Numerical analysis of the rotating viscous flow approaching a solid sphere

A numerical simulation is performed to investigate the flow induced by a sphere moving along the axis of a rotating cylindrical container filled with the viscous fluid. Three‐dimensional incompressible Navier–Stokes equations are solved using a finite element method. The objective of this study is to examine the feature of waves generated by the Coriolis force at moderate Rossby numbers and that to what extent the Taylor–Proudman theorem is valid for the viscous rotating flow at small Rossby number and large Reynolds number. Calculations have been undertaken at the Rossby numbers (R_o) of 1 and 0.02 and the Reynolds numbers (R_e) of 200 and 500. When R_o=O(1), inertia waves are exhibited in the rotating flow past a sphere. The effects of the Reynolds number and the ratio of the radius of the sphere and that of the rotating cylinder on the flow structure are examined. When R_o ? 1, as predicted by the Taylor–Proudman theorem for inviscid flow, the so‐called ‘Taylor column’ is also generated in the viscous fluid flow after an evolutionary course of vortical flow structures. The initial evolution and final formation of the ‘Taylor column’ are exhibited. According to the present calculation, it has been verified that major theoretical statement about the rotating flow of the inviscid fluid may still approximately predict the rotating flow structure of the viscous fluid in a certain regime of the Reynolds number. Copyright © 2004 John Wiley & Sons, Ltd.     

非相干辐照对LiNbO3:Fe晶体光折变非线性的影响与控制作用

研究了非相干辐照对LiNbO3:Fe晶体中从自散焦到自聚焦的动态转换过程的影响和控制作用.无论是从前向还是从背向加入非相干辐照，都能加快自散焦、自聚焦过程以及从自散焦到自聚焦的转换过程，增大折射率的变化值.当非相干辐照以一定的时间间隔重复辐照在晶体上时，透射功率能迅速地上升和下降，具有明显的开关效应.这种在非相干辐照控制下折射率的迅速改变有望应用于全光学开关器件. 关键词： 非相干辐照 光伏效应 自散焦 自聚焦     

n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

液晶分子附着能和盒间隙对响应时间的影响

通过理论分析和实验研究液晶分子附着能和液晶盒间隙对响应时间(τ0)的影响。用液晶盒有效间隙法和表面动力学方程法两种方法推出分析公式,由这两种方法推出的结果是一致的。实验数据与简化方程τ0-dx基本拟合(其中d是液晶盒的间隙,x是指数)。在两种极端的(极大或极小)附着能极限下,指数x分别接近2和1。这个结论有助于优化液晶显示器件的应用。     

Optical investigation of cavitation erosion by laser-induced bubble collapse

By means of a new force sensor based on optical beam deflection (OBD), the mechanical effects of laser-matter interaction underwater at different incident laser energy are investigated in detail. The experimental results show that a target underwater is impacted in turn by laser-plasma ablation force and high-speed liquid-jet impulse induced by bubbles collapse in the vicinity of a solid boundary. Furthermore, the amplitudes of the two forces increase monotonously with laser energy. According to the ablation force detected by the experiment and the theoretical relationship between laser intensity and ablation pressure, the value of liquid-jet impact against a solid boundary can be easily obtained. In addition, based on the model of a collapsing bubble, some characteristic parameters, such as the liquid-jet impact velocity, the maximum bubble radius, the bubble energy can also be obtained at different laser energy, which are valuable in the corresponding research fields.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

受迫振动演示实验装置

本文叙述用示波器显示来演示受迫振动的实验装置，可直观地向学生展示受迫振动的幅频特性和相频特性。     

Endpoint estimates for certain commutators of fractional and singular integrals

In this paper, the authors obtain the endpoint estimates for a class of non-standard commutators with higher order remainders and their variants. Moreover, the authors show that these operators are actually not bounded in certain cases.

     

Techniques and Apparatus for Measuring Rotational Core Losses of Soft Magnetic Materials

In many situations such as the cores of a rotating electrical machine and the T joints of a multiphase transformer, the local flux density varies with time in terms of both magnitude and direction, i.e. the flux density vector is rotating. Therefore, the magnetic properties of the core materials under the rotating flux density vector excitation should be properly measured, modeled and applied in the design and analysis of these electromagnetic devices. This paper presents an extensive review on the development of techniques and apparatus for measuring the rotational core losses of soft magnetic materials based on the experiences of various researchers in the last hundred years.     

Preparation of nanometer MgO by sol-gel auto-combustion

Nanometer MgO was prepared via a sol-gel auto-combustion technique using magnesium nitrate as raw material and citric acid as chelating agent. IR spectra of the dried gel were used to investigate the structure of the precursors. By studying the different TG curves of magnesium citrate gel prepared by different methods, we found that a combustion process occurred and the nitrate ions acted as an oxidant in the combustion process. TEM photographs of synthesized powders from the sol-gel auto-combustion showed that the crystallites were uniform in size. In addition, the XRD pattern of this sample showed that the particle size was 8.9 nm. The BET curves, in turn, showed that the specific surface of the sample was 26.34 m²/g. The mechanism of the frothing process in restraining agglomeration is discussed. __________ Translated from Journal of East China Normal University (Natural Science), 2007, (2): 52–57 [译自: 华东师范大学学报(自然科学版)]