Regularity of the Einstein Equations at Future Null Infinity

When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal factor and thus appear to be ill-behaved at this (exterior) boundary. In this article however we show, through an enforcement of the Hamiltonian and momentum constraints to the needed order in a Taylor expansion, that these apparently singular terms are not only regular at the boundary but can in fact be explicitly evaluated there in terms of conformally regular geometric data. Though we employ a rather rigidly constrained and gauge fixed formulation of the field equations, we discuss the extent to which we expect our results to have a more 'universal' significance and, in particular, to be applicable, after minor modifications, to alternative formulations.Comment: 43 pages, no figures, AMS-TeX. Minor revisions, updated to agree with published versio

Lag time determination in DEC measurements with PTR-MS

The disjunct eddy covariance (DEC) method has emerged as a popular technique for micrometeorological flux measurements of volatile organic compounds (VOCs). It has usually been combined with proton transfer reaction mass spectrometry (PTR-MS), an online technique for VOC concentration measurements. However, the determination of the lag time between wind and concentration measurements has remained an important challenge. To address this issue, we studied the effect of different lag time methods on DEC fluxes. The analysis was based on both actual DEC measurements with PTR-MS and simulated DEC data derived from high frequency H<sub>2</sub>O measurements with an infrared gas analyzer. Conventional eddy covariance fluxes of H<sub>2</sub>O served as a reference in the DEC simulation. The individual flux measurements with PTR-MS were rather sensitive to the lag time methods, but typically this effect averaged out when the median fluxes were considered. The DEC simulation revealed that the maximum covariance method was prone to overestimation of the absolute values of fluxes. The constant lag time methods, one based on a value calculated from the sampling flow and the sampling line dimensions and the other on a typical daytime value, had a tendency to underestimate. The visual assessment method and our new averaging approach utilizing running averaged covariance functions did not yield statistically significant errors and thus fared better than the habitual choice, the maximum covariance method. Given this feature and the potential for automatic flux calculation, we recommend using the averaging approach in DEC measurements with PTR-MS. It also seems well suited to conventional eddy covariance applications when measuring fluxes near the detection limit

Dissecting ion-specific dielectric spectra of sodium-halide solutions into solvation water and ionic contributions

Using extensive equilibrium molecular dynamics simulations we determine the dielectric spectra of aqueous solutions of NaF, NaCl, NaBr, and NaI. The ion- specific and concentration-dependent shifts of the static dielectric constants and the dielectric relaxation times match experimental results very well, which serves as a validation of the classical and non-polarizable ionic force fields used. The purely ionic contribution to the dielectric response is negligible, but determines the conductivity of the salt solutions. The ion- water cross correlation contribution is negative and reduces the total dielectric response by about 5%-10% for 1 M solutions. The dominating water dielectric response is decomposed into different water solvation shells and ion-pair configurations, by this the spectral blue shift and the dielectric decrement of salt solutions with increasing salt concentration is demonstrated to be primarily caused by first-solvation shell water. With rising salt concentration the simulated spectra show more pronounced deviations from a single-Debye form and can be well described by a Cole-Cole fit, in quantitative agreement with experiments. Our spectral decomposition into ionic and different water solvation shell contributions does not render the individual contributions more Debye-like, this suggests the non-Debye-like character of the dielectric spectra of salt solutions not to be due to the superposition of different elementary relaxation processes with different relaxation times. Rather, the non-Debye-like character is likely to be an inherent spectral signature of solvation water around ions

An axisymmetric evolution code for the Einstein equations on hyperboloidal slices

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.Comment: 21 pages, 4 figures. Minor additions, updated to agree with journal versio

Testing outer boundary treatments for the Einstein equations

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman-Penrose scalar Psi_0, and control gauge reflections.Comment: Modified to agree with version accepted for publication in Class. Quantum Gra

The history of NATO TNF policy: The role of studies, analysis and exercises conference proceedings. Volume 3: Papers by Gen. Robert C. Richardson III (Ret.)

This conference was organized to study and analyze the role of simulation, analysis, modeling, and exercises in the history of NATO policy. The premise was not that the results of past studies will apply to future policy, but rather that understanding what influenced the decision process-and how-would be of value. The structure of the conference was built around discussion panels. The panels were augmented by a series of papers and presentations focusing on particular TNF events, issues, studies, or exercises. The conference proceedings consist of three volumes. Volume 1 contains the conference introduction, agenda, biographical sketches of principal participants, and analytical summary of the presentations and discussion panels. Volume 2 contains a short introduction and the papers and presentations from the conference. This volume contains selected papers by Brig. Gen. Robert C. Richardson III (Ret.)

Gowdy waves as a test-bed for constraint-preserving boundary conditions

Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting 200

Axisymmetric evolution of Einstein equations and mass conservation

For axisymmetric evolution of isolated systems, we prove that there exists a gauge such that the total mass can be written as a positive definite integral on the spacelike hypersurfaces of the foliation and the integral is constant along the evolution. The conserved mass integral controls the square of the extrinsic curvature and the square of first derivatives of the intrinsic metric. We also discuss applications of this result for the global existence problem in axial symmetry.Comment: A mistake in the proof of Lemma 5.1 is corrected. This version includes the Corrigendum that appears in Class. Quantum Grav. 26 (2009) 12980

The history of NATO TNF policy: The role of studies, analysis and exercises conference proceedings. Volume 1, Introduction and summary

This conference was organized to study and analyze the role of simulation, analysis, modeling, and exercises in the history of NATO policy. The premise was not that the results of past studies will apply to future policy, but rather that understanding what influenced the decision process -- and how -- would be of value. The structure of the conference was built around discussion panels. The panels were augmented by a series of papers and presentations focusing on particular TNF events, issues, studies or exercise. The conference proceedings consist of three volumes. This volume, Volume 1, contains the conference introduction, agenda, biographical sketches of principal participants, and analytical summary of the presentations and discussion panels. Volume 2 contains a short introduction and the papers and presentations from the conference. Volume 3 contains selected papers by Brig. Gen. Robert C. Richardson III (Ret.)