Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Influence of threshold stress on the estimation of the Weibull statistics

The influence of threshold stress on the estimation of the Weibull statistics is discussed in terms of the Akaike information criterion. Numerical simulations show that, if sample data are limited in number and threshold stress is not too large, the two-parameter Weibull distribution is still a preferred choice. For example, the fit of strength data of glass and ceramics to the two- and three-parameter Weibull distributions is compared.

Statistics of Turbulence in Benthal Boundary Layers

This paper deals with turbulence behavior inbenthalboundarylayers by means of large eddy simulation (LES). The flow is modeled by moving an infinite plate in an otherwise quiescent water with an oscillatory and a steady velocity components. The oscillatory one aims to simulate wave effect on the flow. A number of large-scale turbulence databases have been established, based on which we have obtained turbulencestatisticsof the boundarylayers, such as Reynolds stress, turbulence intensity, skewness and flatness ofturbulence, and temporal and spatial scales of turbulent bursts, etc. Particular attention is paid to the dependences of those statistics on two nondimensional parameters, namely the Reynolds number and the current-wave velocity ratio defined as the steady current velocity over the oscillatory velocity amplitude. It is found that the Reynolds stress and turbulence intensity profile differently from phase to phase, and exhibit two types of distributions in an oscillatory cycle. One is monotonic occurring during the time when current and wave-induced components are in the same direction, and the other inflectional occurring during the time when current and wave-induced components are in opposite directions. Current component makes an asymmetrical time series of Reynolds stress, as well as turbulence intensity, although the mean velocity series is symmetrical as a sine/cosine function. The skewness and flatness variations suggest that the turbulence distribution is not a normal function but approaches to a normal one with the increasing of Reynolds number and the current-wave velocity ratio as well. As for turbulent bursting, the dimensionless period and the mean area of all bursts per unit bed area tend to increase with Reynolds number and current-wave velocity ratio, rather than being constant as in steady channel flows.

The effects of sediment transport on grain-size distributions

Changes in statistics (mean, sorting, and skewness) describing grain-size distributions have long been used to speculate on the direction of sediment transport. We present a simple model whereby the distributions of sediment in transport are related to their source by a sediment transfer function which defines the relative probability that a grain within each particular class interval will be eroded and transported. A variety of empirically derived transfer functions exhibit negatively skewed distributions (on a phi scale). Thus, when a sediment is being eroded, the probability of any grain going into transport increases with diminishing grain size throughout more than half of its size range. This causes the sediment in transport to be finer and more negatively skewed than its source, whereas the remaining sediment (a lag) must become relatively coarser and more positively skewed. Flume experiments show that the distributions of transfer functions change from having a highly negative skewness to being nearly symmetrical (although still negatively skewed) as the energy of the transporting process increases. We call the two extremes low-energy and high-energy transfer functions , respectively. In an expanded sediment-transport model, successive deposits in the direction of transport are related by a combination of two transfer functions. If energy is decreasing and the transfer functions have low-energy distributions, successive deposits will become finer and more negatively skewed. If, however, energy is decreasing, but the initial transfer function has a high-energy distribution, successive deposits will become coarser and more positively skewed. The variance of the distributions of lags, sediment in transport, and successive deposits in the down-current direction must eventually decrease (i.e., the sediments will become better sorted). We demonstrate that it is possible for variance first to increase, but suggest that, in reality, an increasing variance in the direction of transport will seldom be observed, particularly when grain-size distributions are described in phi units. This model describing changes in sediment distributions was tested in a variety of environments where the transport direction was known. The results indicate that the model has real-world validity and can provide a method to predict the directions of sediment transport

Kinetic Assessment of Measured Mass Flow Rates and Streamwise Pressure Distributions in Microchannel Gas Flows

Measured mass flow rates and streamwise pressure distributions of gas flowing through microchannels were reported by many researchers. Assessment of these data is crucial before they are used in the examination of slip models and numerical schemes, and in the design of microchannel elements in various MEMS devices. On the basis of kinetic solutions of the mass flow rates and pressure distributions in microchannel gas flows, the measured data available are properly normalized and then are compared with each other. The 69 normalized data of measured pressure distributions are in excellent agreement, and 67 of them are within 1 +/- 0.05. The normalized data of mass flow-rates ranging between 0.95 and 1 agree well with each other as the inlet Knudsen number Kn (i) < 0.02, but they scatter between 0.85 and 1.15 as Kn (i) > 0.02 with, to some extent, a very interesting bifurcation trend.

