Experimental Frequency Distribution Research Articles

MULTIPLE REGRESSION MODELING THE CHEMICAL COMPOSITION EFFECTS ON THE TENSILE STRENGTH OF Ni-BASED SUPERALLOYS

Based on the previously obtained results of the Data Mining - based Classification and Regression Trees (C&RT) technique application to industrial Ni-based superalloys, multiple regression models were developed to describe quantitatively the chemical composition effects on the alloys tensile strength. The regression models obtained were verified for adequacy in three ways, contrary to the conventional approach requiring only several inadequacy variance values calculations. Namely, the following verification methods were applied: traditional R2 coefficient calculations; comparisons of computer and experimental frequency distributions of the quality indexes; Monte-Carlo simulated and experimental data based scatter plots comparing. It was emphasized that, according to the general statistic principle, close coincidence of the Monte-Carlo simulated and real frequency distributions of any measured characteristic values means full formal (statistical) identity of the real and simulated objects. Hence, in addition, coincidence of the corresponding scatter plots statistical parameters should be considered as a sign of the physical identity of real and modeled regression dependencies. All the applied verification methods show the excellent results that leads to conclusion about high workability of the obtained models in practical and theoretical applications. An additional general advantage of the models was noted: their physically interpretable structure, that provides the opportunity to determine and analyze the effects of individual chemical elements and their interactions under real industrial conditions. Most of the obtained results and the formulated conclusions, especially related to the chemical elements individual effects are in good accordance with the known experimental and theoretic data for polycrystalline Ni-based superalloys. Meantime, some unexpected features, particularly, for the interactions of Nb, Ti, Cu with each other and grain boundaries were revealed, showing necessity of further in dept investigations.

Micro-Mechanical Properties of Individual Phases in Cement Pastes under Brine Solution Using Nanoindentation and Scanning Electron Microscopy

Understanding the micro-mechanical properties and the microstructure of cement-based materials under the saline lake environment in western China can provide a scientific basis for the durability design. In this study, cement pastes ((w/c=0.35) and (w/c=0.53)) were prepared and soaked in brine solution to carry out the dry-wet cycle test, the chemical composition of which is similar to saline lake solution. The micrographs of corroded regions and corrosion products were observed and analyzed under scanning electron microscope (SEM) and energy dispersive spectrometer (EDS). Micro-mechanical properties of different phases were tested by nanoindentation, and multi-peaks fitting was carried out for the experimental frequency distributions of the indentation modulus and indentation hardness by Gaussian function. In the meantime,the statistical distribution of micro-mechanical properties was summarized for the hydrates in corroded cement paste, which has included the low density calcium–silicate–hydrates (LD C-S-H gel), high density calcium–silicate–hydrates (HD C-S-H gel) and calcium hydroxide (CH). The results show that micro mechanical properties of each phase in cement paste after brine corrosion decreased significantly. In addition, the water-cement ratio has little effect on the micro mechanical properties, but much effect on volume fraction of each phase.

Mathematical Modeling of Avidity Distribution and Estimating General Binding Properties of Transcription Factors from Genome-Wide Binding Profiles.

