Science Letters： Research on 3D fiber orientation distribution in arbitrary planar flows

A non-stretchable fiber rotation in planar flows has been solved. The fiber will rotate periodically or run to the asymptotical direction decided by a discriminant defined in the paper involving the fiber aspect ratio and the flow characteristics. Subsequently the fiber orientation distribution is derived directly without the bother of solving the Fokker-Planck equation. The research clearly indicates the overall configuration of a fiber rotation movement in planar flows.     

Research on the orientation distribution of fibers immersed in a pipe flow

The computed orientation distribution of fibers immersed in laminar pipe flows showed that the longitudinal distributions are wide for small Reynolds numbers and become narrower with increasingRe. For lowRe number, the axial orientation distributions are broad with almost no preferred orientations. For highRe number, the axial distribution becomes narrow, with sharp maxima. The mean values of the longitudinal orientation depend strongly on theRe number. The computed results are in qualitative agreement with relevant experimental results. Project (No. 19925210) supported by the National Natural Science Foundation for Outstanding Youth of China     

On the structural features of fiber suspensions in converging channel flow

The structural features of fiber suspensions are dependent on the fiber alignment in the flows. In this work the orientation distribution function and orientation tensors for semi-concentrated fiber suspensions in converging channel flow were calculated, and the evolutions of the fiber alignment and the bulk effective viscosity were analyzed. The results showed that the bulk stress and the effective viscosity were functions of the rate-of-strain tensor and the fiber orientation state; and that the fiber suspensions evolved to steady alignment and tended to concentrate to some preferred directions close to but not same as the directions of local streamlines. The bulk effective viscosity depended on the product of Reynolds number and time. The decrease of effective viscosity near the boundary benefited the increase of the rate of flow. Finally when the fiber alignment went into steady state, the structural features of fiber suspensions were not dependent on the Reynolds number but on the converging channel angle. Projects (No. 19925210) supported by the National Natural Science Foundation of China     

Using Shiny to illustrate the probability density function concept

The transition from the probability mass function for discrete random variables to the probability density function for continuous random variables is not straightforward, especially to students from the health and social sciences. An R Shiny application was created to assist the learning process of probability density function.     

On the structural features of fiber suspensions in converging channel flow

INTRODUCTIONModelingfiber fiberinteractionsinnon di lutefibersuspensionsanddescribinghowtheseinteractionsaffecttherheologicalpropertiesofthesuspensionsintheflowsarefundamentalandimportantinmulti phaseflowsresearch .Ulti matelywewouldliketobeabletodesignan…     

Dynamic Monte Carlo study on the probability distribution functions of tail-like polymer chain

INTRODUCTION Polymer chains with one end attached to a sur- face by means of physical or chemical interaction have become one of the important polymer science subject, which are useful for many applications, such as polymer compatibilizers, copolymer microphases, colloid stabilization, polymeric surfactants (Milner, 1991). Grafting polymers can improve the power efficiency of electrorheological fluids, enhance pho- toluminescence of nano materials, and increase dis- persion stability. On …     

概率论中的二项分布的应用研究

独立重复试验是研究随机现象的重要途径之一,很多概率模型的建立都以独立重复试验为背景,二项分布就是来自于独立重复试验的一个概率模型。我们知道,二项分布的概率公式为简简单单的一个公式,却有着千变万化的应用。下面将对概率论中二项分布的研究做一个仔细的阐述。     

Non-axisymmetric instability in the Taylor-Couette flow of fiber suspension

An analysis of the instability in the Taylor-Couette flow of fiber suspensions with respect to the non-axisymmetric disturbances was performed. The constitutive model proposed by Ericksen was used to represent the role of fiber additives on the stress tensor. The generalized eigenvalue equation governing the hydrodynamic stability of the system was solved using a direct numerical procedure. The results showed that the fiber additives can suppress the instability of the flow. At the same time, the non-axisymmetric disturbance is the preferred mode that makes the fiber suspensions unstable when the ratio of the angular velocity of the outer cylinder to that of the inner cylinder is a large negative number.     

