Explicit solution of the linearized Einstein equations in TT gauge for all multipoles

We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli formalism developed by Sarbach and Tiglio.Comment: 9 pages. Minor corrections, updated references. Final version to appear in Class. Quantum Gra

Implementation of higher-order absorbing boundary conditions for the Einstein equations

We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav

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

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

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

Simple, stable, and affordable : Towards long-term ecosystem scale flux measurements of VOCs

Non peer reviewe

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&lt;sub&gt;2&lt;/sub&gt;O measurements with an infrared gas analyzer. Conventional eddy covariance fluxes of H&lt;sub&gt;2&lt;/sub&gt;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

The Effect of Harvesting Strategy of Grass Silage on Milk Production

Timing of harvest in primary growth of grass is a major factor affecting D-value (digestible organic matter, g/kg DM) of silage and dry matter (DM) consumption and milk production of dairy cows (Rinne, 2000). The objective of this research was to investigate whether there is a similar pattern in regrowths of grass

The Effect of Harvesting Strategy of Grass Silage on Milk Production

Timing of harvest in primary growth of grass is a major factor affecting D-value (digestible organic matter, g/kg DM) of silage and dry matter (DM) consumption and milk production of dairy cows (Rinne, 2000). The objective of this research was to investigate whether there is a similar pattern in regrowths of grass

Strategic Resource Management within the Service Business

Recent development in the global economy from the manufacturing business to the service business has generated increasing interest in the research of services. This paper is a theoretical analysis of the service business and its requirements to the management of organizations in entrepreneurial firms. Identified requirements have direct links to the concept of strategic entrepreneurship, which offers a good theoretical framework for the management of organizations within the service business. Based on the findings in the service business and the concept of strategic entrepreneurship, this theoretical paper conceptualizes a new strategic resource management model for entrepreneurial service organizations