The Entropy of Square-Free Words

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters.Comment: 18 page

UVES observations of QSO 0000-2620: oxygen and zinc abundances in the Damped Ly-alpha galaxy at z_abs=3.3901

Observations of the QSO 0000-2620 with UVES spectrograph at the 8.2m ESO KUEYEN telescope are used for abundance analysis of the damped Ly-alpha system at z_{abs}=3.3901. Several Oxygen lines are identified in the Ly_alpha forest and a measure for the oxygen abundance is obtained at [O/H]=-1.85 +/- 0.1 by means of the unsaturated OI 925 A and OI 950 A lines. This represents the most accurate O measurement in a damped Ly_alpha galaxy so far. We have also detected ZnII 2026 A and CrII 2056, 2062 A redshifted at about 8900 A and found abundances [Zn/H] = -2.07 +/- 0.1 and [Cr/H]=-1.99 +/- 0.1. Furthermore, previous measurements of Fe, Si, Ni and N have been refined yielding [Fe/H]=-2.04 +/- 0.1, [Si/H]=-1.90 +/- 0.1, [Ni/H]=-2.27 +/- 0.1, and [N/H]=-2.68 +/- 0.1. The abundance of the non-refractory element zinc is the lowest among the damped Ly-alpha systems showing that the associated intervening galaxy is indeed in the early stages of its chemical evolution. The fact that the Zn abundance is identical to that of the refractory elements Fe and Cr suggests that dust grains have not formed yet. In this Damped Ly-alpha system the observed [O,S,Si/Zn,Fe,Cr] ratios, in whatever combination are taken, are close to solar (i.e 0.1-0.2 dex) and do not show the [alpha-element/Fe] enhancement observed in Milky Way stars of comparable metallicity. The observed behavior supports a galaxy evolution model characterized by either episodic or low star formation rate rather than a Milky-Way-type evolutionary model.Comment: Accepted by Ap

Scaling of the specific heat in superfluid films

We study the specific heat of the $x-y$ model on lattices $L \times L \times H$ with $L \gg H$ (i.e. on lattices representing a film geometry) using the Cluster Monte--Carlo method. In the $H$--direction we apply Dirichlet boundary conditions so that the order parameter in the top and bottom layers is zero. We find that our results for the specific heat of various thickness size $H$ collapse on the same universal scaling function. The extracted scaling function of the specific heat is in good agreement with the experimentally determined universal scaling function using no free parameters.Comment: 4 pages, uuencoded compressed PostScrip

Formation of Galactic Systems in Light of the Magnesium Abundance in Field Stars: The Thin Disk

We analyze the relations between the relative magnesium abundances in stars and their metallicities, Galactic orbital elements, and ages. The relative magnesium abundances in metal-poor ([Fe/H] < -0.4) thin-disk stars have been found to systematically decrease with increasing stellar orbital radii in such a way that magnesium over abundances ([Mg/Fe]>0.2 dex) are essentially observed only in the stars whose orbits lie almost entirely within the solar circle. At the same time, the range of metallicities in magnesium-poor stars is displaced from (-0.5<[Fe/H]<+0.3 dex) to (-0.7<[Fe/H]<+0.2 dex) as their orbital radii increase. This behavior suggests that, first, the star formation rate decreases with increasing Galactocentric distance and, second, there was no star formation for some time outside the solar circle while this process was continuous within the solar circle. The decrease in the star formation rate with increasing Galactocentric distance is responsible for the existence of a negative radial metallicity gradient (grad_{R}[Fe/H]=(-0.05 \pm 0.01) kpc^{-1}) in the disk, which shows a tendency to increase with decreasing age. At the same time the relative magnesium abundance exhibits no radial gradient. We have confirmed the existence of a steep negative vertical metallicity gradient (grad_Z [Fe/H]=(-0.29 \pm 0.06) kpc^{-1}) and detected a significant positive vertical gradient in relative magnesium abundance (grad_Z [Mg/Fe]=(0.13 \pm 0.02) kpc^{-1}); both gradients increase appreciably in absolute value with decreasing age. We have found that there is not only an age-metallicity relation, but also an age-magnesium abundance relation in the thin disk.Comment: accepted 2006, Astronomy Letters, Vol. 32 No. 6, P.376-392, 14 pages, 10 figure

