Measuring the black hole spin direction in 3D Cartesian numerical relativity simulations

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg's pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\alpha$ and shift $\beta^i$ on the respective timeslice, as they are fixed to Gaussian normal coordinates, while leaving the coordinate labels of the spatial metric $\gamma_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing endows the method with coordinate invariance, which is not present in integral expressions using Weinberg's pseudotensor, as they normally rely on the explicit use of Cartesian coordinates

A model ensemble approach to determine the humus building efficiency of organic amendments in incubation experiments

Organic amendments are important to sustain soil organic matter (SOM) and soil functions in agricultural soils. Information about the contribution of organic amendments to SOM can be derived from incubation experiments. In this study, data from 72 incubated organic amendments including plant residues, digestates and manure were analysed. The incubation data was compiled from three experimental setups with varying incubation times, soils and incubation temperatures, in which CO2 release was measured continuously. The analysis of the incubation data was performed with an approach relying on conceptual parts of C-TOOL, CCB, Century, ICBM, RothC and Yasso which are all well-approved first-order carbon models that differ in structure and abstraction level. All models are an approximation of reality, whereby each model differs in understanding of the processes involved in soil carbon dynamics. To accumulate the advantages from each model a model ensemble was performed for each substrate. With the ability of each carbon model to compute the distribution of carbon into specific SOM pools a new approach for evaluating organic amendments in terms of humus building efficiency is presented that, depends on the weighted model fit of each ensemble member. Depending on the organic substrate added to the soil, the time course of CO2 release in the incubation studies was predicted with different accuracy by the individual model concepts. Averaging the output of the individual models leads to more robust prediction of SOM dynamics. The EHUM value is easy to interpret and the results are in accordance with the literature.Peer Reviewe

Dynamics of a Bose-Einstein Condensate in an Anharmonic Trap

We present a theoretical model to describe the dynamics of Bose-Einstein condensates in anharmonic trapping potentials. To first approximation the center-of-mass motion is separated from the internal condensate dynamics and the problem is reduced to the well known scaling solutions for the Thomas-Fermi radii. We discuss the validity of this approach and analyze the model for an anharmonic waveguide geometry which was recently realized in an experiment \cite{Ott2002c}

Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure