Algebraic treatment of the confluent Natanzon potentials

Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.Comment: 9 page

Dynamical spacetimes and gravitational radiation in a Fully Constrained Formulation

This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be confident in the performances of the upgraded version of CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation of the Einstein equations by the FCF.Comment: 4 pages, 7 figures. Accepted for publication in Journal of Physics: Conference Series, Proceedings of the 8th Edoardo Amaldi Conference on Gravitational Wave

A comparative study of two 47 Tuc giant stars with different s-process enrichment

Here we aim to understand the origin of 47 Tuc's La-rich star Lee 4710. We report abundances for O, Na, Mg, Al, Si, Ca, Sc, Ti, V, Cr, Co, Ni, Zn, Y, Zr, Ba, La, Ce, Pr, Nd, and Eu, and present a detailed abundance analysis of two 47 Tuc stars with similar stellar parameters but different slow neutron-capture (s-)process enrichment. Star Lee 4710 has the highest known La abundance ratio in this cluster ([La/Fe] = 1.14), and star Lee 4626 is known to have normal s-process abundances (e.g., [Ba/Eu]$<0$). The nucleosynthetic pattern of elements with Z$\gtrsim$56 for star Lee 4710 agrees with the predicted yields of a $1.3M_{\odot}$ asymptotic giant branch (AGB) star. Therefore, Lee 4710 may have been enriched by mass transfer from a more massive AGB companion, which is compatible with its location far away from the center of this relatively metal-rich ([Fe/H]$\sim-0.7$) globular cluster. A further analysis comparing the abundance pattern of Lee 4710 with data available in the literature reveals that nine out of the $\sim200$ 47 Tuc stars previously studied show strong s-process enhancements that point towards later enrichment by more massive AGB stars.Comment: ApJL in press. 6 pages, 4 figure

Detailed Abundances for a Large Sample of Giant Stars in the Globular Cluster 47 Tucanae (NGC 104)

47 Tuc is an ideal target to study chemical evolution and GC formation in massive more metal-rich GCs since is the closest, massive GC. We present chemical abundances for O, Na, Al, Si, Ca, Ti, Fe, Ni, La, and Eu in 164 red giant branch (RGB) stars in the massive globular cluster 47 Tuc using spectra obtained with both the Hydra multi-fiber spectrograph at the Blanco 4-m telescope and the FLAMES multi-object spectrograph at the Very Large Telescope. We find an average [Fe/H]=--0.79$\pm$0.09 dex, consistent with literature values, as well as over-abundances of alpha-elements ([\alpha/\mbox{Fe}]\sim0.3 dex). The n-capture process elements indicate that 47 Tuc is r-process dominated ([Eu/La]=+0.24), and the light elements O, Na, and Al exhibit star-to-star variations. The Na-O anti-correlation, a signature typically seen in Galactic globular clusters, is present in 47 Tuc, and extends to include a small number of stars with [O/Fe] $\sim$\,--0.5. Additionally, the [O/Na] ratios of our sample reveal that the cluster stars can be separated into three distinct populations. A KS-test demonstrates that the O-poor/Na-rich stars are more centrally concentrated than the O-rich/Na-poor stars. The observed number and radial distribution of 47 Tuc's stellar populations, as distinguished by their light element composition, agrees closely with the results obtained from photometric data. We do not find evidence supporting a strong Na-Al correlation in 47 Tuc, which is consistent with current models of AGB nucleosynthesis yields.Comment: Accepted for publication in The Astrophysical Journa

Strichartz Estimates for the Vibrating Plate Equation

We study the dispersive properties of the linear vibrating plate (LVP) equation. Splitting it into two Schr\"odinger-type equations we show its close relation with the Schr\"odinger equation. Then, the homogeneous Sobolev spaces appear to be the natural setting to show Strichartz-type estimates for the LVP equation. By showing a Kato-Ponce inequality for homogeneous Sobolev spaces we prove the well-posedness of the Cauchy problem for the LVP equation with time-dependent potentials. Finally, we exhibit the sharpness of our results. This is achieved by finding a suitable solution for the stationary homogeneous vibrating plate equation.Comment: 18 pages, 4 figures, some misprints correcte

Fatty acid composition of Mytilus galloprovincialis larvae fed on different micoralgal diets: effect on larval growth and survival.

