Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Mg I emission lines at 12 and 18 micrometer in K giants

The solar Mg I emission lines at 12 micrometer have already been observed and analyzed well. Previous modeling attempts for other stars have, however, been made only for Procyon and two cool evolved stars, with unsatisfactory results for the latter. We present high-resolution observational spectra for the K giants Pollux, Arcturus, and Aldebaran, which show strong Mg I emission lines at 12 micrometer as compared to the Sun. We also present the first observed stellar emission lines from Mg I at 18 micrometer and from Al I, Si I, and presumably Ca I at 12 micrometer. To produce synthetic line spectra, we employ standard non-LTE modeling for trace elements in cool stellar photospheres. We compute model atmospheres with the MARCS code, apply a comprehensive magnesium model atom, and use the radiative transfer code MULTI to solve for the magnesium occupation numbers in statistical equilibrium. We successfully reproduce the observed Mg I emission lines simultaneously in the giants and in the Sun, but show how the computed line profiles depend critically on atomic input data and how the inclusion of energy levels with n > 9 and collisions with neutral hydrogen are necessary to obtain reasonable fits.Comment: 9 pages, 6 figures, accepted for publication in Astronomy & Astrophysic

Fluorine in the solar neighborhood - is it all produced in AGB-stars?

The origin of 'cosmic' fluorine is uncertain, but there are three proposed production sites/mechanisms: AGB stars, $\nu$ nucleosynthesis in Type II supernovae, and/or the winds of Wolf-Rayet stars. The relative importance of these production sites has not been established even for the solar neighborhood, leading to uncertainties in stellar evolution models of these stars as well as uncertainties in the chemical evolution models of stellar populations. We determine the fluorine and oxygen abundances in seven bright, nearby giants with well-determined stellar parameters. We use the 2.3 $\mu$m vibrational-rotational HF line and explore a pure rotational HF line at 12.2 $\mu$m. The latter has never been used before for an abundance analysis. To be able to do this we have calculated a line list for pure rotational HF lines. We find that the abundances derived from the two diagnostics agree. Our derived abundances are well reproduced by chemical evolution models only including fluorine production in AGB-stars and therefore we draw the conclusion that this might be the main production site of fluorine in the solar neighborhood. Furthermore, we highlight the advantages of using the 12 $\mu$m HF lines to determine the possible contribution of the $\nu$-process to the fluorine budget at low metallicities where the difference between models including and excluding this process is dramatic

TEXES Observations of M Supergiants: Dynamics and Thermodynamics of Wind Acceleration

We have detected [Fe II] 17.94 um and 24.52 um emission from a sample of M supergiants using TEXES on the IRTF. These low opacity emission lines are resolved at R = 50, 000 and provide new diagnostics of the dynamics and thermodynamics of the stellar wind acceleration zone. The [Fe II] lines, from the first excited term, are sensitive to the warm plasma where energy is deposited into the extended atmosphere to form the chromosphere and wind outflow. These diagnostics complement previous KAO and ISO observations which were sensitive to the cooler and more extended circumstellar envelopes. The turbulent velocities, Vturb is about 12 to 13 km/s, observed in the [Fe II] forbidden lines are found to be a common property of our sample, and are less than that derived from the hotter chromospheric C II] 2325 Angstrom lines observed in alpha Ori, where Vturb is about 17 to 19 km/s. For the first time, we have dynamically resolved the motions of the dominant cool atmospheric component discovered in alpha Ori from multi-wavelength radio interferometry by Lim et al. (1998). Surprisingly, the emission centroids are quite Gaussian and at rest with respect to the M supergiants. These constraints combined with model calculations of the infrared emission line fluxes for alpha Ori imply that the warm material has a low outflow velocity and is located close to the star. We have also detected narrow [Fe I] 24.04 um emission that confirms that Fe II is the dominant ionization state in alpha Ori's extended atmosphere.Comment: 79 pages including 10 figures and 2 appendices. Accepted by Ap

Analytical and experimental study of stratification and liquid-ullage coupling, 1 June 1964 - 31 May 1965

Closed-form solution for stratification of subcooled fluids in containers subjected to heating, and for liquid-ullage vapor couplin