36,848 research outputs found
Harmonic coordinate method for simulating generic singularities
This paper presents both a numerical method for general relativity and an
application of that method. The method involves the use of harmonic coordinates
in a 3+1 code to evolve the Einstein equations with scalar field matter. In
such coordinates, the terms in Einstein's equations with the highest number of
derivatives take a form similar to that of the wave equation. The application
is an exploration of the generic approach to the singularity for this type of
matter. The preliminary results indicate that the dynamics as one approaches
the singularity is locally the dynamics of the Kasner spacetimes.Comment: 5 pages, 4 figures, Revtex, discussion expanded, references adde
Hunting Local Mixmaster Dynamics in Spatially Inhomogeneous Cosmologies
Heuristic arguments and numerical simulations support the Belinskii et al
(BKL) claim that the approach to the singularity in generic gravitational
collapse is characterized by local Mixmaster dynamics (LMD). Here, one way to
identify LMD in collapsing spatially inhomogeneous cosmologies is explored. By
writing the metric of one spacetime in the standard variables of another,
signatures for LMD may be found. Such signatures for the dynamics of spatially
homogeneous Mixmaster models in the variables of U(1)-symmetric cosmologies are
reviewed. Similar constructions for U(1)-symmetric spacetimes in terms of the
dynamics of generic -symmetric spacetime are presented.Comment: 17 pages, 5 figures. Contribution to CQG Special Issue "A Spacetime
Safari: Essays in Honour of Vincent Moncrief
Shintani functions, real spherical manifolds, and symmetry breaking operators
For a pair of reductive groups , we prove a geometric criterion
for the space of Shintani functions to be finite-dimensional
in the Archimedean case.
This criterion leads us to a complete classification of the symmetric pairs
having finite-dimensional Shintani spaces.
A geometric criterion for uniform boundedness of is
also obtained.
Furthermore, we prove that symmetry breaking operators of the restriction of
smooth admissible representations yield Shintani functions of moderate growth,
of which the dimension is determined for .Comment: to appear in Progress in Mathematics, Birkhause
Spatio-Temporal Scaling of Solar Surface Flows
The Sun provides an excellent natural laboratory for nonlinear phenomena. We
use motions of magnetic bright points on the solar surface, at the smallest
scales yet observed, to study the small scale dynamics of the photospheric
plasma. The paths of the bright points are analyzed within a continuous time
random walk framework. Their spatial and temporal scaling suggest that the
observed motions are the walks of imperfectly correlated tracers on a turbulent
fluid flow in the lanes between granular convection cells.Comment: Now Accepted by Physical Review Letter
Fluctuations in superconducting rings with two order parameters
Starting from the Ginzburg-Landau energy functional, we discuss how the
presence of two order parameters and the coupling between them influence a
superconducting ring in the fluctuative regime. Our method is exact, but
requires numerical implementation. We also study approximations for which some
analytic expressions can be obtained, and check their ranges of validity. We
provide estimates for the temperature ranges where fluctuations are important,
calculate the persistent current in magnesium diboride rings as a function of
temperature and enclosed flux, and point out its additional dependence on the
cross-section area of the ring. We find temperature regions in which
fluctuations enhance the persistent currents and regions where they inhibit the
persistent current. The presence of two order parameters that can fluctuate
independently always leads to larger averages of the order parameters at Tc,
but only for appropriate parameters this yields larger persistent current. In
cases of very different material parameters for the two coupled condensates,
the persistent current is inhibited
Nonsingular Black Holes and Degrees of Freedom in Quantum Gravity
Spherically symmetric space-times provide many examples for interesting black
hole solutions, which classically are all singular. Following a general
program, space-like singularities in spherically symmetric quantum geometry, as
well as other inhomogeneous models, are shown to be absent. Moreover, one sees
how the classical reduction from infinitely many kinematical degrees of freedom
to only one physical one, the mass, can arise, where aspects of quantum
cosmology such as the problem of initial conditions play a role.Comment: 4 page
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