Hyperbolicity and Constrained Evolution in Linearized Gravity

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them ({\it unconstrained} evolution). Since computational solution of differential equations introduces almost inevitable errors, it is clearly "more correct" to introduce a scheme which actively maintains the constraints by solution ({\it constrained} evolution). This has shown promise in computational settings, but the analysis of the resulting mixed elliptic hyperbolic method has not been completely carried out. We present such an analysis for one method of constrained evolution, applied to a simple vacuum system, linearized gravitational waves. We begin with a study of the hyperbolicity of the unconstrained Einstein equations. (Because the study of hyperbolicity deals only with the highest derivative order in the equations, linearization loses no essential details.) We then give explicit analytical construction of the effect of initial data setting and constrained evolution for linearized gravitational waves. While this is clearly a toy model with regard to constrained evolution, certain interesting features are found which have relevance to the full nonlinear Einstein equations.Comment: 18 page

On income tax avoidance: the case of Germany

In this paper, we present a micro estimate determining taxable income as a function of gross income and all major deduction options depending on household and asset categories. It is shown that tax savings strongly increase with increasing income, resulting in a decreasing effective marginal tax rate for the highest income groups. We compute a lower bound on 1983 aggregate income tax losses to the German fiscal authorities of DM 72b, or of 45 % of wage and income taxes paid in 1983. The estimate of tax loss exceeds estimates for other countries by orders of magnitude. --

Radial flow afterburner for event generators and the baryon puzzle

A simple afterburner including radial flow to the randomized transverse momentum obtained from event generators, Pythia and Hijing, has been implemented to calculate the $p/\pi$ ratios and compare them with available data. A coherent trend of qualitative agreement has been obtained in $pp$ collisions and in $Au+Au$ for various centralities. Those results indicate that the radial flow does play an important role in the so called baryon puzzle anomaly.Comment: 11 pages, 5 figures. To appear in Journal of Physics

Nefazodone in psychotic unipolar and bipolar depression: A retrospective chart analysis and open prospective study on its efficacy and safety versus combined treatment with amitriptyline and haloperidol

Although atypical antipsychotics are on the rise, traditional treatment of psychotic (or delusional) depression mostly includes the addition of classical antipsychotics to antidepressants. As there are only few data supporting this approach compared with antidepressant monotherapy, and almost no data comparing it with antidepressants of the latest generation, we conducted a retrospective chart analysis and a prospective, randomized open study on the efficacy and tolerability of nefazodone monotherapy versus combined treatment with amitriptyline and haloperidol in psychotic depression. The results suggest that the addition of classical antipsychotics should be reserved for those with very severe psychotic symptoms, but may not be needed in milder forms. Copyright (c) 2003 S. Karger AG, Basel

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

Charge transfer between Li ions and Li atoms in the 14-1000-eV energy region

By means of a crossed-beam technique, the absolute cross section for charge transfer between lithium ions and lithium atoms has been measured for incident ions energies ranging from 14 to 1000 eV. The lithium ions are produced thermally in a b-eucryptite source and are accelerated and focused into a ribbon beam in a Peirce gun. The total energy spread of the beam is less than 3% at all energies; mass analysis shows that above 1000 degrees C emitter temperature the impurity ions in the beam are below 0.2%. This ion beam traverses a high-density, collimated lithium vapor beam issuing from an oven. A typical density of neutral lithium atoms in the interaction region is 10(13) atoms/cm(8). The slow ions produced in the charge-transfer interaction are collected on a negatively biased cage surrounding the interaction volume of the two beams. The slow-ion charge-transfer completely accounts for the ion-beam attenuation, thus indicating that all scattered beam ions are collected. The vapor-beam density was determined by condensing the vapor on a cold target, dissolving the metallic lithium thus collected, and titrating the resulting solution. The cross section for charge transfer varies from 240 X 10-(16) cm(2) at 14 eV incident ion energy to 880X10-(16) at 1000 eV, and has the expected energy dependence for resonant charge transfer where in cident ion energy E is in eV and Q is in cm(2).Supported by Advanced Research Project Agency, Project Defender. OH wishes to acknowledge support received from the Office of Naval Research though the U.S. Naval Postgraduate School Research Foundation