The Near-Infrared Extinction Law in Regions of High Av

We present a spectroscopic study of the shape of the dust-extinction law between 1.0 and 2.2um towards a set of nine ultracompact HII regions with Av > 15 mag. We find some evidence that the reddening curve may tend to flatten at higher extinctions, but just over half of the sample has extinction consistent with or close to the average for the interstellar medium. There is no evidence of extinction curves significantly steeper than the standard law, even where water ice is present. Comparing the results to the predictions of a simple extinction model, we suggest that a standard extinction law implies a robust upper limit to the grain-size distribution at around 0.1 - 0.3um. Flatter curves are most likely due to changes in this upper limit, although the effects of flattening due to unresolved clumpy extinction cannot be ruled out.Comment: 9 pages, 7 figure

Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance

In a recent article [M. Olshanii, Phys. Rev. Lett. {\bf 81}, 938 (1998)], an analytic solution of atom-atom scattering with a delta-function pseudopotential interaction in the presence of transverse harmonic confinement yielded an effective coupling constant that diverged at a `confinement induced resonance.' In the present work, we report numerical results that corroborate this resonance for more realistic model potentials. In addition, we extend the previous theoretical discussion to include two-atom bound states in the presence of transverse confinement, for which we also report numerical results hereComment: New version with major revisions. We now provide a detailed physical interpretation of the confinement-induced resonance in tight atomic waveguide

Helium and Hydrogen Line Ratios and The Stellar Content of Compact HII Regions

We present observations and models of the behaviour of the HI and HeI lines between 1.6 and 2.2um in a small sample of compact HII regions. As in our previous papers on planetary nebulae, we find that the `pure' 1.7007um 4^3D-3^3P and 2.16475um 7^(3,1)G-4^(3,1)F HeI recombination lines behave approximately as expected as the effective temperature of the central exciting star(s) increases. However, the 2.058um 2^1P-2^1S HeI line does not behave as the model predicts, or as seen in planetary nebulae. Both models and planetary nebulae showed a decrease in the HeI 2^1P-2^1S/HI Br gamma ratio above an effective temperature of 40000K. The compact HII regions do not show any such decrease. The problem with this line ratio is probably due to the fact that the photoionisation model does not account correctly for the high densities seen in these HII regions, and that we are therefore seeing more collisional excitation of the 2^1P level than the model predicts. It may also reflect some deeper problem in the assumed model stellar atmospheres. In any event, although the normal HeI recombination lines can be used to place constraints on the temperature of the hottest star present, the HeI 2^1P-2^1S/HI Br gamma ratio should not be used for this purpose in either Galactic HII regions or in starburst galaxies, and conclusions from previous work using this ratio should be regarded with extreme caution. We also show that the combination of the near infrared `pure' recombination line ratios with mid-infrared forbidden line data provides a good discriminant of the form of the far ultraviolet spectral energy distribution of the exciting star(s). From this we conclude that CoStar models are a poor match to the available data for our sources, though the more recent WM-basic models are a better fit.Comment: Accepted for publication in MNRA

Topologically Driven Swelling of a Polymer Loop

Numerical studies of the average size of trivially knotted polymer loops with no excluded volume are undertaken. Topology is identified by Alexander and Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration radius, and probability density distributions as functions of gyration radius are generated for loops of up to N=3000 segments. Gyration radii of trivially knotted loops are found to follow a power law similar to that of self avoiding walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200