186 research outputs found

    Some mathematical problems in numerical relativity

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    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

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    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

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    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 100100 judiciously chosen precessing inspiral waveforms are needed for 200200 cycles, mass ratios from 11 to 1010 and spin magnitudes 0.9\le 0.9. In fact, using only the first 1010 reduced basis waveforms yields a maximum mismatch of 0.0160.016 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 100\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

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    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

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    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

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    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 Ψ4\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-Ψ4\Psi_4 waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-Ψ4\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=0m=0 "memory" modes.Comment: 26 pages, 20 figure

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

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    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

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    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][1, 10] and durations corresponding to about 1515 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 2Ym{}_{-2}Y_{\ell m} waveform modes resolved by the NR code up to =8.\ell=8. We compare our surrogate model to Effective One Body waveforms from 5050-300M300 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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