The Construction of Curves and Surfaces Using Numerical Optimization Techniques

Numerical optimization techniques are playing an increasing role in curve and surface construction. Often difficult problems in curve and surface construction, especially when some aspect of shape control is involved, can be phrased as a constrained optimization problem. Four such classes of problems are explored: parametric curve fitting with non-linear shape constraints; explicit surface fitting with linear shape constraints; surface fitting to scattered data giving rise to ill-posed problems; finally, variable knot problems. In each of these problems there is a nonlinear aspect: either the shape of the curve or surface is important for manufacturing or engineering reasons or the shape affects the convergence of numerical algorithms which use the curve or surface or the placement of knots affects the accuracy of the fits. In all cases the class of functions used is that of parametric spline curves and tensor or direct product spline surfaces. The reason for choosing this class is that splines provide flexible models that are easily evaluated and stored. Furthermore, the B-spline representation of splines leads to convenient expressions for shape control over regions

Laboratory studies of Kapton degradation in an oxygen ion beam

Results are presented from a preliminary laboratory investigation of the degradation of the widely used polyimide Kapton under oxygen ion bombardment. Recent space shuttle flights have shown that Kapton and some other materials exposed to the apparent ram flow of residual atmosphere (at orbital velocity in low Earth orbit) lose mass and change their optical properties. It was hypothesized that these changes are caused by chemical interaction with atomic oxygen, aided by the 5-eV impact energy of atmospheric oxygen atoms in the ram. The reaction rate under O(+) bombardment seemed to be independent of incident energy over a wide range of energies. Although the flux of thermal ions in this experiment was much greater than the accelerated flux, the observed Kapton degradation was limited to the beam area and ram flow direction. This is consistent with an activation energy above the thermal energies but well below the beam energies. The results reproduce well the material loss, optical changes, SEM surface structure, and ram directionality of the samples returned by the shuttle. These factors, along with the lack of degradation under argon ion bombardment, are convincing evidence for ram flow oxidation as the mechanism of degradation

Teddy Bear Triage and Treatment: Novel Technique of Mass Casualty Incident Education

Providing education on medical care and triage during mass casualty incidents (MCI) can be challenging. Table top exercises lack the impact of a hands-on experience necessary to emphasize the scale of a real event, while full scale events are often time and resource intensive. We present a novel method using low-cost stuffed bears to expose learners to MCI triage methodology and medical care

Ram-wake effects on plasma current collection of the PIX 2 Langmuir probe

The Plasma Interaction Experiment 2 (PIX 2) Langmuir probe readings of the same polar magnetospheric regions taken on consecutive orbits showed occasional apparent densities as much as 10 times lower than the average, although each pass clearly showed density structures related to the day/night boundary. At other points in the orbit, Langmuir probe currents varied by as much as a factor of 20 on a time scale of minutes. The hypothesis is advanced that these apparent inconsistencies in Langmuir probe current are the results of the probe's orientation relative to the body of the spacecraft and the velocity vector. Theoretical studies predict a possible depletion in collected electron current by a factor of 100 in the wake. Experimental results from other spacecraft indicate that a wake electron depletion by a factor of 10 or so is realistic. This amount of depletion is consistent with the PIX 2 data if the spacecraft was rotating. Both the Sun sensor and temperature sensor data on PIX 2 show a complex variation consistent with rotation of the Langmuir probe into and out of the spacecraft wake on a time scale of minutes. Furthermore, Langmuir probe data taken when the probe was not in the spacecraft wake are consistent from orbit to orbit. This supports the interpretation that ram/wake effects may be the source of apparent discrepancies at other orientations

