A Method for Calculating the Structure of (Singular) Spacetimes in the Large

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity (\Scri{}^+) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.Comment: 29 pages, AGG2

General Relativistic Scalar Field Models in the Large

For a class of scalar fields including the massless Klein-Gordon field the general relativistic hyperboloidal initial value problems are equivalent in a certain sense. By using this equivalence and conformal techniques it is proven that the hyperboloidal initial value problem for those scalar fields has an unique solution which is weakly asymptotically flat. For data sufficiently close to data for flat spacetime there exist a smooth future null infinity and a regular future timelike infinity.Comment: 22 pages, latex, AGG 1

Non-invasive monitoring of renal transplant recipients: Urinary excretion of soluble adhesion molecules and of the complement-split product C4d

Background: The number of inducible adhesion molecules known to be involved in cell-mediated allograft rejection is still increasing. In addition, recent data describe complement activation during acute humoral allograft rejection. The aim of this study was to assess whether specific molecules from either pathway are excreted into urine and whether they can provide useful diagnostic tools for the monitoring of renal transplant recipients. Methods: Urinary concentrations of soluble adhesion molecules (sICAM-1, sVCAM-1) and of the complement degradation product C4d were determined by standardized ELISA technique in 75 recipients of renal allografts and 29 healthy controls. Patient samples were assigned to four categories according to clinical criteria: group 1: acute steroid-sensitive rejection (ASSR, n=14), group 2: acute steroid-resistant rejection (ASRR, n=12), group 3: chronic allograft dysfunction (CAD, n=20) and group 4: stable graft function (SGF, n=29). Results: All patients with rejection episodes (groups 1-3) had significantly higher values of urinary sC4d compared with healthy controls and patients with stable graft function (p<0.05). The urinary levels of sVCAM-1 were significantly higher in group 2 (ASRR) compared with all other groups (p<0.001). Uniformly low amounts of s-VCAM-1 and complement-split product C4d were excreted by healthy controls (group 0). In contrast, urinary sICAM-1 concentration in healthy controls was almost as high as in group 2 (ASRR) whereas patients with a stable functioning graft (group 4) excreted significantly less sICAM-1 (p<0.05). Conclusion: The evaluation of sVCAM-1 and sC4d excretion in urine can provide a valuable tool with regard to the severity and type of allograft rejection. With respect to long-term allograft survival, serial measurements of these markers should have the potential to detect rejection episodes and prompt immediate treatment. Copyright (C) 2003 S. Karger AG, Basel

GW quasiparticle calculations with spin-orbit coupling for the light actinides

We report on the importance of GW self-energy corrections for the electronic structure of light actinides in the weak-to-intermediate coupling regime. Our study is based on calculations of the band structure and total density of states of Np, U, and Pu using a one-shot GW approximation that includes spin-orbit coupling within a full potential LAPW framework. We also present RPA screened effective Coulomb interactions for the f-electron orbitals for different lattice constants, and show that there is an increased contribution from electron-electron correlation in these systems for expanded lattices. We find a significant amount of electronic correlation in these highly localized electronic systems.Comment: Accepted and to appear in Phys. Rev.

Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to physical problems and why there is good hope that this might even be a good idea from the numerical point of view. We describe in detail the derivation of the conformal field equations in the spinor formalism which we use for the implementation of the equations, and present all the equations as a reference for future work. Finally, we discuss the implications of the assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2

How to quantify deterministic and random influences on the statistics of the foreign exchange market

It is shown that prize changes of the US dollar - German Mark exchange rates upon different delay times can be regarded as a stochastic Marcovian process. Furthermore we show that from the empirical data the Kramers-Moyal coefficients can be estimated. Finally, we present an explicite Fokker-Planck equation which models very precisely the empirical probabilitiy distributions.Comment: 3 figure

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page

A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Detection of fixed points in spatiotemporal signals by clustering method

We present a method to determine fixed points in spatiotemporal signals. A 144-dimensioanl simulated signal, similar to a Kueppers-Lortz instability, is analyzed and its fixed points are reconstructed.Comment: 3 pages, 3 figure

Effect of Local Electron-Electron Correlation in Hydrogen-like Impurities in Ge

We have studied the electronic and local magnetic structure of the hydrogen interstitial impurity at the tetrahedral site in diamond-structure Ge, using an empirical tight binding + dynamical mean field theory approach because within the local density approximation (LDA) Ge has no gap. We first establish that within LDA the 1s spectral density bifurcates due to entanglement with the four neighboring sp3 antibonding orbitals, providing an unanticipated richness of behavior in determining under what conditions a local moment hyperdeep donor or Anderson impurity will result, or on the other hand a gap state might appear. Using a supercell approach, we show that the spectrum, the occupation, and the local moment of the impurity state displays a strong dependence on the strength of the local on-site Coulomb interaction U, the H-Ge hopping amplitude, the depth of the bare 1s energy level epsilon_H, and we address to some extent the impurity concentration dependence. In the isolated impurity, strong interaction regime a local moment emerges over most of the parameter ranges indicating magnetic activity, and spectral density structure very near (or in) the gap suggests possible electrical activity in this regime.Comment: 9 pages, 5 figure