Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A new formulation of constraint-preserving boundary conditions of the Sommerfeld type for such systems has recently been proposed. We implement these boundary conditions in a nonlinear 3D evolution code and test their accuracy.Comment: 16 pages, 17 figures, submitted to Phys. Rev.

Problems which are well-posed in a generalized sense with applications to the Einstein equations

In the harmonic description of general relativity, the principle part of Einstein equations reduces to a constrained system of 10 curved space wave equations for the components of the space-time metric. We use the pseudo-differential theory of systems which are well-posed in the generalized sense to establish the well-posedness of constraint preserving boundary conditions for this system when treated in second order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation.Comment: Final version to appear in Classical and Qunatum Gravit

Testing the well-posedness of characteristic evolution of scalar waves

Recent results have revealed a critical way in which lower order terms affect the well-posedness of the characteristic initial value problem for the scalar wave equation. The proper choice of such terms can make the Cauchy problem for scalar waves well posed even on a background spacetime with closed lightlike curves. These results provide new guidance for developing stable characteristic evolution algorithms. In this regard, we present here the finite difference version of these recent results and implement them in a stable evolution code. We describe test results which validate the code and exhibit some of the interesting features due to the lower order terms.Comment: 22 pages, 15 figures Submitted to CQ

Finite difference schemes for second order systems describing black holes

In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.Comment: 19 pages, 9 figure

The Doctrine of the Real Presence of Christ in the Eucharist with special reference to the Doctrine of Transubstantiation

In a Catholic tract of recent date, “The Holy Eucharist Explained” (by Our Sunday Visitor Press, Huntington, Ind.), We read the modest claim that “All Christians for 15 centuries believed the Eucharist to contain the true body and blood, soul and divinity or Jesus Christ, under the appearances or bread and wine” (p. 16); that this is substantiated by the following facts: “In the first place the Greek Church and all the Christian sects or Asia, which are older than Protestantism by 1000 years, believe as we do. Hence such must have been the prevailing belief or Christians during the first centuries. Secondly, writings that come down to us from close successors or the Apostles clearly state the belief of the early Church, and show it to be identical with ours or today

Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations

This paper is concerned with the initial-boundary value problem for the Einstein equations in a first-order generalized harmonic formulation. We impose boundary conditions that preserve the constraints and control the incoming gravitational radiation by prescribing data for the incoming fields of the Weyl tensor. High-frequency perturbations about any given spacetime (including a shift vector with subluminal normal component) are analyzed using the Fourier-Laplace technique. We show that the system is boundary-stable. In addition, we develop a criterion that can be used to detect weak instabilities with polynomial time dependence, and we show that our system does not suffer from such instabilities. A numerical robust stability test supports our claim that the initial-boundary value problem is most likely to be well-posed even if nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added, several minor amendments; version accepted for publication in Class. Quantum Gra

Accurate black hole evolutions by fourth-order numerical relativity

We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite differencing for the BSSN formulation of Einstein's equations, but which is designed to be readily applicable to a broad class of formulations. We apply our techniques to a standard set of numerical relativity test problems, demonstrating the fourth-order accuracy of the solutions. Finally we apply our approach to binary black hole head-on collisions, calculating the waveforms of gravitational radiation generated and demonstrating significant improvements in waveform accuracy over second-order methods with typically achievable numerical resolution.Comment: 17 pages, 25 figure

The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves

The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the worldtube. We establish the well-posedness of this problem for the evolution of a quasilinear scalar wave by means of energy estimates. The treatment is given in characteristic coordinates and thus provides a guide for developing stable finite difference algorithms. A new technique underlying the approach has potential application to other characteristic initial-boundary value problems.Comment: Version to appear in Class. Quantum Gra

Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

We present a set of well-posed constraint-preserving boundary conditions for a first-order in time, second-order in space, harmonic formulation of the Einstein equations. The boundary conditions are tested using robust stability, linear and nonlinear waves, and are found to be both less reflective and constraint preserving than standard Sommerfeld-type boundary conditions.Comment: 18 pages, 7 figures, accepted in CQ

Evidence for induction of humoral and cytotoxic immune responses against devil facial tumor disease cells in Tasmanian devils (Sarcophilus harrisii) immunized with killed cell preparations

Available online 20 February 2015Tasmanian devils (Sarcophilus harrisii) risk extinction from a contagious cancer, devil facial tumour disease (DFTD) in which the infectious agent is the tumor cell itself. Because devils are unable to produce an immune response against the tumor cells no devil has survived 'infection'. To promote an immune response we immunized healthy devils with killed DFTD tumor cells in the presence of adjuvants. Immune responses, including cytotoxicity and antibody production, were detected in five of the six devils. The incorporation of adjuvants that act via toll like receptors may provide additional signals to break 'immunological ignorance'. One of these devils was protected against a challenge with viable DFTD cells. This was a short-term protection as re-challenge one year later resulted in tumor growth. These results suggest that Tasmanian devils can generate immune responses against DFTD cells. With further optimization of immune stimulation it should be possible to protect Tasmanian devils against DFTD with an injectable vaccine.A. Kreiss, G.K. Brown, C. Tovar, A.B. Lyons, G.M. Wood