Statistics of dissipation and enstrophy induced by localized vortices

The ratios of enstrophy and dissipation moments induced by localized vorticity are inferred to be finite. It follows that the scaling exponents for locally averaged dissipation and enstrophy are equal. However, enstrophy and dissipation exponents measured over finite ranges of scales may be different. The cylindrical vortex profile that yields maximal moment ratios is determined. The moment ratios for cylindrical vortices are used to interpret differences in scale dependence of enstrophy and dissipation previously found in numerical simulations.

Thickness And Component Distributions Of Yttrium-Titanium Alloy Films In Electron-Beam Physical Vapor Deposition

Thickness and component distributions of large-area thin films are an issue of international concern in the field of material processing. The present work employs experiments and direct simulation Monte Carlo (DSMC) method to investigate three-dimensional low-density, non-equilibrium jets of yttrium and titanium vapor atoms in an electron-beams physical vapor deposition (EBPVD) system furnished with two or three electron-beams, and obtains their deposition thickness and component distributions onto 4-inch and 6-inch mono-crystal silicon wafers. The DSMC results are found in excellent agreement with our measurements, such as evaporation rates of yttrium and titanium measured in-situ by quartz crystal resonators, deposited film thickness distribution measured by Rutherford backscattering spectrometer (RBS) and surface profilometer and deposited film molar ratio distribution measured by RBS and inductively coupled plasma atomic emission spectrometer (ICP-AES). This can be taken as an indication that a combination of DSMC method with elaborate measurements may be satisfactory for predicting and designing accurately the transport process of EBPVD at the atomic level.

Experimental Investigation Of Particle Velocity Distributions In Windblown Sand Movement

With the PDPA (Phase Doppler Particle Analyzer) measurement technology, the probability distributions of particle impact and lift-off velocities on bed surface and the particle velocity distributions at different heights are detected in a wind tunnel. The results show that the probability distribution of impact and lift-off velocities of sand grains can be expressed by a log-normal function, and that of impact and lift-off angles complies with an exponential function. The mean impact angle is between 28 degrees and 39 degrees, and the mean lift-off angle ranges from 30 degrees to 44 degrees. The mean lift-off velocity is 0.81-0.9 times the mean impact velocity. The proportion of backward-impacting particles is 0.05-0.11, and that of backward-entrained particles ranges from 0.04 to 0.13. The probability distribution of particle horizontal velocity at 4 mm height is positive skew, the horizontal velocity of particles at 20 mm height varies widely, and the variation of the particle horizontal velocity at 80 mm height is less than that at 20 mm height. The probability distribution of particle vertical velocity at different heights can be described as a normal function.

Effects Of Subgrid-Scale Modeling On Lagrangian Statistics In Large-Eddy Simulation

The application of large-eddy simulation (LES) to turbulent transport processes requires accurate prediction of the Lagrangian statistics of flow fields. However, in most existing SGS models, no explicit consideration is given to Lagrangian statistics. In this paper, we focus on the effects of SGS modeling on Lagrangian statistics in LES ranging from statistics determining single-particle dispersion to those of pair dispersion and multiparticle dispersion. Lagrangian statistics in homogeneous isotropic turbulence are extracted from direct numerical simulation (DNS) and the LES with a spectral eddy-viscosity model. For the case of longtime single-particle dispersion, it is shown that, compared to DNS, LES overpredicts the time scale of the Lagrangian velocity correlation but underpredicts the Lagrangian velocity fluctuation. These two effects tend to cancel one another leading to an accurate prediction of the longtime turbulent dispersion coefficient. Unlike the single-particle dispersion, LES tends to underestimate significantly the rate of relative dispersion of particle pairs and multiple-particles, when initial separation distances are less than the minimum resolved scale due to the lack of subgrid fluctuations. The overprediction of LES on the time scale of the Lagrangian velocity correlation is further confirmed by a theoretical analysis using a turbulence closure theory.

