Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade

Almost Block Diagonal Linear Systems: Sequential and Parallel Solution Techniques, and Applications

Almost block diagonal (ABD) linear systems arise in a variety of contexts, specifically in numerical methods for two-point boundary value problems for ordinary differential equations and in related partial differential equation problems. The stable, efficient sequential solution of ABDs has received much attention over the last fifteen years and the parallel solution more recently. We survey the fields of application with emphasis on how ABDs and bordered ABDs (BABDs) arise. We outline most known direct solution techniques, both sequential and parallel, and discuss the comparative efficiency of the parallel methods. Finally, we examine parallel iterative methods for solving BABD systems. Copyright (C) 2000 John Wiley & Sons, Ltd

AlGaAs heterojunction lasers

The characterization of 8300 A lasers was broadened, especially in the area of beam quality. Modulation rates up to 2 Gbit/sec at output powers of 20 mW were observed, waveform fidelity was fully adequate for low BER data transmission, and wavefront measurements showed that phase aberrations were less than lamda/50. Also, individually addressable arrays of up to ten contiguous diode lasers were fabricated and tested. Each laser operates at powers up to 30 mW CW in single spatial mode. Shifting the operating wavelength of the basic CSP laser from 8300 A to 8650 A was accomplished by the addition of Si to the active region. Output power has reached 100 mW single mode, with excellent far field wave front properties. Operating life is currently approx. 1000 hrs at 35 mW CW. In addition, laser reliability, for operation at both 8300 A and 8650 A, has profited significantly from several developments in the processing procedures

A special vortex - vortex scattering process in superconductors

In this thesis we discuss the evidence for scatter in g at right angles o two vortices in a head-on collision. The evidence is given in terms of the approximate solutions of the equations of motion or the Euler-Lagrange equations DiD^+^Wm2- 1) = 0, d,Fij + i/2(o*Djo - (DJy) = 0 where D{ = ( 1. The ordinary differential equations, which result from th e ansatz for th e approximate solutions, are solved by Taylor series a t the origin and a sym p to tic series at infinity