and stronger turbulence strength or higher weight coefficients lead to more severe beam expansion. The on-axis logarithmic intensity probability density distribution of laser beams with different aberrations approximately follows a log-normal distribution. The skewness (S) and kurtosis (K) of the logarithmic intensity distribution are negatively correlated and always satisfy S < 0 and K > 0. Additionally, we found that as turbulence strength increases, turbulence effects significantly raise the required signal-to-noise ratio (SNR) values to achieve a bit error rate of 10⁻⁹. When turbulence strength reaches a certain level, the impact weights of different aberrations on system performance may undergo changes. These results can provide theoretical references for the design and optimization of laser system parameters in marine laser communication. Full article

Wind tunnel test results can be influenced by various factors such as the blockage ratio and scaling ratio. These factors may introduce errors in the experimental outcomes, impacting the accuracy and reliability of the data obtained. This study quantitatively assesses consistency and identifies uncertainty sources to enhance result uniformity across various wind tunnel laboratories. This study conducted a systematic comparison between different wind tunnels in terms of rigid model pressure measurement wind tunnel experiments on the same Commonwealth Advisory Aeronautical Research Council (CAARC) standard tall building model. The study analyzes and discusses the results of mean and root-mean-square (RMS) wind pressure coefficients, peak factors, extreme wind pressure coefficients, probability density distributions, and base overturning force coefficients. The results indicated that in the open-circuit wind tunnel laboratory, the mean wind pressure coefficient is underestimated in the positive pressure region and overestimated in the negative pressure region. This is due to the static pressure which significantly decreases the streamwise direction within the test section, and the difference in static pressure is logarithmically proportional to the mean wind speed. Additionally, dynamic pressure is uniformly distributed along the test section axis. The inaccurate measurement of static pressure leads to these results. To address this issue, an indirect measurement method was employed to correct the static pressure results and reduce the error in the mean wind pressure coefficient to within 10%. Furthermore, differences in turbulence integral scale result in an error of up to 16% in the RMS wind pressure coefficient. Therefore, when conducting rigid model pressure measurement wind tunnel experiments, especially in open-circuit wind tunnel laboratories, careful consideration should be given to the influence of static pressure drop and integral length scale of turbulence. Full article

The isotropic Cauchy distribution is a member of the central $\alpha$-stable family that plays a role in the set of heavy-tailed distributions similar to that of the Gaussian density among finite second-moment laws. Given a sequence of n observations, we are interested in characterizing the performance of Likelihood Ratio Tests, where two hypotheses are plausible for the observed quantities: either isotropic Cauchy or isotropic Gaussian. Under various setups, we show that the probability of error of such detectors is not always exponentially decaying with n, with the leading term in the exponent shown to be logarithmic instead, and we determine the constants in that leading term. Perhaps surprisingly, the optimal Bayesian probabilities of error are found to exhibit different asymptotic behaviors. Full article

This paper primarily presents statistics on the variation of physical characteristics (dimensions and mass) for the coulter discs of double-disc seeders. This statistic was calculated based on actual measurements of the probability density and cumulative probability for the mass of the discs, their average thickness, and outer diameter. These parameters (m = 4000 g, g = 4 mm, D = 380 mm) are tracked from the design phase to the actual realization phase, being the parameters specified in the purchase phase by users from agricultural machinery distributors. The standard deviation and deviation from the mean for a cumulative normal (Gaussian) distribution were calculated, and an analysis was made for the decrease of the mentioned parameters in discs already used for sowing cereals on an area of 80 hectares, due to the wear that appeared as a trace of the contact with the soil and the abrasive wear caused by it. Testing of disk parameters using both logarithmic and Gaussian distributions was performed, and test results are presented through appropriate graphs. With small deviations (which appeared for known or unknown reasons), it can be stated that the distribution of the mentioned parameters is generally a normal-type distribution. If the new discs are 15″ in diameter, experts recommend that they be replaced when they reach a diameter of less than 14.5 inches. This study can provide a reference for improving the physical characteristics of opener discs of seed drills in no-till conditions and beyond. Full article

