Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

Helicopter Anti-Torque System Using Strakes

A helicopter is disclosed with a system for controlling main-rotor torque which reduces the power and size requirements of conventional anti-torque means. The torque countering forces are generated by disrupting the main rotor downwash flowing around the fuselage. The downwash flow is separated from the fuselage surface by a strake positioned at a specified location on the fuselage. This location is determined by the particular helicopter wash pattern and fuselage configuration, generally being located between 20 deg before top dead center (TDC) and 80 deg from TDC on the fuselage side to which the main rotor blade approaches during rotation. The strake extends along the fuselage from the cabin section to the aft end and can be continuous or separated for aerodynamic surfaces such as a horizontal stabilizer

Geometry-induced pulse instability in microdesigned catalysts: the effect of boundary curvature

We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of CO on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.Comment: submitted to Phys. Rev.

Depression, School Performance, and the Veridicality of Perceived Grades and Causal Attributions

An external criterion was assessed to test whether depressives have distorted perceptions of covariation information and whether their attributions are consistent with this information. Students’ actual and self-perceived grades, depression status, and attributions for failures were assessed. Furthermore, partici pants estimated average grades. Generally, self-perceived own past grades were inflated. Depressed students and those with low grades distorted their own grades (but not the average grade) more to their favor than individuals low in depression and those with high grades. Depression went along with lower actual grades and with internal, stable, and global failure attributions. Mood differences in attributions were not due to differences in previous grades. Depressed individuals drew (unrealistically) more depressogenic causal inferences when they perceived average grades to be low than when average grades were perceived to be high. However, they (realistically) attributed failure more in a depressogenic fashion than did nondepressives when their own grade history was low

Self-steepening of light pulses

Self-steepening of light pulses due to propagation in medium with intensity-dependent index of refractio

Temperature dependence of the superconducting gap anisotropy in Bi2_{2}Sr2_{2}Ca1_{1}Cu2_{2}O8+x_{8+x}

We present the first detailed data of the momentum-resolved, temperature dependence of the superconducting gap of $Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+x}$, complemented by similar data on the intensity of the photoemission superconducting condensate spectral area. The gap anisotropy between the $\Gamma-\bar{M}$ and $\Gamma-X$ directions increases markedly with increasing temperature, contrary to what happens for conventional anisotropic-gap superconductors such as lead. Specifically, the size of the superconducting gap along the $\Gamma-X$ direction decreases to values indistinguishable from zero at temperatures for which the gap retains virtually full value along the $\Gamma-\bar{M}$ direction.Comment: APS_REVTEX. 19 pages, including 8 figures, available upon request. UW-Madison preprin

Localization Effects in Bi2Sr2Ca(Cu,Co)2O8+y High Temperature Superconductors

Doping Bi2Sr2Ca1Cu2O8+y with Co causes a superconductor-insulator transition. We study correlations between changes in the electrical resistivity RHOab(T) and the electronic bandstructure using identical single crystalline samples. For undoped samples the resistivity is linear in temperature and has a vanishing residual resistivity. In angle resolved photoemission these samples show dispersing band-like states. Co-doping decreases TC and causes and increase in the residual resistivity. Above a threshold Co-concentration the resistivity is metallic (drab/dT >0) at room temperature, turns insulating below a characteristic temperature Tmin and becomes super- conducting at even lower temperature. These changes in the resistivity correlate with the disappearance of the dispersing band-like states in angle resolved photoemission. We show that Anderson localization caused by the impurity potential of the doped Co-atoms provides a consistent explanation of all experimental features. Therefore the TC reduction in 3d-metal doped high- temperature superconductors is not caused by Abrikosov Gor'kov pair- breaking but by spatial localization of the carriers. The observed suppression of TC indicates that the system is in the homogenous limit of the superconductor-insulator transition. The coexistance of insulating (dRHOab/dT <0) normal state behavior and super- conductivity indicates that the superconducting ground state is formed out of spatially almost localized carriers.Comment: Postscript file 11 pages plus 4 figures available on reques

Implementing Quantum Gates by Optimal Control with Doubly Exponential Convergence

We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude (depending on which one we compare to), particularly for quantum information processing purposes. This substantially enhances the ability to both study the control capabilities of physical systems within their coherence times, and constrain solutions for control tasks to lie within experimentally feasible regions. Natural extensions of the algorithm are also discussed.Comment: 4+2 figures; to appear in PR

Observation of a van Hove Singularity in Bi2Sr2Ca1Cu2O8+xBi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+x} with Angle Resolved Photoemission

We have performed high energy resolution angle-resolved photoemission studies of the normal state band structure of oxygen overdoped $Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+x}$. We find that there is an extended saddle point singularity in the density of states along $\Gamma-\bar{M}-Z$ direction. The data also indicate that there is an asymmetry in the Fermi surface for both the $\Gamma-\bar{M}-Z$ and perpendicular directions.Comment: APS_Revtex. 28 pages, including 16 figures, available upon request. UW-Madison preprint#

Aerodynamic characteristics of several current helicopter tail boom cross sections including the effect of spoilers

Aerodynamic characteristics were determined of three cylindrical shapes representative of tail boom cross sections of the U.S. Army AH-64, UH-60, and UH-1H helicopters. Forces and pressures were measured in a wind-tunnel investigation at the Langley Research Center. Data were obtained for a flow incidence range from -45 to 90 deg and a dynamic pressure range from 1.5 to 50 psf. These ranges provided data representative of full-scale Reynolds numbers and the full range of flow incidence to which these helicopter tail boom shapes would be subjected at low flight speeds. The effects of protuberances such as tail rotor drive-shaft covers and spoilers were evaluated. The data indicate that significant side loads on tail booms of helicopters can be generated and that the addition of spoilers can beneficially alter the side loads. Although an increase in vertical drag occurs, the net effect through reduction of tail rotor thrust required can be an improvement in helicopter performance