Relativistic stars in differential rotation: bounds on the dragging rate and on the rotational energy

For general relativistic equilibrium stellar models (stationary axisymmetric asymptotically flat and convection-free) with differential rotation, it is shown that for a wide class of rotation laws the distribution of angular velocity of the fluid has a sign, say "positive", and then both the dragging rate and the angular momentum density are positive. In addition, the "mean value" (with respect to an intrinsic density) of the dragging rate is shown to be less than the mean value of the fluid angular velocity (in full general, without having to restrict the rotation law, nor the uniformity in sign of the fluid angular velocity); this inequality yields the positivity and an upper bound of the total rotational energy.Comment: 23 pages, no figures, LaTeX. Submitted to J. Math. Phy

Quasi-circular Orbits for Spinning Binary Black Holes

Using an effective potential method we examine binary black holes where the individual holes carry spin. We trace out sequences of quasi-circular orbits and locate the innermost stable circular orbit as a function of spin. At large separations, the sequences of quasi-circular orbits match well with post-Newtonian expansions, although a clear signature of the simplifying assumption of conformal flatness is seen. The position of the ISCO is found to be strongly dependent on the magnitude of the spin on each black hole. At close separations of the holes, the effective potential method breaks down. In all cases where an ISCO could be determined, we found that an apparent horizon encompassing both holes forms for separations well inside the ISCO. Nevertheless, we argue that the formation of a common horizon is still associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR

Seeing Double at Neptune's South Pole

Keck near-infrared images of Neptune from UT 26 July 2007 show that the cloud feature typically observed within a few degrees of Neptune's south pole had split into a pair of bright spots. A careful determination of disk center places the cloud centers at -89.07 +/- 0 .06 and -87.84 +/- 0.06 degrees planetocentric latitude. If modeled as optically thick, perfectly reflecting layers, we find the pair of features to be constrained to the troposphere, at pressures greater than 0.4 bar. By UT 28 July 2007, images with comparable resolution reveal only a single feature near the south pole. The changing morphology of these circumpolar clouds suggests they may form in a region of strong convection surrounding a Neptunian south polar vortex.Comment: 10 pages, 7 figures; accepted to Icaru

Retrieving Neptune's aerosol properties from Keck OSIRIS observations. I. Dark regions

We present and analyze three-dimensional data cubes of Neptune from the OSIRIS integral-field spectrograph on the 10-m Keck telescope, from July 2009. These data have a spatial resolution of 0.035"/pixel and spectral resolution of R~3800 in the H and K broad bands. We focus our analysis on regions of Neptune's atmosphere that are near-infrared dark- that is, free of discrete bright cloud features. We use a forward model coupled to a Markov chain Monte Carlo algorithm to retrieve properties of Neptune's aerosol structure and methane profile above ~4 bar in these near-infrared dark regions. Using a set of high signal-to-noise spectra in a cloud-free band from 2-12N, we find that Neptune's cloud opacity is dominated by a compact, optically thick cloud layer with a base near 3 bar and composed of low albedo, forward scattering particles, with an assumed characteristic size of ~1$\mu$m. Above this cloud, we require a vertically extended haze of smaller (~0.1 $\mu$m) particles, which reaches from the upper troposphere (~0.6 bar) into the stratosphere. The particles in this haze are brighter and more isotropically scattering than those in the deep cloud. When we extend our analysis to 18 cloud-free locations from 20N to 87S, we observe that the optical depth in aerosols above 0.5 bar decreases by a factor of 2-3 or more at mid- and high-southern latitudes relative to low latitudes. We also consider Neptune's methane (CH$_4$) profile, and find that our retrievals indicate a strong preference for a low methane relative humidity at pressures where methane is expected to condense. Our preferred solution at most locations is for a methane relative humidity below 10% near the tropopause in addition to methane depletion down to 2.0-2.5 bar. We tentatively identify a trend of lower CH$_4$ columns above 2.5 bar at mid- and high-southern latitudes over low latitudes.Comment: Published in Icarus: 15 September 201

Exotic Meson Decay Widths using Lattice QCD

A decay width calculation for a hybrid exotic meson h, with JPC=1-+, is presented for the channel h->pi+a1. This quenched lattice QCD simulation employs Luescher's finite box method. Operators coupling to the h and pi+a1 states are used at various levels of smearing and fuzzing, and at four quark masses. Eigenvalues of the corresponding correlation matrices yield energy spectra that determine scattering phase shifts for a discrete set of relative pi+a1 momenta. Although the phase shift data is sparse, fits to a Breit-Wigner model are attempted, resulting in a decay width of about 60 MeV when averaged over two lattice sizes.Comment: 9 pages, 8 figures, RevTex4, minor change to Fig.

Verifying proofs in constant depth

In this paper we initiate the study of proof systems where verification of proofs proceeds by NC circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC proof systems for a variety of languages ranging from regular to NP-complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's

The Effect of Vitamin Deficiency on Blood Pressure in Rats

After devising a very delicate, modified recording mercury manometer, it was found possible to obtain direct blood pressure curves from the abdominal aorta of anaesthetised rats, previously fed upon specific normal and vitamin deficient diets and thus make comparisons. About 75 animals were used, one-half of this number being normals to check about equally against A and B deficient animals. The records from 22 normals, on growing rations, showed an average of 84 mm. Hg, with the exception of one extremely high and one extremely low figure. The majority were close to the general average. This figure is strikingly close to the figure cited by Uhlmann, where he found the normal pressure in rabbits to be about 90 mm. Hg

Collisions of boosted black holes: perturbation theory prediction of gravitational radiation

We consider general relativistic Cauchy data representing two nonspinning, equal-mass black holes boosted toward each other. When the black holes are close enough to each other and their momentum is sufficiently high, an encompassing apparent horizon is present so the system can be viewed as a single, perturbed black hole. We employ gauge-invariant perturbation theory, and integrate the Zerilli equation to analyze these time-asymmetric data sets and compute gravitational wave forms and emitted energies. When coupled with a simple Newtonian analysis of the infall trajectory, we find striking agreement between the perturbation calculation of emitted energies and the results of fully general relativistic numerical simulations of time-symmetric initial data.Comment: 5 pages (RevTex 3.0 with 3 uuencoded figures), CRSR-107