1,430 research outputs found
Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
The principle part of Einstein equations in the harmonic gauge consists of a
constrained system of 10 curved space wave equations for the components of the
space-time metric. A new formulation of constraint-preserving boundary
conditions of the Sommerfeld type for such systems has recently been proposed.
We implement these boundary conditions in a nonlinear 3D evolution code and
test their accuracy.Comment: 16 pages, 17 figures, submitted to Phys. Rev.
Problems which are well-posed in a generalized sense with applications to the Einstein equations
In the harmonic description of general relativity, the principle part of
Einstein equations reduces to a constrained system of 10 curved space wave
equations for the components of the space-time metric. We use the
pseudo-differential theory of systems which are well-posed in the generalized
sense to establish the well-posedness of constraint preserving boundary
conditions for this system when treated in second order differential form. The
boundary conditions are of a generalized Sommerfeld type that is benevolent for
numerical calculation.Comment: Final version to appear in Classical and Qunatum Gravit
Testing the well-posedness of characteristic evolution of scalar waves
Recent results have revealed a critical way in which lower order terms affect
the well-posedness of the characteristic initial value problem for the scalar
wave equation. The proper choice of such terms can make the Cauchy problem for
scalar waves well posed even on a background spacetime with closed lightlike
curves. These results provide new guidance for developing stable characteristic
evolution algorithms. In this regard, we present here the finite difference
version of these recent results and implement them in a stable evolution code.
We describe test results which validate the code and exhibit some of the
interesting features due to the lower order terms.Comment: 22 pages, 15 figures Submitted to CQ
Finite difference schemes for second order systems describing black holes
In the harmonic description of general relativity, the principle part of
Einstein's equations reduces to 10 curved space wave equations for the
componenets of the space-time metric. We present theorems regarding the
stability of several evolution-boundary algorithms for such equations when
treated in second order differential form. The theorems apply to a model black
hole space-time consisting of a spacelike inner boundary excising the
singularity, a timelike outer boundary and a horizon in between. These
algorithms are implemented as stable, convergent numerical codes and their
performance is compared in a 2-dimensional excision problem.Comment: 19 pages, 9 figure
On the well posedness of the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
We give a well posed initial value formulation of the
Baumgarte-Shapiro-Shibata-Nakamura form of Einstein's equations with gauge
conditions given by a Bona-Masso like slicing condition for the lapse and a
frozen shift. This is achieved by introducing extra variables and recasting the
evolution equations into a first order symmetric hyperbolic system. We also
consider the presence of artificial boundaries and derive a set of boundary
conditions that guarantee that the resulting initial-boundary value problem is
well posed, though not necessarily compatible with the constraints. In the case
of dynamical gauge conditions for the lapse and shift we obtain a class of
evolution equations which are strongly hyperbolic and so yield well posed
initial value formulations
Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
This paper is concerned with the initial-boundary value problem for the
Einstein equations in a first-order generalized harmonic formulation. We impose
boundary conditions that preserve the constraints and control the incoming
gravitational radiation by prescribing data for the incoming fields of the Weyl
tensor. High-frequency perturbations about any given spacetime (including a
shift vector with subluminal normal component) are analyzed using the
Fourier-Laplace technique. We show that the system is boundary-stable. In
addition, we develop a criterion that can be used to detect weak instabilities
with polynomial time dependence, and we show that our system does not suffer
from such instabilities. A numerical robust stability test supports our claim
that the initial-boundary value problem is most likely to be well-posed even if
nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added,
several minor amendments; version accepted for publication in Class. Quantum
Gra
Accurate black hole evolutions by fourth-order numerical relativity
We present techniques for successfully performing numerical relativity
simulations of binary black holes with fourth-order accuracy. Our simulations
are based on a new coding framework which currently supports higher order
finite differencing for the BSSN formulation of Einstein's equations, but which
is designed to be readily applicable to a broad class of formulations. We apply
our techniques to a standard set of numerical relativity test problems,
demonstrating the fourth-order accuracy of the solutions. Finally we apply our
approach to binary black hole head-on collisions, calculating the waveforms of
gravitational radiation generated and demonstrating significant improvements in
waveform accuracy over second-order methods with typically achievable numerical
resolution.Comment: 17 pages, 25 figure
Numerical experiments of adjusted BSSN systems for controlling constraint violations
We present our numerical comparisons between the BSSN formulation widely used
in numerical relativity today and its adjusted versions using constraints. We
performed three testbeds: gauge-wave, linear wave, and Gowdy-wave tests,
proposed by the Mexico workshop on the formulation problem of the Einstein
equations. We tried three kinds of adjustments, which were previously proposed
from the analysis of the constraint propagation equations, and investigated how
they improve the accuracy and stability of evolutions. We observed that the
signature of the proposed Lagrange multipliers are always right and the
adjustments improve the convergence and stability of the simulations. When the
original BSSN system already shows satisfactory good evolutions (e.g., linear
wave test), the adjusted versions also coincide with those evolutions; while in
some cases (e.g., gauge-wave or Gowdy-wave tests) the simulations using the
adjusted systems last 10 times as long as those using the original BSSN
equations. Our demonstrations imply a potential to construct a robust evolution
system against constraint violations even in highly dynamical situations.Comment: to be published in PR
The analysis and modeling of dilatational terms in compressible turbulence
It is shown that the dilatational terms that need to be modeled in compressible turbulence include not only the pressure-dilatation term but also another term - the compressible dissipation. The nature of these dilatational terms in homogeneous turbulence is explored by asymptotic analysis of the compressible Navier-Stokes equations. A non-dimensional parameter which characterizes some compressible effects in moderate Mach number, homogeneous turbulence is identified. Direct numerical simulations (DNS) of isotropic, compressible turbulence are performed, and their results are found to be in agreement with the theoretical analysis. A model for the compressible dissipation is proposed; the model is based on the asymptotic analysis and the direct numerical simulations. This model is calibrated with reference to the DNS results regarding the influence of compressibility on the decay rate of isotropic turbulence. An application of the proposed model to the compressible mixing layer has shown that the model is able to predict the dramatically reduced growth rate of the compressible mixing layer
Individual variation in pup vocalizations and absence of behavioral signs of maternal vocal recognition in Weddell seals (Leptonychotes weddellii)
Individually stereotyped vocalizations often play an important role in relocation
of offspring in gregarious breeders. In phocids, mothers often alternate between foraging at sea and attending their pup. Pup calls are individually distinctive in various
phocid species. However, experimental evidence for maternal recognition is rare.
In this study, we recorded Weddell seal (Leptonychotes weddellii) pup vocalizations
at two whelping patches in Atka Bay, Antarctica, and explored individual vocal
variation based on eight vocal parameters. Overall, 58% of calls were correctly classiďŹed according to individual. For males (n = 12) and females (n = 9), respectively,
nine and seven individuals were correctly identiďŹed based on vocal parameters. To
investigate whether mothers respond differently to calls of familiar vs. unfamiliar
pups, we conducted playback experiments with 21 mothers. Maternal responses
did not differ between playbacks of own, familiar, and unfamiliar pup calls. We
suggest that Weddell seal pup calls may need to contain only a critical amount
of individually distinct information because mothers and pups use a combination
of sensory modalities for identiďŹcation. However, it cannot be excluded that pup
developmental factors and differing environmental factors between colonies affect
pup acoustic behavior and the role of acoustic cues in the relocation process
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