5,842 research outputs found
New Formalism for Numerical Relativity
We present a new formulation of the Einstein equations that casts them in an
explicitly first order, flux-conservative, hyperbolic form. We show that this
now can be done for a wide class of time slicing conditions, including maximal
slicing, making it potentially very useful for numerical relativity. This
development permits the application to the Einstein equations of advanced
numerical methods developed to solve the fluid dynamic equations, {\em without}
overly restricting the time slicing, for the first time. The full set of
characteristic fields and speeds is explicitly given.Comment: uucompresed PS file. 4 pages including 1 figure. Revised version adds
a figure showing a comparison between the standard ADM approach and the new
formulation. Also available at http://jean-luc.ncsa.uiuc.edu/Papers/ Appeared
in Physical Review Letters 75, 600 (1995
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.Comment: 5 pages, 1 figure. Contribution to the Spanish Relativity Meeting
200
First order hyperbolic formalism for Numerical Relativity
The causal structure of Einstein's evolution equations is considered. We show
that in general they can be written as a first order system of balance laws for
any choice of slicing or shift. We also show how certain terms in the evolution
equations, that can lead to numerical inaccuracies, can be eliminated by using
the Hamiltonian constraint. Furthermore, we show that the entire system is
hyperbolic when the time coordinate is chosen in an invariant algebraic way,
and for any fixed choice of the shift. This is achieved by using the momentum
constraints in such as way that no additional space or time derivatives of the
equations need to be computed. The slicings that allow hyperbolicity in this
formulation belong to a large class, including harmonic, maximal, and many
others that have been commonly used in numerical relativity. We provide details
of some of the advanced numerical methods that this formulation of the
equations allows, and we also discuss certain advantages that a hyperbolic
formulation provides when treating boundary conditions.Comment: To appear in Phys. Rev.
Three dimensional numerical relativity: the evolution of black holes
We report on a new 3D numerical code designed to solve the Einstein equations
for general vacuum spacetimes. This code is based on the standard 3+1 approach
using cartesian coordinates. We discuss the numerical techniques used in
developing this code, and its performance on massively parallel and vector
supercomputers. As a test case, we present evolutions for the first 3D black
hole spacetimes. We identify a number of difficulties in evolving 3D black
holes and suggest approaches to overcome them. We show how special treatment of
the conformal factor can lead to more accurate evolution, and discuss
techniques we developed to handle black hole spacetimes in the absence of
symmetries. Many different slicing conditions are tested, including geodesic,
maximal, and various algebraic conditions on the lapse. With current
resolutions, limited by computer memory sizes, we show that with certain lapse
conditions we can evolve the black hole to about , where is the
black hole mass. Comparisons are made with results obtained by evolving
spherical initial black hole data sets with a 1D spherically symmetric code. We
also demonstrate that an ``apparent horizon locking shift'' can be used to
prevent the development of large gradients in the metric functions that result
from singularity avoiding time slicings. We compute the mass of the apparent
horizon in these spacetimes, and find that in many cases it can be conserved to
within about 5\% throughout the evolution with our techniques and current
resolution.Comment: 35 pages, LaTeX with RevTeX 3.0 macros. 27 postscript figures taking
7 MB of space, uuencoded and gz-compressed into a 2MB uufile. Also available
at http://jean-luc.ncsa.uiuc.edu/Papers/ and mpeg simulations at
http://jean-luc.ncsa.uiuc.edu/Movies/ Submitted to Physical Review
Development of an experimental 10 T Nb3Sn dipole magnet for the CERN LHC
An experimental 1-m long twill aperture dipole magnet developed using a high-current Nb3Sn conductor in order to attain a magnetic field well beyond 10 T at 4.2 K is described. The emphasis in this Nb3Sn project is on the highest possible field within the known Large Hadron Collider (LHC) twin-aperture configuration. A design target of 11.5 T was chosen
First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
We find a one-parameter family of variables which recast the 3+1 Einstein
equations into first-order symmetric-hyperbolic form for any fixed choice of
gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in
