About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.

Conditions for the local manipulation of tripartite Gaussian states

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

CSRe束流动力学研究

非线性动力学对于环形加速器，尤其是对现代新型的加速器来说，起着越来越重要的作用。非线性力的引入使得束流在真空管道中的稳定性大大降低，对物理实验产生较大的影响。所以对束流动力学尤其是非线性动力学的研究已成为加速器研究中的一个必要的、重要的课题。 本文首先对加速器物理的基础知识和兰州重离子加速器冷却储存环及其实验环（HIRFL-CSRe）做了一定的介绍。然后给出了非线性力存在时的动力学孔径的理解和此时动力学孔径的多种研究方法。 接着本论文对束流的共振情况做了推导和描述，用映射的观点，通过Normal Form这一数学工具研究了CSRe的非线性动力学。然后用加速器常用的软件（COSY INFINITY）研究了HIRFL-CSRe在各种状态下由于高阶场误差带来的非线性力对各阶共振力的影响。 最后，也是本文的核心部分。用MAD程序研究了CSRe横向动力学。对CSRe色品进行了校正，并计算了色品六极铁对CSRe Lattice的影响。对CSRe理想Lattice的动力学孔径进行了计算，然后根据实际测磁数据计算了CSRe在有二极铁和四极铁高阶误差等多种情况下的动力学孔径，最后通过实际实验时的束流的各种参数的测量说明了理论计算和实际情况一致，强度和稳定性都能够满足物理实验的要求。 本论文对CSRe系统的运行和CSRe各项实验有着一定的实际意义

CSRm横向动力学研究

随着现代加速器向高能、强流、长寿命束流方向的发展，非线性动力学己成为现代加速器研究中一个非常重要的课题。本文从解析和数值模拟两方面对CSRm在存在各种场缺陷和安装准直误差情况下的非线性动力学进行了研究，并探讨研究了环型加速器中随时间变化驱动力-tune调制对粒子稳定性的影响。在解析研究方面，本文给出了储存环非线性束流动力学中基本理论、常用的表达式及研究方法做了详细介绍和推导。作为对非线性束流动力学解析研究的典型例子，本文给出了高杰推导出的存在不同非线性磁铁高阶场时动力学孔径解析表达式的详细推导过程。解析表达式能直观表示影响粒子运动稳定性的关键因素，但解析表达式所描述的lattice结构过子简单，只能看作是实际储存环lottice的近似。通过解析法可以研究主导粒子运动不稳定性的机制，但用来确定储存环动力学孔径强有力的工具是数值跟踪。用映射的观点，通过非线性变换，将表示通常粒子非线性运动的单圈映射用Normal Form来表示。用Normal Form这一数学工具，通过计算粒子运动稳定相空间体积确定了CSRm动力学孔径，求出了CSRm的高阶共振参数，半解析的研究了CSRm中tune随粒子振荡振幅的变换-Detuning效应。同时，跟用其他的数值方法的计算结果进行了比较。储存环中影响粒子运动稳定性的因素，除各种场缺陷和安装准直误差外，还有电源纹波效应等所引起随时间变化驱动力的影响。本文先从理论上分析研究了tune调制所引起的随机层宽度，扩散速度等，然后通过单粒子跟踪研究了tune调制对简单的FODo 1 ottice和CSRm的影响。用加速器中常用的MAD程序研究了CSRm横向动力学。对CSRm色品进行校正，并计算了色品六极铁对CSRmlattice的影响。通过实际的测量数据计算了二极铁的离散性和四极铁的安装准直误差所引起的闭轨畸变。由于CsRm二极铁黔的四极分量所引起 Tune移动时粒子在加速过程中经过共振线，所以对lattice黔行了修正。最后跟踪研究了lattice修正后的动力学孔径。

Experimental study on two-phase gas-liquid flow patterns at normal and reduced gravity conditions

Experimental studies have been performed for horizontal two-phase air-water flows at normal and reduced gravity conditions in a square cross-section channel. The experiments at reduced gravity are conducted on board the Russian IL-76 reduced gravity airplane. Four flow patterns, namely bubble, slug, slug-annular transition and annular flows, are observed depending on the liquid and gas superficial velocities at both conditions. Semi-theoretical Weber number model is developed to include the shape influence on the slug-annular transition. It is shown that its prediction is in reasonable agreement with the experimental slug-annular transition under both conditions. For the case of two-phase gas-liquid flow with large value of the Froude number, the drift-flux model can predict well the observed boundary between bubble and slug flows.

Shock-Induced Near-Wall Two-Phase Flow Structure Over a Micron-Sized Particles Bed

The present paper studies numerical modelling of near-wall two-phase flows induced by a normal shock wave moving at a constant speed, over a micronsized particles bed. In this two-fluid model, the possibility of particle trajectory intersection is considered and a full Lagrangian formulation of the dispersed phase is introduced. The finiteness of the Reynolds and Mach numbers of the flow around a particle as well as the fineness of the particle sizes are taken into account in describing the interactions between the carrier- and dispersed- phases. For the small mass-loading ratio case, the numerical simulation of flow structure of the two phases is implemented and the profiles of the particle number density are obtained under the constant-flux condition on the wall. The effects of the shock Mach number and the particle size and material density on particle entrainment motion are discussed in detail.The obtained results indicate that interphase non-equilibrium in the velocity and temperature is a common feature for this type of flows and a local particle accumulation zone may form near the envelope of the particle trajectory family.