A flight dynamics investigation of compound helicopter configurations

Compounding has often been proposed as a method to increase the maximum speed of the helicopter. There are two common types of compounding known as wing and thrust compounding. Wing compounding offloads the rotor at high speeds delaying the onset of retreating blade stall, hence increasing the maximum achieveable speed, whereas with thrust compounding, axial thrust provides additional propulsive force. The concept of compounding is not new but recently there has been a resurgence of interest in the configuration due to the emergence of new requirements for speeds greater than those of conventional helicopters. The aim of this paper is to investigate the dynamic stability characteristics of compound helicopters and compare the results with a conventional helicopter. The paper discusses the modelling of two compound helicopters, with the first model featuring a coaxial rotor and pusher propeller. This configuration is known as the coaxial compound helicopter. The second model, known as the hybrid compound helicopter, features a wing and two propellers providing thrust compounding. Their respective trim results are presented and contrasted with a baseline model. Furthermore, using a numerical differentiation technique, the compound models are linearised and their dynamic stability assessed. The results show that the frequency of the coaxial compound helicopter’s dutch roll mode is less than that of the baseline helicopter and there is also greater roll damping. With regards to the hybrid compound helicopter the results show greater heave damping and the stabilisation of the phugoid due to the addition of the wing and propellers

Laboratory degradation of Kapton in a low energy oxygen ion beam

An atomic oxygen ion beam, accelerated from a tunable microwave resonant cavity, was used at Lewis Research Center to bombard samples of the widely used polyimide Kapton. The Kapton experienced degradation and mass loss at high rates, which may be comparable to those found in Space Shuttle operations if the activation energy supplied by the beam enabled surface reactions with the ambient oxygen. The simulation reproduced the directionality (ram-wake dependence) of the degradation, the change in optical properties of the degraded materials, and the structure seen in scanning electron micrographs of samples returned on the Shuttle Trails with a substituted argon ion beam produced no rapid degradation. Energy Dispersive X-ray Analysis (EDAX) showed significant surface composition changes in all bombarded samples. Mass loss rates and surface composition changes are discussed in terms of the possible oxidation chemistry of the interaction. Finally, the question of how the harmful degradation of materials in low Earth orbit can be minimized is addressed

The voltage threshold for arcing for solar cells in LEO: Flight and ground test results

Ground and flight results of solar cell arcing in low Earth orbit (LEO) conditions are compared and interpreted. It is shown that an apparent voltage threshold for arcing may be produced by a strong power law dependence of arc rate on voltage, combined with a limited observation time. The change in this apparent threshold with plasma density is a reflection of the density dependence of the arc rate. A nearly linear dependence of arc rate on density is inferred from the data. A real voltage threshold for arcing for 2 by 2 cm solar cells may exist however, independent of plasma density, near -230 V relative to the plasma. Here, arc rates may change by more than an order of magnitude for a change of only 30 V in array potential. For 5.9 by 5.9 solar cells, the voltage dependence of the arc rate is steeper, and the data are insufficient to indicate the existence of an arcing increased by an atomic oxygen plasma, as is found in LEO, and by arcing from the backs of welded-through substrates

Hedge funds and systemic risk.

A hedge fund is a privately offered investment vehicle that pools the contributions of investors in order to invest in a variety of assets, such as securities, futures, options, bonds and currencies. Hedge funds have attracted growing attention from policy makers, financial market participants and the general public due to their rapid growth and substantial scale, their importance to banks as clients and the impact of their trading activity on global capital markets. Because of their rapid growth and the market disruptions caused by Long-Term Capital Management (LTCM) in 1998, some analysts believe that hedge funds pose systemic risks. However, this is unlikely. A thorough review of the avenues through which hedge funds could cause systemic problems indicates that, although a major disruption emanating from the hedge fund sector is possible, it would be diffi cult for the sector to be highly disruptive to fi nancial markets. Post-LTCM, regulatory authorities have encouraged banks to monitor their hedge fund clients through constraints on their leverage. This has thus far proven effective, as the recent failure of Amaranth demonstrates. That failure, the largest yet, caused hardly a ripple in the wider financial markets. Hedge funds support the robustness of markets in many ways. They provide attractive investment alternatives and improve economy-wide risk sharing. In addition, they promote fi nancial market stability by assuming risks that other market participants are unwilling or unable to bear; by providing liquidity; and by placing trades that move mispriced assets toward their “fundamental” values. Of course, hedge funds could raise problems through their dominant role in some markets, active trading strategies, use of leverage and relative lack of transparency. Counterparties must therefore be cognizant of the risks they bear from hedge funds. Also, regulators must continue to promote better hedge fund risk management and transparency through their regulation of counterparties while remaining vigilant about potential systemic risks emanating from the sector. On balance, however, hedge funds enhance market stability and are unlikely to be the source of a systemic failure.