Stability of the Dividing Distribution Function Method for ParticleSize Distribution Analysis in Small Angle X－Ray Scattering

The Dividing Distribution Function (DDF) method is one of the methods by which the particle size distribution of ultrafine powder can be evaluated from its small angle X-ray scattering data. In this paper, the stability of the solution obtained from DDF method has been investigated through optimizing the coefficient matrix, introducing a damping factor and a least square treatment. All calculations were accomplished with a microcomputer. It was shown that the average deviations of the size distribution obtained are not larger than the assigned random errors to the scattering intensities as long as the corresponding requirements are satisfied.

NUMERICAL SIMULATION OF ORIENTATION DISTRIBUTION FUNCTION OF CYLINDRICAL PARTICLE SUSPENSIONS

The orientation distribution function of cylindrical particle suspensions was deduced and numerically simulated, and an application was taken in a wedge-shaped flow field. The relationship between the orientation distribution function and particle orientation angles was obtained. The results show that comparing with the most probable angle distribution which comes to being in short time, the distribution of the steady state doesn't vary much. in range; the main difference is the anti-clockwise rotation in the right and upper field, that is, particles rotate more at the points where the velocity gradients are larger. The most probable orientations are close to the direction of local streamlines. In the direction of streamlines, with poleradius decreasing, the most probable angles increase, but the angles between their orientations and the local streamlines decrease.

Resolution Increase and Noise Removal in Particle Size Distribution Measurement with Shifrin Transform

Based on the laser diffraction and Shifrin transform,the measurement method of particle size distribution has been improved extensively.While in real measurements,some noise peaks exist in the inversion data and are easily to be misread as particle distribution peaks.The improved method used a truncation function as a filter is hard to distinguish adjacent peaks.Here,by introducing the bimodal resolution criterion,the filter function is optimized,and to a quasi truncation function with the optimized filter function is studied to achieve optimal bimodal resolution and to remove noise peaks.This new quasi truncation function fits multimode distribution very well.By combining the quasi truncation function with Shifrin transform,noise peaks are removed well and the adjacent peaks are distinguished clearly.Finally,laser diffraction experiments are conducted and the particle size distribution is analyzed by adoping the method.The results show that the quasi truncation function has better bimodal resolution than the truncation function.Generally,by combining the quasi truncation function with the Shifrin transform,in particle size distribution measurements with laser diffraction,the bimodal resolution is greatly increased and the noise is removed well.And the results can restore the original distribution perfectly.Therefore,the new method with combination of the quasi truncation function and the Shifrin transform provides a feasible and effective way to measure the multimode particle size distribution by laser diffraction.

Effects of shear rates on radial distribution of different types of heavy particles in light media

In order to study distribution properties of different types of heavy particles in light media and to link macro-properties of a system with its micro-structures,radial distribution functions(RDF)of partly charged metallic particles in uni-and bi-polar systems at various shear rates were investigated by Brownian dynamics simulation.The results are good in agreement qualitatively or quantitatively compared with ones in non-polar systems and other works.The investigation indicates that dispersibility of the particles in the uni-polar system of high ionic concentrations is the largest.Therefore,it is the most unfavored to grow into clusters for precipitation.The dispersibility in the bi-polar systems is less than that in uni-polar systems,but larger than that in non-polar systems.Furthermore,all the RDFs at the same shear rates in three systems approach a limit,which implies that a threshold value exists.

Pair distribution function analysis: Fundamentals and application to battery materials

Battery materials are of vital importance in powering a clean and sustainable society.Improving their performance relies on a clear and fundamental understanding of their properties,in particular,structural properties.Pair distribution function(PDF)analysis,which takes into account both Bragg scattering and diffuse scattering,can probe structures of both crystalline and amorphous phases in battery materials.This review first introduces the principle of PDF,followed by its application in battery materials.It shows that PDF is an effective tool in studying a series of key scientific topics in battery materials.They range from local ordering,nano-phase quantification,anion redox reaction,to lithium storage mechanism,and so on.

