Probability Distribution Function Method Research Articles

Eulerian–Eulerian RSTM-PDF Modeling of Turbulent Particulate Flow

A novel 3D computational model was developed for the turbulent particulate two-phase flow simulation in the rectangular channel. The model is based on the Eulerian approach applied to 3D Reynolds-averaged Navier–Stokes modeling and statistical Probability Distribution Function method. The uniqueness of the method lies in the direct calculation of normal and transverse components of the Reynolds stresses for both gas and particles. Two cases were examined: a conventional channel flow and grid-generated turbulence flow. The obtained numerical results have been verified and validated by the experimental data, received from the turbulent particle dispersion test. The computed values of the particles’ turbulent dispersion and the maximum value of the particulate concentration distribution show good agreement with the experimental results. The examples are ranged from coal and other bulk material pneumatic transport, vertical fluidized beds, coal gasifiers, and chemical reactors.

Universality and Nonuniversality in Distributed Nuclear Burning in Homogeneous Isotropic Turbulence.

Nuclear burning plays a key role in a wide range of astrophysical stellar transients, including thermonuclear, pair instability, and core collapse supernovae, as well as kilonovae and collapsars. Turbulence is now understood to also play a key role in these astrophysical transients. Here, we demonstrate that turbulent nuclear burning may lead to large enhancements above the uniform background burning rate, since turbulent dissipation gives rise to temperature fluctuations, and in general the nuclear burning rates are highly sensitive to temperature. We derive results for the turbulent enhancement of the nuclear burning rate under the influence of strong turbulence in the distributed burning regime in homogeneous isotropic turbulence, using probability distribution function methods. We demonstrate that the turbulent enhancement obeys a universal scaling law in the limit of weak turbulence. We further demonstrate that, for a wide range of key nuclear reactions, such as C^{12}(O^{16},α)Mg^{24} and 3-α, even relatively modest temperature fluctuations, of the order of 10%, can lead to enhancements of 1-3 orders of magnitude in the turbulent nuclear burning rate. We verify the predicted turbulent enhancement directly against numerical simulations, and find very good agreement. We also present an estimation for the onset of turbulent detonation initiation, and discuss implications of our results for stellar transients.

Comparison of three different deconvolution methods for analyzing nanoindentation test data of hydrated cement paste

The micromechanical properties of hydrated cement paste were investigated by nanoindentation with a large data set (4000 indentation points) to reveal the influences of multiple factors on analysis results. Three different deconvolution analysis methods, i.e. the Gaussian mixture model (GMM) with the maximum likelihood evaluation (MLE) algorithm, the probability distribution function (PDF) and the cumulative distribution function (CDF) with least square estimate (LSE) algorithm, were employed to analyze the nanoindentation test data. It was found that the GMM with a diagonal-unshared matrix is the most appropriate for the deconvolution of nanoindentation data of hydrated cement paste for the MLE algorithm. The PDF and CDF methods are equally effective for the LSE algorithm, but the former is subjected to the influences of bin sizes and the optimal bin size is 1.5–2 GPa for elastic modulus and 0.075–0.1 GPa for hardness. The threshold number of indentation points necessary to obtain reliable micromechanical parameters and phase contents by all three deconvolution methods is approximately 800-1000, significantly higher than the values used in the literature. The phase content seems to show more variations than elastic modulus and hardness when the number of indentation point is insufficient. With sufficient number of indentation points, the three different deconvolution methods give consistent results regarding the properties and contents of six phases identified. The various phase contents calculated by deconvolution of nanoindentation test data are in reasonable agreement with that estimated by QXRD and SEM except for the pore phase.

