Density Distribution Function Research Articles

Wind resource assessment for turbine class identification in Bayanzhaganxiang, China

Abstract The wind resource assessment has been used effectively to identify the classification of wind turbines at a particular wind farm site. The current study used WAsP software and various statistical methods such as graphical, energy pattern factor, standard deviation, and Rayleigh distribution methods to find the Weibull parameters by evaluating the raw data collected from August 2005 until July 2006 at four (4) different heights of the meteorological mast station in Bayanzhaganxiang, China. The Weibull parameters were utilized to find the annual mean wind speed, probability density, and cumulative distribution functions of wind conditions at the reference heights of 70 m, 50 m, 30 m, and 10 m. The wind shear coefficient was 0.130 with an overall roughness factor of 0.0385 m, suggesting the site vicinity is an open country with no significant structures and vegetation. The results also showed that the post-processed output from WAsP and standard deviation method at the sensor’s height of 70 m have a correlation coefficient and confidence level of 0.99977 and above 95%, respectively. Based on the turbine classification from GL Wind 2003 and IEC 61400-1 Ed.2, it was found that the turbine class ideal for the site is class III wind turbines with an annual mean wind speed of 7.439 m/s at a hub height of 99 m. The measured wind power density at hub height was calculated according to IEC 61400-12-1, which yields 464.36 W/m2. The characteristic wind turbulence at 70 m high is IEC subclass B. Among the selected wind turbines, the net annual energy production with efficiency is 8,059.57 MWh/year using Avantis AV1010, with the highest capacity factor of 40.05%. It has been found that the lowest energy generation cost is US$ 0.0292/kWh for a period of 20 years.

Control Charts for a Novel Exponent Power Rayleigh Distribution

Abstract: In this Paper, we presented the distribution as A Novel Exponent Power Rayleigh (NovEPRD) probability density function, Distribution, and Survival and Hazard functions introduced by Bharathi et al (2022) and A Novel Exponent Power Rayleigh (NovEPR) distribution Properties and its Applications studied by Bharathi et al (2022) and then here we derived the Weighted Variance (WV), Weighted Standard Deviation (WSD) and Correction Factor (CF) for existed A Novel Exponent Power Rayleigh (NovEPR) distribution , this paper obtains the parameters of the control lines X̅ and R drawn from the A Novel Exponent Power Rayleigh (NovEPR) distribution. These methods are compared with Newton Raphson’s simulations. For these control charts, Type I risk is compared with different groups of A Novel Exponent Power Rayleigh (NovEPR) distribution. Simulation results show that the Skewness Correction (SC) method of Type I carries less risk than other methods. When the distribution is approximately equal, the type I risk of the Shewhart, W V, WSD and SC X̅ plans is comparable, while the type I risk of the SC R plan is smaller

Density estimation via measure transport: Outlook for applications in the biological sciences

AbstractOne among several advantages of measure transport methods is that they allow or a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results from computational studies aimed at assessing the potential of measure transport techniques, specifically, the use of triangular transport maps, as part of a workflow intended to support research in the biological sciences. Scenarios characterized by the availability of limited amount of sample data, which are common in domains such as radiation biology, are of particular interest. We find that when estimating a distribution density function given limited amount of sample data, adaptive transport maps are advantageous. In particular, statistics gathered from computing series of adaptive transport maps, trained on a series of randomly chosen subsets of the set of available data samples, leads to uncovering information hidden in the data. As a result, in the radiation biology application considered here, this approach provides a tool for generating hypotheses about gene relationships and their dynamics under radiation exposure.

Molecular dynamics simulation of the interaction between aggregates and calcium silicate hydrate and influence of ethylene vinyl acetate copolymer modifier

ABSTRACT It is known that the bonding strength of the aggregate/cement interface affects the overall durability of concrete. However, whether the modification of ethylene vinyl acetate (EVA) copolymer affects the interface interaction between aggregates and cementitious materials is unclear. This study analyzed the interface's static structure, dynamic characteristics, and binding energy. The interaction mechanisms between acid and alkali aggregates and hydrated calcium silicate and the modification effect of EVA were compared. The calculation results of relative density distribution and radial distribution function verified the difference in the structure of EVA-modified acidic or alkaline interfaces. EVA polymer chains significantly blocked the flow of Ca atoms in CaO at the CaO/C-S-H interface and weakened the van der Waals effect at the interface. The mean square displacement and time correlation function analysis indicate that all unmodified interfaces have stable interface structures. After EVA modification, the stability of CaCa-HW decreased significantly, hindered the generation of hydration products, and verified the weak Ca atom transport at the CaO/C-S-H interface. In addition, the adhesion energy of SiO2/C-S-H and CaO/C-S-H after EVA modification decreased by 6% and 14.8%, respectively, quantifying the modification effect of EVA.