To analyze the intensity of atmospheric turbulence in a satellite–ground laser communication link, it is important to consider the effect of increased atmospheric turbulence caused by wind speed. Atmospheric turbulence causes a change in the refractive index, which negatively impacts the quality and focusing ability of the laser beam by altering its phase front. To simulate the changes in amplitude and phase characteristics of laser beam propagation in atmospheric turbulence caused by wind speed, a transverse translation phase screen is used. To better understand and address the influence of atmospheric wind speed on the phase of optical signals in satellite–ground laser communication links, this paper proposes a Monte Carlo simulation method. This method utilizes the spatial and temporal variations in the refractive index in the atmosphere and integrates the principles of optical signal propagation in the atmosphere to simulate changes in the phase of optical signals under different wind speed conditions. By analyzing the variations in the received optical signal’s power, the Monte Carlo method is employed to simulate phase screens and logarithmic amplitude screens. Additionally, it models the probability density of the statistical behavior of received optical signal’s fluctuations, as well as the time autocorrelation coefficient of optical signals. This paper, under the coupling condition in satellite–ground laser communication links, conducted a Monte Carlo simulation experiment to analyze the characteristics of the optical signal’s fluctuations in the link and discovered that atmospheric wind speed affects the shape of the power spectral density model of the received optical signal. Increasing wind speed leads to a decrease in the time autocorrelation coefficient of the received optical signal and affects the coupling efficiency. The paper then used a cubic spline interpolation fitting method to verify the models of the power spectral density and the autocorrelation time coefficient of the optical signal. This provides a theoretical foundation and practical guidance for the optimization of satellite–ground laser communication systems. Full article

Aquifer properties, such as hydraulic transmissivity T and its spatial variability, are fundamental for sustainable groundwater exploitation in arid regions. Especially in karst aquifers, spatial variability can be considerable, and the application of geostatistical methods allows for spatial interpolation and mapping based on observations combined with the quantification of uncertainties. Moreover, direct measurements of T are typically scarce, while those of specific capacity S_c are more frequent. In this study, we establish the linear regression relationship between the logarithms of T and S_c measured in 51 wells in a semi-arid karst region in Northeastern Brazil. This relationship is used to estimate empirical values logT_emp based on measurements of logS_c at 269 wells. LogT_emp values are found to be normally distributed with an isotropic variogram of a significant nugget effect (attributed to local-scale karst features) and approximately 10 km range (attributed to larger-scale gradual changes in karst feature density). Ordinary kriging cross-validation indicates an optimum number of 25 neighboring wells for interpolation, which is used in a conditional sequential Gaussian simulation (SGSIM) to generate 500 realizations of logT_emp with respective maps of standard deviations and probabilities of (not) exceeding threshold values. High-transmissivity areas mostly coincide with karstified river valleys, while low-transmissivity areas occur toward the edges where aquifer thickness decreases. The resulting transmissivity maps are relevant for optimizing regional water management strategies, which includes stochastic approaches where transmissivity realizations can be used to parameterize multiple runs of numerical groundwater models. Full article

Coarse-grained molecular dynamic simulations are employed to investigate the spatiotemporal evolution of vesicles (polymersomes) via self-assembly of randomly distributed amphiphilic diblock copolymers PB-PEO (Poly(Butadiene)-b-Poly(Ethylene Oxide)) in water. The vesiculation pathway consists of several intermediate structures, such as spherical/rodlike aggregates, wormlike micelles, lamellae, and cavities. The lamella-to-vesicle transition occurs at a constant aggregation number and is accompanied by a reduction in the solvent-accessible surface area. Simulation predictions are in qualitative agreement with the mechanism of vesicle formation in which the unfavorable hydrophobic interactions between water molecules and polymer segments, along the edge of the lamella, are eliminated at the expense of gaining curvature energy. However, rod–lamella–vesicle transition is accompanied by an increase in copolymer packing density. Hence, the change in the surface area accompanying vesiculation predicted by the simulations is significantly lower than theoretical estimates. Changes in information entropy, quantified by the expectation of the logarithm of the probability distribution function of the segmental stretch parameter s, defined as the difference between the maximum and instantaneous segmental extension, are statistically insignificant along the vesiculation pathway. For rods, lamellae, and polymersomes, s follows a log normal distribution. This is explained based on the configurational dynamics of a single diblock chain in water. Full article

