Factorization of Spanning Trees on Feynman Graphs

In order to use the Gaussian representation for propagators in Feynman amplitudes, a representation which is useful to relate string theory and field theory, one has to prove first that each $\alpha$- parameter (where $\alpha$ is the parameter associated to each propagator in the $\alpha$-representation of the Feynman amplitudes) can be replaced by a constant instead of being integrated over and second, prove that this constant can be taken equal for all propagators of a given graph. The first proposition has been proven in one recent letter when the number of propagators is infinite. Here we prove the second one. In order to achieve this, we demonstrate that the sum over the weighted spanning trees of a Feynman graph $G$ can be factorized for disjoint parts of $G$. The same can also be done for cuts on $G$, resulting in a rigorous derivation of the Gaussian representation for super-renormalizable scalar field theories. As a by-product spanning trees on Feynman graphs can be used to define a discretized functional space.Comment: 47 pages, Plain Tex, 3 PostScript figure

Regge behaviour and Regge trajectory for ladder graphs in scalar Φ3\Phi^3 field theory

Using the gaussian representation for propagators (which can be proved to be exact in the infinite number of loops limit) we are able to derive the Regge behaviour for ladder graphs of $\phi^3$ field theory in a completely new way. An analytic expression for the Regge trajectory $\alpha (t/m^2)$ is found in terms of the mean-values of the Feynman $\alpha$-parameters. $\alpha (t/m^2)$ is calculated in the range $- 3.6 < t/m^2 < 0.8$. The intercept $\alpha (0)$ agrees with that obtained from earlier calculations using the Bethe-Salpeter approach for \alpha (0) \gsim 0.3.Comment: 10 PlainTex pages, 2 PostScript Figures include

Separation of aqueous salt solution by pervaporation through hybrid organic-inorganic membrane: effect of operating conditions

Hybrid polymer-inorganic membranes were prepared by crosslinking poly(vinyl alcohol) (PVA), maleic acid (MA) and silica via an aqueous sol–gel route. Membrane characterisation results revealed silica nanoparticles (b10 nm) were well dispersed in the polymer matrix and significantly reduced swelling of the membrane. The membranes were tested for pervaporation separation of aqueous salt solution with NaCl concentrations of 0.2–5.0 wt% at temperatures 20–65 °C, feed flowrates 30–150 mL/min and permeate pressures 2–40 Torr. The salt rejection remained high (up to 99.9%) under all operating conditions. A high water flux of 11.7 kg/m2 h could be achieved at a feed temperature of 65 °C and a vacuum of 6 Torr. The effect of operating conditions on water flux is discussed in relation to diffusion coefficients of water and fundamental transport mechanism through the membrane. The activation energy for water permeation was found to vary from 23.8 to 20.1 kJ/kmol when the salt concentration in the feed was increased from 0.2 to 5.0 wt%

Discovery of low-metallicity stars in the central parsec of the Milky Way

We present a metallicity analysis of 83 late-type giants within the central 1 pc of the Milky Way. K-band spectroscopy of these stars were obtained with the medium-spectral resolution integral-field spectrograph NIFS on Gemini North using laser-guide star adaptive optics. Using spectral template fitting with the MARCS synthetic spectral grid, we find that there is large variation in metallicity, with stars ranging from [M/H] $<$ -1.0 to above solar metallicity. About 6\% of the stars have [M/H] $<$ -0.5. This result is in contrast to previous observations, with smaller samples, that show stars at the Galactic center have approximately solar metallicity with only small variations. Our current measurement uncertainties are dominated by systematics in the model, especially at [M/H] $>$ 0, where there are stellar lines not represented in the model. However, the conclusion that there are low metallicity stars, as well as large variations in metallicity is robust. The metallicity may be an indicator of the origin of these stars. The low-metallicity population is consistent with that of globular clusters in the Milky Way, but their small fraction likely means that globular cluster infall is not the dominant mechanism for forming the Milky Way nuclear star cluster. The majority of stars are at or above solar metallicity, which suggests they were formed closer to the Galactic center or from the disk. In addition, our results indicate that it will be important for star formation history analyses using red giants at the Galactic center to consider the effect of varying metallicity.Comment: 11 pages, 10 figures, ApJ Accepte

