1,057 research outputs found
Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity
The harmonic formulation of Einstein's field equations is considered, where
the gauge conditions are introduced as dynamical constraints. The difference
between the fully constrained approach (used in analytical approximations) and
the free evolution one (used in most numerical approximations) is pointed out.
As a generalization, quasi-stationary gauge conditions are also discussed,
including numerical experiments with the gauge-waves testbed. The complementary
3+1 approach is also considered, where constraints are related instead with
energy and momentum first integrals and the gauge must be provided separately.
The relationship between the two formalisms is discussed in a more general
framework (Z4 formalism). Different strategies in black hole simulations follow
when introducing singularity avoidance as a requirement. More flexible
quasi-stationary gauge conditions are proposed in this context, which can be
seen as generalizations of the current 'freezing shift' prescriptions.Comment: Talk given at the Spanish Relativity Meeting, Tenerife, September
200
A new dissipation term for finite-difference simulations in Relativity
We present a new numerical dissipation algorithm, which can be efficiently
used in combination with centered finite-difference methods. We start from a
formulation of centered finite-volume methods for Numerical Relativity, in
which third-order space accuracy can be obtained by employing just
piecewise-linear reconstruction. We obtain a simplified version of the
algorithm, which can be viewed as a centered finite-difference method plus some
'adaptive dissipation'. The performance of this algorithm is confirmed by
numerical results obtained from 3D black hole simulations.Comment: Talk presented at the Spanish Relativity Meeting (Tenerife 2007
General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars
We have studied the dynamics of an equal-mass magnetized neutron-star binary
within a resistive magnetohydrodynamic (RMHD) approach in which the highly
conducting stellar interior is matched to an electrovacuum exterior. Because
our analysis is aimed at assessing the modifications introduced by resistive
effects on the dynamics of the binary after the merger and through to collapse,
we have carried out a close comparison with an equivalent simulation performed
within the traditional ideal magnetohydrodynamic approximation. We have found
that there are many similarities between the two evolutions but also one
important difference: the survival time of the hyper massive neutron star
increases in a RMHD simulation. This difference is due to a less efficient
magnetic-braking mechanism in the resistive regime, in which matter can move
across magnetic-field lines, thus reducing the outward transport of angular
momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried
here have been performed at higher resolutions and with a different grid
structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L.
Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732,
L6 (2011)], but confirm the formation of a low-density funnel with an ordered
magnetic field produced by the black hole--torus system. In both regimes the
magnetic field is predominantly toroidal in the highly conducting torus and
predominantly poloidal in the nearly evacuated funnel. Reconnection processes
or neutrino annihilation occurring in the funnel, none of which we model, could
potentially increase the internal energy in the funnel and launch a
relativistic outflow, which, however, is not produced in these simulations.Comment: 26 pages, 17 figures; animations available at
http://www.southampton.ac.uk/~kd10g13/movies/index.shtm
Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars
Following previous work in vacuum spacetimes, we investigate the
constraint-damping properties in the presence of matter of the recently
developed traceless, conformal and covariant Z4 (CCZ4) formulation of the
Einstein equations. First, we evolve an isolated neutron star with an ideal gas
equation of state and subject to a constraint-violating perturbation. We
compare the evolution of the constraints using the CCZ4 and
Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima (BSSNOK) systems. Second, we
study the collapse of an unstable spherical star to a black hole. Finally, we
evolve binary neutron star systems over several orbits until the merger, the
formation of a black hole, and up to the ringdown. We show that the CCZ4
formulation is stable in the presence of matter and that the constraint
violations are one or more orders of magnitude smaller than for the BSSNOK
formulation. Furthermore, by comparing the CCZ4 and the BSSNOK formulations
also for neutron star binaries with large initial constraint violations, we
investigate their influence on the errors on physical quantities. We also give
a new, simple and robust prescription for the damping parameter that removes
the instabilities found when using the fully covariant version of CCZ4 in the
evolution of black holes. Overall, we find that at essentially the same
computational costs the CCZ4 formulation provides solutions that are stable and
with a considerably smaller violation of the Hamiltonian constraint than the
BSSNOK formulation. We also find that the performance of the CCZ4 formulation
is very similar to another conformal and traceless, but noncovariant
formulation of the Z4 system, i.e. the Z4c formulation.Comment: 15 pages, 11 figures; accepted for publication in Phys. Rev.
