Geometric Interpretation of Half-Plane Capacity

Schramm-Loewner Evolution describes the scaling limits of interfaces in certain statistical mechanical systems. These interfaces are geometric objects that are not equipped with a canonical parametrization. The standard parametrization of SLE is via half-plane capacity, which is a conformal measure of the size of a set in the reference upper half-plane. This has useful harmonic and complex analytic properties and makes SLE a time-homogeneous Markov process on conformal maps. In this note, we show that the half-plane capacity of a hull A is comparable up to multiplicative constants to more geometric quantities, namely the area of the union of all balls centered in A tangent to R, and the (Euclidean) area of a 1-neighborhood of A with respect to the hyperbolic metric.National Science Foundation (U.S.) (Grant DMS-0805755)National Science Foundation (U.S.) (Grant DMS-0734151

Shear Strength of Continuous Lightly Reinforced Concrete Joist Systems

The objective of this research is to study the shear strength of continuous lightly reinforced concrete joist systems. Six two span joists, with and without web reinforcement, and two multiple web joists without web reinforcement were tested. The main focus of this study was to determine the shear cracking capacity and to investigate load sharing between joists. Shear cracking loads are determined using crack pattern and stirrup strain analyses. Behavior is evaluated in both the .o,.irive and the negative moment regions. The primary variables in this research are the longitudinal reinforcement ratio, p,.. (0.76% and 1.04% for negative moment regions and from 0.79% to 2.43% for positive moment regions), and nominal stirrup strength, Pvfvy (0 to 70 psi) for single web joists and placement of the load in multiple web joists. Stirrup effectiveness in joists is analyzed based upon ACI provisions and the number of stirrups intercepted by the critical shear crack. Nominal shear stresses and load sharing between the joists are compared with current ACI design pro , The tests indicate that ACI 318-89 overestimates the shear cracking load and shear capacity of lightly reinforced concrete joists in negative moment regions, and under estimates the shear cracking load but not the shear capacity in positive moment regiOns. In the study, the stirrup contribution in both the negative and positive moment regions equaled or exceeded the value predicted by ACI 318-89. In the positive moment regions of members with stirrups, the concrete contribution to shear capacity was often below the shear cracking load, contrary to the usual assumption. The study indicates that significant load sharing occurs between the joists, but that the load sharing is adequate only to distribute local overloads. The additional I 0% in the concrete contribution to shear capacity, as allowed by ACI 318-89, is not available for joist systems as a whole

Shear Strength of Continuous Lightly Reinforced T-Beams

The shear strength of continuous lightly reinforced concrete T -beams is studied. Six twospan T -beams with and without web reinforcement are tested. The primary variables are longitudinal reinforcement ratio (0.75% and 1.0%) and nominal stirrup strength (0 to 82 psi). The test results are analyzed and compared with the shear design provisions of "Building Code Requirements for Reinforced Concrete (ACI 318-89)" and predictions of other investigators, including predictions obtained using the modified compression field theory. The tests indicate that ACI 318-89 overpredicts the concrete shear capacity of lightly reinforced beams without shear reinforcement. Little difference exists between shear cracking stresses in the negative and positive moment regions for beams in the current study. For both the negative and positive moment regions, the stirrup contribution to shear strength exceeds the value predicted by ACI 318-89. Stirrup contribution to shear strength increases with increasing flexural reinforcement ratio. Overall, the ACI 318-89 shear provisions are conservative for the beams tested in the current study. Two procedures based on the modified compression field theory are also conservative. ACI 318-89 better predicts the nominal shear strength of the beams in the current study than either of the modified compression field theory procedures

The Carnegie Astrometric Planet Search Program

We are undertaking an astrometric search for gas giant planets and brown dwarfs orbiting nearby low mass dwarf stars with the 2.5-m du Pont telescope at the Las Campanas Observatory in Chile. We have built two specialized astrometric cameras, the Carnegie Astrometric Planet Search Cameras (CAPSCam-S and CAPSCam-N), using two Teledyne Hawaii-2RG HyViSI arrays, with the cameras' design having been optimized for high accuracy astrometry of M dwarf stars. We describe two independent CAPSCam data reduction approaches and present a detailed analysis of the observations to date of one of our target stars, NLTT 48256. Observations of NLTT 48256 taken since July 2007 with CAPSCam-S imply that astrometric accuracies of around 0.3 milliarcsec per hour are achievable, sufficient to detect a Jupiter-mass companion orbiting 1 AU from a late M dwarf 10 pc away with a signal-to-noise ratio of about 4. We plan to follow about 100 nearby (primarily within about 10 pc) low mass stars, principally late M, L, and T dwarfs, for 10 years or more, in order to detect very low mass companions with orbital periods long enough to permit the existence of habitable, Earth-like planets on shorter-period orbits. These stars are generally too faint and red to be included in ground-based Doppler planet surveys, which are often optimized for FGK dwarfs. The smaller masses of late M dwarfs also yield correspondingly larger astrometric signals for a given mass planet. Our search will help to determine whether gas giant planets form primarily by core accretion or by disk instability around late M dwarf stars.Comment: 48 pages, 9 figures. in press, Publ. Astron. Soc. Pacifi

Multispin correlations and pseudo-thermalization of the transient density matrix in solid-state NMR: free induction decay and magic echo

Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately "rewind" the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered - simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics.Comment: 12 Pages, 9 figure

Evaluation of denoising strategies to address motion-correlated artifacts in resting-state functional magnetic resonance imaging data from the human connectome roject

Like all resting-state functional connectivity data, the data from the Human Connectome Project (HCP) are adversely affected by structured noise artifacts arising from head motion and physiological processes. Functional connectivity estimates (Pearson's correlation coefficients) were inflated for high-motion time points and for high-motion participants. This inflation occurred across the brain, suggesting the presence of globally distributed artifacts. The degree of inflation was further increased for connections between nearby regions compared with distant regions, suggesting the presence of distance-dependent spatially specific artifacts. We evaluated several denoising methods: censoring high-motion time points, motion regression, the FMRIB independent component analysis-based X-noiseifier (FIX), and mean grayordinate time series regression (MGTR; as a proxy for global signal regression). The results suggest that FIX denoising reduced both types of artifacts, but left substantial global artifacts behind. MGTR significantly reduced global artifacts, but left substantial spatially specific artifacts behind. Censoring high-motion time points resulted in a small reduction of distance-dependent and global artifacts, eliminating neither type. All denoising strategies left differences between high- and low-motion participants, but only MGTR substantially reduced those differences. Ultimately, functional connectivity estimates from HCP data showed spatially specific and globally distributed artifacts, and the most effective approach to address both types of motion-correlated artifacts was a combination of FIX and MGTR