MICROSTRUCTURE OF AGGREGATES IN DISPERSIONS DESCRIBED IN TERMS OF RADIAL DISTRIBUTION FUNCTION

Following a sticky particle model and its computer simulation scheme proposed in the previous papers, the motions of particles in both 2-and 3-dimensional shear flow fields are simulated. At a steady state of clustering process, the radial distribution functions are calculated to precisely describe the microstructure of aggregates in dispersions, and the configuration of particles is displayed,which gives a direct view of microstructure. It is found that (1) the kind of the microstructure transforms from compact clusters to a loose network as the concentration of particles increases; (2) the microstructure is independent of shear rate which only dominates the size of clusters formed at steady state.

Reconstruction of Probability Density Function for Gamma Distribution

The probability distributions of small sample data are difficult to determine,while a large proportion of samples occur in the early failure period,so it is particularly important to make full use of these data in the statistical analysis.Based on gamma distribution,four methods of probability density function(PDF)reconstruction with early failure data are proposed,and then the mean time between failures(MTBF)evaluation expressions are concluded from the reconstructed PDFs.Both theory analysis and an example show that method 2 is the best evaluation method in dealing with early-failure-small-sample data.The reconstruction methods of PDF also have certain guiding significance for other distribution types.

Particle swarm optimization algorithm for simultaneous optimal placement and sizing of shunt active power conditioner(APC)and shunt capacitor in harmonic distorted distribution system

Due to development of distribution systems and increase in electricity demand,the use of capacitor banks increases.From the other point of view,nonlinear loads generate and inject considerable harmonic currents into power system.Under this condition if capacitor banks are not properly selected and placed in the power system,they could amplify and propagate these harmonics and deteriorate power quality to unacceptable levels.With attention of disadvantages of passive filters,such as occurring resonance,nowadays the usage of this type of harmonic compensator is restricted.On the other side,one of parallel multi-function compensating devices which are recently used in distribution system to mitigate voltage sag and harmonic distortion,performs power factor correction,and improves the overall power quality as active power conditioner(APC).Therefore,the utilization of APC in harmonic distorted system can affect and change the optimal location and size of shunt capacitor bank under harmonic distortion condition.This paper presents an optimization algorithm for improvement of power quality using simultaneous optimal placement and sizing of APC and shunt capacitor banks in radial distribution networks in the presence of voltage and current harmonics.The algorithm is based on particle swarm optimization(PSO).The objective function includes the cost of power losses,energy losses and those of the capacitor banks and APCs.

基于λ-PDF和一次二阶矩的不确定性反求方法

为了有效评价测量响应中不确定性对结构参量识别结果的影响,提出一种基于λ概率密度函数(Probability distribution function,PDF)和一次二阶矩的不确定性计算反求方法。采用二次衍生λ-PDF对待识不确定性参量的PDF进行建模。内层通过对参量呈λ-PDF的功能函数采用一次二阶矩法进行正问题求解,得到计算响应的概率分布;外层通过最小化测量响应与计算响应之间的概率分布特征量将不确定性反问题转化为确定性的最优化问题,并用隔代映射遗传算法识别未知参量λ-PDF的参数。本方法不仅有效地实现了结构未知参量PDF的估计,而且与传统基于抽样的统计方法相比,计算效率较高。数值算例和工程应用验证了本方法的可行性和有效性。

ATLAS 2.76 TeV单喷注实验数据对CT18NNLO部分子分布函数的影响

通过ePump(error PDF(parton distribution function)updating method package)研究了大型强子对撞机(large hadron collider,LHC)在质心能量√s=2:76TeV时,来自ATLAS(a toroidal LHC apparatus)探测器单喷注的双微分散射截面的实验数据对CT18NNLO(next-to-next-to-leading order)部分子分布函数(PDF)的影响.首先,使用CT18NNLO部分子分布函数计算了单喷注的双微分散射截面,观察到理论预测与实验数据符合得较好;其次,计算了单喷注双微分散射截面的理论预测值与CT18NNLO胶子部分子分布函数的关联余弦cosϕ;最后,使用ePump更新了CT18NNLO部分子分布函数,并研究了实验数据与全局拟合数据间的冲突.通过比较在Q=100GeV时CT18NNLO胶子部分子分布函数和ePump更新的胶子部分子分布函数,发现ATLAS 2.76 TeV单喷注双微分散射截面实验数据在大和小的动量分数区域对CT18NNLO胶子部分子分布函数的约束较小.