Thermal and Structural Analysis on Simulated Model of a Beam Dump

This paper deals with the design, thermal and structural analysis for stopping the proton beam. A conical beam dump is being designed to handle the thermal and structural stresses resulting due to high heat load and hydraulic pressure of coolant, while handling 600 KW proton beam power in CW operation at 20 MeV energy. Pressure drop and heat transfer calculations are done considering spiral channel cooling system. The heat flux has been calculated by using Bi-Gaussian distribution density function of particles in beam. Nickel is selected as the beam dump material because of its favorable properties. In order to understand the thermal performance of beam dump a finite element model has been developed to predict the steady state temperature and stress distributions within the beam stop material. Key Word: Beam dump design, FEM, Thermal and Structural stress.

Nano structure of CO2-Brine-Kaolinite Interface: Implications for CO2 Geological Sequestration

CO2-Brine-Rock interaction has been identified to govern CO2 multiphase flow and affect the integrity of the underground reservoirs. However, limited investigations address the role of brine salinity, rock mineralogy, and organic matter in CO2 wettability at nano scale. To solve this problem, a molecular dynamics (MD) simulation is performed. The interfacial properties, including density distribution and radial distribution function (RDF, g(r)), are calculated for CO2 saturated high salinity water and CO2 saturated low salinity water. The density distribution profile shows that mineralogy is a critical parameter for CO2 wettability: lowering salinity leads to a more CO2 wet siloxane surface while the aluminol surface becomes less CO2 wet. g(r) reveals that the type of organic matter plays a critical role: base functional group (-N) renders a CO2 wet surface whereas the acid functional group (-COOH) causes a water wet surface. This investigation integrates the effects of brine salinity, mineralogy, and organic matter to evaluate CO2 wettability. This MD simulation reveals the principal factors controlling the CO2 wettability at the nano scale and provides a general paradigm to reduce the leakage risk of CO2 geological sequestration.

Transform coefficient distribution modeling based frame-level adaptive rate control for VVC

Rate control is a key issue in the research of video coding optimization. In this work, we propose a statistical modeling based frame-level distortion estimation model and a distortion dependency based rate control optimization algorithm for Versatile Video Coding (VVC). VVC has incorporated into more advanced coding tools, resulting in the distribution of transform coefficient more sharper. In response to this phenomenon, the TCD of VVC is modeled by the probability density function (PDF) of Cauchy distribution and generalized Gaussian distribution (GGD) individually. Then, a sliding window-based frame-level distortion model is proposed, which is used for derivation of inter-frame distortion dependency factor. According to the derived distortion dependency factor, a frame-level rate control optimization algorithm is presented to update the coding parameters in practical coding process. Experiments have shown that the proposed method could effectively improve rate–distortion performance, achieving an average rate distortion performance improvement of 0.72% in sequences blow 4K resolution, and 1.47% in 4K sequences in low delay P frame (LDP) configuration.

A T-splines-oriented isogeometric topology optimization for plate and shell structures with arbitrary geometries using Bézier extraction

Recently, the non-uniform rational B-splines (NURBS) have been considerably employed in modeling plate and shell structures, or developing the related size, shape or topology optimization methods for their design. However, the NURBS with the tensor product feature strongly hinders the effectiveness of the optimization on complex structures. The primary intention of the current research is to propose a new T-splines-oriented Isogeometric Topology Optimization (T-ITO) method and then address the critical design problem of plate and shell structures with arbitrary shapes in practical applications. Firstly, the Bézier extraction is utilized in the T-splines to map the geometrical model into a family of Bézier elements, each of which is presented by a local Density Distribution Function (DDF) for elementary topology. A global DDF is constructed by an assembly of all local DDFs with a natural connection to the present structural topology. Secondly, the T-splines-based IsoGeometric Analysis (T-IGA) formulation with the Bézier extraction for complex plate and shell structures is developed using the Kirchhoff-Love theory, where a universal numerical implementation framework is constructed, including the Rhino, MATLAB, export modules with all geometric information and import modules for the analysis. Thirdly, a mathematical formulation for plate and shell structures with arbitrary geometries is developed using the T-ITO method to improve structural loading-capability, and the sensitivity analysis with respect to design variables is rigorously derived in detail. Finally, several numerical examples of plate and shell structures with both regular and elaborate geometries are tested to demonstrate the validity, effectiveness, superiorities and indispensability of the T-ITO method.