The shape of the experimental frequency distributions (EFD) of diverse molecular interaction events quantifying genome-wide binding is often skewed to the rare but abundant quantities. Such distributions are systematically deviated from standard power-law functions proposed by scale-free network models suggesting that more explanatory and predictive probabilistic model(s) are needed. Identification of the mechanism-based data-driven statistical distributions that provide an estimation and prediction of binding properties of transcription factors from genome-wide binding profiles is the goal of this analytical survey. Here, we review and develop an analytical framework for modeling, analysis, and prediction of transcription factor (TF) DNA binding properties detected at the genome scale. We introduce a mixture probabilistic model of binding avidity function that includes nonspecific and specific binding events. A method for decomposition of specific and nonspecific TF-DNA binding events is proposed. We show that the Kolmogorov-Waring (KW) probability function (PF), modeling the steady state TF binding-dissociation stochastic process, fits well with the EFD for diverse TF-DNA binding datasets. Furthermore, this distribution predicts total number of TF-DNA binding sites (BSs), estimating specificity and sensitivity as well as other basic statistical features of DNA-TF binding when the experimental datasets are noise-rich and essentially incomplete. The KW distribution fits equally well to TF-DNA binding activity for different TFs including ERE, CREB, STAT1, Nanog, and Oct4. Our analysis reveals that the KW distribution and its generalized form provides the family of power-law-like distributions given in terms of hypergeometric series functions, including standard and generalized Pareto and Waring distributions, providing flexible and common skewed forms of the transcription factor binding site (TFBS) avidity distribution function. We suggest that the skewed binding events may be due to a wide range of evolutionary processes of creating weak avidity TFBS associated with random mutations, while the rare high-avidity binding sites (i.e., high-avidity evolutionarily conserved canonical e-boxes) rarely occurred. These, however, may be positively selected in microevolution.

Constraining Frequency Distributions with the Probable Maximum Precipitation for the Stochastic Generation of Realistic Extreme Events

Stochastic weather generators are widely used to produce large ensembles of climate time series for assessing risk-based environmental impacts. However, they often perform poorly at generating extreme values since the fitting of traditionally used distribution functions is limited by short historical records. In such cases, extreme values are generated by extrapolating the fitted distributions far outside of observations, and can result in values outside of the physically possible range. This work uses a curve-fitting approach constrained on the probable maximum precipitation (PMP) to allow for the generation of realistic precipitation over the entire range of daily precipitation amounts. The method differs from the traditional parametric approach which assumes that the daily precipitation follows a specific probability distribution. Instead, the curve-fitting approach uses a second-degree polynomial to fit the Weibull experimental frequency distribution of observed daily precipitation. In this process, the PMP is specifically represented with its associated probability of occurrence, thus ensuring the realistic representation of extreme precipitation events. The proposed algorithm is compared to three distribution functions (of varied complexity) for simulating daily precipitation amounts at 35 stations dispersed across central and southern Quebec, Canada. The curve-fitting approach is presented in two versions: with and without constraint on the PMP. The results show that compound distribution functions perform better than their single distribution counterparts at representing the overall distribution of daily precipitation amounts, especially when simulating the upper tail. The unconstrained curve-fitting approach consistently performs better than all of the distribution functions with respect to preserving the statistical characteristics (e.g., mean, standard deviation and overall distribution) of daily precipitation amounts. Constraining the second-degree polynomial to the PMP is an effective way to generate the entire range of daily precipitation amounts with no risk of generating physically impossible values for events with extremely small probability. However, its overall performance is slightly less than that of its unconstrained counterpart.

A generic statistical methodology to predict the maximum pit depth of a localized corrosion process

This paper outlines a new methodology to predict accurately the maximum pit depth related to a localized corrosion process. It combines two statistical methods: the Generalized Lambda Distribution (GLD), to determine a model of distribution fitting with the experimental frequency distribution of depths, and the Computer Based Bootstrap Method (CBBM), to generate simulated distributions equivalent to the experimental one. In comparison with conventionally established statistical methods that are restricted to the use of inferred distributions constrained by specific mathematical assumptions, the major advantage of the methodology presented in this paper is that both the GLD and the CBBM enable a statistical treatment of the experimental data without making any preconceived choice neither on the unknown theoretical parent underlying distribution of pit depth which characterizes the global corrosion phenomenon nor on the unknown associated theoretical extreme value distribution which characterizes the deepest pits. Considering an experimental distribution of depths of pits produced on an aluminium sample, estimations of maximum pit depth using a GLD model are compared to similar estimations based on usual Gumbel and Generalized Extreme Value (GEV) methods proposed in the corrosion engineering literature. The GLD approach is shown having smaller bias and dispersion in the estimation of the maximum pit depth than the Gumbel approach both for its realization and mean. This leads to comparing the GLD approach to the GEV one. The former is shown to be relevant and its advantages are discussed compared to previous methods.

