Gravity from Rational Curves

This paper presents a new formula which is conjectured to yield all tree amplitudes in N=8 supergravity. The amplitudes are described in terms of higher degree rational maps to twistor space. The resulting expression has manifest N=8 supersymmetry and is manifestly permutation symmetric in all external states. It depends monomially on the infinity twistor that explicitly breaks conformal symmetry to Poincare. The formula has been explicitly checked to yield the correct amplitudes for the 3-point MHV-bar and for the n-point MHV, where it reduces to an expression of Hodges. We have also carried out numerical checks of the formula at NMHV and NNMHV level, for up to eight external states.Comment: 8 page

A Rich Population of X-ray Emitting Wolf-Rayet Stars in the Galactic Starburst Cluster Westerlund 1

Recent optical and IR studies have revealed that the heavily-reddened starburst cluster Westerlund 1 (Wd 1) contains at least 22 Wolf-Rayet (WR) stars, comprising the richest WR population of any galactic cluster. We present results of a senstive Chandra X-ray observation of Wd 1 which detected 12 of the 22 known WR stars and the mysterious emission line star W9. The fraction of detected WN stars is nearly identical to that of WC stars. The WN stars WR-A and WR-B as well as W9 are exceptionally luminous in X-rays and have similar hard heavily-absorbed spectra with strong Si XIII and S XV emission lines. The luminous high-temperature X-ray emission of these three stars is characteristic of colliding wind binary systems but their binary status remains to be determined. Spectral fits of the X-ray bright sources WR-A and W9 with isothermal plane-parallel shock models require high absorption column densities log N$_{H}$ = 22.56 (cm$^{-2}$) and yield characteristic shock temperatures kT_shock ~ 3 keV (T ~ 35 MK).Comment: ApJL, 2006, in press (3 figures, 1 table

The Fantastic Four: A plug 'n' play set of optimal control pulses for enhancing nmr spectroscopy

We present highly robust, optimal control-based shaped pulses designed to replace all 90{\deg} and 180{\deg} hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90{\deg} and 180{\deg} point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1 ms pulses provide uniform performance over resonance offsets of 20 kHz (1H) and 35 kHz (13C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of (+/-)15% (1H) and (+/-)10% (13C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600 MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).Comment: 28 pages, 19 figure

Saturation-Dependence of Dispersion in Porous Media

In this study, we develop a saturation-dependent treatment of dispersion in porous media using concepts from critical path analysis, cluster statistics of percolation, and fractal scaling of percolation clusters. We calculate spatial solute distributions as a function of time and calculate arrival time distributions as a function of system size. Our previous results correctly predict the range of observed dispersivity values over ten orders of magnitude in experimental length scale, but that theory contains no explicit dependence on porosity or relative saturation. This omission complicates comparisons with experimental results for dispersion, which are often conducted at saturation less than 1. We now make specific comparisons of our predictions for the arrival time distribution with experiments on a single column over a range of saturations. This comparison suggests that the most important predictor of such distributions as a function of saturation is not the value of the saturation per se, but the applicability of either random or invasion percolation models, depending on experimental conditions

Connections of the Mesencephalic Locomotor Region (MLR) in the Cat

The cat entopeduncular nucleus (EN), which is the main output of the basal ganglia, is known to project to the mesencephalic tegmentum. We have been able to elicit antidromic responses in single EN neurons from the region of the mesencephalic locomotor region (MLR), then transect (precollicular-postmamillary) the brainstem and elicit rhythmic movements of the limbs by stimulation of the same site in the same animal. Injections of the fluorescent dye 2,4 diamidino phenylindole 2 HCL (DAPI) into this area induces retrograde labeling of cell bodies in EN and motor cortex. Injections of a tritiated amino acid (leucine) into the motor cortex induce terminal labeling in the area of the MLR. These studies describe convergent projections from EN and motor cortex to the MLR. These connections may be involved in the sequencing and ordering of voluntary movements in which locomotion is necessary