Generalized Variational Inference via Optimal Transport

Variational Inference (VI) has gained popularity as a flexible approximate inference scheme for computing posterior distributions in Bayesian models. Original VI methods use Kullback-Leibler (KL) divergence to construct variational objectives. However, KL divergence has zero-forcing behavior and is completely agnostic to the metric of the underlying data distribution, resulting in bad approximations. To alleviate this issue, we propose a new variational objective by using Optimal Transport (OT) distance, which is a metric-aware divergence, to measure the difference between approximate posteriors and priors. The superior performance of OT distance enables us to learn more accurate approximations. We further enhance the objective by gradually including the OT term using a hyperparameter λ for over-parameterized models. We develop a Variational inference method with OT (VOT) which presents a gradient-based black-box framework for solving Bayesian models, even when the density function of approximate distribution is not available. We provide the consistency analysis of approximate posteriors and demonstrate the practical effectiveness on Bayesian neural networks and variational autoencoders.

SIR epidemic model with non-Lipschitz stochastic perturbations

This paper investigates a stochastic SIR epidemic model with non-Lipschitz coefficients in the diffusion term. Firstly, we study the existence and uniqueness of the global positive solution of this model. Then, we prove that the stochastic process has a stationary distribution, and we also establish an exact expression of the density function of the stationary distribution under certain parameter constraints. Finally, we discuss the extinction of the epidemic and the asymptotic properties around the equilibrium points of the deterministic SIR model.

A P–S–N curve fitting method based on mixed Weibull distribution and expectation-maximization algorithm

In practical engineering, there are many factors affecting the fatigue life of actual components, and a single Weibull distribution is insufficient to accurately describe the impact of various factors on fatigue life. In order to solve the above problems, 316L stainless steel is taken as the experimental object to study the effects of phase difference and stress levels on fatigue life based on the mixed Weibull distribution model. Firstly, the mixed Weibull distribution model is converted into the mixed extreme value distribution model, and used Euler's constant to calculate relevant parameters of extreme value distribution and Expectation-Maximization (EM) algorithm to determine the probability density function of the mixed Weibull distribution. Secondly, the probability density function is integrated to obtain the distribution function and the fatigue life under different failure probabilities is calculated. Finally, the influence of non-proportional additional reinforcement and stress amplitude on fatigue life is studied by taking them as hidden variables of mixed Weibull distribution, which is used to obtain P-S-N curves for various failure probabilities. Through the proposed method, the influence of different factors on fatigue life can be considered from the perspective of statistics, and the accuracy of fatigue life prediction can be promoted.

Droplet coalescence in coupled shear and electric fields: A molecular dynamics study

Water droplet coalescence in coupled flow and electric fields is a phenomenon extensively observed in petrochemical, microfluidic, and chemical synthesis processes; however, the existing research in this domain lacks the necessary depth. This paper employs a molecular dynamics approach to elucidate the microscopic mechanisms governing droplet aggregation in water-in-oil emulsions. The investigation spans various shear rates and droplet angles, considering droplet morphology and molecular interactions. The study reveals an interrelation between shear rate and droplet angle effects on droplet coalescence, both seeking to understand the impact of the flow field's shear effect on the electrocoalescence of water droplets. Increasing the shear rate proves advantageous to droplet aggregation up to a certain threshold; however, complete coalescence is hindered beyond the critical shear rate, γ = 7.5 × 109 s−1. Augmenting the droplet angle amplifies the shear force exerted by the flow field on the droplets, while diminishing the radial electric field force. Consequently, an optimal droplet angle of θ = 25° facilitates comprehensive droplet merging. The analysis of the coalescence process, interaction energy, charge density and radial distribution function shows that the approximate process of droplet motion is as follows: the shear effect drives the droplets to approach, and then the directional migration of charge and electrostatic attraction between water molecules drive the coalescence. The existence of a moderate shear effect enables complete droplet coalescence. This study offers theoretical guidance for the exploration of dynamic electrocoalescence technology.

