Modeling of composite beams and plates for static and dynamic analysis

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal

XMM-Newton Observations of NGC 507: Super-solar Metal Abundances in the Hot ISM

We present the results of the X-ray XMM-Newton observations of NGC 507, a dominant elliptical galaxy in a small group of galaxies, and report 'super-solar' metal abundances of both Fe and a-elements in the hot ISM of this galaxy. We find Z_Fe = 2-3 times solar inside the D25 ellipse of NGC 507. This is the highest Z_Fe reported so far for the hot halo of an elliptical galaxy; this high Iron abundance is fully consistent with the predictions of stellar evolution models, which include the yield of both type II and Ia supernovae. The spatially resolved, high quality XMM spectra provide enough statistics to formally require at least three emission components: two soft thermal components indicating a range of temperatures in the hot ISM, plus a harder component, consistent with the integrated output of low mass X-ray binaries (LMXBs). The abundance of a-elements (most accurately determined by Si) is also found to be super-solar. The a-elements to Fe abundance ratio is close to the solar ratio, suggesting that ~70% of the Iron mass in the hot ISM was originated from SNe Type Ia. The a-element to Fe abundance ratio remains constant out to at least 100 kpc, indicating that SNe Type II and Ia ejecta are well mixed in a scale much larger than the extent of the stellar body.Comment: 29 pages, 6 figures, Accepted in ApJ (v613, Oct. 1, 2004); Minor revisions after referee's comments; A high-resolution pdf file available at http://hea-www.harvard.edu/~kim/pap/N507_XMM.pd

Detectability of dissipative motion in quantum vacuum via superradiance

We propose an experiment for generating and detecting vacuum-induced dissipative motion. A high frequency mechanical resonator driven in resonance is expected to dissipate energy in quantum vacuum via photon emission. The photons are stored in a high quality electromagnetic cavity and detected through their interaction with ultracold alkali-metal atoms prepared in an inverted population of hyperfine states. Superradiant amplification of the generated photons results in a detectable radio-frequency signal temporally distinguishable from the expected background.Comment: 4 pages, 2 figure

On the distribution of career longevity and the evolution of home run prowess in professional baseball

Statistical analysis is a major aspect of baseball, from player averages to historical benchmarks and records. Much of baseball fanfare is based around players exceeding the norm, some in a single game and others over a long career. Career statistics serve as a metric for classifying players and establishing their historical legacy. However, the concept of records and benchmarks assumes that the level of competition in baseball is stationary in time. Here we show that power-law probability density functions, a hallmark of many complex systems that are driven by competition, govern career longevity in baseball. We also find similar power laws in the density functions of all major performance metrics for pitchers and batters. The use of performance-enhancing drugs has a dark history, emerging as a problem for both amateur and professional sports. We find statistical evidence consistent with performance-enhancing drugs in the analysis of home runs hit by players in the last 25 years. This is corroborated by the findings of the Mitchell Report [1], a two-year investigation into the use of illegal steroids in major league baseball, which recently revealed that over 5 percent of major league baseball players tested positive for performance-enhancing drugs in an anonymous 2003 survey.Comment: 5 pages, 5 figures, 2-column revtex4 format. Revision has change of title, a figure added, and minor changes in response to referee comment

Efficiency of Energy Transduction in a Molecular Chemical Engine

A simple model of the two-state ratchet type is proposed for molecular chemical engines that convert chemical free energy into mechanical work and vice versa. The engine works by catalyzing a chemical reaction and turning a rotor. Analytical expressions are obtained for the dependences of rotation and reaction rates on the concentrations of reactant and product molecules, from which the performance of the engine is analyzed. In particular, the efficiency of energy transduction is discussed in some detail.Comment: 4 pages, 4 fugures; title modified, figures 2 and 3 modified, content changed (pages 1 and 4, mainly), references adde

AGN Black Hole Masses and Bolometric Luminosities

Black hole mass, along with mass accretion rate, is a fundamental property of active galactic nuclei. Black hole mass sets an approximate upper limit to AGN energetics via the Eddington limit. We collect and compare all AGN black hole mass estimates from the literature; these 177 masses are mostly based on the virial assumption for the broad emission lines, with the broad-line region size determined from either reverberation mapping or optical luminosity. We introduce 200 additional black hole mass estimates based on properties of the host galaxy bulges, using either the observed stellar velocity dispersion or using the fundamental plane relation to infer $\sigma$; these methods assume that AGN hosts are normal galaxies. We compare 36 cases for which black hole mass has been generated by different methods and find, for individual objects, a scatter as high as a couple of orders of magnitude. The less direct the method, the larger the discrepancy with other estimates, probably due to the large scatter in the underlying correlations assumed. Using published fluxes, we calculate bolometric luminosities for 234 AGNs and investigate the relation between black hole mass and luminosity. In contrast to other studies, we find no significant correlation of black hole mass with luminosity, other than those induced by circular reasoning in the estimation of black hole mass. The Eddington limit defines an approximate upper envelope to the distribution of luminosities, but the lower envelope depends entirely on the sample of AGN included. For any given black hole mass, there is a range in Eddington ratio of up to three orders of magnitude.Comment: 43 pages with 10 figures. Accepted for publication in Ap