277 research outputs found
Discovering an active subspace in a single-diode solar cell model
Predictions from science and engineering models depend on the values of the
model's input parameters. As the number of parameters increases, algorithmic
parameter studies like optimization or uncertainty quantification require many
more model evaluations. One way to combat this curse of dimensionality is to
seek an alternative parameterization with fewer variables that produces
comparable predictions. The active subspace is a low-dimensional linear
subspace defined by important directions in the model's input space; input
perturbations along these directions change the model's prediction more, on
average, than perturbations orthogonal to the important directions. We describe
a method for checking if a model admits an exploitable active subspace, and we
apply this method to a single-diode solar cell model with five input
parameters. We find that the maximum power of the solar cell has a dominant
one-dimensional active subspace, which enables us to perform thorough parameter
studies in one dimension instead of five
Where post-Newtonian and numerical-relativity waveforms meet
We analyze numerical-relativity (NR) waveforms that cover nine orbits (18
gravitational-wave cycles) before merger of an equal-mass system with low
eccentricity, with numerical uncertainties of 0.25 radians in the phase and
less than 2% in the amplitude; such accuracy allows a direct comparison with
post-Newtonian (PN) waveforms. We focus on one of the PN approximants that has
been proposed for use in gravitational-wave data analysis, the restricted 3.5PN
``TaylorT1'' waveforms, and compare these with a section of the numerical
waveform from the second to the eighth orbit, which is about one and a half
orbits before merger. This corresponds to a gravitational-wave frequency range
of to 0.1. Depending on the method of matching PN and NR
waveforms, the accumulated phase disagreement over this frequency range can be
within numerical uncertainty. Similar results are found in comparisons with an
alternative PN approximant, 3PN ``TaylorT3''. The amplitude disagreement, on
the other hand, is around 6%, but roughly constant for all 13 cycles that are
compared, suggesting that only 4.5 orbits need be simulated to match PN and NR
waves with the same accuracy as is possible with nine orbits. If, however, we
model the amplitude up to 2.5PN order, the amplitude disagreement is roughly
within numerical uncertainty up to about 11 cycles before merger.Comment: 14 pages, 18 figures. Modifications resulting from bug fixes in LAL,
and extended analysis of numerical errors and phase agreement with PN, now
including the 3PN TaylorT3 approximant. No change to main conclusion
Accretion onto a Supermassive Black Hole Binary Before Merger
While supermassive binary black holes (SMBBHs) inspiral toward merger they
may also accrete significant amounts of matter. To study the dynamics of such a
system requires simultaneously describing the evolving spacetime and the
dynamics of magnetized plasma. Here we present the first relativistic
calculation simulating two equal-mass, non-spinning black holes as they
inspiral from an initial separation of () almost to merger,
, while accreting gas from a surrounding disk, where is the
total binary mass. We find that the accretion rate onto the black
holes first decreases during this period and then reaches a plateau, dropping
by only a factor of despite its rapid inspiral. An estimated
bolometric light curve follows the same profile. The minidisks through which
the accretion reaches the black holes are very non-standard. Reynolds, not
Maxwell, stresses dominate, and they oscillate between two distinct structural
states. In one part of the cycle, ``sloshing" streams transfer mass from one
minidisk to the other through the L1 point at a rate the
accretion rate, carrying kinetic energy at a rate that can be as large as the
peak minidisk bolometric luminosity. We also discover that the minidisks have
time-varying tilts with respect to the orbital plane similar in magnitude to
the circumbinary disk's aspect ratio. The unsigned poloidal flux on the black
hole event horizon is roughly constant at a dimensionless level ,
but doubles just before merger; if the black holes had significant spin, this
flux could support jets whose power could approach the radiated luminosity.
This simulation is the first to employ our multipatch infrastructure \pwmhd,
decreasing computational expense per physical time to of similar
runs using conventional single-grid methods.Comment: Comments welcom
Modeling the source of GW150914 with targeted numerical-relativity simulations
In fall of 2015, the two LIGO detectors measured the gravitational wave
signal GW150914, which originated from a pair of merging black holes. In the
final 0.2 seconds (about 8 gravitational-wave cycles) before the amplitude
reached its maximum, the observed signal swept up in amplitude and frequency,
from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging
black holes, as predicted by general relativity, can be computed only by full
numerical relativity, because analytic approximations fail near the time of
merger. Moreover, the nearly-equal masses, moderate spins, and small number of
orbits of GW150914 are especially straightforward and efficient to simulate
with modern numerical-relativity codes. In this paper, we report the modeling
of GW150914 with numerical-relativity simulations, using black-hole masses and
spins consistent with those inferred from LIGO's measurement. In particular, we
employ two independent numerical-relativity codes that use completely different
analytical and numerical methods to model the same merging black holes and to
compute the emitted gravitational waveform; we find excellent agreement between
the waveforms produced by the two independent codes. These results demonstrate
the validity, impact, and potential of current and future studies using
rapid-response, targeted numerical-relativity simulations for better
understanding gravitational-wave observations.Comment: 11 pages, 3 figures, submitted to Classical and Quantum Gravit
Can Cosmic Parallax Distinguish Between Anisotropic Cosmologies?
In an anisotropic universe, observers not positioned at a point of special
symmetry should observe cosmic parallax - the relative angular motion of test
galaxies over cosmic time. It was recently argued that the non-observance of
this effect in upcoming precision astrometry missions such as Gaia may be used
to place strong bounds on the position of off-center observers in a void-model
universe described by the Lemaitre-Tolman-Bondi metric. We consider the
analogous effect in anisotropic cosmological models described by an
axisymmetric homogeneous Bianchi type I metric and discuss whether any
observation of cosmic parallax would distinguish between different anisotropic
evolutions.Comment: 24 pages, 6 figure
Error-analysis and comparison to analytical models of numerical waveforms produced by the NRAR Collaboration
The Numerical-Relativity-Analytical-Relativity (NRAR) collaboration is a
joint effort between members of the numerical relativity, analytical relativity
and gravitational-wave data analysis communities. The goal of the NRAR
collaboration is to produce numerical-relativity simulations of compact
binaries and use them to develop accurate analytical templates for the
LIGO/Virgo Collaboration to use in detecting gravitational-wave signals and
extracting astrophysical information from them. We describe the results of the
first stage of the NRAR project, which focused on producing an initial set of
numerical waveforms from binary black holes with moderate mass ratios and
spins, as well as one non-spinning binary configuration which has a mass ratio
of 10. All of the numerical waveforms are analysed in a uniform and consistent
manner, with numerical errors evaluated using an analysis code created by
members of the NRAR collaboration. We compare previously-calibrated,
non-precessing analytical waveforms, notably the effective-one-body (EOB) and
phenomenological template families, to the newly-produced numerical waveforms.
We find that when the binary's total mass is ~100-200 solar masses, current EOB
and phenomenological models of spinning, non-precessing binary waveforms have
overlaps above 99% (for advanced LIGO) with all of the non-precessing-binary
numerical waveforms with mass ratios <= 4, when maximizing over binary
parameters. This implies that the loss of event rate due to modelling error is
below 3%. Moreover, the non-spinning EOB waveforms previously calibrated to
five non-spinning waveforms with mass ratio smaller than 6 have overlaps above
99.7% with the numerical waveform with a mass ratio of 10, without even
maximizing on the binary parameters.Comment: 51 pages, 10 figures; published versio
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