Instability Analysis of Nonlinear Surface Waves in a Circular Cylindrical Container Subjected to a Vertical Excitation

Singular perturbation theory of two-time scale expansions was developed both in inviscid and weak viscous fluids to investigate the motion of single surface standing wave in a liquid-filled circular cylindrical vessel, which is subject to a vertical periodical oscillation. Firstly, it is assumed that the fluid in the circular cylindrical vessel is inviscid, incompressible and the motion is irrotational, a nonlinear evolution equation of slowly varying complex amplitude, which incorporates cubic nonlinear term, external excitation and the influence of surface tension, was derived from solvability condition of high-order approximation. It shows that when forced frequency is low, the effect of surface tension on mode selection of surface wave is not important. However, when forced frequency is high, the influence of surface tension is significant, and can not be neglected. This proved that the surface tension has the function, which causes free surface returning to equilibrium location. Theoretical results much close to experimental results when the surface tension is considered. In fact, the damping will appear in actual physical system due to dissipation of viscosity of fluid. Based upon weakly viscous fluids assumption, the fluid field was divided into an outer potential flow region and an inner boundary layer region. A linear amplitude equation of slowly varying complex amplitude, which incorporates damping term and external excitation, was derived from linearized Navier-Stokes equation. The analytical expression of damping coefficient was determined and the relation between damping and other related parameters (such as viscosity, forced amplitude and depth of fluid) was presented. The nonlinear amplitude equation and a dispersion, which had been derived from the inviscid fluid approximation, were modified by adding linear damping. It was found that the modified results much reasonably close to experimental results. Moreover, the influence both of the surface tension and the weak viscosity on the mode formation was described by comparing theoretical and experimental results. The results show that when the forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when the forcing frequency is high, the surface tension of the fluid is prominent. Finally, instability of the surface wave is analyzed and properties of the solutions of the modified amplitude equation are determined together with phase-plane trajectories. A necessary condition of forming stable surface wave is obtained and unstable regions are illustrated. (c) 2005 Elsevier SAS. All rights reserved.

Nonlinear Faraday Waves in a Parametrically Excited Circular Cylindrical Container

In the cylindrical coordinate system, a singular perturbation theory of multiple-scale asymptotic expansions was developed to study single standing water wave mode by solving potential equations of water waves in a rigid circular cylinder, which is subjec

Function Innovation in Combined Surface Technologies for Metals

表面技术能够显著提高材料功能而成为工程和产品设计的重要组成部分, 但前提是表面技术必须具有可设计性。为此, 需要开拓和发展表面组合加工技术, 进行创新。该技术的内涵体现了新材料与新技术、基础研究与产业化有机结合的特点, 具有重要的价值和广阔的前景。

Computer Simulation Of Random Sphere Packing In An Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4 similar to 0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.

Surface waves in a vertically excited circular cylindrical container

The nonlinear free surface amplitude equation, which has been derived from the inviscid fluid by solving the potential equation of water waves with a singular perturbation theory in a vertically oscillating rigid circular cylinder, is investigated successively in the fourth-order Runge-Kutta approach with an equivalent time-step. Computational results include the evolution of the amplitude with time, the characteristics of phase plane determined by the real and imaginary parts of the amplitude, the single-mode selection rules of the surface waves in different forced frequencies, contours of free surface displacement and corresponding three-dimensional evolution of surface waves, etc. In addition, the comparison of the surface wave modes is made between theoretical calculations and experimental measurements, and the results are reasonable although there are some differences in the forced frequency.

Instability of the vertically forced surface wave in a circular cylindrical container

The nonlinear amplitude equation, which was derived by Jian Yongjun employing expansion of two-time scales in inviscid fluids in a vertically oscillating circular cylindrical vessel, is modified by introducing a damping term due to the viscous dissipation of this system. Instability of the surface wave is analysed and properties of the solutions of the modified equation are determined together with phase-plane trajectories. A necessary condition of forming a stable surface wave is obtained and unstable regions are illustrated. Research results show that the stable pattern of surface wave will not lose its stability to an infinitesimal disturbance.

Dynamic interaction of an elastic container with fluid

The vibration analysis of an elastic container with partially filled fluid was investigated in this paper. The container is made of a thin cylinder and two circular plates at the ends. The axis of the cylinder is in the horizontal direction. It is difficult to solve this problem because the complex system is not axially symmetric. The equations of motion for this system were derived. An incompressible and ideal fluid model is used in the present work. Solutions of the equations were obtained by the generalized variational method. The solution was expressed in a series of normalized generalized Fourier's functions. This series converged rapidly, and so its approximate solution was obtained with high precision. The agreement of the calculated values with the experimental result is good. It should be mentioned that with our method, the computer time is less than that with the finite-element method.

Quadratic nonlinear technologies for femtosecond lasers

Quadratic optical nonlinearity chi((2)) can be exploited in femtosecond lasers and regarded as a significant new degree of freedom for the design of short-pulse sources. We will review our recent progress on developing nonlinear quadratic technologies for femtosecond lasers. Our nonlinear laser technology offers new properties for femtosecond lasers, including optical parametric amplifier with novel working regime, efficient second harmonic generation, and time telescope.

