186 research outputs found

### Some mathematical problems in numerical relativity

The main goal of numerical relativity is the long time simulation of highly
nonlinear spacetimes that cannot be treated by perturbation theory. This
involves analytic, computational and physical issues. At present, the major
impasses to achieving global simulations of physical usefulness are of an
analytic/computational nature. We present here some examples of how analytic
insight can lend useful guidance for the improvement of numerical approaches.Comment: 17 pages, 12 graphs (eps format

### Lattice Boltzmann Approach to Viscous Flows Between Parallel Plates

Four different kinds of laminar flows between two parallel plates are
investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is
estimated in two cases using numerical fits of the parabolic velocity profiles
and the kinetic energy decay curves, respectively. The error relative to the
analytical kinematic viscosity values was found to be less than one percent in
both cases. The LBM results for the unsteady development of the flow when one
plate is brought suddenly at a constant velocity, are found in excellent
agreement with the analytical solution. Because the classical Schlichting's
approximate solution for the entrance--region flow is not valid for small
Reynolds numbers, a Finite Element Method solution was used in order to check
the accuracy of the LBM results

### A sparse representation of gravitational waves from precessing compact binaries

Many relevant applications in gravitational wave physics share a significant
common problem: the seven-dimensional parameter space of gravitational
waveforms from precessing compact binary inspirals and coalescences is large
enough to prohibit covering the space of waveforms with sufficient density. We
find that by using the reduced basis method together with a parametrization of
waveforms based on their phase and precession, we can construct ultra-compact
yet high-accuracy representations of this large space. As a demonstration, we
show that less than $100$ judiciously chosen precessing inspiral waveforms are
needed for $200$ cycles, mass ratios from $1$ to $10$ and spin magnitudes $\le
0.9$. In fact, using only the first $10$ reduced basis waveforms yields a
maximum mismatch of $0.016$ over the whole range of considered parameters. We
test whether the parameters selected from the inspiral regime result in an
accurate reduced basis when including merger and ringdown; we find that this is
indeed the case in the context of a non-precessing effective-one-body model.
This evidence suggests that as few as $\sim 100$ numerical simulations of
binary black hole coalescences may accurately represent the seven-dimensional
parameter space of precession waveforms for the considered ranges.Comment: 5 pages, 3 figures. The parameters selected for the basis of
precessing waveforms can be found in the source file

### Spin Diagrams for Equal-Mass Black-Hole Binaries with Aligned Spins

Binary black-hole systems with spins aligned with the orbital angular
momentum are of special interest as they may be the preferred end-state of the
inspiral of generic supermassive binary black-hole systems. In view of this, we
have computed the inspiral and merger of a large set of binary systems of
equal-mass black holes with spins aligned with the orbital angular momentum but
otherwise arbitrary. By least-square fitting the results of these simulations
we have constructed two "spin diagrams" which provide straightforward
information about the recoil velocity |v_kick| and the final black-hole spin
a_fin in terms of the dimensionless spins a_1 and a_2 of the two initial black
holes. Overall they suggest a maximum recoil velocity of |v_kick|=441.94 km/s,
and minimum and maximum final spins a_fin=0.3471 and a_fin=0.9591,
respectively.Comment: 4 pages, 3 figs; small changes matching published versio

### Black hole-neutron star mergers for 10 solar mass black holes

General relativistic simulations of black hole-neutron star mergers have
currently been limited to low-mass black holes (less than 7 solar mass), even
though population synthesis models indicate that a majority of mergers might
involve more massive black holes (10 solar mass or more). We present the first
general relativistic simulations of black hole-neutron star mergers with 10
solar mass black holes. For massive black holes, the tidal forces acting on the
neutron star are usually too weak to disrupt the star before it reaches the
innermost stable circular orbit of the black hole. Varying the spin of the
black hole in the range a/M = 0.5-0.9, we find that mergers result in the
disruption of the star and the formation of a massive accretion disk only for
large spins a/M>0.7-0.9. From these results, we obtain updated constraints on
the ability of BHNS mergers to be the progenitors of short gamma-ray bursts as
a function of the mass and spin of the black hole. We also discuss the
dependence of the gravitational wave signal on the black hole parameters, and
provide waveforms and spectra from simulations beginning 7-8 orbits before
merger.Comment: 11 pages, 11 figures - Updated to match published versio

### Comparing Gravitational Waveform Extrapolation to Cauchy-Characteristic Extraction in Binary Black Hole Simulations

We extract gravitational waveforms from numerical simulations of black hole
binaries computed using the Spectral Einstein Code. We compare two extraction
methods: direct construction of the Newman-Penrose (NP) scalar $\Psi_4$ at a
finite distance from the source and Cauchy-characteristic extraction (CCE). The
direct NP approach is simpler than CCE, but NP waveforms can be contaminated by
near-zone effects---unless the waves are extracted at several distances from
the source and extrapolated to infinity. Even then, the resulting waveforms can
in principle be contaminated by gauge effects. In contrast, CCE directly
provides, by construction, gauge-invariant waveforms at future null infinity.
We verify the gauge invariance of CCE by running the same physical simulation
using two different gauge conditions. We find that these two gauge conditions
produce the same CCE waveforms but show differences in extrapolated-$\Psi_4$
waveforms. We examine data from several different binary configurations and
measure the dominant sources of error in the extrapolated-$\Psi_4$ and CCE
waveforms. In some cases, we find that NP waveforms extrapolated to infinity
agree with the corresponding CCE waveforms to within the estimated error bars.
However, we find that in other cases extrapolated and CCE waveforms disagree,
most notably for $m=0$ "memory" modes.Comment: 26 pages, 20 figure

### Brain Tumor Segmentation from MRI Data Using Ensemble Learning and Multi-Atlas

Atlases are frequently employed to assist medical image segmentation with prior information. This paper
introduces a multi-atlas architecture that is trained to locally characterize the appearance (average intensity and standard deviation) of normal tissues in various observed and computed data channels of brain MRI records. The multiple atlas is then deployed to enhance the accuracy of an ensemble learning based brain tumor segmentation procedure that uses binary decision
trees. The proposed method is validated using the low-grade tumor volumes of the BraTS 2016 train data set. The use of atlases improve the segmentation quality, causing a rise of up to 1.5% in average Dices scores

### Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models

Simulating a binary black hole (BBH) coalescence by solving Einstein's
equations is computationally expensive, requiring days to months of
supercomputing time. Using reduced order modeling techniques, we construct an
accurate surrogate model, which is evaluated in a millisecond to a second, for
numerical relativity (NR) waveforms from non-spinning BBH coalescences with
mass ratios in $[1, 10]$ and durations corresponding to about $15$ orbits
before merger. We assess the model's uncertainty and show that our modeling
strategy predicts NR waveforms {\em not} used for the surrogate's training with
errors nearly as small as the numerical error of the NR code. Our model
includes all spherical-harmonic ${}_{-2}Y_{\ell m}$ waveform modes resolved by
the NR code up to $\ell=8.$ We compare our surrogate model to Effective One
Body waveforms from $50$-$300 M_\odot$ for advanced LIGO detectors and find
that the surrogate is always more faithful (by at least an order of magnitude
in most cases).Comment: Updated to published version, which includes a section comparing the
surrogate and effective-one-body models. The surrogate is publicly available
for download at http://www.black-holes.org/surrogates/ . 6 pages, 6 figure

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