Calibration of the CH and CN Variations Among Main Sequence Stars in M71 and in M13

An analysis of the CN and CH band strengths measured in a large sample of M71 and M13 main sequence stars by Cohen (1999a,b) is undertaken using synthetic spectra to quantify the underlying C and N abundances. In the case of M71 it is found that the observed CN and CH band strengths are best matched by the {\it{identical}} C/N/O abundances which fit the bright giants, implying: 1) little if any mixing is taking place during red giant branch ascent in M71, and 2) a substantial component of the C and N abundance inhomogeneities is in place before the main sequence turn-off. The unlikelihood of mixing while on the main sequence requires an explanation for the abundance variations which lies outside the present stars (primordial inhomogeneities or intra-cluster self enrichment). For M13 it is shown that the 3883\AA CN bands are too weak to be measured in the spectra for any reasonable set of expected compositions. A similar situation exists for CH as well. However, two of the more luminous program stars do appear to have C abundances considerably greater than those found among the bright giants thereby suggesting deep mixing has taken place on the M13 red giant branch.Comment: 14 pages, 4 figures, accepted for publication by A

Modeling the Black Hole Excision Problem

We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between. Proofs of well-posed evolution and boundary algorithms for a second differential order treatment of the system are given for the separate pieces underlying the finite difference problem. These are implemented in a numerical code which gives accurate long term simulations of the quasi-linear excision problem. Excitation of long wavelength exponential modes, which are latent in the problem, are suppressed using conservation laws for the discretized system. The techniques are designed to apply directly to recent codes for the Einstein equations based upon the harmonic formulation.Comment: 21 pages, 14 postscript figures, minor contents updat

Szego coordinates, quadrature domains, and double quadrature domains

We define Szego coordinates on a finitely connected smoothly bounded planar domain which effect a holomorphic change of coordinates on the domain that can be as close to the identity as desired and which convert the domain to a quadrature domain with respect to boundary arc length. When these Szego coordinates coincide with Bergman coordinates, the result is a double quadrature domain with respect to both area and arc length. We enumerate a host of interesting and useful properties that such double quadrature domains possess, and we show that such domains are in fact dense in the realm of bounded finitely connected domains with smooth boundaries.Comment: 19 page

Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity

Two new formulations of general relativity are introduced. The first one is a parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived by addition of combinations of the constraints and their derivatives to the right-hand-side of the ADM evolution equations. The desirable property of this modification is that it turns the surface of constraints into a local attractor because the constraint propagation equations become second-order parabolic independently of the gauge conditions employed. This system may be classified as mixed hyperbolic - second-order parabolic. The second formulation is a parabolization of the Kidder, Scheel, Teukolsky formulation and is a manifestly mixed strongly hyperbolic - second-order parabolic set of equations, bearing thus resemblance to the compressible Navier-Stokes equations. As a first test, a stability analysis of flat space is carried out and it is shown that the first modification exponentially damps and smoothes all constraint violating modes. These systems provide a new basis for constructing schemes for long-term and stable numerical integration of the Einstein field equations.Comment: 19 pages, two column, references added, two proofs of well-posedness added, content changed to agree with submitted version to PR

Neutron electric form factor at large momentum transfer

Based on the recent, high precision data for elastic electron scattering from protons and deuterons, at relatively large momentum transfer $Q^2$, we determine the neutron electric form factor up to $Q^2=3.5$ GeV$^2$. The values obtained from the data (in the framework of the nonrelativistic impulse approximation) are larger than commonly assumed and are in good agreement with the Gari-Kr\"umpelmann parametrization of the nucleon electromagnetic form factors.Comment: 11 pages 2 figure

Quadrature domains and kernel function zipping

It is proved that quadrature domains are ubiquitous in a very strong sense in the realm of smoothly bounded multiply connected domains in the plane. In fact, they are so dense that one might as well assume that any given smooth domain one is dealing with is a quadrature domain, and this allows access to a host of strong conditions on the classical kernel functions associated to the domain. Following this string of ideas leads to the discovery that the Bergman kernel can be zipped down to a strikingly small data set. It is also proved that the kernel functions associated to a quadrature domain must be algebraic.Comment: 13 pages, to appear in Arkiv for matemati