The research and progress of micro-fabrication technologies of two-dimensional photonic crystal

The novel material of photonic crystal makes it possible to control a photon, and the photonic integration will have breakthrough progress due to the application of photonic crystal. It is based on the photonic crystal device that the photonic crystal integration could be realized. Therefore, we should first investigate photonic crystal devices based on the active and the passive semiconductor materials, which may have great potential application in photonic integration. The most practical and important method to fabricate two-dimensional photonic crystal is the micro-manufacture method. In this paper, we summarize and evaluate the fabrication methods of two-dimensional photonic crystal in near-infrared region, including electron beam lithography, selection of mask, dry etching, and some works of ours. This will be beneficial to the study of the photonic crystal in China.

Web容器性能关键技术研究

基于Java EE技术的Web容器已经成为面向Web计算环境的主流中间件平台，它为创建、部署、运行、集成和管理企业Web组件提供了基础设施支持。然而，企业用户规模的不断增长与企业Web应用程序的日趋复杂使得Web容器的性能面临严峻的威胁。 影响服务器性能的主要因素是服务器的资源与负载。在传统服务器设计领域，研究者已经取得了一系列的研究成果，如资源管理、准入控制、动态缓存、差分服务等。然而，上述传统服务器领域的研究成果难以满足开放、动态的Web计算环境需求。首先，Web容器无法预先获知企业Web应用程序的资源需求与负载特征，这使得它不得不采用一种“尽力而为”的服务策略。其次，传统资源管理技术难以解决不同资源之间的管理冲突，影响了资源的利用率。最后，传统的负载管理技术侧重于负载规模的变化，很少考虑负载的组成特征与行为特征。为解决上述问题，论文提出了一种面向资源的分阶段体系结构ROSA，并研究了基于ROSA的动态缓存技术与差分服务技术，具体研究内容如下： 论文首先提出了面向资源的分阶段体系结构ROSA，它将请求处理所需的处理资源（主要指线程）与共享资源加以区分，并且通过分阶段体系结构设计来有效解决处理资源阻塞。同时，论文扩展Petri网模型给出了ROSA体系结构的描述模型RDM与性能模型RPM，前者用于验证ROSA体系结构设计方案的结构性质与行为性质，后者用于定量的计算ROSA体系结构设计方案的平均响应时间、吞吐率等性能指标。最后，论文提出了相关设计模式用于ROSA体系结构的开发。 论文提出了一种访问模式驱动的动态缓存机制，消除了Web容器、Web组件与动态缓存机制的耦合，并能够利用客户访问模式提高Web容器的缓存效率。首先，论文设计了Web容器动态缓存框架来缓存Web组件动态生成的Web内容，减少Web组件的重复执行。然后，论文设计了模式图描述客户的访问行为，有效的消除了传统马尔可夫模型引入的无效访问行为。最后，论文在模式图基础上分别基于会话和缓存对象设计了两个预测概率函数以及访问模式驱动的缓存替换算法，有效的提高了动态缓存机制的效率。 论文提出了一种自适应差分服务机制以满足Web容器剧烈变化的负载，同时为企业Web应用程序的差分服务需求提供支持。首先，论文基于客户行为特征设计了动态的会话优先级，弥补了传统静态优先级定义（客户优先级、请求优先级）无法描述客户行为优先级的缺点。然后，通过扩展ROSA体系结构设计，提供了准入控制、优先级调度、资源预留等多种差分服务策略，从而适应Web容器的不同负载。最后，论文设计了自适应差分服务策略选择算法，根据Web容器负载状况自适应选择差分服务策略，消除了单一差分服务策略在某些情况下出现的资源浪费、请求“饿死”、不必要的请求丢失现象，保障了关键请求的性能指标。 最后，以上研究成果已经应用在一个高性能的Web容器系统Once Web容器中。在Java EE性能测试基准TPC-W的测试中取得了较好的效果。

Electrochemiluminescent microoptoprobe with mini-grid working electrode and self-contained sample container

A new electrochemiluminescence (ECL) microoptoprobe with simple structure. small sampling volume and high efficiency was developed. It was constructed by fixing the transparent gold mini-grid on the end surface of the optical fiber, and by surrounding the fiber with the counter- and reference electrodes to form a self-contained three-electrode system. The use of mini-grid electrode increased the surface area and collection efficiency. which resulted in higher ECL signal and better sensitivity. The counter electrode together with one end of the fiber formed a mini-vessel, which eliminated the need of additional container and allowed to perform ECL detection in a very small volume (about 10 mul). The microoptoprobe obtained was characterized with the Ru(bpy)(3)(2-)-tripropylamine system and was applied for the determination of oxalate and chlorpromazine (CPZ). Detection limits (S/N = 3) were 5 x 10(-7) and 1 x 10(-6) mol l(-1) for oxalate and CPZ. respectively. The linear range for oxalate and CPZ extended from 1 x 10(-6) to 1 x 10(-3) mol l(-1), and from 5 x 10(-6) to 5 x 10(-4) mol l(-1). respectively.