4,417 research outputs found
Modeling the Black Hole Excision Problem
We analyze the excision strategy for simulating black holes. The problem is
modeled by the propagation of quasi-linear waves in a 1-dimensional spatial
region with timelike outer boundary, spacelike inner boundary and a horizon in
between. Proofs of well-posed evolution and boundary algorithms for a second
differential order treatment of the system are given for the separate pieces
underlying the finite difference problem. These are implemented in a numerical
code which gives accurate long term simulations of the quasi-linear excision
problem. Excitation of long wavelength exponential modes, which are latent in
the problem, are suppressed using conservation laws for the discretized system.
The techniques are designed to apply directly to recent codes for the Einstein
equations based upon the harmonic formulation.Comment: 21 pages, 14 postscript figures, minor contents updat
Perturbation theorems for Hele-Shaw flows and their applications
In this work, we give a perturbation theorem for strong polynomial solutions
to the zero surface tension Hele-Shaw equation driven by injection or suction,
so called the Polubarinova-Galin equation. This theorem enables us to explore
properties of solutions with initial functions close to but are not polynomial.
Applications of this theorem are given in the suction or injection case. In the
former case, we show that if the initial domain is close to a disk, most of
fluid will be sucked before the strong solution blows up. In the later case, we
obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows
in terms of invariant Richardson complex moments. This rescaling behavior
result generalizes a recent result regarding large-time rescaling behavior for
small data in terms of moments. As a byproduct of a theorem in this paper, a
short proof of existence and uniqueness of strong solutions to the
Polubarinova-Galin equation is given.Comment: 25 page
Mixed Hyperbolic - Second-Order Parabolic Formulations of General Relativity
Two new formulations of general relativity are introduced. The first one is a
parabolization of the Arnowitt, Deser, Misner (ADM) formulation and is derived
by addition of combinations of the constraints and their derivatives to the
right-hand-side of the ADM evolution equations. The desirable property of this
modification is that it turns the surface of constraints into a local attractor
because the constraint propagation equations become second-order parabolic
independently of the gauge conditions employed. This system may be classified
as mixed hyperbolic - second-order parabolic. The second formulation is a
parabolization of the Kidder, Scheel, Teukolsky formulation and is a manifestly
mixed strongly hyperbolic - second-order parabolic set of equations, bearing
thus resemblance to the compressible Navier-Stokes equations. As a first test,
a stability analysis of flat space is carried out and it is shown that the
first modification exponentially damps and smoothes all constraint violating
modes. These systems provide a new basis for constructing schemes for long-term
and stable numerical integration of the Einstein field equations.Comment: 19 pages, two column, references added, two proofs of well-posedness
added, content changed to agree with submitted version to PR
Sensitivity of Baltic Sea deep water salinity and oxygen concentration to variations in physical forcing
The Initial-Boundary Value Problem in General Relativity
In this article we summarize what is known about the initial-boundary value
problem for general relativity and discuss present problems related to it.Comment: 11 pages, 2 figures. Contribution to a special volume for Mario
Castagnino's seventy fifth birthda
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
Constraint preserving boundary conditions for the Z4c formulation of general relativity
We discuss high order absorbing constraint preserving boundary conditions for
the Z4c formulation of general relativity coupled to the moving puncture family
of gauges. We are primarily concerned with the constraint preservation and
absorption properties of these conditions. In the frozen coefficient
approximation, with an appropriate first order pseudo-differential reduction,
we show that the constraint subsystem is boundary stable on a four dimensional
compact manifold. We analyze the remainder of the initial boundary value
problem for a spherical reduction of the Z4c formulation with a particular
choice of the puncture gauge. Numerical evidence for the efficacy of the
conditions is presented in spherical symmetry.Comment: 18 pages, 8 figure
Towards a gauge-polyvalent Numerical Relativity code
The gauge polyvalence of a new numerical code is tested, both in
harmonic-coordinate simulations (gauge-waves testbed) and in
singularity-avoiding coordinates (simple Black-Hole simulations, either with or
without shift). The code is built upon an adjusted first-order
flux-conservative version of the Z4 formalism and a recently proposed family of
robust finite-difference high-resolution algorithms. An outstanding result is
the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates
(zero shift) without excision.Comment: to appear in Physical Review
Adherence to artemether/lumefantrine treatment in children under real-life situations in rural Tanzania.
A follow-up study was conducted to determine the magnitude of and factors related to adherence to artemether/lumefantrine (ALu) treatment in rural settings in Tanzania. Children in five villages of Kilosa District treated at health facilities were followed-up at their homes on Day 7 after the first dose of ALu. For those found to be positive using a rapid diagnostic test for malaria and treated with ALu, their caretakers were interviewed on drug administration habits. In addition, capillary blood samples were collected on Day 7 to determine lumefantrine concentrations. The majority of children (392/444; 88.3%) were reported to have received all doses, in time. Non-adherence was due to untimeliness rather than missing doses and was highest for the last two doses. No significant difference was found between blood lumefantrine concentrations among adherent (median 286 nmol/l) and non-adherent [median 261 nmol/l; range 25 nmol/l (limit of quantification) to 9318 nmol/l]. Children from less poor households were more likely to adhere to therapy than the poor [odds ratio (OR)=2.45, 95% CI 1.35-4.45; adjusted OR=2.23, 95% CI 1.20-4.13]. The high reported rate of adherence to ALu in rural areas is encouraging and needs to be preserved to reduce the risk of emergence of resistant strains. The age-based dosage schedule and lack of adherence to ALu treatment guidelines by health facility staff may explain both the huge variability in observed lumefantrine concentrations and the lack of difference in concentrations between the two groups
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.
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