Dynamical Identification of Urban-Rural Gradient and Ecosystem Service Response: A Case Study of Jinghong City, China

Understanding ecosystem service characteristics along urban-rural gradients is vital for enhancing the well-being of urban and rural residents. Despite this importance, prior research has neglected the dynamic evolution of urban-rural gradients during urbanization. This study investigates the spatiotemporal variations of four ecosystem services—habitat quality, carbon sequestration, water yield, and soil retention—along the urban-rural gradient in Jinghong City, China. We propose a method for identifying the gradient using the inverse S function of urban land density distribution and concentric analysis. From 2000 to 2020, ecosystem service supply capacity in Jinghong City continuously declined, indicating degradation over the two decades. The urban-rural gradient zone is classified as core area, inner urban area, suburban area, and urban periphery, each experiencing outward expansion, reflecting significant urbanization. Changes in ecosystem services along the gradient revealed consistently high losses in habitat quality, carbon sequestration, and overall services in the inner urban area, while water yield and soil retention suffered the greatest losses in the urban periphery. As urbanization expanded outward, the loss of these services shifted from the inner urban area to the suburban and urban periphery. These results support decision-making in urban planning and sustainable development for urban-rural regions.

Quantitative Methods for Evaluating Long-Term Career Attitudes of the Subjects of Modern Society («Model of the Life Trajectory»)

The article is devoted to the problems of ideas of the subjects of modern society about the long-term prospects for the development of their life path (the so-called “life trajectories”). Particular attention is paid to methods for formalizing such representations based on the approximation of life trajectories using curves from the family of beta distribution density functions. The parameters of the beta-density function can be used as the basis for the formal typification of subjects within society. Their changes can be used as indicators of structural changes in society. First of all, in terms of shifts in ideas about the «ideal» (reference) configurations of the life path. In part, these conclusions can be incorporated into procedures for identifying generations.

A New Sparse Bayesian Learning-Based Direction of Arrival Estimation Method with Array Position Errors

In practical applications, the hydrophone array has element position errors, which seriously degrade the performance of the direction of arrival estimation. We propose a direction of arrival (DOA) estimation method based on sparse Bayesian learning using existing array position errors to solve this problem. The array position error and angle grid error parameters are introduced, and the prior distribution of these two errors is determined. The joint probability density distribution function is established by means of a sparse Bayesian learning model. At the same time, the unknown parameters are optimized and iterated using the expectation maximum algorithm and the corresponding parameters are solved to obtain the spatial spectrum. The results of the simulation and the lake experiments show that the proposed method effectively overcomes the problem of array element position errors and has strong robustness. It shows a good performance in terms of its estimation accuracy, meaning that the resolution ability can be greatly improved in the case of a low signal-to-noise ratio or small number of snapshots.

Transient quasi-periodic oscillations in the gamma-ray light curves of bright blazars

ABSTRACT Transient quasi-periodic oscillations (QPOs) are extremely interesting observational phenomena. However, the precise physical mechanisms leading to their generation are still hotly debated. We performed a systematic search for transient QPO signals using Weighted Wavelet Z-transforms on the gamma-ray light curves of 134 bright blazars with peak flux exceeding 1 × 10−6 ph cm−2 s−1 as monitored by Fermi-LAT. Artificial light curves were generated from the power spectral density and probability distribution functions of the original light curves to assess the significance level of transient QPO. We discuss several physical mechanisms that produce transient QPOs, with the helical jet model providing the best explanation. This study identified four new transient QPO events. Interestingly, repetitive transient QPOs are observed in PKS 0537-441, and nested transient QPOs are detected in PKS 1424−41. Additionally, we find that transient QPOs tend to occur in the flare state of the blazar. Finally, we estimate the incidence of transient QPO events to be only about 3 per cent.

On the Existence of Global Solutions for the Vlasov–Poisson System in a Half-space and Plasma Confinement

We consider the Vlasov–Poisson system with external magnetic field in a half-space with the Neumann boundary condition for the electric potential and specular reflection on a boundary. For arbitrary compactly supported initial density distribution functions, we obtain sufficient conditions for external magnetic field, which provide global existence of density distribution functions with compact supports lying at some distance from a boundary.

