Configuration Design Sensitivity Analysis of Kinematic Responses of Mechanical Systems∗

Abstract

A continuum-based configuration design sensitivity analysis method is presented for kinematically driven mechanical systems. Configuration design variable for mechanical systems are defined. The 3-1-3 Euler angle is used as the orientation design variable. The reassembly process for a mechanical system after a configuration design change is eliminated by imposing kinematic admissibility conditions of the velocity field. The direct differentiation method is used to derive design sensitivity equations. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.     

A least‐square weighted residual method for level set formulation

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three‐dimensional (3D) problems. An LSWRM was adopted for two semi‐discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time‐reversed single‐vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non‐oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier–Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Design of a 50 kW, wideband Ka-band slow wave cyclotron amplifier

A two-stage slow wave cyclotron amplifier is investigated to demonstrate a high power, stable, and broad Ka-band radiation source, operating at a low beam power (~60 kV, ~5 amps) and a low magnetic field (~7 kG). A linear theory predicts that the second harmonic gyro-BWO is competing in the amplifier and can be stabilized by inserting a sever in the interaction circuit. A slow-time-scale non-linear code, with a sever included, predicts a saturated gain of 24-28 dB, an efficiency of 15-17%, and an instantaneous bandwidth of 15-20% at a beam axial velocity spread of 2%. A broadband RF coupler, a mode converter, and a RF vacuum window are designed by the use of a 3D electromagnetic, finite element code. Measured RF characteristics are in good agreement with predictions     

The M/G/1 retrial queue with bernoulli schedule

We consider anM/G/1 retrial queue with infinite waiting space in which arriving customers who find the server busy join either (a) the retrial group with probabilityp in order to seek service again after a random amount of time, or (b) the infinite waiting space with probabilityq(=1–p) where they wait to be served. The joint generating function of the numbers of customers in the two groups is derived by using the supplementary variable method. It is shown that our results are consistent with known results whenp=0 orp=1.     

Liminf results on the increments of an (N,d)-Gaussian process

We establish some liminf theorems on the increments of a (N,d)-Gaussian process with the usual Euclidean norm, via estimating upper bounds of large deviation probabilities on the suprema of the (N,d)-Gaussian process. This revised version was published online in June 2006 with corrections to the Cover Date.     

The Chern Conjecture for Affinely Flat Manifolds Using Combinatorial Methods

An affine manifold is a manifold with a flat affine structure, i.e. a torsion-free flat affine connection. We slightly generalize the result of Hirsch and Thurston that if the holonomy of a closed affine manifold is isomorphic to amenable groups amalgamated or HNN-extended along finite groups, then the Euler characteristic of the manifold is zero confirming an old conjecture of Chern. The technique is from Kim and Lee's work using the combinatorial Gauss–Bonnet theorem and taking the means of the angles by amenability. We show that if an even-dimensional manifold is obtained from a connected sum operation from K(, 1)s with amenable fundamental groups, then the manifold does not admit an affine structure generalizing a result of Smillie.