From Tensor Equations to Numerical Code -- Computer Algebra Tools for Numerical Relativity
In this paper we present our recent work in developing a computer-algebra
tool for systems of partial differential equations (PDEs), termed "Kranc". Our
work is motivated by the problem of finding solutions of the Einstein equations
through numerical simulations. Kranc consists of Mathematica based
computer-algebra packages, that facilitate the task of dealing with symbolic
tensorial calculations and realize the conversion of systems of partial
differential evolution equations into parallelized C or Fortran code.Comment: LaTeX llncs style, 9 pages, 1 figure, to appaer in the proceedings of
"SYNASC 2004 - 6th International Symposium on Symbolic and Numeric Algorithms
for Scientific Computing", Timisoara, Romania, September 26-30 200
Dynamical damping terms for symmetry-seeking shift conditions
Suitable gauge conditions are fundamental for stable and accurate
numerical-relativity simulations of inspiralling compact binaries. A number of
well-studied conditions have been developed over the last decade for both the
lapse and the shift and these have been successfully used both in vacuum and
non-vacuum spacetimes when simulating binaries with comparable masses. At the
same time, recent evidence has emerged that the standard "Gamma-driver" shift
condition requires a careful and non-trivial tuning of its parameters to ensure
long-term stable evolutions of unequal-mass binaries. We present a novel gauge
condition in which the damping constant is promoted to be a dynamical variable
and the solution of an evolution equation. We show that this choice removes the
need for special tuning and provides a shift damping term which is free of
instabilities in our simulations and dynamically adapts to the individual
positions and masses of the binary black-hole system. Our gauge condition also
reduces the variations in the coordinate size of the apparent horizon of the
larger black hole and could therefore be useful when simulating binaries with
very small mass ratios.Comment: 11 pages, 8 figure
Multi-state Boson Stars
Motivated by the increasing interest in models which consider scalar fields
as viable dark matter candidates, we have constructed a generalization of
relativistic Boson Stars (BS) composed of two coexisting states of the scalar
field, the ground state and the first excited state. We have studied the
dynamical evolution of these Multi-state Boson Stars (MSBS) under radial
perturbations, using numerical techniques. We show that stable MSBS can be
constructed, when the number of particles in the first excited state, N2, is
smaller than the number of particles in the ground state, N1. On the other
hand, when N2 > N1, the configurations are initially unstable. However, they
evolve and settle down into stable configurations. In the stabilization
process, the initially ground state is excited and ends in a first excited
state, whereas the initially first excited state ends in a ground state. During
this process, both states emit scalar field radiation, decreasing their number
of particles. This behavior shows that even though BS in the first excited
state are intrinsically unstable under finite perturbations, the configuration
resulting from the combination of this state with the ground state produces
stable objects. Finally we show in a qualitative way, that stable MSBS could be
realistic models of dark matter galactic halos, as they produce rotation curves
that are flatter at large radii than the rotation curves produced by BS with
only one state.Comment: 14 pages. Extended discussion and new figures added. Conclusions
unchanged. Accepted for publication in Physical Review
Optimal price-based scheduling of a pumped-storage hydropower plant considering environmental constraints
publishedVersio
Financial Market Surveillance Decision Support: An Explanatory Design Theory
In this paper, an explanatory design theory for Financial Market Surveillance Systems is presented, which addresses both user requirements and regulatory demands. The identified general requirements and generated general components of the proposed design theory provides a theoretical foundation for design of implementation of highly flexible and real-time surveillance systems for capital markets
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