The possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator

We find the possibility of the non-perturbative an-harmonic correction to Mehler's formula for propagator of the harmonic oscillator. We evaluate the conditional Wiener measure functional integral with a term of the fourth order in the exponent by an alternative method as in the conventional perturbative approach. In contrast to the conventional perturbation theory, we expand into power series the term linear in the integration variable in the exponent. We discuss the case, when the starting point of the propagator is zero. We present the results in analytical form for positive and negative frequency.Comment: The detailed "pedagogical" evaluations are postponed to appendices, 1 figur

A Thorium Metal-Organic Framework with Outstanding Thermal and Chemical Stability.

A new thorium metal-organic framework (MOF), Th(OBA)2 , where OBA is 4,4'-oxybis(benzoic) acid, has been synthesized hydrothermally in the presence of a range of nitrogen-donor coordination modulators. This Th-MOF, described herein as GWMOF-13, has been characterized by single-crystal and powder X-ray diffraction, as well as through a range of techniques including gas sorption, thermogravimetric analysis (TGA), solid-state UV/Vis and luminescence spectroscopy. Single-crystal X-ray diffraction analysis of GWMOF-13 reveals an interesting, high symmetry (cubic Ia 3 ‾ d) structure, which yields a novel srs-a topology. Most notably, TGA analysis of GWMOF-13 reveals framework stability to 525 °C, matching the thermal stability benchmarks of the UiO-66 series MOFs and zeolitic imidazolate frameworks (ZIFs), and setting a new standard for thermal stability in f-block based MOFs

A Comparison of Cosmological Hydrodynamic Codes

We present a detailed comparison of the simulation results of various cosmological hydrodynamic codes. Starting with identical initial conditions based on the Cold Dark Matter scenario for the growth of structure, we integrate from redshift $z=20$ to $z=0$ to determine the physical state within a representative volume of size $L^3$ where $L=64 h^{-1} {\rm Mpc}$. Five independent codes are compared: three of them Eulerian mesh based and two variants of the Smooth Particle Hydrodynamics "SPH" Lagrangian approach. The Eulerian codes were run at $N^3=(32^3,~64^3,~128^3,~{\rm and},~256^3)$ cells, the SPH codes at $N^3= 32^3$ and $64^3$ particles. Results were then rebinned to a $16^3$ grid with the expectation that the rebinned data should converge, by all techniques, to a common and correct result as $N \rightarrow \infty$. We find that global averages of various physical quantities do, as expected, tend to converge in the rebinned model, but that uncertainties in even primitive quantities such as $\langle T \rangle$, $\langle \rho^2\rangle^{1/2}$ persists at the 3\%-17\% level after completion of very large simulations. The two SPH codes and the two shock capturing Eulerian codes achieve comparable and satisfactory accuracy for comparable computer time in their treatment of the high density, high temperature regions as measured in the rebinned data; the variance among the five codes (at highest resolution) for the mean temperature (as weighted by $\rho^2$) is only 4.5\%. Overall the comparison allows us to better estimate errors, it points to ways of improving this current generation of hydrodynamic codes and of suiting their use to problems which exploit their individually best features.Comment: 20p plaintex to appear in The Astrophysical Journal on July 20, 199

Cross-correlation Weak Lensing of SDSS galaxy Clusters II: Cluster Density Profiles and the Mass--Richness Relation

We interpret and model the statistical weak lensing measurements around 130,000 groups and clusters of galaxies in the Sloan Digital Sky Survey presented by Sheldon et al. 2007 (Paper I). We present non-parametric inversions of the 2D shear profiles to the mean 3D cluster density and mass profiles in bins of both optical richness and cluster i-band luminosity. We correct the inferred 3D profiles for systematic effects, including non-linear shear and the fact that cluster halos are not all precisely centered on their brightest galaxies. We also model the measured cluster shear profile as a sum of contributions from the brightest central galaxy, the cluster dark matter halo, and neighboring halos. We infer the relations between mean cluster virial mass and optical richness and luminosity over two orders of magnitude in cluster mass; the virial mass at fixed richness or luminosity is determined with a precision of 13% including both statistical and systematic errors. We also constrain the halo concentration parameter and halo bias as a function of cluster mass; both are in good agreement with predictions of LCDM models. The methods employed here will be applicable to deeper, wide-area optical surveys that aim to constrain the nature of the dark energy, such as the Dark Energy Survey, the Large Synoptic Survey Telescope and space-based surveys

Radial Temperature Profiles of X-Ray--Emitting Gas Within Clusters of Galaxies

Previous analyses of ASCA data of clusters of galaxies have found conflicting results regarding the slope of the temperature profile of the hot X-ray gas within clusters, mainly because of the large, energy-dependent point spread function (PSF) of the ASCA mirrors. We present a summary of all ASCA-determined cluster temperature profiles found in the literature, and find a discrepancy in the radial temperature trend of clusters based on which PSF-correction routine is used. This uncertainty in the cluster temperature profile in turn can lead to large uncertainties in the amount of dark matter in clusters. In this study, we have used ROSAT PSPC data to obtain independent relative temperature profiles for 26 clusters, most of which have had their temperature profiles determined by ASCA. Our aim is not to measure the actual temperature values of the clusters, but to use X-ray color profiles to search for a hardening or softening of the spectra with radius for comparison to ASCA-derived profiles. The radial color profiles indicate that outside of the cooling flow region, the temperature profiles of clusters are in general constant. Within 35% of the virial radius, we find a temperature drop of 20% at 10 keV and 12% at 5 keV can be ruled out at the 99% confidence level. A subsample of non-cooling flow clusters shows that the condition of isothermality applies at very small radii too, although cooling gas complicates this determination in the cooling flow subsample. The colors predicted from the temperature profiles of a series of hydrodynamical cluster simulations match the data very well, although they cannot be used to discriminate among different cosmologies. An additional result is that the color profiles show evidence for a central peak in metallicity in low temperature clusters.Comment: 39 pages, 15 embedded Postscript figures, uses aaspp4.sty, accepted for publication in Astrophysical Journa

Modeling the Near-Infrared Luminosity Functions of Young Stellar Clusters

We present the results of numerical experiments designed to evaluate the usefulness of near-infrared luminosity functions for constraining the Initial Mass Function (IMF) of young stellar populations. From this numerical modeling, we find that the luminosity function of a young stellar population is considerably more sensitive to variations in the underlying initial mass function than to either variations in the star forming history or assumed pre-main-sequence (PMS) mass-to-luminosity relation. To illustrate the potential effectiveness of using the KLF of a young cluster to constrain its IMF, we model the observed K band luminosity function of the nearby Trapezium cluster. Our derived mass function for the Trapezium spans two orders of magnitude in stellar mass (5 Msun to 0.02 Msun), has a peak near the hydrogen burning limit, and has an IMF for Brown Dwarfs which steadily decreases with decreasing mass.Comment: To appear in ApJ (1 April 2000). 37 pages including 11 figures, AAS: ver 5.

Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background

The effective potential for a dynamical Wick field (dynamical signature) induced by the quantum effects of massive fields on a topologically non-trivial $D$ dimensional background is considered. It is shown that when the radius of the compactified dimension is very small compared with $\Lambda^{1/2}$ (where $\Lambda$ is a proper-time cutoff), a flat metric with Lorentzian signature is preferred on ${\bf R}^4 \times {\bf S}^1$. When the compactification radius becomes larger a careful analysis of the 1-loop effective potential indicates that a Lorentzian signature is preferred in both $D=6$ and $D=4$ and that these results are relatively stable under metrical perturbations