Dryland farming improvement by considering the relation between rainfall variability and crop yield

About 40% of the global cultivable land practices dryland farming. An improvement of dryland farming is imperative to ensure food security for expanding populations in the developing world. This paper presents a method to assess the impact of precipitation variability on the annual yield of dryland farmed crops. All probable periods of precipitation in three dryland farming seasons (autumn, winter, and spring) are considered. The effect of each period of precipitation on the annual yield of dryland farmed crops is assessed, and the most effective period of precipitation on the annual yield of each crop is identified. Subsequently, annual yield versus effective precipitation regressions for each crop are developed. The annual crop yields are calculated with annual yield versus effective precipitation regressions and with the probability distribution function method. The presented methodology is illustrated with an application to wheat and barley production in Hamedan Province, Iran. The most effective period of precipitation for predicting the annual yield of dryland farmed wheat and barley in all conditions is March 30–May 7. The predictive skill of the annual yield versus effective precipitation regressions is evaluated and found to yield crop yield estimates that are very similar to those obtained with the probability distribution function method.

Bayes theorem–based and copula-based estimation for failure probability function

The failure probability function (FPF), aiming to decouple the nested-loop reliability-based design optimization solution into a single-loop optimization problem, has attracted a great deal of interest from designers and researchers. It is defined as a function of failure probability with respect to the design parameter. Among the estimation methods for the FPF, the Bayes theorem based on probability distribution function methods is competitive. It transforms the FPF as the estimation of the conditional joint probability density function (PDF) of design parameters on the failure event and the augmented failure probability. The augmented failure probability can be estimated by Monte Carlo simulation, while for the joint multi-dimensional PDF, the existing estimation methods are unavailable. To alleviate this issue, a novel FPF estimation method is proposed by Bayes theorem and copula. In the proposed method, the FPF is derived as a product of the conditional copula density and the augmented failure probability, in which the vine copula is employed to disassemble the multi-dimensional conditional copula density into several bivariate copula density functions, and they can be completed by the existing PDF estimation methods. In contrast to the existing Bayes theorem–based estimation methods for the FPF, the proposed method interprets the FPF as the dependence function between design parameters and the augmented failure probability in terms of copula, which involuntarily breaks the limitation of the multi-dimensional design parameters. In addition, the adaptive Kriging surrogate model is embedded in the proposed method to improve the efficiency of the proposed method. The presented examples demonstrate the efficiency and accuracy of the proposed method.

Multi-sensor network for industrial metal plate structure monitoring via time reversal ultrasonic guided wave

Active ultrasonic guided wave is considered to be the most effective and important on-line damage monitoring method for industrial steel plates structure health monitoring. Aiming at the problem of poor practicability of extracting damage scattering signal from baseline signal, a baseline-free time reversal probabilistic imaging algorithm (BFTRPI algorithm) is proposed in this paper based on ultrasound guided waves time reversal theory and probability statistics principle. Firstly, the time reversal of signal and the adaptive focusing mechanism of wave source are used to eliminate the dispersion effect of Lamb wave by the multi-sensor network. Secondly, the energy characteristic difference coefficient between the reconstructed Lamb wave signal and the original excitation signal, is taken as the damage factor. Finally, the relative distance between the damage and the direct path of the sensor-actuator channel is used to adjust the weight distribution function. The weighted probabilistic values of each sensor path in the sensor network are mapped to the discrete coordinates in the detection area, and the probabilistic imaging of the damage appearing on these discrete coordinates is constructed for multiple damages imaging and location. Experiments on aluminium sheets show that the method can clearly separate the damage scattering signals without baseline signals, achieve the focus of the original excitation signal, and obtain the damage probability images of structure. Compared to traditional probability distribution function method, it has better imaging accuracy and imaging quality. The positioning accuracy of the BFTRPI algorithm is obviously higher than that of traditional algorithm. The estimated position by BFTRPI algorithm is more close to the actual damage position. The location area of damage and artifact for traditional algorithm are both higher than that of BFTRPI algorithm. This method can accurately identify and locate multiple damages in aluminium sheet, which verifies the validity of this method and has certain engineering application value.