By using Weather Research and Forecasting Model (WRF) to simulate a southwest vortex precipitation process, this work studies the correlations between entrainment rate (λ) and dynamical parameters in the cloud and further fit λ. We relate the probability density distribution (PDF) to the parameterization of λ and find that the greater the probability, the larger the slope of the logarithmic liner function. The slope of the log-linear fitting function in fitting decreases for developing and enhancing cumulus clouds, which is related to the increase in updraft motion and the decrease in λ. Then, we group clouds according to cloud top heights and calculate average λ and dynamic parameters, and the results indicate that when only one dynamic parameter is used, vertical wind velocity (w) is more suitable than buoyancy (B) to be used to fit λ. The fitting functions combing one single parameter and more parameters by principal components regression are compared with two traditional schemes, and we found that λ obtained by our fitting schemes are between the two traditional schemes. Because the principal component regression method takes into account the interaction between more dynamic factors and entrainment, the fitting function, including w and B, is suitable to be applied to fit λ in the parameterization scheme for cumulus clouds. Full article

Turbulence can cause effects such as light intensity fluctuations and phase fluctuations when a laser is transmitted in the atmosphere, which has serious impacts on a number of optical engineering application effects and on climate improvement. Therefore, accurately obtaining real-time turbulence intensity information using lidar-active remote sensing technology is of great significance. In this paper, based on residual turbulent scintillation theory, a Mie-scattering lidar method was developed to detect atmospheric turbulence intensity. By extracting light intensity fluctuation information from a Mie-scattering lidar return signal, the atmospheric refractive index structure constant, $C_n^2$, representing the atmospheric turbulence intensity, could be obtained. Specifically, the scintillation effect on the detection path was analyzed, and the probability density distribution of the light intensity of the Mie-scattering lidar return signal was studied. It was verified that the probability density of logarithmic light intensity basically follows a normal distribution under weak fluctuation conditions. The $C_n^2$ profile based on Kolmogorov turbulence theory was retrieved using a layered, iterative method through the scintillation index. The method for detecting Kolmogorov turbulence intensity was applied to the detection of the non-Kolmogorov turbulence intensity. Through detection using the scintillation index, the corresponding ${\tilde{C}}_n^2$ profile could be calculated. The detection of the ${\tilde{C}}_n^2$ and $C_n^2$ profiles were compared with the Hufnagel–Valley (HV) night model in the Yinchuan area. The results show that the detection results are consistent with the overall change trend of the model. In general, it is feasible to detect a non-Kolmogorov turbulence profile using Mie-scattering lidar. Full article

In this paper, we develop the new extended Kumaraswamy generated (NEKwG) family of distributions. It aims to improve the modeling capability of the standard Kumaraswamy family by using a one-parameter exponential-logarithmic transformation. Mathematical developments of the NEKwG family are provided, such as the probability density function series representation, moments, information measure, and order statistics, along with asymptotic distribution results. Two special distributions are highlighted and discussed, namely, the new extended Kumaraswamy uniform (NEKwU) and the new extended Kumaraswamy exponential (NEKwE) distributions. They differ in support, but both have the features to generate models that accommodate versatile skewed data and non-monotone failure rates. We employ maximum likelihood, least-squares estimation, and Bayes estimation methods for parameter estimation. The performance of these methods is discussed using simulation studies. Finally, two real data applications are used to show the flexibility and importance of the NEKwU and NEKwE models in practice. Full article

The famous Selberg class is defined axiomatically and consists of Dirichlet series satisfying four axioms (Ramanujan hypothesis, analytic continuation, functional equation, multiplicativity). The Selberg–Steuding class $\mathcal{S}$ is a complemented Selberg class by an arithmetic hypothesis related to the distribution of prime numbers. In this paper, a joint universality theorem for the functions L from the class $\mathcal{S}$ on the approximation of a collection of analytic functions by shifts $\left(L(s+i{a}_1\tau ),\dots ,L(s+i{a}_r\tau )\right)$, where $a_1,\dots ,a_r$ are real algebraic numbers linearly independent over the field of rational numbers, is obtained. It is proved that the set of the above approximating shifts is infinite, its lower density and, with some exception, density are positive. For the proof, a probabilistic method based on weak convergence of probability measures in the space of analytic functions is applied together with the Backer theorem on linear forms of logarithms and the Mergelyan theorem on approximation of analytic functions by polynomials. Full article