Steady-state convection of a non-Newtonian fluid in a vertical layer

Steady-state thermal convection is investigated for a non-Newtonian fluid with a power-law rheological characteristic in a plane vertical channel bounded by parallel planes x=±h maintained at different temperatures.perm'. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–139, July–August, 1972.     

Homotopy Classes of Self-Maps of Annuli, Generalised Twists and Spin Degree

Let X be a [generalised] annulus and consider the space of continuous self-maps of X, that is,

2维各向异性弹性力学中的Stroh公式和某些不变量

本文简要综述了各向异性弹性体2维变形的Stroh公式。该公式数学上优美而应用上有力。它的最近进展使我们将已有的复数形式的解转变成实数形式,进而可去解决一些迄今尚未解出的问题。结果,发现了许多有趣的而在物理上难以预料的现象。例如,对于界面包含x_3轴的各向异性双介质体,如果线力和线位错都沿x_3轴,那末包含x_3轴的任意径向平面上的面拉力将不随径向平面的选择而变化。而且,在任何固定点上的应力与界面的方位无关。要揭示的其他一些不变性质是:双介质材料中的虚拟力,界面裂纹上的应力奇异,界面裂纹表面上的振荡,等等;另外,在具有一个有限裂纹,或一个椭圆孔,或一个刚性椭圆核的无穷大均匀介质中的某些应力和位移也是不变量。这些不变量的大部分尚未有它们的物理解释。在实数形式的解中,Barnett-Lothe张量常常出现。在绕x_3轴转动时,这些张量的分量的某些组合是不变的。这些组合将在本文中推导并列出。最后我们给出了某些各向异性弹性材料,它们的Barnett-Lothe张量是不变量,即这些张量的所有分量在绕x_3轴转动时是不变的。     

Microradiographic strain measurement using markers

A method for measuring strain on interior planes of some real structural materials is presented. X-ray images are formed of small (10–40 micron) gold markers placed on selected interior planes of optically opaque X-ray transparent materials. The use of well collimated monochromatic synchrotron radiation makes possible high contrast images of the small markers. Images of the particles before and after straining are recorded photographically. Photographs are enlarged 33X and measured using a simple electro-optical setup. In calibration experiments using approximately a 300-micron gage length, the strain measured by this method agreed with extensometer measured strains to within 100 microstrain. Example applications in a graphite-epoxy composite are presented, including measurement of the strain drop off near the free edge, strain concentration around a hole, and the strain field on a particular plane near a hole after local delamination. The technique is currently limited to materials no less X-ray transparent than titanium.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Analysis of sloping elastic pile under arbitrary loads by line-loaded integral equation method

ＩｎｔｒｏｄｕｃｔｉｏｎＳｌｏｐｉｎｇｐｉｌｅｉｓｏｆｔｅｎｕｓｅｄｉｎｆｏｕｎｄａｔｉｏｎｓｏｆｐｉｅｒ,ｂｒｉｄｇｅ,ｏｆｓｈｏｒｅｓｔｒｕｃｔｕｒｅ,ｓｔｒｕｃｔｕｒｅａｎｄｂｕｉｌｄｉｎｇ．Ｔｈｅｓｔｕｄｙｈａｓｂｅｎｃｏｎｄｕｃｔｅｄｂｙｔ...     

Extended graphical representation of polynomials with applications to cybernetics

In this paper,the polynomial of a complex variable s(≡x iy)with realcoefficients K=a_0s~n a_1s~(n-1) …… a_(n-1)s a_n.is graphically represented by three plane curves which are the projections of aspace curve on three coordinate planes of the coordinate system(x,iy.K)inwhich K is confined to be real.The projection on(x,iy)plane is just the rootlocus of the polynomial with K as a real parameter.It is remarkable thatthe equation of the root-locus is m-th degree in y~2,whether n=2m 1 orn=2m 2.In addition to the real curve K.=f(x)in the figure(K,x)thereexists another curve K.which is plotted by the real parts of all complexroots against K.The(K,x)curve is particularly important to determine theabsolute as well as the relative stable interval of K for linear systems.For cybernetics,the(K,iy)curve can be used to show the relation betweenthe nature frequency ω and the gain K.Such three figures are useful forstudying the theory of equation and cybernetics.     

On Approximations of First Integrals for Strongly Nonlinear Oscillators

In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations. In particularthe generalized Rayleigh oscillator equation will be studied in detail, and it will beshown that at least five limit cycles can occur.     

Centers and Uniform Isochronous Centers of Planar Polynomial Differential Systems

For planar polynomial vector fields of the form

$$\begin{aligned} (-y+X(x,y))\dfrac{\partial }{\partial x}+(x+Y(x,y))\dfrac{\partial }{\partial y}, \end{aligned}$$

where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers.

     

Stagnation point heat flux in hypersonic high enthalpy flow

The paper describes stagnation point heat flux measurements at a range of enthalpies relevant to re-entry speeds of aero-assisted space transfer vehicles (ASTVs) and proposed space planes, using the Australian National University Free Piston Shock Tunnel T3. The unique feature of these experiments is that they were conducted in the straight through (reflectionless) mode which enabled higher enthalpies and densities hitherto unattained.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1992 and the AMS fonts, developed by the American Mathematical Society.     