Classification of Selected Citrus Fruits Based on Color Using Machine Vision System

This article evaluated some of the machine vision techniques to classify selected citrus fruits like oranges, sweet-lime, and lemon based on color analysis using single view fruit images. The methods carried out analyze the fruit images to extract the hue and classify using methods like color distance, linear discriminant analysis, and probability distribution function. The performance was evaluated in terms of classification accuracy relative to human classification and computational complexity. Classification accuracy above 90% could be obtained based on color classification. The probability distribution function method was found to be computationally less intensive and providing better accuracy when compared to other two methods. Since surface color is one of the indicators of maturity, color determination was also extended to find the maturity of fruits based on color variations within the same variety of fruits using red/green value ratio. The analysis also showed that the color information found in terms of hue mean and hue median can be utilized to classify the fruits based on maturity. Appropriate algorithms were developed and implemented to classify the fruits based on color and maturity using the above methods.

Prospects of Wind Energy in Bagwai for Irrigation Scheme

A 10 years data (2002-2012) was used to analyse the possibility of using weibull probability distribution function method to generate power for irrigational pumping machine, the mean and extractable power densities were found to be 22.75w/m 2 and 13.49 Kwh/m 2 at 25m height respectively, this indicate strongly

Develop Probability Distribution Function to Select Pavement Preventive Maintenance Materials and Methods

Maintenance and protection of road pavements are one of important tasks of highway agencies. Many studies are done about specifying suitable time for pavement preventive maintenance. The probability distribution isn't used in this study, although the significant factor in decision making is relevant to probability function. In present paper, the suitable time between two preventive repairs is determined by Erlangen probability distribution function method. Economical factors are one of important parameters in this method, so, maintenance and repairing process cost, the useful life of maintenance process and the cutting of traffic flow are applied in calculation of suggested method.

Evolution and collapse of quasistationary states of an electron in planar symmetric three-barrier resonance-tunneling structures

A theory of the evolution and collapse of pairs of resonances because of a change in the strength (thickness) of the inner barrier is developed in a model of effective masses and symmetric, square, potential barriers for an electron in a planar three-barrier structure. Analytical and numerical calculations of the spectral parameters (resonance energies and widths) are performed by the transmission coefficient and probability distribution function method using the transfer and S matrices. It is shown that the collapse of the resonance energies and widths of all quasistationary states in a symmetric three-barrier structure occurs for practically the same thicknesses of the inner barriers, somewhat greater than the total thickness of the outer barriers. It is established that with respect to the square-barrier model the δ model overestimates the resonance energies by 10% and the resonance widths by almost a factor of 2.

Comparison of the RANS and PDF methods for air-particle flows

Two simulation methods, namely Reynolds-Averaged Navier–Stokes (RANS) equations, and Probability Distribution Function (PDF) are currently widely used for the modeling of multiphase flows. These two approaches are supplemented with appropriate closure equations that take into account all the pertinent forces and interaction effects on the solid particles, such as: particle–turbulence interactions; turbulence modulation; particle–particle interactions; particle–wall interactions; gravitation, drag and lift forces. The two methods have been used in order to simulate the turbulent particulate flow in upward pipes. The flow domain in all cases was a cylindrical pipe and the computations were carried for upward pipe flow. Monodisperse as well as polydisperse mixtures of particles have been considered. In general, the average velocity results obtained from the two methods are in close agreement, because the methods predict well the average velocity distribution of the carrier fluid as well as the solids. Thus, the differences in the average axial velocities predicted by the methods are not substantial. Differences in the turbulence intensity are more significant. A comparison of the numerical results obtained shows the relative importance of retaining the diffusion terms in both the axial and radial directions in the RANS method. Also the comparisons of the results show the relative effect of the lift forces in the distribution of solid particles.

MAD techniques applied to powder data: finding the structure given the substructure

The joint probability distribution function method is applied to multiple-wavelength anomalous dispersion (MAD) powder data. The distributions are calculated by assuming prior knowledge of the scattering intensities at two wavelengths and of the anomalous-scatterer substructure. The method leads to formulas estimating the full structure phases and their reliability. The procedure has been applied to two structures, one unknown and one known; the second was used as a control for the phasing procedure. In spite of the unavoidable peak overlapping in the diffraction pattern, the formulas proved to be very effective. Combined with a new algorithm for phase extension, they enabled the solution of both crystal structures.

