SOl-based radial-contour-mode micromechanical disk resonator

This paper reports a radial-contour-mode micromechanical disk resonator for radio frequency applications.This disk resonator with a gold plated layer as the electrodes,was prepared on a silicon-on-insulator wafer,which is supported by an anchor on another silicon wafer through Au-Au thermo-compression bonding.The gap between the disk and the surrounding gold electrodes is 100 nm.The radius of the disk is 20 μm and the thickness is 4.5μm.In results,the resonator shows a resonant frequency of 143 MHz and a quality factor of 5600 in vacuum.     

Exact solutions for the incompressible viscous magnetohydrodynamic fluid of a rotating-disk flow with Hall current

The focus of the present study is to obtain exact solutions for the flow of a viscous hydromagnetic fluid due to the rotation of an infinite disk in the presence of an axial uniform steady magnetic field with the inclusion of Hall current effect. In place of the traditional von Karman's axisymmetric evolution of the flow, the rotational non-axisymmetric stationary conducting flow is taken into consideration here, whose governing equations allow an exact solution to develop bounded everywhere in the normal direction to the wall.The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions, which differ from those of corresponding to the classical von Karman's conducting flow. Making use of this solution, analytical formulas for the angular velocity components, for the current density field as well as for the wall shear stresses are extracted. The critical peripheral locations at which extrema of the local skin friction occur are also determined. It is proved from the analytical results that for the specific flow the properly defined thicknesses decay as the magnetic field strength increases in magnitude, approaching their hydrodynamic value in the limit of large Hall numbers.Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation function. According to the Fourier's heat law, a constant heat transfer from the disk to the fluid occurs, though it increases by the presence of magnetic field, the increase is slowed down by the Hall effect eventually reaching its hydrodynamic limit.     

Flow due to non-coaxial rotation of a porous disk and a second grade fluid rotating at infinity

An exact solution for the three-dimensional flow due to non-coaxial rotation of a porous disk and a second grade fluid at infinity is obtained. It is shown that for uniform suction or uniform blowing at the disk, an asymptotic profile exists for the velocity distribution. The velocity depends on two parameters: one of them is the suction parameter or blowing parameter and the other is the visco-elastic parameter. Furthermore, it is found that when the value of the visco-elastic parameter is fixed, the velocity decreases with an increase in the value of the suction parameter and when the value of the suction parameter is fixed, the velocity increases with an increase in the value of the visco-elastic parameter.     

Study on the dynamical characteristics of a supersonic high pressure ratio underexpanded impinging ideal gas jet through numerical simulations

The impingement of an axisymmetric underexpanded ideal gas jet on a flat surface is investigated through numerical simulations. Different injection conditions, characterized by the nozzle pressure ratio (NPR), have been considered and for each, several standoff distances were studied. The study was conducted using the commercial finite volume general purpose code Fluent^®. The numerical results are presented in terms of Mach number and static pressure to characterize the structure of the flow. Furthermore, the influence of the standoff distance upon the position and diameter of Mach disk is analysed. Some results are compared with literature data and good agreement is obtained.     

L波段强流单束团注入器的束流动力学计算

自由电子激光器要求高亮度、低能散度的电子束注入波荡器(Undulator)。本文叙述提供高亮度电子束的高频电子直线加速器中的注入器部分的设计计算。注入器由L波段(1300MHz)的十二分频和三分频两个谐振腔预聚束器和一个基波频率的变相速聚束器组成。粒子运动方程中考虑了空间电荷效应和束流负载效应。电子枪的注入参数:脉冲宽度T=4ns;电流I=5A;电子的初始动能E_0=100keV;电子束分布为高斯型。参数优化设计结果:单束团宽度小于25ps,峰值电流达400A以上,电子的平均归一化能量>4,束团内的能量差小于200keV。     

Transverse disks, symbolic dynamics, homology direction vectors, and Thurston-Nielson theory

We review some properties of transverse disks and use symbolic dynamics to determine rotation vectors from the return map to a transverse disk. We also prove connections between the symbolic dynamics and Nielson equivalence of orbits.     

On Minimal Annuli with a Straight Line Boundary

Shiffman proved that if a minimal annulus A in a slab is bounded by two convex Jordan curves contained respectively in the two boundary planes P and Q of the slab, then A intersects all parallel planes between P and Q in strictly convex curves. We generalize Shiffman's result to the case that A is bounded by a strictly convex C² Jordan curve and a straight line. We show that in this case Shiffman's result is still true.     

Investigation of Elliptical Gaussian Beam in Optical Disk System

1.IntroductionLaserdiodehasbeenx`idelyusedinfibrc-opticcommunicat:onandopticaldisk$yctems.LaserbeamIsradiationangle(fullangu1aratha1f-maximumintensitypoint)ismeasuredbothparllelandPerpendiculartothcjunctionp1anclgenera1ly.o//=6,~1o",oJ-=2o"~5O':Inerasableopticaldisksystemsasmagneto-optica1disksystems,thelaserbcamiscollimatedandshapedtobecircularsymInetricbeaminordcrtoaquireahighintensityandhighqualityscanningbeamiPot,butitsoptica1systemiscomplicatedandeasyaddingassocialaberration.usingaellip…     

Regular points for Lagrange interpolation on the unit disk

A set of points on the unit disk of the Euclidean plane is given, which admits unique Lagrange interpolation. The points have rotational symmetry and they form an example of natural lattices of Chung and Yao [2]. Properties of Lagrange interpolation with respect to these points are studied.Work done when visiting the University of Oregon at Eugene, Oregon.Supported by National Science Foundation under Grant No. 9302721.