Transformation of Chord Length Distributions into Particle Size Distributions Using Least Squares Techniques

For the characterization of particulate systems, various measuring techniques exist. Many of these assume that the particles are spherical in order to compute a particle size distribution (PSD) from the measured data. However, in many applications the shape of the particles deviates from a sphere, and as a consequence the computed PSD will contain errors because of this violated assumption. Measuring techniques that do not require this a priori assumption are, for example, those that measure the chord lengths of the particles. A disadvantage of the latter techniques is that the interpretation of the chord length distribution (CLD) is less transparent than the interpretation of a shape-based PSD (the PSD given an assumed particle shape). To facilitate the interpretation of a CLD, an algorithm based on least squares optimization techniques is presented. This algorithm computes the shape-based PSD that best explains the measured CLD and can, for example, discriminate spheres from rods using information of the CLD only. Knowledge about the type of PSD (e.g., Gaussian or log-normal) is not required.     

Transformation of Chord Length Distributions into Particle Size Distributions Using Least Squares Techniques

ABSTRACT

For the characterization of particulate systems, various measuring techniques exist. Many of these assume that the particles are spherical in order to compute a particle size distribution (PSD) from the measured data. However, in many applications the shape of the particles deviates from a sphere, and as a consequence the computed PSD will contain errors because of this violated assumption. Measuring techniques that do not require this a priori assumption are, for example, those that measure the chord lengths of the particles. A disadvantage of the latter techniques is that the interpretation of the chord length distribution (CLD) is less transparent than the interpretation of a shape-based PSD (the PSD given an assumed particle shape). To facilitate the interpretation of a CLD, an algorithm based on least squares optimization techniques is presented. This algorithm computes the shape-based PSD that best explains the measured CLD and can, for example, discriminate spheres from rods using information of the CLD only. Knowledge about the type of PSD (e.g., Gaussian or log-normal) is not required.     

The small-angle scattering correlation function of the hemisphere

The analytical expression of the correlation function of the hemisphere is given. The calculation is based on the chord length distribution of this figure, calculated by the author. It is discussed here, too. Details of these structure functions at certain r-positions are analyzed. An expansion into a Taylor series at r=0 is possible. The first coefficients are given. The asymptotic scattering intensity I_∞(h) is formulated and compared with that of the hemisphere in a Porod plot.     

应用Voronoi图的点群范围自动识别

运用动态阈值对点群Delaunay三角网进行"蚕食"处理,获得不同视觉邻近距离下的点群分布范围多边形,在多边形边界外侧构建一系列虚拟边界点,在构建中使用两个重要参数:扩展距离、扩展方向.由虚拟边界点与初始点群共同组成新点群,通过对新点群Voronoi图的构建,确定边界点Voronoi区域的准确范围.最后,以点群状分布的教育资源优化配置为例,说明了该方法的具体应用.     

光纤灰度分布的高斯函数拟合法测量光纤几何参数

光纤的几何参数影响着光纤的光学传输和机械性能等,是衡量光纤质量的重要指标。近场光分布法是国标GB 15972.20-2008中推荐的几何参数测量方法。该方法在对光纤纤芯的测量中需对光纤通光照明,以区分纤芯和包层的边界。通光的纤芯端面是一个边缘并不清晰的发光亮斑,因而无法准确判断纤芯与包层的真实边缘。本文分析了光纤内光传播模场的分布,理论上光纤模场电磁矢量的解满足贝塞尔函数,但在近似情况下也可以用高斯函数代表光纤模场分布。因此本文利用高斯函数拟合光纤纤芯端面灰度分布,进而由拟合后的高斯函数得到纤芯与包层的真实边缘。本方法是对国标GB15972.20-2008的测量方法的进一步完善。实验测量结果表明,当光纤的切割效果不佳或成像质量较差时,模场灰度分布的高斯函数拟合法仍能保证测量的重复精度和测量数据的稳定性。     

Non-local line method for notched elements with use of effective length calculated in an elasto-plastic condition

The paper presents a non-local line method used to the fatigue life calculation of notched elements. The presented method is based on the concept of an effective length which determines the size of the equivalent fatigue zone. Effective values of normal stress calculated in the critical plane with a weight function were applied when determining the equivalent fatigue zone. Simulation studies were performed for two types of steel and two types of loading. Five different series of tests and simulations were used. Experimental studies were carried out for 40 HM-T and EA4T steels. These materials are used in railway industry, including the manufacturing of coupling bars. The notched test specimens contained notches with a tip radius of 0.2, 0.5, 0.8 and 1 mm. Stress calculations were performed using the finite element method by adopting cyclic material properties described by the model of a multi-linear hardening. Non-local calculations were performed in a defined critical plane for normal stress distribution and a weight function. As a result, the function of variation of the effective length depending on the loading level and geometry of the notch has been determined.     

Optimal design of one-sided exponential cumulative sum charts with known and estimated parameters based on the median run length

As a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high-quality processes. Considering both known and estimated parameter cases, the one-sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run length (RL ) distribution of the one-sided exponential CUSUM charts is skewed and it also changes with the mean shift size and the number of Phase I samples used to estimate the process parameter, the median run length (MRL ) is employed as a good alternative performance measure for the charts. The optimal design procedures based on MRL of the one-sided exponential CUSUM charts with known and estimated parameters are discussed. By comparing the MRL performance of the chart with known parameters with the one of the chart with estimated parameters, we investigate the effect of estimated process parameters on the properties of the chart. Finally, an application is illustrated to show the implementation of the chart.     

Elasticity Theories with Higher-order Gradients of Inertia and Stiffness for the Modelling of Wave Dispersion in Laminates

Dispersive wave propagation is simulated with a continuum elasticity theory that incorporates gradients of strain and inertia. The additional parameters are the Representative Volume Element (RVE) sizes in statics and dynamics, respectively. For the special case of a periodic laminate, expressions for these two RVE sizes can be provided based on the properties of the two components. The fourth-order governing equations are rewritten in two sets of coupled second-order equations, whereby the two sets of unknowns are the macroscopic displacements and the microscopic displacements. The resulting formulation is thus a true multi-scale continuum. In a numerical wave propagation example it is shown that the higher-order continuum model provides an excellent approximation of an explicit model of the heterogeneous laminate.     

Diffusion length of photoexcited carriers in GaN

When additional carriers are introduced in a material with a non uniform concentration, they tend to diffuse on a scale given by their diffusion length. This parameter can be measured by different methods. Depending on the conditions, different values can be found as the recombination mechanisms differ. In this paper, we present the situation in GaN with various experiments including the photocarrier grating method, photoluminescence and the spectral response in photoconductors. We show that the diffusion length varies from 0.1 μm to a few μm depending on experimental conditions. The interpretation is given based on the diffusion equations and on the analysis of the recombinations.     

黄麻纤维束力学性能的尺寸和应变率效应

为了探究黄麻纤维束的尺寸效应和应变率敏感性,利用C43电子式万能试验机和CEAST 9340落锤试验冲击系统分别在静动载条件下对黄麻纤维束进行测试,获得了杨氏模量、强度、峰值应变和韧性随标距和应变率的变化关系静载试验在1/600s-1应变率条件下进行,测试了6组不同标距(25、50、100、150、200和300mm)的试件;动载试验以应变率为变量,在4组不同的应变率(40、80、120和160s-1)条件下进行了测试,试件标距均为25mm。测试结果表明:随着试件标距增大,杨氏模量初始增大,当标距大于100mm时趋于稳定;强度、峰值应变和韧性均减小。随着应变率增大,杨氏模量和强度均增大;峰值应变初始减小后趋于稳定;韧性先减小后增大。鉴于植物纤维束材料较大的性能离散性,采用Weibull分布对试验数据进行拟合,获得了黄麻纤维束强度在不同试验条件(标距和应变率)下的分布规律。     

南海深海体积混响及散射特性试验研究

深海中存在着众多的不均匀"水团"、分层、深海生物圈以及海底逸出气泡等,这些散射体对入射声信号的散射构成了深海体积混响。通过测量获取深海水体散射目标的散射强度,研究不同海区不同时间的体积混响,对进一步认识深海声学特性具有重要的作用,也有助于主动声呐系统的性能预报。从深海中的主要散射体的组成、分类及其特征出发,介绍了一种深海体积混响及散射特性的研究方法。通过垂直向下发射窄波束测量各个深度层上的散射强度,用直观的声学图像显示强度值。构建试验系统在南海进行了深海试验,通过处理和分析测量数据发现,深度100 m以内的鱼类和处于深海散射层的海洋生物是深海体积混响的主要贡献者。     

An acceptance diagram analysis of the contaminant pulse removal problem with direct geometry neutron chopper spectrometers

Phased choppers are used to produce pulsed beams of monochromatic neutrons at research reactors and spallation neutron sources. Depending on the design of the instrument, it is very possible that the choppers will transmit neutrons with wavelengths other than those within the desired band of wavelengths. One or more additional choppers are typically needed to remove these contaminant pulses. We describe a method of determining the wavelength- and time-dependent transmission of a system of choppers using acceptance diagrams. The method is illustrated with calculations for the Disk Chopper Spectrometer at the NIST Center for Neutron Research and the proposed Cold Neutron Chopper Spectrometer at the Spallation Neutron Source (Oak Ridge, TN).     