Multiple-wavelength anomalous dispersion techniques applied to powder data: a probabilistic method for finding the substructureviajoint probability distribution functions

A new joint probability distribution function method is described to find the anomalous scatterer substructure from powder data. The method requires two wavelengths; the conclusive formulas provide estimates of the substructure structure factor moduli, from which the anomalous scatterer positions can be found by Patterson or direct methods. The theory has been preliminarily applied to two compounds, the first having Pt and the second having Fe as anomalous scatterer. Both substructures were correctly identified.

INVESTIGATION OF SPONTANEOUS CHIRAL-SYMMETRY BREAKING FROM LATTICE QCD WITH MASSLESS QUARKS

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, zeros of the Bessel function and eigenvalue of Dirac operator is also given. The chiral condensate in this limit can be measured with small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. Results for lattice QCD with Kogut-Susskind quarks are shown.

Spontaneous chiral-symmetry breaking of lattice QCD with massless dynamical quarks

One of the most challenging issues in QCD is the investigation of spontaneous chiral-symmetry breaking, which is characterized by the non-vanishing chiral condensate when the bare fermion mass is zero. In standard methods of the lattice gauge theory, one has to perform expensive simulations at multiple bare quark masses, and employ some modeled functions to extrapolate the data to the chiral limit. This paper applies the probability distribution function method to computing the chiral condensate in lattice QCD with massless dynamical quarks, without any ambiguous mass extrapolation. The results for staggered quarks indicate that this might be a promising and efficient method for investigating the spontaneous chiral-symmetry breaking in lattice QCD, which deserves further investigation.

Chiral condensate of lattice QCD with massless quarks from the probability distribution function method

We apply the probability distribution function method to the study of chiral properties of QCD with quarks in the exact massless limit. A relation among the chiral condensate, the zeros of the Bessel function, and the eigenvalue of the Dirac operator is also given. The chiral condensate in this limit can be measured with a small number of eigenvalues of the massless Dirac operator and without any ambiguous mass extrapolation. The results for SU(3) gauge theory with quenched Kogut-Susskind quarks on the ${10}^{4}$ lattice are shown.

The probability distribution function of structure factors with non-integral indices. III. The joint probability distribution in the P1; case.

The joint probability distribution function method has been developed in P1; for reflections with rational indices. The positional atomic parameters are considered to be the primitive random variables, uniformly distributed in the interval (0, 1), while the reflection indices are kept fixed. Owing to the rationality of the indices, distributions like P(F(p1), F(p2)) are found to be useful for phasing purposes, where p1 and p2 are any pair of vectorial indices. A variety of conditional distributions like P(|F(p1)| | |F(p2)|), P(|F(p1)| |F(p2)), P(varphi(p1)| |F(p1)|, F(p2)) are derived, which are able to estimate the modulus and phase of F(p1) given the modulus and/or phase of F(p2). The method has been generalized to handle the joint probability distribution of any set of structure factors, i.e. the distributions P(F(1), F(2),ellipsis, F(n+1)), P(|F(1)| |F(2),ellipsis, F(n+1)) and P(varphi(1)| |F|(1), F(2),ellipsis, F(n+1)) have been obtained. Some practical tests prove the efficiency of the method.

Characterization of Cast Metals with Probability Distribution Functions

AbstractCharacterization of microstructure using a probability distribution function (PDF) provides a means for extracting useful information about material properties. In the extension of classical PDF methods developed in our research, material characteristics are evolved by propagating an initial PDF through time, using growth laws derived from consideration of heat flow and species diffusion, constrained by the Gibbs-Thomson law. A model is described here that allows for nucleation, followed by growth of nominally spherical grains according to a stable or unstable growth law. Results are presented for the final average grain size as a function of cooling rate for various nucleation parameters. In particular we show that the model describes linear variation of final grain size with the inverse cube root of cooling rate. Within a subset of casting parameters, the stable-to-unstable manifests itself as a bimodal distribution of final grain size. Calculations with the model are described for the liquid to epsilon phase transition in a plutonium I weight percent gallium alloy.