terms of an arbitrary factor times a power of the determinant of the 3-metric;
under certain assumptions, the exponent can be chosen arbitrarily, but
positive, with no implication of gauge-fixing.Comment: 5 pages; Latex with Revtex v3.0 macro package and style; to appear in
Phys. Rev. Let
Type 2 myocardial infarction: a diagnostic and therapeutic challenge in contemporary cardiology
In the expanding world of cardiovascular diseases, rapidly reaching pandemic proportions, the main focus is still on coronary atherosclerosis and its clinical consequences. However, at least in the Western world, middle-aged male patients with acute myocardial infarction are no more the rule. Due to a higher life expectancy and major medical advances, physicians are to treat older and frailer individuals, usually with multiple comorbidities. In this context, myocardial ischaemia and infarction frequently result from an imbalance between myocardial oxygen supply and demand\u2014i.e., type 2 myocardial infarction (T2MI), according to the current universal definition\u2014rather than coronary atherothrombosis. Moreover, the increasing use of high-sensitivity cardiac troponin assays has led to a heightened detection of T2MI\u2014often causing relatively little myocardial injury\u2014, which seems to have doubled its numbers in recent years. Nevertheless, owing to its multifaceted pathophysiology and clinical presentation, T2MI is still underdiagnosed. Perhaps more importantly, T2MI is also victim of undertreatment, as drugs that constitute the cornerstone of therapy in most cardiovascular diseases are much more unlikely to be prescribed in T2MI than in coronary atherothrombosis. In this paper, we review the recent literature on the classification, pathophysiology, epidemiology, and management of T2MI, trying to summarise the state-of-the-art knowledge about this increasingly important pathologic condition. Finally, based on the current scientific evidence, we also propose an algorithm that may be easily utilised in clinical practice, in order to improve T2MI diagnosis and risk stratification
Robustness of the Blandford-Znajek mechanism
The Blandford-Znajek mechanism has long been regarded as a key ingredient in
models attempting to explain powerful jets in AGNs, quasars, blazzars etc. In
such mechanism, energy is extracted from a rotating black hole and dissipated
at a load at far distances. In the current work we examine the behaviour of the
BZ mechanism with respect to different boundary conditions, revealing the
mechanism robustness upon variation of these conditions. Consequently, this
work closes a gap in our understanding of this important scenario.Comment: 7 pages, accepted in CQ
A hyperbolic slicing condition adapted to Killing fields and densitized lapses
We study the properties of a modified version of the Bona-Masso family of
hyperbolic slicing conditions. This modified slicing condition has two very
important features: In the first place, it guarantees that if a spacetime is
static or stationary, and one starts the evolution in a coordinate system in
which the metric coefficients are already time independent, then they will
remain time independent during the subsequent evolution, {\em i.e.} the lapse
will not evolve and will therefore not drive the time lines away from the
Killing direction. Second, the modified condition is naturally adapted to the
use of a densitized lapse as a fundamental variable, which in turn makes it a
good candidate for a dynamic slicing condition that can be used in conjunction
with some recently proposed hyperbolic reformulations of the Einstein evolution
equations.Comment: 11 page
Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks
I study the Bona-Masso family of hyperbolic slicing conditions, considering
in particular its properties when approaching two different types of
singularities: focusing singularities and gauge shocks. For focusing
singularities, I extend the original analysis of Bona et. al and show that both
marginal and strong singularity avoidance can be obtained for certain types of
behavior of the slicing condition as the lapse approaches zero. For the case of
gauge shocks, I re-derive a condition found previously that eliminates them.
Unfortunately, such a condition limits considerably the type of slicings
allowed. However, useful slicing conditions can still be found if one asks for
this condition to be satisfied only approximately. Such less restrictive
conditions include a particular member of the 1+log family, which in the past
has been found empirically to be extremely robust for both Brill wave and black
hole simulations.Comment: 11 pages, revtex4. Change in acknowledgment
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