Closed form solutions of T-stress in plane elasticity crack problems

The T-stress is considered as an important parameter in linear elastic fracture mechanics. In this paper, several closed form solutions of T-stress in plane elasticity crack problems in an infinite plate are investigated using the complex potential theory. In the line crack case, if the applied loading is the remote stress or the concentrated forces, the T-stress can be derived from the basic field. Here, the basic field is defined as the field caused by the applied loading in the infinite plate without the crack. For the circular are crack, the T-stress can be abstracted from a known solution. For the cusp crack problems, the T-stress can be separated from the obtained stress solution for which the conformal mapping technique is used.

Fracture statistics of brittle materials: Weibull or normal distribution

The fit of fracture strength data of brittle materials (Si3N4, SiC, and ZnO) to the Weibull and normal distributions is compared in terms of the Akaike information criterion. For Si3N4, the Weibull distribution fits the data better than the normal distribution, but for ZnO the result is just the opposite. In the case of SiC, the difference is not large enough to make a clear distinction between the two distributions. There is not sufficient evidence to show that the Weibull distribution is always preferred to other distributions, and the uncritical use of the Weibull distribution for strength data is questioned.

Variable power singular interface elements for a crack normal to the bimaterial interface

Zero thickness crack tip interface elements for a crack normal to the interface between two materials are presented. The elements are shown to have the desired r(lambda-1) (0 < lambda < 1) singularity in the stress field at the crack tip and are compatible with other singular elements. The stiffness matrices of the quadratic and cubic interface element are derived. Numerical examples are given to demonstrate the applicability of the proposed interface elements for a crack perpendicular to the bimaterial interface.

Computation of turbulent-flow in a square duct - aspects of the secondary flow and its origin

A numerical study of turbulent flow in a straight duct of square cross-section is made. An order-of-magnitude analysis of the 3-D, time-averaged Navier-Stokes equations resulted in a parabolic form of the Navier-Stokes equations. The governing equations, expressed in terms of a new vector-potential formulation, are expanded as a multi-deck structure with each deck characterized by its dominant physical forces. The resulting equations are solved using a finite-element approach with a bicubic element representation on each cross-sectional plane. The numerical integration along the streamwise direction is carried out with finite-difference approximations until a fully-developed state is reached. The computed results agree well with other numerical studies and compare very favorably with the available experimental data. One important outcome of the current investigation is the interpretation analytically that the driving force of the secondary flow in a square duct comes mainly from the second-order terms of the difference in the gradients of the normal and transverse Reynolds stresses in the axial vorticity equation.

Collapsed isoparametric element as a singular element for a crack normal to the bi-material interface

It is shown that the variable power singularity of the strain field at the crack tip can be obtained by the simple technique of collapsing quadrilateral isoparametric elements into triangular elements around the crack tip and adequately shifting the side-nodes adjacent to this crack tip. The collapsed isoparametric elements have the desired singularity at crack tip along any ray. The strain expressions for a single element have been derived and in addition to the desired power singularity, additional singularities are revealed. Numerical examples have shown that triangular elements formed by collapsing one side lead to excellent results.

Some theoretical aspects of the simplified Navier-Stokes(SNS) equations

This study deals with the formulation, mathematical property and physical meaning of the simplified Navier-Stokes (SNS) equations. The tensorial SNS equations proposed is the simplest in form and is applicable to flow fields with arbitrary body boundaries. The zones of influence and dependence of the SNS equations, which are of primary importance to numerical solutions, are expounded for the first time from the viewpoint of subcharacteristics. Besides, a detailed analysis of the diffusion process in flow fields shows that the diffusion effect has an influence zone globally windward and an upwind propagation greatly depressed by convection. The maximum upwind influential distance of the viscous effect and the relative importance of the viscous effect in the flow direction to that in the direction normal to the flow are represented by the Reynolds number, which illustrates the conversion of the complete Navier-Stokes (NS) equations to the SNS equations for flows with large Reynolds number.

High-speed streams from coronal holes and the accelerating mechanism of the solar-wind

In this paper, the general Mach number equation is derived, and the influence of typical energy forms in the solar wind is analysed in detail. It shows that the accelerating process of the solar wind is influenced critically by the form of heating in the corona, and that the transonic mechanism is mainly the result of the adjustment of the variation of the crosssection of flowing tubes and the heat source term.The accelerating mechanism for both the high-speed stream from the coronal hole and the normal solar wind is similar. But, the temperature is low in the lower level of the coronal hole and more heat energy supply in the outside is required, hence the high speed of the solar wind; while the case with the ordinary coronal region is just the opposite, and the velocity of the solar wind is therefore lower. The accelerating process for various typical parameters is calculated, and it is found that the high-speed stream may reach 800 km/sec.

Adhesive behavior of two-dimensional power-law graded materials

In this paper, we investigate the adhesive contact between a rigid cylinder of radius R and a graded elastic half-space with a Young's modulus varying with depth according to a power-law, E = E-0(y/c(0))(k) (0 < k < 1), while the Poisson's ratio v remains constant. The results show that, for a given value of ratio R/C-0, a critical value of k exists at which the pull-off force attains a maximum; for a fixed value of k, the larger the ratio R/c(0), the larger the pull-off force is. For Gibson materials (i.e., k = 1 and v = 0.5), closed-form analytical solutions can be obtained for the critical contact half-width at pull-off and pull-off force. We further discuss the perfect stick case with both externally normal and tangential loads.

Precipitation of nanocrystals in glasses by electron irradiation: An alternative path to form glass ceramics?

This letter demonstrates an alternative method to form gallium silicate glass ceramics using high-energy electron irradiation. Compared with glass ceramics obtained from the conventional thermal treatment method, the distribution and crystal sizes of the precipitated Ga2O3 nanoparticles are the same. An advantage of this method is that the spatial distribution of the precipitated nanoparticles can be easily controlled. However, optically active dopants Ni2+ ions do not participate in the precipitation during electron irradiation. (c) 2007 American Institute of Physics.