Properties of the Remnant Clockwise Disk of Young Stars in the Galactic Center

We present new kinematic measurements and modeling of a sample of 116 young stars in the central parsec of the Galaxy in order to investigate the properties of the young stellar disk. The measurements were derived from a combination of speckle and laser guide star adaptive optics imaging and integral field spectroscopy from the Keck telescopes. Compared to earlier disk studies, the most important kinematic measurement improvement is in the precision of the accelerations in the plane of the sky, which have a factor of six smaller uncertainties (~10 uas/yr/yr). We have also added the first radial velocity measurements for 8 young stars, increasing the sample at the largest radii (6"-12") by 25%. We derive the ensemble properties of the observed stars using Monte-Carlo simulations of mock data. There is one highly significant kinematic feature (~20 sigma), corresponding to the well-known clockwise disk, and no significant feature is detected at the location of the previously claimed counterclockwise disk. The true disk fraction is estimated to be ~20%, a factor of ~2.5 lower than previous claims, suggesting that we may be observing the remnant of what used to be a more densely populated stellar disk. The similarity in the kinematic properties of the B stars and the O/WR stars suggests a common star formation event. The intrinsic eccentricity distribution of the disk stars is unimodal, with an average value of = 0.27 +/- 0.07, which we show can be achieved through dynamical relaxation in an initially circular disk with a moderately top-heavy mass function.Comment: 65 pages, 22 figures, 8 tables, submitted to Ap

Recent Results and Perspectives for Precision Astrometry and Photometry with Adaptive Optics

Large ground-based telescopes equipped with adaptive optics (AO) systems have ushered in a new era of high-resolution infrared photometry and astrometry. Relative astrometric accuracies of <0.2 mas have already been demonstrated from infrared images with spatial resolutions of 55-95 mas resolution over 10-20'' fields of view. Relative photometric accuracies of 3% and absolute photometric accuracies of 5%-20% are also possible. I will review improvements and current limitations in astrometry and photometry with adaptive optics of crowded stellar fields. These capabilities enable experiments such as measuring orbits for brown dwarfs and exoplanets, studying our Galaxy's supermassive black hole and its environment, and identifying individual stars in young star clusters, which can be used test the universality of the initial mass function.Comment: SPIE Conference Proceedin

Mapping the Outer Edge of the Young Stellar Cluster in the Galactic Center

We present new near-infrared spectroscopic observations of the outer edges of the young stellar cluster around the supermassive black hole at the Galactic center. The observations show a break in the surface-density profile of young stars at approximately 13 arcsec (0.52 pc). These observations spectroscopically confirm previous suggestions of a break based on photometry. Using Gemini North's Near-Infrared Integral Field Spectrometer (NIFS) we are able to detect and separate early- and late-type stars with a 75% completeness at Ks = 15.5. We sample a region with radii between 7" to 23" (0.28 pc to 0.92 pc) from Sgr A*, and present new spectral classifications of 144 stars brighter than Ks = 15.5, where 140 stars are late-type (> 1 Gyr) and only four stars are early-type (young, 4-6 Myr). A broken power-law fit of the early-type surface-density matches well with our data and previously published values. The projected surface-density of late-type stars is also measured and found to be consistent with previous results. We find that the observed early-type surface-density profile is inconsistent with the theory of the young stars originating from a tightly bound infalling cluster, as no significant trail of young stars is found at radii above 13". We also note that either a simple disk instability criterion or a cloud-cloud collision could explain the location of the outer edge, though we lack information to make conclusive remarks on either alternative. If this break in surface-density represents an edge to the young stellar cluster it would set an important scale for the most recent episode of star formation at the Galactic center.Comment: 17 pages, 11 figures, 3 tables, ApJ accepte

A profiling analysis of contributions of cigarette smoking, dietary calcium intakes, and physical activity to fragility fracture in the elderly

Fragility fracture and bone mineral density (BMD) are influenced by common and modifiable lifestyle factors. In this study, we sought to define the contribution of lifestyle factors to fracture risk by using a profiling approach. The study involved 1683 women and 1010 men (50+ years old, followed up for up to 20 years). The incidence of new fractures was ascertained by X-ray reports. A “lifestyle risk score” (LRS) was derived as the weighted sum of effects of dietary calcium intake, physical activity index, and cigarette smoking. Each individual had a unique LRS, with higher scores being associated with a healthier lifestyle. Baseline values of lifestyle factors were assessed. In either men or women, individuals with a fracture had a significantly lower age-adjusted LRS than those without a fracture. In men, each unit lower in LRS was associated with a 66% increase in the risk of total fracture (non-adjusted hazard ratio [HR] 1.66; 95% CI, 1.26 to 2.20) and still significant after adjusting for age, weight or BMD. However, in women, the association was uncertain (HR 1.30; 95% CI, 1.11 to 1.53). These data suggest that unhealthy lifestyle habits are associated with an increased risk of fracture in men, but not in women, and that the association is mediated by BMD