Fractal features of oscillatory convection in the half-floating zone

Unsteady and two-dimensional numerical simulation is applied to study the transition process from steady convection to turbulence via subharmonic bifurcation in thermocapillary convection of a liquid bridge in the half-floating zone. The results of numerical tests show clearly the fractal structure of period-doubling bifurcations, and frequency-locking at f/4, f/8, f/16 with basic frequency f is observed with increasing temperature difference. The Feigenbaum universal constant is given by the present paper as delta(4) = 4.853, which can be compared with the theoretical value 4.6642016.

Formation of shear bands in plane sheet

The formation of shear bands in plane sheet is studied, both analytically and experimentally, to enhance the fundamental understanding of this phenomenon and to develop a capability for predicting material failure. The evolution of voids is measured and its interaction with the process of shear banding is examined. The evolving dilatancy in plasticity is shown to have a vital role in analysing the shear-band type of bifurcation, and tremendously reduces the theoretical value of critical stresses. The analyses, referring to both localized and diffuse modes of bifurcation, fairly explain the corresponding observations obtained through testing a dual-phase steer sheet and provide a justification of the constitutive model used.

Predicting chaotic time-series with wavelet networks

A new technique, wavelet network, is introduced to predict chaotic time series. By using this technique, firstly, we make accurate short-term predictions of the time series from chaotic attractors. Secondly, we make accurate predictions of the values and bifurcation structures of the time series from dynamical systems whose parameter values are changing with time. Finally we predict chaotic attractors by making long-term predictions based on remarkably few data points, where the correlation dimensions of predicted attractors are calculated and are found to be almost identical to those of actual attractors.

Transition from steady to oscillatory convection with chaotic feature in thermocapillary convection

The transition process from steady to turbulent convection via subharmonic bifurcation in thermocapillary convection of half floating zone was studied by numerical simulation and experimental test. Both approaches gave structure of period doubling bifurcations in the present paper, and the Feigenbaum universal law was checked for the system of thermocapillary convection.

Elastodynamic stress-intensity factors for a semiinfinite crack under 3-d combined mode loading

The dynamic stress intensity factor histories for a half plane crack in an otherwise unbounded elastic body are analyzed. The crack is subjected to a traction distribution consisting of two pairs of suddenly-applied shear point loads, at a distance L away from the crack tip. The exact expression for the combined mode stress intensity factors as the function of time and position along the crack edge is obtained. The method of solution is based on the direct application of integral transforms together with the Wiener-Hopf technique and the Cagniard-de Hoop method, which were previously believed to be inappropriate. Some features of solutions are discussed and the results are displayed in several figures.

Elastodynamic stress intensity factor history for a semi-infinite crack under three-dimensional transient loading

The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.

On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.

一种新的二维平板分叉流槽的设计

目的 解决平行平板流槽每次实验只能观测壁面培养细胞受一种剪应力作用的问题。方法 作者在平行平板流槽的基础上，首次提出了一种改进后的流槽-二维平板分叉流槽。通过数值模拟，给出了流体作定常流动时，流速和壁面剪应力的分布。结果 结果发现，利用这种二维平板分流槽可以研究壁面培养的细胞在不同大小剪应力作用下的力学行为。结论 该研究结果为流槽的合理设计和使用，并分析剪应力空间分布对内皮细胞的影响有重要实际意义。

T型分叉流槽中前列环素和内皮素分泌的研究

动脉粥样硬化（atherosclerosis）的非随机分布与当地的血流动力环境有关，借助平行平板式平直流槽和以T型分叉流槽为代表的平行平板式异型流槽，可以模拟血管的主要形状特征，首,先在数值模拟的基础上分布了流型特征参数，确定了流的设计尺寸。然后，通过实验研究，探讨流型改变对内皮细胞血管活性物质分泌的影响，发现扩张效应流线偏转和驻点效应使得异型流槽前列环素和内定素的沁泌水平与相同入口雷诺数（Re）条件下的平直流槽分别有降低趋势和显著差异。为进一步研究流型对血管内皮细胞的影响提供了实验数据。

多热源分布时薄层液体中热毛细对流的分叉特征

研究一个液体薄层在热源作用下的流动特征.Pimputakar和Ostrach给出了单热源作用下薄层液体的高度和流场方程.在此基础上具体分析比较了多个热源分布作用下的流动图像随各参数尤其是随热源间距离不同的变化情况,着重讨论产生的分叉现象.

Information Preservation (IP) Method in Simulation

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

湍流研究最近半世纪的一些发展

<正>内容一、绪言(Ⅰ)研究湍流的意义(Ⅱ)国外开展湍流研究的情况二、湍流理论的进展(Ⅰ)先把流体动力学方程组平均的理论(a)1950年以前发展情况简述(1)Reynolds方程和混合长度理论(2)各向同性湍流的统计理论(3)具有剪应力的普通湍流理论(b)最近的剪切湍流的半经验理论(c)最近的湍流统计理论(1)E.Hopf理论(2)R.H.Kraichnan直接相互作用理论(8)Lewis等人的分子运动理论(4)Meecham理论。(5)S.Grossmann重正化群法(8)陈善谟统计动力学重复级串法

Floating zone convection

The microgravity research, as a branch of the advanced sciences and a spe- cialized field of high technology, has been made in China since the late 1980's. The research group investigating microgravity fluid physics consisted of our col- leagues and the authors in the Institute of Mechanics of the Chinese Academy of Sciences (CAS), and we pay special attention to the floating zone convection as our first research priority. Now, the research group has expanded and is a part of the National Microgravity Laboratory of the CAS, and the research fields have been extended to include more subjects related to microgravity science. Howev- er, the floating zone convection is still an important topic that greatly holds our research interests.