A New Approach to Predict the Pit Depth Extreme Value of a Localized Corrosion Process

Depth of pits that propagate during a pitting corrosion process is an important characteristic of the damage of steels; the greater the depth, the more dramatic the damage. For evident reasons of safety and reliability of industrial installations, statistical procedures must be constructed to assess the maximum pit depth to perform proper maintenance from limited inspection data. This paper outlines a new methodology to predict accurately the pit depth extreme value related to a localized corrosion process independently of the nature of the unknown parent distribution of the experimental data. Based on computer calculations and simulations, this methodology combines the Generalized Lambda Distribution (GLD) and the Bootstrap statistical methods. The GLD method was used in this study to determine a modeled distribution that fits the experimental frequency distribution of pit depths produced on a ferritic stainless steel sample during an accelerated corrosion test. This modeled distribution was used to generate, thanks to the Computer-Based Bootstrap Method (CBBM), simulated distributions of corrosion pit depths equivalent to the experimental one. An estimation of the mean with a 90% confidence interval of the maximum pit depth can be finally deduced not only for these simulated samples of equivalent surface size than the experimental one but also for a large scale installation.

Generalized frequency spectra of water at both sides of the freezing transition

We report a comparison of the experimental frequency distributions of heavy water on both sides of the melting transition. The spectra for ice about 3 ∘ below melting point shows a still narrow first peak at about 6.5 meV as well as a gap centered at about 40 meV separating both the “translational” and “librational” bands. Such features are profoundly modified upon melting. The first peak is still present in the liquid as a well-defined entity although significantly broader than that shown by the hot crystal. The derived Z( ε) spectra is then used for a tentative assignment of features appearing on the Raman spectrum of the liquid.

Copper electrodissolution in 1M HCl at low current densities. II. Electrochemical impedance spectroscopy study

Abstract Anodic oxidation of a copper rotating disk in 1 M HCl is studied by electrochemical impedance spectroscopy (EIS). Experimental impedance diagrams show two capacitive loops separated in frequency. These diagrams validated with Kramers–Kronig relationships reveal a change in the frequency fc, at the apex of the low frequency loop, with the electrode potential. The theoretical expression for the impedance is derived and the possible limiting shapes of the impedance diagrams are discussed. The low frequency loop can take different forms as a convective-diffusion loop, a first order semi-circle or a mixed graph. An increase in fc with the electrode potential should be observed. Fitting of the impedance diagrams by the kinetic model gives good agreement with the experimental frequency distribution. A discussion is presented between the theoretical and experimental results.

The platinum‐carbon replication of a homogenous population of gold particles makes log‐normal distributions of shadow widths and lengths

Gold particles were prepared, dried on grids and shadowed at 45° with a 1.2 nm platinum‐carbon (Pt‐C) film using the shadowing conditions previously described for the freeze‐fracture of gastric parietal cell membranes. The particle diameters and the particle shadow widths and lengths were measured using an image analysis system. Statistical analysis of 2000 diameters, shadow widths and shadow lengths indicated that a homogenous population of particles had a normal frequency distribution of diameters (mean diameter 14.5 ± 1.5 nm) and that the Pt‐C shadowing transformed that normal curve into a log‐normal frequency distribution of shadow widths. The frequency distribution of shadow lengths was log‐normal too. We conclude that a statistical partition of experimental frequency distributions of particle shadow widths and lengths of natural membranes to determine the number and parameters of individual components should involve log‐normal subdistributions rather than normal ones.

Preferential deformation in a mild steel specimen under fast rate compressive loading

Specimens of mild steel were subjected to fast-rate uniaxial compressive loading at liquid nitrogen temperatures such that overall plastic deformation was slight. These conditions should also represent the initial phase of more severe deformation treatments. Deformation seemed to have occurred completely by twinning. By studying and analysing the inclinations of the twin traces with the loading direction as observed on sections of the specimens containing the applied force direction it was found that twinning had occurred preferentially along certain directions relative to the applied force direction. A statistical model based on a minimum threshold value of 0.25 of the Schmid factor for twinning and a suppression factor for twinning in directions opposing the applied force was adopted and found to be successful in accounting for the observed experimental frequency distribution of different inclinations of the twin planes to the applied force direction.

