Axial symmetry and conformal Killing vectors

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in conformally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, we prove that in axisymmetric spacetimes with another symmetry (such as stationary and axisymmetric or cylindrically symmetric spacetimes) and a conformal symmetry, the commutator of the axial Killing vector with the two others mush vanish or else the symmetry is larger than that originally considered. The results are completely general and do not depend on Einstein's equations or any particular matter content.Comment: 15 pages, Latex, no figure

Wave packet approach to transport in mesoscopic systems

Wave packets provide a well established and versatile tool for studying time-dependent effects in molecular physics. Here, we demonstrate the application of wave packets to mesoscopic nanodevices at low temperatures. The electronic transport in the devices is expressed in terms of scattering and transmission coefficients, which are efficiently obtained by solving an initial value problem (IVP) using the time-dependent Schroedinger equation. The formulation as an IVP makes non-trivial device topologies accessible and by tuning the wave packet parameters one can extract the scattering properties for a large range of energies.Comment: 12 pages, 4 figure

Spherical Orbifolds for Cosmic Topology

Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1011.427

A Twisting Electrovac Solution of Type II with the Cosmological Constant

An exact solution of the current-free Einstein-Maxwell equations with the cosmological constant is presented. It is of Petrov type II, and its double principal null vector is geodesic, shear-free, expanding, and twisting. The solution contains five constants. Its electromagnetic field is non-null and aligned. The solution admits only one Killing vector and includes, as special cases, several known solutions.Comment: 4 pages, LaTeX 2e, no figures. The present (second) version, identical to that published in General Relativity and Gravitation, is derived from the first version by presenting the admitted Killing vector, and by adding the last paragraph, two footnotes (here Footnotes 1 and 3), and two references (here Refs. [3,4]

Supporting context-aware engineering based on stream reasoning

In a world of increasing dynamism, context-awareness gives promise through the ability to detect changes in the context of devices, environment, and people. Equally, with stream reasoning using languages including C-SPARQL, continuous streams of raw data in RDF can be reasoned over for context awareness. Writing many context queries and rules this way can however be error prone, and often contains boilerplate. In this paper, we present a context modelling notation designed to support the creation of context-awareness based on stream reasoning systems. In validating our language there is tool support which, amongst other benefits, can generate context queries in C-SPARQL and context aggregation rules for higher level context knowledge processing. An Android compatible mobile platform context reasoner was developed which can handle these deployable context rules. This methodology and associated tools has been validated as part of an EU funded project

On some geometric features of the Kramer interior solution for a rotating perfect fluid

Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian features of the bounding surface for some rotation rates, we show, by means of a detailed analysis of the three-dimensional spatial geodesics, that the standard Newtonian convexity properties do hold. A central role is played by a family of geodesics that are introduced here, and provide a generalization of the Newtonian straight lines parallel to the axis of rotation.Comment: LaTeX, 15 pages with 4 Poscript figures. To be published in Classical and Quantum Gravit

A Spherically Symmetric Closed Universe as an Example of a 2D Dilatonic Model

We study the two-dimensional (2D) dilatonic model describing a massless scalar field minimally coupled to the spherically reduced Einstein-Hilbert gravity. The general solution of this model is given in the case when a Killing vector is present. When interpreted in four dimensions, the solution describes either a static or a homogeneous collision of incoming and outgoing null dust streams with spherical symmetry. The homogeneous Universe is closed.Comment: 5 pages, 2 figures, to appear in Physical Review

A Bayesian method for pulsar template generation

Extracting Times of Arrival from pulsar radio signals depends on the knowledge of the pulsars pulse profile and how this template is generated. We examine pulsar template generation with Bayesian methods. We will contrast the classical generation mechanism of averaging intensity profiles with a new approach based on Bayesian inference. We introduce the Bayesian measurement model imposed and derive the algorithm to reconstruct a "statistical template" out of noisy data. The properties of these "statistical templates" are analysed with simulated and real measurement data from PSR B1133+16. We explain how to put this new form of template to use in analysing secondary parameters of interest and give various examples: We implement a nonlinear filter for determining ToAs of pulsars. Applying this method to data from PSR J1713+0747 we derive ToAs self consistently, meaning all epochs were timed and we used the same epochs for template generation. While the average template contains fluctuations and noise as unavoidable artifacts, we find that the "statistical template" derived by Bayesian inference quantifies fluctuations and remaining uncertainty. This is why the algorithm suggested turns out to reconstruct templates of statistical significance from ten to fifty single pulses. A moving data window of fifty pulses, taking out one single pulse at the beginning and adding one at the end of the window unravels the characteristics of the methods to be compared. It shows that the change induced in the classical reconstruction is dominated by random fluctuations for the average template, while statistically significant changes drive the dynamics of the proposed method's reconstruction. The analysis of phase shifts with simulated data reveals that the proposed nonlinear algorithm is able to reconstruct correct phase information along with an acceptable estimation of the remaining uncertainty.Comment: 21 pages, 16 figures, submitted to MNRA

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models

New Non-Diagonal Singularity-Free Cosmological Perfect-Fluid Solution

We present a new non-diagonal G2 inhomogeneous perfect-fluid solution with barotropic equation of state p=rho and positive density everywhere. It satisfies the global hyperbolicity condition and has no curvature singularity anywhere. This solution is very simple in form and has two arbitrary constants.Comment: Latex, no figure