颗粒流体两相流基本方程中压差力和曳力系数的计算

本文总结了颗粒流体两相流基本方程的压差力表达方式和推导颗粒流体系统曳力系数计算公式的力平衡原理，提出了一种分析压差力的简单方法，阐明了各种压差力表达方式间的关系及对应的两相流基本方程的曳力系数的计算方法     

Shape optimization of a micromixer with staggered herringbone groove

Shape optimization of a staggered herringbone groove micromixer using three-dimensional Navier-Stokes analysis has been carried out. The analysis of the degree of mixing is performed by the calculation of spatial data statistics. The calculation of the variance of the mass fraction at various nodes on a plane in the channel is used to quantify mixing. A numerical optimization technique is applied to optimize the shape of the grooves on a single wall of the channel. Two design variables, namely, the ratio of the groove depth to channel height ratio and the angle of the groove, are selected for optimization. A mixing index is used as the objective function. The results of the optimization show that the mixing is very sensitive to the shape of the groove which can be used in controlling the mixing in microdevices. The mixing is affected by the depth of the groove much more than the angle of the groove.     

Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with uncertainty

Student academic underachievement is a concern of paramount importance in Europe, where around 15% of the students in the last high school courses do not achieve the minimum knowledge academic requirement. In this paper, we propose a model based on a system of differential equations to study the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia. This approach is supported by the idea that both good and bad study habits, are a mixture of personal decisions and influence of classmates. This model allows us to forecast the student academic performance by means of confidence intervals over the next few years.     

Comparison of Three‐Dimensional Korean Male Anthropometric Data with Modeling Data Generated by Digital Human Models

The purpose of this study was first to extract the anthropometric data of typical Korean male adults, based on the three‐dimensional anthropometric data measured through the Size Korea project. The data were then analyzed to identify the differences in the anthropometric characteristics between typical Koreans and 3D Korean mannequinmannequins generated by digital human models. Revision equations were then suggested to improve the inaccuracy of digital human models. Typical Korean adults subject to the 3D body scan data were selected by factor analysis with respect to the 5th, 50th, and 95th percentiles. Comparisons of anthropometric differences included the differences of the height and length variables in the vertical direction and the breadth, depth, and circumference variables in the horizontal direction. These comparisons demonstrated the differences in the anthropometric characteristics between typical Koreans and Korean mannequins based on differences in body shape and proportions between Korean and Western populations. Typical Koreans have shorter legs and longer torso than those of such mannequins generated from their own modeling algorithms, and the body shape of Koreans is more of an inverted triangular shape compared to the models. Although 3D digital human models are required to be modified to appropriately reflect the Asian body shape, modification of the modeling algoritms is not available to the public. The revision equations that convert the Korean modeling data of RAMSIS and Human in CATIA into typical Korean anthropometric data were instead suggested by regression analysis. It is expected that the proposed revision equations will help the designer evaluate design alternatives and improve the suitability of ergonomic evaluation for Korean customers. © 2012 Wiley Periodicals, Inc.     

PHASE-SPACE DIFFUSION EQUATIONS FOR SINGLE BROWNIAN PARTICLE MOTION NEAR SURFACES

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method.

In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the Liouville equation for the Brownian particle and n-fluid molecules present in the system, thus, establishing a firm theoretical foundation for the Fokker-Planck equation and the various other phase-space diffusion equations that follow from it.

Based on diagonalization of the Fokker-Planck equation, its short-time behavior is also derived here which enables a generalization of the Brownian dynamics method for the study of particle motion near surfaces including fluid dynamic interactions. Additionally, a perturbation solution of the Fokker-Planck equation under the conditions of small, but finite particle Stokes number is also derived. These solutions are shown to agree with previously given representations of the Smoluchowski or convective-diffusion equation for Brownian particle motion near surfaces, as well as with inertial corrections to the Smoluchowski equation available in the literature. This latter equation is also generalized here to include particle-surface fluid dynamic interactions.     

一类燃烧模型方程组的整体经典解

燃烧模型是拟线性双曲方程组中一类重要的物理模型.考虑燃烧模型方程组的Cauchy问题,利用特征线和局部经典解延拓的方法证明了经典解的整体存在性.     

一类高阶非线性差分方程的吸引性

在文献[1-2]的基础上,研究了非线性差分方程xn+1=a-bxpn-k/A-x2n的全局稳定性和正解的周期性,其中a,A为非负实数,b为正实数,k,p∈{1,2,…},p≥2.证明了该方程的一个正平衡点是一个全局吸引子,并给出了相应的吸引域.     

Maxwell-Cattaneo方程组的非标准问题的衰减界

主要研究当温度和热量流满足非标准初始条件时的Maxwell-Cattaneo方程组.通过一些微分不等式,在参数的适当的范围上,结合非标准的初始条件,证明了温度和热量流的指数衰减界可由数据项确定.同时我们也推出了一个特例的解的指数衰减界.     

改进型Boussinesq方程高精度紧致差分显格式

采用一种高精度的紧致差分显格式对改进型Boussinesq方程进行数值求解;采用具有TVD性质的三阶Runge-Kutta方法进行预报,用三次样条函数进行校正,时间精度可达到四阶;在空间离散上采用六阶精度的三点紧致显格式进行计算;运用以上数值格式对Beji和Nadaoka改进型Boussinesq方程进行了求解,求解证明:高精度的数值结果和已知的试验结果吻合良好.作为验证算例,同时对波浪在台阶上的传播进行了模拟,从效果对比上可以看出,所得结果明显比Kittitanasuan的计算结果更靠近试验值.     

电路模拟中非线性方程的周期波形响应

用范数估计方法对非线性高阶微分方程的周期边值问题进行了讨论,通过对非线性二阶微分方程周期边值问题的详细讨论,给出了系统函数对某些变量偏导数的某种范数小于1时,非线性二阶微分方程的波形松弛算法产生的迭代序列收敛到该方程的周期解.用类似的方法给出了非线性高阶微分方程的波形松弛算法产生的迭代序列收敛到该方程周期解的充分性条件.