Fragmentation of56Fe in Al at 1.88A GeV

The production of fragmented nuclei from relativistic56Fe beam available from LBL Bevalac at 1.88A GeV has been studied using CR-39 (DOP) passive detector placed at an angle of 60° with respect to the beam. The histogram showing the experimental frequency distribution of minor axes of the elliptic etch pit shows the presence of the fragmented nuclei produced with charge numberZ from 25 up to 21. The histogram further reveals the presence of nuclei withZ=27 and 28. The production of nuclei heavier than56Fe is possibly due to the charge exchange or pick-up phenomena.

About the anisotropy of the polarizability of a pair of argon atoms

Available models of the anisotropy of the polarizability of a pair of argon atoms are used to compute the collision-induced Raman spectrum. It is seen that the point-dipole model allows the best fit of the experimental frequency distribution and absolute intensity, which have been measured previously. Other models of the anisotropy appear by these criteria to be overcorrected or, if successful, not significantly different from the point-dipole expression.

Some Stereological Principles in Morphometric Cytology

In this paper several statistical methods are developed that are of use in morphometric cytology, for the purpose of obtaining three-dimensional information from two-dimensional measurements made on cell sections. An estimator is described for counting $N_V $, the number of organelles (e.g., mitochondria) per unit of cellular volume. Unlike those currently employed, this estimator for $N_V $ does not depend on the sizes of the organelle bodies. The remainder of the paper discusses the axis ratios, t, of elliptical cross sections that are the intersections of an ellipsoid with random planes. For prolate spheroids, an explicit formula is developed for the probability density. For general ellipsoids, a numerical method is presented for calculating the distribution function. As one approach toward deriving information about organelle shape, frequency distributions of t derived by these techniques may be compared with experimental frequency distributions of the axis ratios of organelle cross sections.

Frequency Spectra of Body-Centered-Cubic Lattices

A Born-von Karman model has been used to determine the frequency spectrum for a body-centered cubic lattice. The model used contains noncentral angular stiffness forces as well as central forces between nearest and next-nearest neighbors. Frequency distributions have been calculated for vanadium and compared with experimental frequency distributions available from slow neutron experiments. Qualitative agreement was found between the shapes of the experimental and theoretical distributions. The calculated maximum frequency for vanadium was within 2% of that derived from the experimental frequency distribution. Dispersion curves for iron were also calculated, and were found to be in good agreement with experiment.

Frequency Spectra of Body-Centered Cubic Lattices

A Born-von Karman model has been used to determine the frequency spectrum for a body-centered cubic lattice. The model used contains noncentral angular stiffness forces as well as central forces between nearest and next-nearest neighbors. Frequency distributions have been calculated for vanadium and compared with experimental frequency distributions available from slow neutron experiments. Qualitative agreement was found between the shapes of the experimental and theoretical distributions. The calculated maximum frequency for vanadium was within 2% of that derived from the experimental frequency distribution. Dispersion curves for iron were also calculated, and were found to be in good agreement with experiment.

FREQUENCY DISTRIBUTIONS OF VELOCITIES IN TURBULENT FLOW

Abstract A conventional anemometer used in the atmosphere or in a wind tunnel measures velocities projected on a plane independently of their directions in the plane. The relation between the frequency distribution of those velocities and the frequency distribution of the turbulent components parallel to the direction of the mean velocity is discussed. At small intensities of the longitudinal turbulence the two distributions are approximately the same. However, at intensities of turbulence of the order of those measured in the atmosphere, the difference between the two frequency distributions becomes appreciable. Some experimental frequency distributions of wind velocities are presented, and the intensities of atmospheric turbulence are determined from the experiments.