基于Copula函数对二维正态分布中常见认识误区的分析

针对二维正态分布讨论联合分布与边缘分布的关系问题。在对二维正态分布中常见的认识误区进行举例辨析的基础上,借助不同的Copula函数对两个一维正态分布的联合分布进行了多种构造,并对两个正态分布的联合分布为二维正态分布的条件进行了说明。     

激光聚焦光斑形状对溅射产物角分布的影响

讨论了将线形聚焦光斑看作是点溅射的线性迭加时．对衬底平面上溅射产物角分布影响的推导．推导结果间接证明了溅射产物中粒子之间有更强烈的相互作用。     

应用型本科高校概率统计课程教学方法探讨

概率统计课程是应用型本科高校理工科学生必修课程之一,具有很强的理论性和应用性。文章主要探讨了应如何加强课程教学内容的改革,注重概率统计思想讲授,加强实践环节的教学,如何结合实例将数学建模思想融入到概率统计教学中,培养学生的应用和创新能力。     

熵损失函数下正态分布参数的E--Bayes估计

在正态分布的先验分布为逆分布时,研究了刻度参数在熵损失函数下的E—Bayes估计和多层Bayes估计,证明了该参数的Bayes估计是容许的,并证明了在熵损失函数下计算出的正态分布参数的E—Bayes估计与多层Bayes估计是渐近相等的．     

一类随机向量函数序列的依概率收敛性

将依概率收敛的一维随机变量序列的连续函数仍依概率收敛的结论推广到随机向量序列的情形。     

服从均匀分布的多个独立随机变量和的密度函数公式

通过简单枚举一些特例,列出服从均匀分布的多个独立随机变量和的密度函数一般公式,然后用数学归纳法进行严格的证明.     

Motion and orientation of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio

Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The transient impulse model of 3D collisions between particles and between particle and wall is proposed. The numerical results are qualitatively in agreement with and quantitatively comparable to the experiment data. The results show that the increases of both the cylindrical particle to pipe size ratio and the particle aspect ratio decrease the rotation about all axes. All rotations of cubic particles decrease with increasing the particle concentration. The cubic particles, rotating more drastically in the flow with large Reynolds number, rotate faster than the cylindrical particles with the same size. The cylindrical particles align with the flow direction more obviously with decreasing Reynolds numbers. However, the orientations of cubic particles are spread all over the range with no significant difference in magnitude, and the Reynolds numbers have no obvious effect on the orientations of cubic particles.     

N-E-V分布的实用性研究

本文推导了统计热力学中粒子数N、能量E、体积V和熵S在第八种分布(N-E-V分布)情况下的计算公式,并以单原子理想气体和量子气体为例说明了N-E-V分布具有其实用性.     

刻度平方误差损失下Lomax分布形状参数的Bayes估计

对于给定容量为n的一个Lomax样本X1,X2,…,Xn,在刻度平方误差损失函数下,给出了Lomax分布参数的Bayes估计,可容许性及置信下限,同时也得到了参数的多层Bayes估计的表达式.     

关于调和函数与次调和函数的几个性质的研究

根据调和函数与次调和函数的概念，对调和函数与次调和函数作了进一步的研究，并给出了关一调和函数与次调和函数的几个性质定理。     

大学的文化功能初探

大学的文化功能体现在文化的选择、传递和创新上。大学同其它社会组织一道,共同与文化体系发生相互作用。大学对文化发生影响的作用,将会随社会发展而越来越得到加强。大学"文化"应该定位在知识、信仰、艺术以及道德、法律、习俗等社会规范的精神层面含义上。     

随机变量的特征函数在恒等式证明中的探讨

本文重点阐述了随机变量的特征函数在恒等式证明中的应用方法,说明它比用分 布函数证明恒等式更方便,并用实例加以说明.