The influence of dietary essential fatty acid on bivalve larval growth and survival has been reported by several authors. The objectives of the current research were (1) to describe fatty acid composition of Mytilus galloprovincialis D-larvae and (2) to investigate the influence of algal lipid composition on larval growth and survival. Larvae were fed with two diets, A (Tetraselmis suecica + Isochrisis galbana) and B (Tetraselmis suecica + Chaetoceros sp). After fifteen days the larval growth was significantly higher with diet B than with diet A. The survival was also different, being 28% in diet A and 22.4 % in diet B. The percentages of veliger, pediveliger and amorphous larvae were higher in group A than in B, while in the latter there were not amorphous larvae and the 21 % were postlarvae. So, the microalgae Chaetoceros sp seems to enhance larvae growth and development. The difference in diet also produced changes in fatty acid profiles being the most important change ones (1) the increase of 14:0 in both groups, (2) 16:0 decreased in group A but it increased in group B and (3) total MUFA showed higher levels in both trials. Total PUFA n-6 level was higher in group A due to the 18:2n-6 increase. Arachidonic acid level was augmented with both diets. EPA level diminished in group A but it augmented in group B, DHA behaviour was opposite, increasing in group A but decreasing in group B. This is due to the high level of EPA in Chaetoceros sp and DHA in Isochrysis galbana (Fern&aacute;ndez-Reiriz et al., 2006). These results do not coincide with other studies which suggest that DHA is a key requirement for larval development and growth of other bivalve species (Caers et al., 1999). In our case diet rich in EPA seems to be better in mussel larva culture than the diet rich in DHA. This work was supported by Interreg Project 0251_ECOAQUA_5_E, financed by the EDRF (European Regional Development Fund). www.juntadeandalucia.es/agriculturaypesca/ifapa/ecoaqua. &nbsp;La influencia de la composici&oacute;n en &aacute;cidos grasos de la dieta ha sido estudiada por diversos autores. Los objetivos de este trabajo fuero (1) describir la composici&oacute;n en &aacute;cidos grasos de las larvas D de Mytilus galloprovincialis y (2) investigar la influencia de la composici&oacute;n lip&iacute;dica de las microalgas en el crecimiento y supervivencia larvario. Las larvas se fueron alimentadas con dos dietas,A (Tetraselmis suecica + Isochrisis galbana) y B (Tetraselmis suecica + Chaetoceros sp). Tras quince d&iacute;as el crecimiento larvario fue significativamente mayor con la dieta B que con la dieta A. La supervivencia tambi&eacute;n fue diferente, siendo 28 % en la dieta A y 22.4% en la dieta B. El porcentaje de las larvas veliger, pediveliger y amorfas fue mayor en A que en B, mientras que en &eacute;ste no hubo amorfas y el 21 % fueron postlarvas. Por lo tanto la microalga Chaetoceros sp mejora el cultivo larvario. La diferencia en la dieta tambi&eacute;n produjo cambios en el perfil de &aacute;cidos grasos siendo los m&aacute;s importantes (1) el incremento del 14:0 en ambos grupos, (2) el 16:0 decreci&oacute; en el grupo A pero aument&oacute; en el B y (3) el total de monoinsaturados mostr&oacute; mayores valores en ambos grupos. El total de PUFA n-6 fue mayor en el grupo A debido al incremento de 18:2n-6. El nivel de &aacute;cido araquid&oacute;nico aument&oacute; en ambos grupos. El nivel de EPA disminuy&oacute; en el grupo A pero aument&oacute; en el grupo B, el comportamiento del DHA fue el contrario, incrementando en el grupo A y disminuyendo en el B. Esto fue debido al alto nivel de EPA en Chaetoceros sp y DHA en Isochrysis galbana (Fern&aacute;ndez-Reiriz et al., 2006). Estos resultados no coinciden con otros estudios que sugieren que el DHA es un requerimiento clave para el desarrollo y crecimiento larvarios de otras especies de bivalvos (Caers et al., 1999). En nuestro caso la dieta rica en EPA parece ser mejor para el cultivo larvario de mejillones que la dieta rica en DHA. Este trabajo fue apoyado por el proyecto Interreg 0251_ECOAQUA_5_E, financiado por el FEDER (Fondo Europeo de Desarrollo Regional). www.juntadeandalucia.es/agriculturaypesca/ifapa/ecoaqua.</p

Phase transitions and phase diagram of the ferroelectric perovskite NBT-BT by anelastic and dielectric measurements

The complex elastic compliance and dielectric susceptibility of (Na_{0.5}Bi_{0.5})_{1-x}Ba_{x}TiO_{3} (NBT-BT) have been measured in the composition range between pure NBT and the morphotropic phase boundary included, 0 <= x <= 0.08. The compliance of NBT presents sharp peaks at the rhombohedral/tetragonal and tetragonal/cubic transitions, allowing the determination of the tetragonal region of the phase diagram, up to now impossible due to the strong lattice disorder and small distortions and polarizations involved. In spite of ample evidence of disorder and structural heterogeneity, the R-T transition remains sharp up to x = 0.06, whereas the T-C transition merges into the diffuse and relaxor-like transition associated with broad maxima of the dielectric and elastic susceptibilities. An attempt is made at relating the different features in the anelastic and dielectric curves to different modes of octahedral rotations and polar cation shifts. The possibility is also considered that the cation displacements locally have monoclinic symmetry, as for PZT near the morphotropic phase boundary.Comment: 11 pages, 9 figures, submitted to Phys. Rev.