An efficient discrete unified gas-kinetic scheme for compressible thermal flows

In this paper, an efficient discrete unified gas-kinetic scheme (DUGKS) is developed for compressible thermal flows based on the total energy kinetic model for natural convection with a large relative temperature difference. A double distribution function model is designed with the second distribution representing the total energy. This efficient DUGKS enables the simulation of compressible thermal flows, governed by the compressible Navier–Stokes–Fourier system, using only a seventh-order, off-lattice Gauss–Hermite quadrature (GHQ) D3V27A7 combined with a fifth-order GHQ D3V13A5. The external force is included by truncated Hermite expansions. Based on the Chapman–Enskog approximation and Hermite projection, we propose a systematic approach to derive the discrete kinetic boundary conditions for the density and total energy distribution functions. The discrete kinetic boundary treatments are provided for the no-slip boundary condition, Dirichlet boundary condition and Neumann boundary condition. To validate our scheme, we perform simulations of steady natural convection (Ra=103−106) in two- and three-dimensional cavities with differentially heated sidewalls and a large temperature difference (ε=0.6), where the Oberbeck–Boussinesq approximation is invalid. The results demonstrate that the current efficient DUGKS is robust and accurate for thermal compressible flow simulations. With the D3V27A7 and D3V13A5 off-lattice discrete particle velocity model, the computational efficiency of the DUGKS is improved by a factor of 3.09 when compared to the previous partial energy kinetic model requiring the ninth-order Gauss–Hermite quadrature.

Heliospheric Diffusion of Stochastic Parker Spirals in Radially Evolving Solar Wind Turbulence

We present a stochastic field line mapping model where the interplanetary magnetic field lines are described by a density distribution function satisfying a Fokker–Planck equation that is solved numerically. Due to the spiral geometry of the nominal Parker field and to the evolving nature of solar wind turbulence, the heliospheric diffusion of the magnetic field lines is both heterogeneous and anisotropic, including a radial component. The longitudinal distributions of the magnetic field lines are shown to be close to circular Gaussian distributions, although they develop a noticeable skewness. The magnetic field lines emanating from the Sun are found to differ, on average, from the spirals predicted by Parker. Although the spirals remain close to Archimedean, they are here underwound, on average. Our model predicts a spiral angle that is smaller by ∼5° than the Parker spiral angle at Earth’s orbit for the same solar wind speed of V sw = 400 km s−1. It also predicts an angular position on the solar disk of the best magnetically connected footpoint to an observer at 1 au that is shifted westward by ∼10° with respect to the Parker’s field model. This significantly changes the angle of the most probable magnetic connection between possible sources on the Sun and observers in the inner heliosphere. The results have direct implications for the heliospheric transport of “scatter-free” electrons accelerated in the aftermath of solar eruptions.

An accelerated lattice Boltzmann method for natural convection coupled with convolutional neural network

A novel approach is proposed in the present study, which combines the lattice Boltzmann method (LBM) with convolutional neural networks and is suitable for square cavity natural convection and conjugate natural convection problems, exhibiting remarkable acceleration capabilities and potentials. The density distribution function obtained from LBM at time t and the temperature distribution function at time t+Δt under different Rayleigh numbers (Ra) are, respectively, utilized as input and output datasets for training and comparison in three convolutional neural networks, aiming to select the optimal coupling model, namely, half-Res-Unet. The coupling model can accurately simulate the natural convection in a square cavity within six times the upper limit of the Ra under the training condition, which can save the central processing unit (CPU) calculation time and the iteration steps by up to 29.2% and 30.3%, respectively. The coupling model is further extended in the current study to incorporate conjugate natural convection, enabling the accurate simulation of temperature distribution under training conditions with a thermal conductivity ratio (Ka) of 25 and an upper limit of Ra increased by 20 times. The corresponding maximum relative errors for the average Nusselt numbers (Nu) are found to be 1.8% and 0.7%, respectively, providing strong evidence for the generalization capability of the coupling model. Furthermore, the coupling model demonstrates a remarkable acceleration performance, as evidenced by its ability to reduce the CPU calculation time by up to 39.6% and iteration steps in the simulation process by 36.5%. It offers valuable insights into the integration of LBM with machine learning techniques, thereby enhancing the computational efficiency of LBM.