抽样定理法重建流场的三维温度分布

结合气流场温度较低，只能得到较少干涉条纹的实际情况，提出了采用轴样定理法重建流场的三维温度分布的模型，并考查了该方法的计算机模拟运算结果，对具体的对象，进行了实验，并采用图像处理方法对条纹进行了一系列处理，最后重建了二个截面上的温度分布。     

Asymptotic Behavior of Quasi-Autonomous Expansive Type Evolution Systems in a Hilbert Space

We introduce the notion of almost expansive sequences and curves and study their ergodic and asymptotic properties in a Hilbert space H. We apply our results to study the asymptotic behavior of solutions to the quasi-autonomous expansive type evolution system (du/dt)(t) + f(t) ∈ Au(t) on [0, ∞).     

A 3D Model of One-Legged Hopping Machine

The paper models the spatial motion of a hopping machine with allowance for the inertial properties of its leg. A control system is synthesized and a program trajectory is determined in view of the collision processes accompanying touchdowns. The synthesis procedure is based on optimization of periodic systems. The results from numerical simulation of the hopper's nonstationary motion are demonstrative of the high efficiency of the control system     

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

Phragmen-Lindelöf alternative results for the initial boundary problem of stokes equation

In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation, i. e. we show that the energy expression for the solution of the initial boundary problem must either grow exponentially or decay exponentially with axial distance from the end of a semi-infinite strip. For the case of decay, we also establish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.Project supported by the National Natural Science Foundation of China and Zhongshan University Science Foundation     

Stationary problem of third-grade fluids in two and three dimensions: existence and uniqueness

This paper is devoted to the stationary problem of third-grade fluids in two and three dimensions. In two dimensions, we show existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, by generalizing the method used by J.M. Bernard for the stationary problem of second-grade fluids (we deal with a polynomial of four degrees instead of two degrees). Contrary to the case of two dimensions, the resolution of the problem of third-grade fluids in three dimensions requires the physical condition |α₁+α₂|<(24νβ)^1/2. From this condition, we derive two “pseudo ellipticities” for the operator ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, where A(u) is a 3-order symmetric matrix such that tr(A(u))=0. Thus, with, in addition, a sharp estimate of the scalar product (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), we are able to prove existence of solutions and uniqueness, for a boundary of class C^2,1 and small data, in three dimensions.

Résumé

Cet article est consacré au problème stationnaire des fluides de grade trois en dimension deux et trois. En dimension deux, nous montrons l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en généralisant la méthode utilisée par J.M. Bernard pour le problème stationnaire des fluides de grade deux (nous avons affaire à un polynôme de degré quatre au lieu de deux). Contrairement au cas de la dimension deux, la résolution du problème des fluides de grade trois en dimension trois requière la condition physique |α₁+α₂|<(24νβ)^1/2. De cette condition, nous déduisons deux “pseudo matrice” pour l’opérateur ν|A(u)|²+(α₁+α₂)tr(A(u)³)+β|A(u)|⁴, où A(u) est une matice symétrique d’ordre 3 à trace nulle. De là, avec, en plus, une fine estimation du produit scalaire (|A(u)|²A(u)-|A(v)|²A(v),A(u)-A(v)), nous sommes capables de prouver l’existence de solutions et l’unicité, pour une frontière de classe C^2,1 et une donnée petite, en dimension trois.     

Uniqueness in the water-wave problem for bodies intersecting the free surface at arbitrary anglesL'unicité du problème des ondes de surface pour les corps qui intersectent la surface libre sous des angles arbitraires

This Note deals with the linearized water-wave problem involving a surface-piercing cylinder in water of infinite depth. A solution to this problem is proved to be unique for all values of the radian frequency when the cylinder intersecting the free surface at arbitrary angles is subjected to certain geometric arrangements. To cite this article: N. Kuznetsov, C. R. Mecanique 332 (2004).     

用波晶片相位板产生角动量可调的无衍射涡旋空心光束

本文提出了一种用波晶片产生无衍射涡旋空心光束的新方案. 根据晶体双折射的性质, 设计波晶片的厚度, 在一块晶体薄片上对o光和e光分别形成各自的四台阶相位板, 线偏振光入射到该相位板后, o光和e光衍射按强度叠加, 利用准伽利略望远镜系统聚焦, 得到近似无衍射涡旋空心光束. 光路简单, 调节方便. 在近轴条件下, 运用菲涅耳衍射理论和经典电磁场角动量理论, 数值模拟计算了周期数不同的两块波晶片相位板衍射光强和角动量的分布, 结果表明: 两块相位板都能在较长距离内产生近似无衍射涡旋空心光束, 光强和轨道角动量的分布与螺旋相位板产生的涡旋光束基本相同. 在衍射光路中加入相位补偿器, 调节o光和e光的相位差可以调节自旋角动量的大小, 从而可以调节总角动量密度和平均光子角动量的大小. 用这种空心光束导引冷原子或冷分子, 原子在与光子相互作用过程中可获得可调的转动力矩.     

悬链曲面上的点粒子动力学及扩展空间约束系统量子化

扩张型正则量子化方案的核心内容是位置、动量以及哈密顿量同时量子化. 通过分析悬链面上粒子的扩张型正则量子化方案, 并且与薛定谔理论进行比较, 发现内禀几何中二维悬链面给不出与薛定谔理论相一致的结果, 而考虑将二维悬链面嵌入在三维欧氏空间之后, 还需要将正则量子化方案进行扩张, 可以得到体系的几何势能和几何动量, 并与薛定谔理论相一致.