Some Aspects of Stability for Semigroup Actions and Control Systems

The present paper introduces both the notions of Lagrange and Poisson stabilities for semigroup actions. Let \(S\) be a semigroup acting on a topological space \(X\) with mapping \(\sigma :S\times X\rightarrow X\) , and let \(\mathcal {F}\) be a family of subsets of \(S\) . For \(x\in X\) the motion \(\sigma _{x}:S\rightarrow X\) is said to be forward Lagrange stable if the orbit \(Sx\) has compact closure in \(X\) . The point \(x\) is forward \(\mathcal {F}\) -Poisson stable if and only if it belongs to the limit set \(\omega \left( x,\mathcal {F}\right) \) . The concept of prolongational limit set is also introduced and used to describe nonwandering points. It is shown that a point \(x\) is \( \mathcal {F}\) -nonwandering if and only if \(x\) lies in its forward \(\mathcal {F} \) -prolongational limit set \(J\left( x,\mathcal {F}\right) \) . The paper contains applications to control systems.     

大瑞铁路澜沧江大桥工程边坡岩体结构特征研究

岩体中结构面的展布及其组合特征决定了岩体的工程地质性质和力学性状,影响着岩体的破坏方式。大瑞铁路澜沧江大桥所处的澜沧江构造带,具有高地震烈度、活跃的新构造运动、活跃的外动力地质条件、活跃的岸坡浅表改造过程等地质特征。工程区两岸节理裂隙等弱面发育,岸坡浅表改造过程强烈,导致岩体结构复杂。通过野外现场调查,对两岸边坡岩体结构面数据进行统计分析,采用^x2检验与K-S检验法对结构面进行概率密度拟合,分析岩体结构特征。结果表明：(1)右岸的优势结构面有三组; (2)左岸的优势结构面有四组; (3)各组优势结构面产出状态数据均服从正态分布。在统计分析结果的基础上,建立两岸岩体结构的统计模型,并对边坡破坏模式进行定性分析,认为：(1)右岸边坡变形破坏模式为滑移 压致拉裂; (2)左岸结构面贯通性不好,主要的破坏模式是局部块体滑移。
     

地下工程中岩土结构面的影响分析

研究已表明岩土体中都存在结构面,工程岩土体的变形破坏一般受结构面控制。本文依据结构面 (断层 )优势指标综合值 (Ri)的量化比较,可得出各结构面 (断层 )对隧道稳定影响程度的大小,从而针对各结构面 (断层 )采取不同的工程措施。本文分析还表明,结构面和地下工程中的水害、瓦斯突出、岩体质量好坏等也有密切关系。     

On a gas source in a constant force field

The nonbarochronic regular partially invariant submodel of the equations of gas dynamics is studied. The submodel reduces to an implicit ordinary differential equation of the first order for an auxiliary function X = X(x). The physical quantities (velocity, density, and pressure) are expressed in terms of the function X. The properties of the solutions of the equation are investigated and interpreted physically in terms of gas motion. The existence of a shock-wave solution is proved. The properties of the shock adiabat are studied. It is shown that the results obtained are new and differ significantly from the results for the case of no constant force. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 3–16, November–December, 2006.     

多裂面斜坡滑动面聚类分析

斜坡中通常发育有多种裂面 ,这些裂面能否在滑坡发育过程中形成滑面 ,将取决于裂面所处的应力状态、裂面的性质、形态、发育密集程度等因素。裂面聚类分析就是通过对裂面所处应力状态的分析 ,确定斜坡中存在的多组潜在滑面 ,然后对斜坡中多组裂面进行聚类分析。其基本方法是将所研究的一组样本 (裂隙或潜在滑面 )中的每一个样本看成一类 ,根据样品间相似系数或距离的大小 ,每次将最为相近的合并 ,计算合并后新类与其他类之间的距离 ,再选择最小距离合并 ,最后将一组样本合并成所需要的类 ,确定斜坡中最有可能发育成滑动面的裂面 (或变形带).     

Anti-plane shear cracks in ideally plastic crystals

Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

Fixed point theorem of nonexpansive mappings in convex metric spaces

Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:d(T_x,T_y)≤ad(x,t)+b{d(x,T_x)+d(y,T_y)}+c{d(x,T_x)+d(y,T_y)}for all x,y in K,where 0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1, then T has a unique fixed point in K.     

Temperature distributions in a periodically stratified layer with slant lamination

The paper deals with the two-dimensional stationary temperature distribution in a composite layer. The nonhomogenous body is assumed to be composed of periodically repeated two-layered laminae. The layering is inclined with an arbitrary angle to the boundary planes. The lower and upper boundary planes are assumed to be kept at given temperatures. The considered problem is solved within the framework of the homogenized model with microlocal parameters, where the continuity thermal conditions on interfaces are satisfied.