Bounds and optimization of the minimum eigenvalue for a vibrating system

We consider the problem of the oscillation of a string fixed at one end with a mass connected to a spring at the other end. The problem of minimizing the first eigenvalue of the system subject to a fixed total mass constraint is investigated. We discuss both a Sturm-Liouville and a Stieltjes integral formulation of the boundary value problem. For small spring constant, the minimum eigenvalue for both formulations is obtained by concentrating all the mass at the end with the spring. For large spring constants, the Stieltjes eigenvalue is minimized by a point mass at an interior point. We also formulate the problem with an $\alpha$-norm constraint on the density $\rho$ in which case the optimal eigenpair satisfies a nonlinear boundary value problem. Numerical evidence suggests that this case tends to the point-mass case at the end as $\alpha\rightarrow 1+.

An Infrared Determination of the Reddening and Distance to Dwingeloo 1

We present for the first time infrared observations of the nearby highly obscured galaxy Dwingeloo 1 (Dw1), including deep H-band imaging covering a total of 4.9x4.9 arcmin, together with J and Ks imaging of the central 2.5x2.5 arcmin. We used the small dispersion of the intrinsic infrared colors of spiral galaxies to determine an infrared H-band extinction of A_H = 0.47+/-0.11 mag towards Dw1. In using infrared colors, the uncertainties in the reddening and distance are reduced by a factor of three. The H-band magnitude corrected for extinction and the infrared Tully-Fisher relation are then used to estimate a distance modulus of (m-M)_0 = 28.62+/-0.27, and thus a distance of d = 5.3 {+0.7/-0.6} Mpc, which puts Dw1 at the far end of the IC342/Maffei 1 & 2 group. Our result is largely independent of the nature of the reddening law because we estimated both the reddening and the distance at the same wavelength range.Comment: 20 pages, 2 figures, see http://nicmos2.as.arizona.edu/~aalonso/Dw1/dw1_paper.htm

Eleven New Heavily Reddened Field Wolf–Rayet Stars

We report the results of a medium-narrowband 2 μm line survey covering 5.8 deg^2 near the Galactic plane. We confirm 11 new field Wolf-Rayet stars along three lines of sight probing the inner Galaxy, demonstrating the capability to uncover distant and highly reddened populations of Galactic wind-borne emission-line stars suffering extinction as high as A_V ~ 40 and as distant as 9 kpc down to modest magnitude limits of K_s ~ 12.5. All stars are of subtype WC7-8, with median distance d = 6 kpc and median extinction A_(Ks) = 2.5. Over the fields surveyed, the density of Wolf-Rayet stars to limiting magnitude K_s ~ 12.5 was found to be 1.9 deg^(–2). We compare this to models which predict their distribution within the Galaxy and find that, even neglecting survey and subtype incompleteness, they consistently underpredict the number of newly discovered stars along the surveyed lines of sight

Commissioning the MMT ground-layer and laser tomography adaptive optics systems

A multi-laser adaptive optics system, at the 6.5 m MMT telescope, has been undergoing commissioning in preparation for wide-field, partially corrected as well as narrow-field, diffraction limited science observations in the thermal and near infrared. After several delays due to bad weather, we have successfully closed the full high order ground-layer adaptive optics (GLAO) control loop for the first time in February 2008 using five Rayleigh laser guide stars and a single tilt star. Characterization and automated correction of static aberrations such as non-common path errors were addressed in May 2008. Calibration measurements in preparation for laser tomography adaptive optics (LTAO) operation are planned for the fall of 2008 along with the start of shared-risk GLAO science observations. We present the results of GLAO observations with the PISCES imager, a 1 - 2.5 µm camera with a field of view of 110 arc seconds. The status of the remaining GLAO commissioning work is also reviewed. Finally, we present plans for commissioning work to implement the LTAO operating mode of the system

Universal Controller for Spacecraft Mechanisms

An electronic control unit has been fabricated and tested that can be replicated as a universal interface between the electronic infrastructure of a spacecraft and a brushless-motor (or other electromechanical actuator) driven mechanism that performs a specific mechanical function within the overall spacecraft system. The unit includes interfaces to a variety of spacecraft sensors, power outputs, and has selectable actuator control parameters making the assembly a mechanism controller. Several control topologies are selectable and reconfigurable at any time. This allows the same actuator to perform different functions during the mission life of the spacecraft. The unit includes complementary metal oxide/semiconductor electronic components on a circuit board of a type called rigid flex (signifying flexible printed wiring along with a rigid substrate). The rigid flex board is folded to make the unit fit into a housing on the back of a motor. The assembly has redundant critical interfaces, allowing the controller to perform time-critical operations when no human interface with the hardware is possible. The controller is designed to function over a wide temperature range without the need for thermal control, including withstanding significant thermal cycling, making it usable in nearly all environments that spacecraft or landers will endure. A prototype has withstood 1,500 thermal cycles between 120 and +85 C without significant deterioration of its packaging or electronic function. Because there is no need for thermal control and the unit is addressed through a serial bus interface, the cabling and other system hardware are substantially reduced in quantity and complexity, with corresponding reductions in overall spacecraft mass and cost

On-sky wide field adaptive optics correction using multiple laser guide stars at the MMT

We describe results from the first astronomical adaptive optics system to use multiple laser guide stars, located at the 6.5-m MMT telescope in Arizona. Its initial operational mode, ground-layer adaptive optics (GLAO), provides uniform stellar wavefront correction within the 2 arc minute diameter laser beacon constellation, reducing the stellar image widths by as much as 53%, from 0.70 to 0.33 arc seconds at lambda = 2.14 microns. GLAO is achieved by applying a correction to the telescope's adaptive secondary mirror that is an average of wavefront measurements from five laser beacons supplemented with image motion from a faint stellar source. Optimization of the adaptive optics system in subsequent commissioning runs will further improve correction performance where it is predicted to deliver 0.1 to 0.2 arc second resolution in the near-infrared during a majority of seeing conditions.Comment: 13 pages, 1 table, 7 figures. Accepted for publication in Astrophysical Journal. Expected March 200