On Killing vectors in initial value problems for asymptotically flat space-times

The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the asymptotic characteristic and in the hyperboloidal initial value problem (both of them are formulated on the conformally compactified space-time manifold)

On the Effect of Constraint Enforcement on the Quality of Numerical Solutions in General Relativity

In Brodbeck et al 1999 it has been shown that the linearised time evolution equations of general relativity can be extended to a system whose solutions asymptotically approach solutions of the constraints. In this paper we extend the non-linear equations in similar ways and investigate the effect of various possibilities by numerical means. Although we were not able to make the constraint submanifold an attractor for all solutions of the extended system, we were able to significantly reduce the growth of the numerical violation of the constraints. Contrary to our expectations this improvement did not imply a numerical solution closer to the exact solution, and therefore did not improve the quality of the numerical solution.Comment: 14 pages, 9 figures, accepted for publication in Phys. Rev.

Closing the gap between spatial and spin dynamics of electrons at the metal-to-insulator transition

We combine extensive precision measurements of the optically detected spin dynamics and magneto-transport measurements in a contiguous set of n-doped bulk GaAs structures in order to unambiguously unravel the intriguing but complex contributions to the spin relaxation at the metal-to-insulator transition (MIT). Just below the MIT, the interplay between hopping induced loss of spin coherence and hyperfine interaction yields a maximum spin lifetime exceeding 800~ns. At slightly higher doping concentrations, however, the spin relaxation deviates from the expected Dyakonov-Perel mechanism which is consistently explained by a reduction of the effective motional narrowing with increasing doping concentration. The reduction is attributed to the change of the dominant momentum scattering mechanism in the metallic impurity band where scattering by local conductivity domain boundaries due to the intrinsic random distribution of donors becomes significant. Here, we fully identify and model all intricate contributions of the relevant microscopic scattering mechanisms which allows the complete quantitative modeling of the electron spin relaxation in the entire regime from weakly interacting up to fully delocalized electrons

Ultrafast Spin Dynamics in Nickel

The spin dynamics in Ni is studied by an exact diagonalization method on the ultrafast time scale. It is shown that the femtosecond relaxation of the magneto-optical response results from exchange interaction and spin-orbit coupling. Each of the two mechanisms affects the relaxation process differently. We find that the intrinsic spin dynamics occurs during about 10 fs while extrinsic effects such as laser-pulse duration and spectral width can slow down the observed dynamics considerably. Thus, our theory indicates that there is still room to accelerate the spin dynamics in experiments.Comment: 4 pages, Latex, 4 postscript figure

Electronic Theory for the Nonlinear Magneto-Optical Response of Transition-Metals at Surfaces and Interfaces: Dependence of the Kerr-Rotation on Polarization and on the Magnetic Easy Axis

We extend our previous study of the polarization dependence of the nonlinear optical response to the case of magnetic surfaces and buried magnetic interfaces. We calculate for the longitudinal and polar configuration the nonlinear magneto-optical Kerr rotation angle. In particular, we show which tensor elements of the susceptibilities are involved in the enhancement of the Kerr rotation in nonlinear optics for different configurations and we demonstrate by a detailed analysis how the direction of the magnetization and thus the easy axis at surfaces and buried interfaces can be determined from the polarization dependence of the nonlinear magneto-optical response, since the nonlinear Kerr rotation is sensitive to the electromagnetic field components instead of merely the intensities. We also prove from the microscopic treatment of spin-orbit coupling that there is an intrinsic phase difference of 90$^{\circ }$ between tensor elements which are even or odd under magnetization reversal in contrast to linear magneto-optics. Finally, we compare our results with several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. We conclude that the nonlinear magneto-optical Kerr-effect determines uniquely the magnetic structure and in particular the magnetic easy axis in films and at multilayer interfaces.Comment: 23 pages Revtex, preprintstyle, 2 uuencoded figure

Theory for Spin-Polarized Oscillations in Nonlinear Magneto-Optics due to Quantum Well States

Using an electronic tight-binding theory we calculate the nonlinear magneto-optical response from an x-Cu/1Fe/Cu(001) film as a function of frequency and Cu overlayer thickness (x=3 ... 25). We find very strong spin-polarized quantum well oscillations in the nonlinear magneto-optical Kerr effect (NOLIMOKE). These are enhanced by the large density of Fe $d$ states close to the Fermi level acting as intermediate states for frequency doubling. In good agreement with experiment we find two oscillation periods of 6-7 and 11 monolayers the latter being more pronounced.Comment: 12 pages, Revtex, 3 postscript figure

Normal classification of 3D occupancy grids for voxel-based indoor reconstruction from point clouds

In this paper, we present an automated method for classification of binary voxel occupancy grids of discretized indoor mapping data such as point clouds or triangle meshes according to normal vector directions. Filled voxels get assigned normal class labels distinguishing between horizontal and vertical building structures. The horizontal building structures are further differentiated into those with normal directions pointing upwards or downwards with respect to the building interior. The derived normal grids can be deployed in the context of an existing voxel-based indoor reconstruction pipeline, which so far was only applicable to indoor mapping triangle meshes that already contain normal vectors consistently oriented with respect to the building interior. By means of quantitative evaluation against reference data, we demonstrate the performance of the proposed method and its applicability in the context of voxel-based indoor reconstruction from indoor mapping point clouds without normal vectors. The code of our implementation is made available to the public at https://github.com/huepat/voxir

Voxel-Based Indoor Reconstruction From HoloLens Triangle Meshes

Current mobile augmented reality devices are often equipped with range sensors. The Microsoft HoloLens for instance is equipped with a Time-Of-Flight (ToF) range camera providing coarse triangle meshes that can be used in custom applications. We suggest to use the triangle meshes for the automatic generation of indoor models that can serve as basis for augmenting their physical counterpart with location-dependent information. In this paper, we present a novel voxel-based approach for automated indoor reconstruction from unstructured three-dimensional geometries like triangle meshes. After an initial voxelization of the input data, rooms are detected in the resulting voxel grid by segmenting connected voxel components of ceiling candidates and extruding them downwards to find floor candidates. Semantic class labels like 'Wall', 'Wall Opening', 'Interior Object' and 'Empty Interior' are then assigned to the room voxels in-between ceiling and floor by a rule-based voxel sweep algorithm. Finally, the geometry of the detected walls and their openings is refined in voxel representation. The proposed approach is not restricted to Manhattan World scenarios and does not rely on room surfaces being planar.Comment: 8 pages, 4 figure