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.     

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.     

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。     

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.     

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).     

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.     

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.     

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.     

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.     

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.     

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.     

Effect of small notch and absorbed hydrogen on the fatigue fracture in two-step stress test within fatigue limit diagram

It is usually regarded as a common understanding that fatigue failure would not occur if all stresses were kept within fatigue limit diagram. However, it was shown that fatigue failure occurred in some special cases of variable amplitude loading condition even when all stresses were kept within fatigue limit diagram in the case of small-notched specimen. The cause of such a phenomenon was examined using two-step stress pattern for low alloy steel SCM440H. In the case of constant stress amplitude loading, non-propagating crack was formed only at low mean stress and not formed at high mean stress. However, in the case of two-step stress pattern in which the first step stress was chosen as  R  =−1 and the second step stress was with high mean stress, a non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred by the stresses within fatigue limit diagram. In this study, the effect of notch size and shape were examined. The effect of absorbed hydrogen was also investigated. Absorption of 0.3 ppm hydrogen caused more reduction of fatigue limit.     

A probabilistic model for cleavage fracture with a length scale-influence of material parameters and constraint

A probabilistic model for the cumulative probability of failure by cleavage fracture with a material related length scale is developed in this study. The model aims at describing the random nature of fracture in ferritic steels in the brittle-to-ductile transition temperature region. The model derives from use of an exponential function to describe the distribution of microstructural entities eligible to take part in the fracture initiation process, where also a dependence on effective plastic strain is incorporated. A nonlocal stress measure, calculated as the average stress in a spherical volume, drives the contribution to failure probability of an infinitesimal material volume. The radius of the spherical volume enters as the material length in this model. This length has a significant influence on failure probability predictions in geometries exposed to strong stress gradients as found ahead of cracks. The material length is associated with a fracture toughness threshold value. In a fracture application three model parameters need to be estimated based on testing; a parameter directly related to the mean fracture toughness, a parameter that primarily is related to crack-tip constraint effects and the material length parameter. The model is explored in a parametric study showing model features in concord with typical features found in toughness distributions from fracture mechanics testing in the transition region.     

The transfer length in concrete structures repaired with composite materials: a survey of some analytical models and simplified approaches

This work focuses on the closed-form solutions for the shear distribution that takes place in the adhesive between composite and concrete in RC structures repaired with composite plates. Three different loading cases are studied. It is shown that the exact shear stress distributions, which are rather complicated, can be simplified to provide very similar expressions in the three studied cases. The main parameters that govern the shear distribution are then clearly highlighted. This leads to an easy understanding of the influence of some geometrical and material parameters on the shear distribution, as illustrated through a parametric study.     

分配管长度补偿方案对多回路蒸发器换热性能影响的试验研究

针对一台空气源屋顶式空调(热泵)机组,对多回路蒸发器出口有带液风险的回路进行分配管长度改进方案设计,并进行相关测试,结果表明,适当增加过热度较低回路的分配管长度对于提高蒸发器换热均匀性和换热效率有着改善作用,是优化机组性能行之有效的方法之一;在3个分配管长度改进方案中,方案3效果最佳,机组制热量相比原方案增加约1.8％...     

Application of a feasible formability diagram for the effective design in stamping processes of automotive panels

The objective of this study is to propose a method of process design that uses a feasible formability diagram, which denotes the safe region without fracture and wrinkle, for the effective and rapid design of stamping processes. To determine the feasible formability diagram, FE-analyses have been performed for combinations of process variables that correspond to the orthogonal array of design of experiments. Subsequently, the characteristic values for fracture and wrinkle have been estimated from the results of FE-analyses on the basis of the forming limit diagram. The characteristic values for all combinations within a whole range of process variables have been predicted through the training of an artificial neural network. The feasible formability diagram has been finally determined for all combinations of process variables. The stamping processes of automotive panels to support suspension module, such as the turret suspension and the wheel house, have been taken as examples to verify the effectiveness of process design through feasible formability diagram. A comparison of the FE-simulation results with the experimental results reveals that the design of stamping processes through feasible formability diagram is efficient and suitable for actual processes.