球磨法制备芡实超微粉及其理化功能性质分析

芡实淀粉属小颗粒淀粉,且以超聚合的复粒形式存在。为了解超微粉碎对淀粉复粒结构及其中功效组分溶出的影响,文中采用球磨法制备超微芡实粉,分析了不同球磨参数对芡实粉理化功能性质的影响。研究显示,芡实粉的适宜球磨参数为:转速200 r/min,m(用料量)∶m(研磨球)=1∶30,研磨球直径4 mm,研磨时间30 min。与对照相比,所得超微芡实粉中超细粉末(粒径0~1μm)占比达到85.04%,其中总黄酮溶出量增加不显著,但总酚溶出量有明显增加(P≤0.05)。所得超微芡实粉吸水性和吸油性显著提高,分别达到3.88、2.46 g/g,分别增加了3.26、1.34倍。X-衍射图谱和扫描电子显微镜照片显示,超微芡实粉中淀粉的复粒结构发生碎裂,淀粉颗粒完整性及其晶体结构也被严重破坏,印证了超微芡实粉理化功能性质改变的内在原因。研究结果表明,球磨处理不仅改善了芡实粉的理化功能性质,也有利于其中功效组分的溶出。

Shape control on probability density function in stochastic systems

A novel strategy of probability density function （PDF） shape control is proposed in stochastic systems. The control er is designed whose parameters are optimal y obtained through the improved particle swarm optimization algorithm. The parameters of the control er are viewed as the space position of a particle in particle swarm optimization algorithm and updated continual y until the control er makes the PDF of the state variable as close as possible to the expected PDF. The proposed PDF shape control technique is compared with the equivalent linearization technique through simulation experiments. The results show the superiority and the effectiveness of the proposed method. The control er is excellent in making the state PDF fol ow the expected PDF and has the very smal error between the state PDF and the expected PDF, solving the control problem of the PDF shape in stochastic systems effectively.

Hypoexponential Distribution with Different Parameters

The Hypoexponential distribution is the distribution of the sum of n ≥ 2 independent Exponential random variables. This distribution is used in moduling multiple exponential stages in series. This distribution can be used in many domains of application. In this paper we consider the case of n exponential Random Variable having distinct parameters. Using convolution, some properties ofLaplacetransform and the moment generating function, we analyse this case and give new properties and identities. Moreover, we shall study particular cases when are arithmetic and geometric.

LHCb 7 TeV W和Z数据对CT14HERA2 PDFs的影响

为了研究LHCb 7 TeV W+、W-和Z实验数据对CT14HERA2部分子分布函数(Parton Distribution Functions,PDFs)的影响,首先将收集到的数据进行了理论预测并将其和实验测量结果进行了比较,在误差允许的范围内理论和实验符合的很好。其次,用误差PDFs更新软件包(Error PDFs Updated Method Package,EPUMP)更新了CT14HERA2 PDFs,并和全局拟合的PDFs进行了比较。最后,加入协方差矩阵后的实验数据可以在较大和较小的x区域减少d(x,Q)/u(x,Q)误差,同时也对CT14HERA2 PDFs进行了优化。验证结果表明,LHCb 7 TeV W+、W-和Z产生的实验数据在较大的x区域对g(x,Q)、d(x,Q)、d(x,Q)/u(x,Q)、d(x,Q)/u(x,Q)、u(x,Q)、d(x,Q)和u(x,Q)PDFs的中心值约束较大,可以用前4个误差PDFs代替原来全局拟合或优化后得到的56个误差集。

磨浆过程输出纤维长度随机分布预测PDF控制

磨浆过程作为制浆和造纸工业最为重要的生产环节之一,其输出纤维长度随机分布(Fiber length stochastic distribution,FLSD)形状直接决定着后续造纸过程的能耗和纸品质量.针对传统的均值和方差难以描述输出FLSD特征,即具有非高斯分布特性,本文提出一种磨浆过程输出FLSD的预测概率密度函数(Probability density function,PDF)控制方法.首先,采用径向基函数(Radical basis function,RBF)神经网络逼近输出FLSD的PDF,在采用迭代学习方法完成基函数参数整定基础上对相应权值向量进行估计.其次,针对权值之间存在强耦合特点,利用随机权神经网络(Random vector functional-networks,RVFLNs)建立表征输入变量和权值之间关系的预测模型.最后,基于建立的输出FLSD模型设计预测PDF控制器,最终实现对期望输出PDF的跟踪控制.基于工业数据实验验证了所提方法的有效性,为磨浆过程优化运行和控制提供理论依据.

