6,799 research outputs found
Constraint-preserving boundary conditions in the 3+1 first-order approach
A set of energy-momentum constraint-preserving boundary conditions is
proposed for the first-order Z4 case. The stability of a simple numerical
implementation is tested in the linear regime (robust stability test), both
with the standard corner and vertex treatment and with a modified
finite-differences stencil for boundary points which avoids corners and
vertices even in cartesian-like grids. Moreover, the proposed boundary
conditions are tested in a strong field scenario, the Gowdy waves metric,
showing the expected rate of convergence. The accumulated amount of
energy-momentum constraint violations is similar or even smaller than the one
generated by either periodic or reflection conditions, which are exact in the
Gowdy waves case. As a side theoretical result, a new symmetrizer is explicitly
given, which extends the parametric domain of symmetric hyperbolicity for the
Z4 formalism. The application of these results to first-order BSSN-like
formalisms is also considered.Comment: Revised version, with conclusive numerical evidence. 23 pages, 12
figure
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
Thermodynamics of the Stephani Universes
We examine the consistency of the thermodynamics of the most general class of
conformally flat solution with an irrotational perfect fluid source (the
Stephani Universes). For the case when the isometry group has dimension
, the Gibbs-Duhem relation is always integrable, but if it is only
integrable for the particular subclass (containing FRW cosmologies)
characterized by and by admitting a conformal motion parallel to the
4-velocity. We provide explicit forms of the state variables and equations of
state linking them. These formal thermodynamic relations are determined up to
an arbitrary function of time which reduces to the FRW scale factor in the FRW
limit of the solutions. We show that a formal identification of this free
parameter with a FRW scale factor determined by FRW dynamics leads to an
unphysical temperature evolution law. If this parameter is not identified with
a FRW scale factor, it is possible to find examples of solutions and formal
equations of state complying with suitable energy conditions and reasonable
asymptotic behavior and temperature laws.Comment: 25 pages, Plain.TeX, four figure
Robust evolution system for Numerical Relativity
The paper combines theoretical and applied ideas which have been previously
considered separately into a single set of evolution equations for Numerical
Relativity. New numerical ingredients are presented which avoid gauge
pathologies and allow one to perform robust 3D calculations. The potential of
the resulting numerical code is demonstrated by using the Schwarzschild black
hole as a test-bed. Its evolution can be followed up to times greater than one
hundred black hole masses.Comment: 11 pages, 4 figures; figure correcte
Formulations of the 3+1 evolution equations in curvilinear coordinates
Following Brown, in this paper we give an overview of how to modify standard
hyperbolic formulations of the 3+1 evolution equations of General Relativity in
such a way that all auxiliary quantities are true tensors, thus allowing for
these formulations to be used with curvilinear sets of coordinates such as
spherical or cylindrical coordinates. After considering the general case for
both the Nagy-Ortiz-Reula (NOR) and the Baumgarte-Shapiro-Shibata-Nakamura
(BSSN) formulations, we specialize to the case of spherical symmetry and also
discuss the issue of regularity at the origin. Finally, we show some numerical
examples of the modified BSSN formulation at work in spherical symmetry.Comment: 19 pages, 12 figure
Strongly hyperbolic second order Einstein's evolution equations
BSSN-type evolution equations are discussed. The name refers to the
Baumgarte, Shapiro, Shibata, and Nakamura version of the Einstein evolution
equations, without introducing the conformal-traceless decomposition but
keeping the three connection functions and including a densitized lapse. It is
proved that a pseudo-differential first order reduction of these equations is
strongly hyperbolic. In the same way, densitized Arnowitt-Deser-Misner
evolution equations are found to be weakly hyperbolic. In both cases, the
positive densitized lapse function and the spacelike shift vector are arbitrary
given fields. This first order pseudodifferential reduction adds no extra
equations to the system and so no extra constraints.Comment: LaTeX, 16 pages, uses revtex4. Referee corections and new appendix
added. English grammar improved; typos correcte
A 3+1 covariant suite of Numerical Relativity Evolution Systems
A suite of three evolution systems is presented in the framework of the 3+1
formalism. The first one is of second order in space derivatives and has the
same causal structure of the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system
for a suitable choice of parameters. The second one is the standard first order
version of the first one and has the same causal structure of the Bona-Masso
system for a given parameter choice. The third one is obtained from the second
one by reducing the space of variables in such a way that the only modes that
propagate with zero characteristic speed are the trivial ones. This last system
has the same structure of the ones recently presented by Kidder, Scheel and
Teukolski: the correspondence between both sets of parameters is explicitly
given. The fact that the suite started with a system in which all the dynamical
variables behave as tensors (contrary to what happens with BSSN system) allows
one to keep the same parametrization when passing from one system to the next
in the suite. The direct relationship between each parameter and a particular
characteristic speed, which is quite evident in the second and the third
systems, is a direct consequence of the manifest 3+1 covariance of the
approach
RNA secondary structure prediction using large margin methods
The secondary structure of RNA is essential for its biological role. Recently, Do, Woods, Batzoglou, (ISMB 2006) proposed a probabilistic approach that generalizes SCFGs using conditional maximum likelihood to estimate the model parameters. We propose an alternative approach to parameter estimation which is based on an SVM-like large margin method
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