Parametric control of solutions to an evolution problem in a neighborhood of an unstable stationary regime

We study a controlled system of ordinary differential equations in a neighborhood of an unstable stationary regime. We seek for a control under which the solution remains in the neighborhood however long. We find conditions under which such control is possible and prove an existence theorem. The results are of a constructive character and can be applied to controlling actual processes.     

正交各向异性旋转壳的塑性拉伸失稳

研究了正交各向异性旋转壳的拉伸塑性失稳，给出了失稳条件下强化材料旋转壳的应力和应变。     

Effect of small parameters on the structure of the front formed by unstable viscous-fluid displacement from a Hele-Shaw cell

The process of displacement of a viscous fluid from a Hele-Shaw cell consisting of two plates separated by a small gap is investigated. The front formed when the fluid is displaced from the cell by another, lower-viscosity fluid is unstable. The lower-viscosity fluid breaks through the layer of displaced fluid and forms channels called viscous fingers. As a result, a mixing zone occupied by both displaced and displacing fluids is formed. The structure of the unstable displacement front is investigated when the surface tension forces have no effect on the shape of the fingers. This situation is realized when a water-glycerin mixture is rapidly displaced from the cell by water. Equations taking the inertial and viscous forces acting in the plane of the plates into account are obtained by averaging the Navier-Stokes equations over the cell gap. Using the equations obtained the stability of a plane displacement front traveling in the direction of its normal and the stability of the lateral surfaces of the viscous fingers is investigated when the fluid velocities are parallel to the interface. From the solution for stability of the transverse displacement front it follows that the viscous forces acting in the plane of the plates determine the finger width (when there is no surface tension). Instability also develops in the flow on the longitudinal fluid interface. In this case the destabilizing factor is the inertial forces. Under the action of this instability the fingers, in their turn, lose stability and disintegrate into viscous bubbles.     

Accessibility of partially hyperbolic endomorphisms with 1D center-bundles

We prove that partially hyperbolic endomorphisms with one dimensional center-bundles and non-trivial unstable bundles are stably accessible. And there is residual subset $\Res$ of partially hyperbolic volume preserving endomorphisms with one dimensional center-bundles such that every $f \in \Res$ is stably accessible. In the end, we prove the accessibility of Gan''s example.     

Stability of command economies

We consider the impact of fluctuations in the technology matrix A on two command input- output models. In the first, resources and goals are fixed and the model is solved for industrial production. If the growth rate can be zero, expected values of fluctuations of industrial goods are infinite. In the second, produced goods are scaled down to fit resources. Here we derive a criterion that

$\text{2log n}\text{k}$

should be small, where k is the number of significant ingredients in a good efficiency of aggregated economies, with n replaced by n₁/2 where n₁ is the number of goods aggregated into one.     

Invariant manifolds near a minimizer

A classical result, studied, among others, by Carathéodory [C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989], states that, for second-order, scalar equations, nondegenerate periodic minimizers are hyperbolic. Consequently, the Stable/Unstable Manifold Theorem applies, and implies that, at least locally, the stable and unstable sets are regular curves intersecting transversally at the nondegenerate minimizer.For analytic equations, there is a version of this fact which holds for isolated, but possibly degenerate, minimizers.     

第八种统计分布、涨落及热力学平衡态的稳定性

由Jaynes最大信息熵原理及拉格朗日乘子法推导出第八种统计分布,通过引入非广延熵常数的方法解决了零系综的困难.理论验证表明:本文推导出的第八种分布(N-E-V分布)不仅适用于小系统,而且适用于大系统.由此分布计算的理想量子系统的热力学量与7种分布相同,但广延量相对涨落却是正比于1的.这不仅可以解释临界现象, 也说明热力学平衡态及近平衡定态并不总是稳定的.     

Variable reflectivity unstable resonators for a long pulse XeCl excimer laser

The divergence of a long pulse, low gain XeCl excimer laser has been improved using confocal positive branch unstable resonators with variable reflectivity mirrors as outcouplers. With variable reflectivity unstable resonators, nearly diffraction limited beams are obtained. Variable reflectivity resonators lead to high brightness beams (9.1 10 W/(cm sr)). Different reflection profiles were studied with respect to their influence on the beam quality and the energy extraction.     

变物性条件下管内加速流时湍流换热与流动过程的数值模拟

对圆管内变物性流体在加速流时考虑了非定常流的影响,采用新的湍流迁移模型,对换热过程和流动特性进行了数值模拟研究。与实验相比较,得到较一致的结果。模拟计算在很大的参量范围内进行,结果标明:努谢尔特数及阻力系数与其准静态时的量值的比值在所定义的无量纲特征时间上有一最小值;在加速流时变物性的影响是导致不稳定过程加大的因素。     

Pion parton distributions in a nonlocal Lagrangian

We use phenomenological nonlocal Lagrangians, which lead to nontrivial forms for the quark propagator, to describe the pion. We define a procedure based on previous studies on nonlocal Lagrangians for the calculation of the pion parton distributions at low Q². The obtained parton distributions fulfill all the wishful properties. Using a convolution approach we incorporate the composite character of the constituent quarks. We evolve, using the Renormalization Group, the calculated parton distributions to the experimental scale and compare favorably with the data and draw conclusions.