Past and future gauge in numerical relativity

Numerical relativity describes a discrete initial value problem for general relativity. A choice of gauge involves slicing space-time into space-like hypersurfaces. This introduces past and future gauge relative to the hypersurface of present time. Here, we propose solving the discretized Einstein equations with a choice of gauge in the future and a dynamical gauge in the past. The method is illustrated on a polarized Gowdy wave.Comment: To appear in Class Quantum Grav, Let

Oscillations of Thick Accretion Discs Around Black Holes

We present a numerical study of the response of a thick accretion disc to a localized, external perturbation with the aim of exciting internal modes of oscillation. We find that the perturbations efficiently excite global modes recently identified as acoustic p--modes, and closely related to the epicyclic oscillations of test particles. The two strongest modes occur at eigenfrequencies which are in a 3:2 ratio. We have assumed a constant specific angular momentum distribution within the disc. Our models are in principle scale--free and can be used to simulate accretion tori around stellar or super massive black holes.Comment: 4 pages, 4 figures, accepted for publication as a letter in the Monthly Notices of the Royal Astronomical Societ

Oscillations of Thick Accretion Discs Around Black Holes - II

We present a numerical study of the global modes of oscillation of thick accretion discs around black holes. We have previously studied the case of constant distributions of specific angular momentum. In this second paper, we investigate (i) how the size of the disc affects the oscillation eigenfrequencies, and (ii) the effect of power-law distributions of angular momentum on the oscillations. In particular, we compare the oscillations of the disc with the epicyclic eigenfrequencies of a test particle with different angular momentum distributions orbiting around the central object. We find that there is a frequency shift away from the epicyclic eigenfrequency of the test particle to lower values as the size of the tori is increased. We have also studied the response of a thick accretion disc to a localized external perturbation using non constant specific angular momentum distributions within the disc. We find that in this case it is also possible (as reported previously for constant angular momentum distributions) to efficiently excite internal modes of oscillation. In fact we show here that the local perturbations excite global oscillations (acoustic p modes) closely related to the epicyclic oscillations of test particles. Our results are particularly relevant in the context of low mass X-ray binaries and microquasars, and the high frequency Quasi-Periodic Oscillations (QPOs) observed in them. Our computations make use of a Smooth Particle Hydrodynamics (SPH) code in azimuthal symmetry, and use a gravitational potential that mimics the effects of strong gravity.Comment: 10 pages, 8 figures, accepted for publication as a paper in the Monthly Notices of the Royal Astronomical Societ

Scattering Lens Resolves sub-100 nm Structures with Visible Light

The smallest structures that conventional lenses are able to optically resolve are of the order of 200 nm. We introduce a new type of lens that exploits multiple scattering of light to generate a scanning nano-sized optical focus. With an experimental realization of this lens in gallium phosphide we have succeeded to image gold nanoparticles at 97 nm optical resolution. Our work is the first lens that provides a resolution in the nanometer regime at visible wavelengths.Comment: 4 pages, 3 figure

Salpingitis. A rare cause of acute abdomen in a sexually inactive girl: a case report

Salpingitis is an acute inflammation of the fallopian tubes, most commonly caused by sexually transmitted micro-organisms in adolescent and adult women. It is rarely found in sexually inactive girls and generally the result of a blood-borne or genitourinary infection. In young girls without a history of consensual sexual contact, the possibility of sexual abuse should be considered

Non-Imaging Speckle Interferometry forHigh Speed Nanometer-Scale Position Detection

We experimentally demonstrate a non-imaging approach to displacement measurement for complex scattering materials. By spatially controlling the wave front of the light that incidents on the material we concentrate the scattered light in a focus on a designated position. This wave front acts as an unique optical fingerprint that enables precise position detection of the illuminated material by simply measuring the intensity in the focus. By combining two optical fingerprints we demonstrate position detection along one dimension with a displacement resolution of 2.1 nm. As our approach does not require an image of the scattered field, it is possible to employ fast non-imaging detectors to enable high-speed position detection of scattering materials.Comment: 4 pages, 3 figure

Entropic force in black hole binaries and its Newtonian limits

We give an exact solution for the static force between two black holes at the turning points in their binary motion. The results are derived by Gibbs' principle and the Bekenstein-Hawking entropy applied to the apparent horizon surfaces in time-symmetric initial data. New power laws are derived for the entropy jump in mergers, while Newton's law is shown to derive from a new adiabatic variational principle for the Hilbert action in the presence of apparent horizon surfaces. In this approach, entropy is strictly monotonic such that gravity is attractive for all separations including mergers, and the Bekenstein entropy bound is satisfied also at arbitrarily large separations, where gravity reduces to Newton's law. The latter is generalized to point particles in the Newtonian limit by application of Gibbs' principle to world-lines crossing light cones.Comment: Accepted for publication in Phys. Rev.

Spatial amplitude and phase modulation using commercial twisted nematic LCDs

We present a method for full spatial phase and amplitude control of a laser beam using a twisted nematic liquid crystal display combined with a spatial filter. By spatial filtering we combine four neighboring pixels into one superpixel. At each superpixel we are able to independently modulate the phase and the amplitude of light. We demonstrate experimentally the independent phase and amplitude modulation using this novel technique. Our technique does not impose special requirements on the spatial light modulator and allows precise control of fields even with imperfect modulators.Comment: 10 pages, 6 figure