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+.

Full Optical Potential for the Electron-Hydrogen Entrance Channel

Differential and total elastic and total reaction cross sections are calculated for electron-hydrogen scattering at 30, 100, and 400 eV using an ab initio optical potential that treats bound and continuum nonelastic channels in the distorted-wave Born approximation. Multichannel and partial wave expansions are carried out to numerical convergence. Convergence criteria and quadratures for the continuum-energy integration are chosen for 1% overall accuracy. Results are compared with experiment and less detailed calculations

Coupled-Channel Optical Calculation of Electron-Hydrogen Scattering: The Distorted-Wave Optical Potential

The coupled-channel optical method solves a set of coupled momentum-space integral equations for a finite set of reaction channels. The remaining channels, including the target continuum, are described by the polarization potential operator, which formally depends on the full three-body state vectors for these channels. The distorted-wave optical potential makes the distorted-wave Born approximation for these state vectors, using exact target states. No other approximation is made. Calculations and comparison with experiment are reported for total ionization cross sections and asymmetries, total excitation cross sections, entrance-channel phenomena, and the coupled 1s,2s,2p channels, at a range of energies

Effect of Second-Order Exchange in Electron-Hydrogen Scattering

The electron-hydrogen scattering problem has been a nemesis to theoretical atomic physicists due to the fact that even the most sophisticated of theoretical calculations, both perturbative and nonperturbative, do not agree with experiment. The current opinion is that the perturbative approach cannot be used for this problem since recent second-order calculations are not in agreement with the experimental data and higher-order calculations are deemed impractical However, these second-order calculations neglected second-order exchange. We have now added exchange to the second-order calculation and have found that the primary source of disagreement between experiment and theory for intermediate energies is attributable not to higher-order terms but to second-order exchang

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