Diffractive point sets with entropy

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition

Keck-Nirspec Infrared OH Lines: Oxygen Abundances in Metal-Poor Stars Down to [Fe/H] = -2.9

Infrared OH lines at 1.5 - 1.7 um in the H band were obtained with the NIRSPEC high-resolution spectrograph at the 10m Keck Telescope for a sample of seven metal-poor stars. Detailed analyses have been carried out, based on optical high-resolution data obtained with the FEROS spectrograph at ESO. Stellar parameters were derived by adopting infrared flux method effective temperatures, trigonometric and/or evolutionary gravities and metallicities from FeII lines. We obtain that the sample stars with metallicities [Fe/H] < -2.2 show a mean oxygen abundance [O/Fe] ~ 0.54, for a solar oxygen abundance of epsilon(O) = 8.87, or [O/Fe] ~ 0.64 if epsilon(O) = 8.77 is assumed.Comment: To be published in ApJ 575 (August 10

A RAVE investigation on Galactic open clusters I. Radial velocities and metallicities

Context. Galactic open clusters (OCs) mainly belong to the young stellar population in the Milky Way disk, but are there groups and complexes of OCs that possibly define an additional level in hierarchical star formation? Current compilations are too incomplete to address this question, especially regarding radial velocities (RVs) and metallicities ([M/H]). Aims. Here we provide and discuss newly obtained RV and [M/H] data, which will enable us to reinvestigate potential groupings of open clusters and associations. Methods. We extracted additional RVs and [M/H] from the RAdial Velocity Experiment (RAVE) via a cross-match with the Catalogue of Stars in Open Cluster Areas (CSOCA). For the identified OCs in RAVE we derived (RV) over bar and ([M/H]) over bar from a cleaned working sample and compared the results with previous findings. Results. Although our RAVE sample does not show the same accuracy as the entire survey, we were able to derive reliable (RV) over bar for 110 Galactic open clusters. For 37 OCs we publish (RV) over bar for the first time. Moreover, we determined ([M/H]) over bar for 81 open clusters, extending the number of OCs with ([M/H]) over bar by 69

A Compiled Catalogue of Spectroscopically Determined Elemental Abundances for Stars with Accurate Parallaxes. I.Magnesium

We present a compiled catalogue of effective temperatures, surface gravities, iron and magnesium abundances, distances, velocity components, and orbital elements for stars in the solar neighborhood. The atmospheric parameters and iron abundances are averages of published values derived from model synthetic spectra for a total of about 2000 values in 80 publications. Our relative magnesium abundances were found from 1412 values in 31 publications for 876 dwarfs and subgiants using a three-step iteration averaging procedure, with weights assigned to each source of data as well as to each individual determination and taking into account systematic deviations of each scale relative to the reduced mean scale. The estimated assumed completeness for data sources containing more than five stars, up to late December 2003, exceeds 90%. For the vast majority of stars in the catalogue, the spatial velocity components were derived from modern high-precision astrometric observations, and their Galactic orbit elements were computed using a three-component model of the Galaxy, consisting of a disk, a bulge, and a massive extended halo.Comment: Accepted for Astron. Rep. 2005, v.49, No.5, p.405-416, 12 pages, 10 figure

Random Tilings: Concepts and Examples

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical change

Critical behavior of the three-dimensional XY universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a discrepancy with the most recent experimental estimate of alpha; this discrepancy calls for further theoretical and experimental investigations. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods, and high-temperature expansions. Two improved models (with suppressed leading scaling corrections) are selected by Monte Carlo computation. The critical exponents are computed from high-temperature expansions specialized to these improved models. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine the specific-heat amplitude ratio.Comment: 61 pages, 3 figures, RevTe