不规则铜钼矿颗粒断裂强度分布实验研究

不规则矿石颗粒的断裂是矿物加工过程中常见的现象,其强度分布决定了矿石破碎特性。为了定量分析不规则颗粒的强度分布,通过对5种不同粒级的铜钼矿颗粒进行准静态单轴压缩实验,确定破碎过程中的最大破碎力和断裂能。选取3种常见的统计学模型分别对不同定义下的(最大破碎力、断裂应力、断裂能和断裂比能)颗粒强度进行拟合,并研究了其与颗粒尺寸和材料特性之间的定量关系。试验结果表明:Weibull模型较Lognormal和Lmogintic两种模型更适合描述铜钼矿颗粒的强度分布,其模型中强度分布的离散程度D只与材料特性有关,与颗粒尺寸呈弱函数关系;F_(63.20)、E_(63.20)与颗粒尺寸呈正比关系,而σ_(63.20)和Em_(63.20)随着颗粒尺寸的增大呈幂函数规律减小;不同定义下的颗粒强度之间(最大破碎力-断裂能和断裂应力-断裂比能)的关系都只与材料特性有关,而与颗粒尺寸无关,在双对数坐标系下斜率分别为1.49与0.67。

基于圆柱形纳米颗粒的纳米流体导热特性模拟

纳米流体是将纳米颗粒分散在基液形成的一种介质,具有较强的导热性能,在诸多领域具有重要的应用。纳米流体的悬浮颗粒多为球形颗粒,而在实际应用中很多颗粒为非球形。基于平衡态分子动力学模拟方法,研究了含有圆柱形纳米颗粒的纳米流体导热性能。计算结果表明,随着纳米颗粒球形度降低,纳米流体的热导率明显增大。基于纳米流体径向分布函数以及基液和纳米颗粒扩散系数的分析表明,对于相同体积的纳米颗粒,圆柱形纳米颗粒的比表面积较大,颗粒表面的类固液体层效应是非球形纳米颗粒提高纳米流体热导率的主导机制,并且颗粒的布朗运动有可能削弱此效应。该研究结果为强化纳米流体热导率提供了新的思路。

基于多策略粒子群优化RBF的云资源预测模型

针对云计算资源利用率低等问题,构建基于多策略粒子群优化RBF神经网络的云资源预测模型(MPSO-RBF)。采用改进的粒子群算法对RBF神经网络参数进行优化,避免随机初始化参数引起的预测精度低等问题;对于粒子群容易陷入局部最优解等问题,采用动态惯性权重、自适应学习因子和变异粒子位置3种策略对粒子群进行改进,提高算法的寻优能力。基于云计算资源负载数据,将该模型与BP、RBF和PSO-RBF模型进行对比实验,验证了该模型具有良好的性能。

Calculation method for particle mean diameter and particle size distribution function under dependent model algorithm

In total light scattering particle sizing technique, the relationship among Sauter mean diameter D32, mean extinction efficiency Q, and particle size distribution function is studied in order to inverse the mean diameter and particle size distribution simply. We propose a method which utilizes the mean extinction efficiency ratio at only two selected wavelengths to solve D32 and then to inverse the particle size distribution associated with Q and D32. Numerical simulation results show that the particle size distribution is inversed accurately with this method, and the number of wavelengths used is reduced to the greatest extent in the measurement range. The calculation method has the advantages of simplicity and rapidness.

改进粒子群算法在柔性作业加工时间问题研究

为了减少柔性作业加工时长,在柔性作业加工问题中,提出一种改进粒子群算法(β-PSO)。该算法以最小加工时间为目标函数,惯性权重幂函数自适应调节,随机数采用贝塔分布进行改进,选取Kacem算例进行验证,通过对比β-PSO算法与标准粒子群算法(PSO)、余弦惯性权重改进粒子群算法(CPSO)的优化结果,β-PSO算法加工时间均较低。实验结果表明,β-PSO算法在减少柔性作业加工时间问题上的有效性。