Diffusion length variation in photovoltaic cells with Bridgman-grown CuInSe2 substrates

In a group of CuInSe₂-CdS-ZnO photovoltaic cells, where the absorber was a layer cut from Bridgman-grown p-type CuInSe₂ ingots, electron diffusion lengths at room temperature (L_n) were estimated by the photocurrent-capacitance method. Dark capacitance measurements were also made on the same cells against reverse bias and from Mott-Schottky plots, slope concentrations p_MS were determined at a reverse bias of 1.5 V. In a plot of L_n against p_MS, it was found that, despite much scatter in the experimental points, there was an apparent trend of L_n decreasing by about an order of magnitude with increase of p_MS from 10¹⁶ to 10¹⁷ cm^− 3. Detailed proposals were then made to explain this trend. These were reduction of lifetime via Shockley-Read trapping with mobility decrease by impurity scattering, shunt resistance lowering by light and optical penetration depth reduction at shorter illumination wavelengths.     

EXAFS: Determination of cation distribution in spinels

In oxidic spinels containing transition metal ions, the tetrahedral and octahedral bond distances differ by less than 0·25 Å. Therefore, in the case of a cation occupying both the sites, the normalized EXAFS for first coordination shell gives the average bond distance and average coordination number respectively over all the bonds and the positions of the cation under investigation. EXAFS analysis of fourteen mixed lithium ferrite spinels was carried out to show how the average bond distance can fruitfully be used to obtain the exact cation distribution, in conformity with X-ray diffraction data.     

Measurement of the temperature-field distribution in the volume of a dielectric material treated in a microwave resonator chamber

The problem of producing a uniform temperature-field distribution in the volume of a dielectric material, treated in a microwave chamber, is considered. An experimental procedure for determining the temperature distribution inside a heated object is described. Translated from Metrologiya No. 1, pp. 22–27, January, 2009.     

Variable wall thickness scroll geometry modeling with use of a control volume approach

In a scroll-type compressor, compression is achieved through relative contact between two spiral curves. Since the scroll invention by Leon Creux (1905), multiple methods have been developed for calculating scroll geometry. What can generally be considered the most classical method, is defining each scroll curve as the involute of a circle. Gravesen and Henriksen (2001) introduced a new method to calculate scroll geometry by deriving each scroll curve from the radius of curvature parameterized with involute angle. This allows a wide range of involute geometries to be considered not included in the classical method. In this paper, Gravesen's method is extended to the tip region to include all tip geometries involved in a two arc configuration resulting in a more comprehensive scroll geometry definition. Lastly, with parametric representation of all scroll geometry, the pocket volume can be easily solved using a derived control volume approach.     

Improved stability of solid dispersions of manidipine with polyethylene glycol 4000/copovidone blends: application of ternary phase diagram

Context: Manidipine (MDP) is generally used clinically as an antihypertensive agent; however, the bioavailability of orally administered MDP is limited due to their very low water solubility.

Objective: The objectives of this research were, therefore, to increase the solubility of MDP by the formation of ternary solid dispersions (tSD) with polyethylene glycol 4000 (PEG4000) and copovidone and to improve their stability.

Methods: Solid ternary phase diagram was constructed to find homogeneous solid dispersion region after melting and solidifying at low temperature with different quenching substances. The pulverized powder of solid dispersions was then determined, for their physicochemical properties, by differential scanning calorimetry, powder X-ray diffractometry, Fourier transform infrared (FTIR) spectroscopy and hot stage microscopy. The solubility and dissolution of MDP from the tSD were investigated. The physical stability of tSD was also determined under accelerated condition at 40?°C/75% relative humidity (RH) for 6 months.

Results and discussion: The results showed that MDP was molecularly dispersed in PEG4000 and copovidone when the tSD was created from homogeneous region of solid ternary phase diagram. FTIR results confirmed that strong hydrogen bonding was presented between MDP and copovidone, leading to a significant increase in the solubility and dissolution of MDP. After storage at accelerated condition (40?°C/75%RH) for 6 months, the tSD still showed a good appearance and high solubility.

Conclusion: The results of this study suggest that tSD prepared by melting has promising potential for oral administration and may be an efficacious approach for improving the therapeutic potential of MDP.     

Corrections to the theory and the optimal line in the swimming diagram of Taylor (1952)

The analysis of undulatory swimming gaits requires knowledge of the fluid forces acting on the animal body during swimming. In his classical 1952 paper, Taylor analysed this problem using a ‘resistive-force’ theory. The theory was used to characterize the undulatory gaits that result in the smallest energy dissipation to the fluid for a given swim velocity. The optimal gaits thus found were compared with data recorded from movies of a snake and a leech swimming. This report identifies and corrects a mathematical error in Taylor’s paper, showing that his theory applies even better to animals of circular cross section.     

Control charts for monitoring the median parameter of Birnbaum-Saunders distribution

In this paper, we propose control charts for monitoring the Birnbaum-Saunders (BS) median parameter (scale parameter) on the basis of three estimators. Comparison of the control charts in terms of average run length using probability control limits and those based on asymptotic distribution of three estimators for the median parameter is developed. We also present guidelines for practitioners about the minimum sample size needed to match out-of-control average run length with the asymptotic control limits in function of the median parameter after an extensive simulation study. Numerical example illustrates the applied monitoring of BS median parameter.