13,191 research outputs found
Falloff of the Weyl scalars in binary black hole spacetimes
The peeling theorem of general relativity predicts that the Weyl curvature
scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an
asymptotically flat spacetime, fall off asymptotically as r^(n-5) along
outgoing radial null geodesics. This leads to the interpretation of Psi_4 as
outgoing gravitational radiation at large distances from the source. We have
performed numerical simulations in full general relativity of a binary black
hole inspiral and merger, and have computed the Weyl scalars in the standard
tetrad used in numerical relativity. In contrast with previous results, we
observe that all the Weyl scalars fall off according to the predictions of the
theorem.Comment: 7 pages, 3 figures, published versio
The Asymptotic Falloff of Local Waveform Measurements in Numerical Relativity
We examine current numerical relativity computations of gravitational waves,
which typically determine the asymptotic waves at infinity by extrapolation
from finite (small) radii. Using simulations of a black hole binary with
accurate wave extraction at , we show that extrapolations from the
near-zone are self-consistent in approximating measurements at this radius,
although with a somewhat reduced accuracy. We verify that is the
dominant asymptotic contribution to the gravitational energy (as required by
the peeling theorem) but point out that gauge effects may complicate the
interpretation of the other Weyl components
Study of noise effects in electrical impedance tomography with resistor networks
We present a study of the numerical solution of the two dimensional
electrical impedance tomography problem, with noisy measurements of the
Dirichlet to Neumann map. The inversion uses parametrizations of the
conductivity on optimal grids. The grids are optimal in the sense that finite
volume discretizations on them give spectrally accurate approximations of the
Dirichlet to Neumann map. The approximations are Dirichlet to Neumann maps of
special resistor networks, that are uniquely recoverable from the measurements.
Inversion on optimal grids has been proposed and analyzed recently, but the
study of noise effects on the inversion has not been carried out. In this paper
we present a numerical study of both the linearized and the nonlinear inverse
problem. We take three different parametrizations of the unknown conductivity,
with the same number of degrees of freedom. We obtain that the parametrization
induced by the inversion on optimal grids is the most efficient of the three,
because it gives the smallest standard deviation of the maximum a posteriori
estimates of the conductivity, uniformly in the domain. For the nonlinear
problem we compute the mean and variance of the maximum a posteriori estimates
of the conductivity, on optimal grids. For small noise, we obtain that the
estimates are unbiased and their variance is very close to the optimal one,
given by the Cramer-Rao bound. For larger noise we use regularization and
quantify the trade-off between reducing the variance and introducing bias in
the solution. Both the full and partial measurement setups are considered.Comment: submitted to Inverse Problems and Imagin
HYPERION: An open-source parallelized three-dimensional dust continuum radiative transfer code
HYPERION is a new three-dimensional dust continuum Monte-Carlo radiative
transfer code that is designed to be as generic as possible, allowing radiative
transfer to be computed through a variety of three-dimensional grids. The main
part of the code is problem-independent, and only requires an arbitrary
three-dimensional density structure, dust properties, the position and
properties of the illuminating sources, and parameters controlling the running
and output of the code. HYPERION is parallelized, and is shown to scale well to
thousands of processes. Two common benchmark models for protoplanetary disks
were computed, and the results are found to be in excellent agreement with
those from other codes. Finally, to demonstrate the capabilities of the code,
dust temperatures, SEDs, and synthetic multi-wavelength images were computed
for a dynamical simulation of a low-mass star formation region. HYPERION is
being actively developed to include new features, and is publicly available
(http://www.hyperion-rt.org).Comment: Accepted for publication in Astronomy & Astrophysics. HYPERION is
being prepared for release at the start of 2012, but you can already sign up
to the mailing list at http://www.hyperion-rt.org to be informed once it is
available for downloa
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