2,284 research outputs found
Numerical stability of a new conformal-traceless 3+1 formulation of the Einstein equation
There is strong evidence indicating that the particular form used to recast
the Einstein equation as a 3+1 set of evolution equations has a fundamental
impact on the stability properties of numerical evolutions involving black
holes and/or neutron stars. Presently, the longest lived evolutions have been
obtained using a parametrized hyperbolic system developed by Kidder, Scheel and
Teukolsky or a conformal-traceless system introduced by Baumgarte, Shapiro,
Shibata and Nakamura. We present a new conformal-traceless system. While this
new system has some elements in common with the
Baumgarte-Shapiro-Shibata-Nakamura system, it differs in both the type of
conformal transformations and how the non-linear terms involving the extrinsic
curvature are handled. We show results from 3D numerical evolutions of a
single, non-rotating black hole in which we demonstrate that this new system
yields a significant improvement in the life-time of the simulations.Comment: 7 pages, 2 figure
Implementation of higher-order absorbing boundary conditions for the Einstein equations
We present an implementation of absorbing boundary conditions for the
Einstein equations based on the recent work of Buchman and Sarbach. In this
paper, we assume that spacetime may be linearized about Minkowski space close
to the outer boundary, which is taken to be a coordinate sphere. We reformulate
the boundary conditions as conditions on the gauge-invariant
Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated
by rewriting the boundary conditions as a system of ODEs for a set of auxiliary
variables intrinsic to the boundary. From these we construct boundary data for
a set of well-posed constraint-preserving boundary conditions for the Einstein
equations in a first-order generalized harmonic formulation. This construction
has direct applications to outer boundary conditions in simulations of isolated
systems (e.g., binary black holes) as well as to the problem of
Cauchy-perturbative matching. As a test problem for our numerical
implementation, we consider linearized multipolar gravitational waves in TT
gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We
demonstrate that the perfectly absorbing boundary condition B_L of order L=l
yields no spurious reflections to linear order in perturbation theory. This is
in contrast to the lower-order absorbing boundary conditions B_L with L<l,
which include the widely used freezing-Psi_0 boundary condition that imposes
the vanishing of the Newman-Penrose scalar Psi_0.Comment: 25 pages, 9 figures. Minor clarifications. Final version to appear in
Class. Quantum Grav
Critical analysis of cerebrovascular autoregulation during repeated head-up tilt.
BACKGROUND AND PURPOSE: Cerebrovascular autoregulation has been described with a phase lead of cerebral blood flow preceding changes in cerebral perfusion pressure (CPP), but there has been less focus on the effect of CPP on cerebral vascular resistance. We investigated these relations during spontaneous fluctuations (control) and repeated head-up tilt.
METHODS: Eight healthy adults were studied in supine rest and repeated tilt with 10-second supine, 10 seconds at 45 degrees head-up tilt for a total of 12 cycles. Cerebral blood flow was estimated from mean flow velocity (MFV) by transcranial Doppler ultrasound, CPP was estimated from corrected finger pressure (CPP(F)), and cerebrovascular resistance index (CVRi) was calculated in the supine position from CPP(F)/MFV. Gain and phase relations were assessed by cross-spectral analysis.
RESULTS: In the supine position, MFV preceded CPP(F), but changes in CVRi followed CPP(F). Gain and phase relations for CPP(F) as input and MFV as output were similar in supine and repeated tilt experiments. Thus, changes in cerebrovascular resistance must have had a similar pattern in the supine and tilt experiments.
CONCLUSIONS: Cerebrovascular autoregulation is achieved by changes in resistance in response to modulations in perfusion pressure whether spontaneous or induced by repeated tilt. The phase lead of MFV before CPP(F) is a mathematical and physiological consequence of the relation the input variable (CPP(F)) and the manipulated variable (cerebrovascular resistance) that should not be taken as an indication of independent control of cerebral blood flow
Semi-supervised multi-task learning for predicting interactions between HIV-1 and human proteins
Motivation: Protein–protein interactions (PPIs) are critical for virtually every biological function. Recently, researchers suggested to use supervised learning for the task of classifying pairs of proteins as interacting or not. However, its performance is largely restricted by the availability of truly interacting proteins (labeled). Meanwhile, there exists a considerable amount of protein pairs where an association appears between two partners, but not enough experimental evidence to support it as a direct interaction (partially labeled)
Impact of densitized lapse slicings on evolutions of a wobbling black hole
We present long-term stable and second-order convergent evolutions of an
excised wobbling black hole. Our results clearly demonstrate that the use of a
densitized lapse function extends the lifetime of simulations dramatically. We
also show the improvement in the stability of single static black holes when an
algebraic densitized lapse condition is applied. In addition, we introduce a
computationally inexpensive approach for tracking the location of the
singularity suitable for mildly distorted black holes. The method is based on
investigating the fall-off behavior and asymmetry of appropriate grid
variables. This simple tracking method allows one to adjust the location of the
excision region to follow the coordinate motion of the singularity.Comment: 10 pages, 8 figure
Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
We study gravitational perturbations of Schwarzschild spacetime by solving a
hyperboloidal initial value problem for the Bardeen-Press equation.
Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us
to have access to the gravitational waveform at null infinity in a general
setup. We argue that this hyperboloidal approach leads to a more accurate and
efficient calculation of the radiation signal than the common approach where a
timelike outer boundary is introduced. The method can be generalized to study
perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure
Control sideband generation for dual-recycled laser interferometric gravitational wave detectors
We present a discussion of the problems associated with generation of multiple control sidebands for length sensing and control of dual-recycled, cavity-enhanced Michelson interferometers and the motivation behind more complicated sideband generation methods. We focus on the Mach–Zehnder interferometer as a topological solution to the problem and present results from tests carried out at the Caltech 40 m prototype gravitational wave detector. The consequences for sensing and control for advanced interferometry are discussed, as are the implications for future interferometers such as Advanced LIGO
Momentum constraint relaxation
Full relativistic simulations in three dimensions invariably develop runaway
modes that grow exponentially and are accompanied by violations of the
Hamiltonian and momentum constraints. Recently, we introduced a numerical
method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint
violation and helps improve the quality of the numerical model. We present here
a method that controls the violation of the momentum constraint. The method is
based on the addition of a longitudinal component to the traceless extrinsic
curvature generated by a vector potential w_i, as outlined by York. The
components of w_i are relaxed to solve approximately the momentum constraint
equations, pushing slowly the evolution toward the space of solutions of the
constraint equations. We test this method with simulations of binary neutron
stars in circular orbits and show that effectively controls the growth of the
aforementioned violations. We also show that a full numerical enforcement of
the constraints, as opposed to the gentle correction of the momentum relaxation
scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More
detailed description of the algorithms are provided. Final published versio
Toward a dynamical shift condition for unequal mass black hole binary simulations
Moving puncture simulations of black hole binaries rely on a specific gauge
choice that leads to approximately stationary coordinates near each black hole.
Part of the shift condition is a damping parameter, which has to be properly
chosen for stable evolutions. However, a constant damping parameter does not
account for the difference in mass in unequal mass binaries. We introduce a
position dependent shift damping that addresses this problem. Although the
coordinates change, the changes in the extracted gravitational waves are small.Comment: 15 pages, submitted to CQG for NRDA 2009 conference proceeding
Structural and magnetic characterization of the complete delafossite solid solution (CuAlO2){1-x}(CuCrO2){x}
We have prepared the complete delafossite solid solution series between
diamagnetic CuAlO2 and the t2g^3 frustrated antiferromagnet CuCrO2. The
evolution with composition x in CuAl(1-x)Cr(x)O2 of the crystal structure and
magnetic properties has been studied and is reported here. The room-temperature
unit cell parameters follow the Vegard law and increase with x as expected. The
effective moment is equal to the Cr^3+ spin-only S = 3/2 value throughout the
entire solid solution. Theta is negative, indicating that the dominant
interactions are antiferromagnetic, and its magnitude increases with Cr
substitution. For dilute Cr compositions, J_BB was estimated by mean-field
theory to be 2.0 meV. Despite the sizable Theta, long-range antiferromagnetic
order does not develop until very large x, and is preceeded by glassy behavior.
Data presented here, and that on dilute Al-substitution from Okuda et al.,
suggest that the reduction in magnetic frustration due to the presence of
non-magnetic Al does not have as dominant an effect on magnetism as chemical
disorder and dilution of the magnetic exchange. For all samples, the 5 K
isothermal magnetization does not saturate in fields up to 5 T and minimal
hysteresis is observed. The presence of antiferromagnetic interactions is
clearly evident in the sub-Brillouin behavior with a reduced magnetization per
Cr atom. An inspection of the scaled Curie plot reveals that significant
short-range antiferromagnetic interactions occur in CuCrO2 above its Neel
temperature, consistent with its magnetic frustration. Uncompensated
short-range interactions are present in the Al-substituted samples and are
likely a result of chemical disorder
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