Distributions of temperature, velocity and viscosity at symmetrical axis of cylindrical plume in earth's mantle with variable viscosity

The parameters at the symmetrical axis of a cylindrical plume characterize the strength of this plume and provide a boundary condition which must be given to investigate the structure of a plume. For Newtonian fluid with a temperature-and pressure-dependence viscosity, an asymptotical solution of hydrodynamic equations at the symmetrical axis of the plume is found in the present paper. The temperature, upward velocity and viscosity at the symmetrical axis have been obtained as functions of depth, The calculated results have been given for two typical sets of Newtonian rheological parameters. The results obtained show that the temperature distribution along the symmetrical axis is nearly independent of the theological parameters. The upward velocity at the symmetrical axis, however, is strongly dependent on the rheological parameters.

Effect of coal-over-coal reburn on furnace temperature and heat flux distributions in 1 MW tangentially fired furnace

The furnace temperature and heat flux distributions of 1 MW tangentially fired furnace were studied during coal-over-coal reburn, and the influences of the position of reburn nozzle and reburn fuel fraction on furnace temperature and heat flux distributions were investigated. Compared with the baseline, the flue gas temperature is 70–90 C lower in primary combustion and 130–150 C higher at furnace exit, and the variations of the flue gas temperature distributions along furnace height are slower. The temperature distribution along the width of furnace wall decreases with the increase of the relative furnace height. In the primary combustion zone and the reburn zone, the temperature and heat flux distributions of furnace wall are much non-uniform and asymmetric along the width of furnace wall, those of furnace wall in the burnout zone are relatively uniform, and the temperature non-uniformity coefficients of the primary combustion zone, the reburn zone and the burnout zone are 0.290, 0.100 and 0.031, respectively.

The calculation of photoelectron angular distributions with jet-like structure from scattering theory

Photoelectron angular distributions produced in above-threshold ionization (ATI) are analysed using a nonperturbative scattering theory. The numerical results are in good qualitative agreement with recent measurements. Our study shows that the origin of the jet-like structure arises from the inherent properties of the ATI process and not from the angular momentum of either the initial or the excited states of the atom.

A scaling law of photoelectron angular distributions in one-cycle laser pulses

The photoelectron angular distributions (PADs) from above-threshold ionization of atoms irradiated by one-cycle laser pulses satisfy a scaling law. The scaling law denotes that the main features of the PADs are determined by four dimensionless parameters: (1) the ponderomotive number u(p) = U-p/hw, the ponderomotive energy U-p in units of laser photon energy; (2) the binding number E-b = E-b/h(w), the atomic binding energy E-b in units of laser photon energy; (3) the number of absorbed photons q; (4) the carrier-envelope phase phi(0), the phase of the carrier wave with respect to the envelope. We verify the scaling law by theoretical analysis and numerical calculation, compared to that in long-pulse case. A possible experimental test to verify the scaling law is suggested.

The intensity distributions of collected signals in coherent anti-Stokes Raman scattering microscopy

Coherent anti-Stokes Raman scattering (CARS) microscopy with the combining of confocal and CARS techniques is a remarkable alternative for imaging chemical or biological specimens that neither fluoresce nor tolerate labeling. The CARS is a nonlinear optical process, the imaging properties of CARS microscopy will be very different from the conventional confocal microscopy. In this paper, we calculated the propagation of CARS signals by using the wave equation in medium and the slowly varying envelope approximation (SVEA), and find that the intensity angular distributions vary considerably with the different experimental configurations and the different specimen shapes. So the conventional description of microscopy (e.g.. the point spread function) will fail to descript the imaging properties of CARS microscopy. (c) 2004 Elsevier B.V. All rights reserved.

Photoelectron angular distributions of molecules in bichromatic laser fields of circular polarization

Photoelectron angular distributions (PADs) from above-threshold ionization of O-2 and N-2 molecules irradiated by a bichromatic laser field of circular polarization are Studied. The bichromatic laser field is specially modulated such that it can be used to mimic a sequence of one-cycle laser pulses. The PADs are greatly affected by the molecular alignment, the symmetry of the initial electronic distribution, and the carrier-envelope phase of the laser pulses. Generally, the PADs do not show any symmetry, and become symmetric about an axis only when the symmetric axis of laser field coincides with the symmetric axis of molecules. This study shows that the few-cycle laser pulses call be used to steer the photoelectrons and perform the selective ionization of molecules. (C) 2008 Elsevier B.V. All rights reserved.