267 research outputs found
Formation of singularities for equivariant 2+1 dimensional wave maps into the two-sphere
In this paper we report on numerical studies of the Cauchy problem for
equivariant wave maps from 2+1 dimensional Minkowski spacetime into the
two-sphere. Our results provide strong evidence for the conjecture that large
energy initial data develop singularities in finite time and that singularity
formation has the universal form of adiabatic shrinking of the degree-one
harmonic map from into .Comment: 14 pages, 5 figures, final version to be published in Nonlinearit
Dispersion and collapse of wave maps
We study numerically the Cauchy problem for equivariant wave maps from 3+1
Minkowski spacetime into the 3-sphere. On the basis of numerical evidence
combined with stability analysis of self-similar solutions we formulate two
conjectures. The first conjecture states that singularities which are produced
in the evolution of sufficiently large initial data are approached in a
universal manner given by the profile of a stable self-similar solution. The
second conjecture states that the codimension-one stable manifold of a
self-similar solution with exactly one instability determines the threshold of
singularity formation for a large class of initial data. Our results can be
considered as a toy-model for some aspects of the critical behavior in
formation of black holes.Comment: 14 pages, Latex, 9 eps figures included, typos correcte
Black holes have no short hair
We show that in all theories in which black hole hair has been discovered,
the region with non-trivial structure of the non-linear matter fields must
extend beyond 3/2 the horizon radius, independently of all other parameters
present in the theory. We argue that this is a universal lower bound that
applies in every theory where hair is present. This {\it no short hair
conjecture} is then put forward as a more modest alternative to the original
{\it no hair conjecture}, the validity of which now seems doubtful.Comment: Published in Physical Review Letters, 13 pages in Late
Stratified horizontal flow in vertically vibrated granular layers
A layer of granular material on a vertically vibrating sawtooth-shaped base
exhibits horizontal flow whose speed and direction depend on the parameters
specifying the system in a complex manner. Discrete-particle simulations reveal
that the induced flow rate varies with height within the granular layer and
oppositely directed flows can occur at different levels. The behavior of the
overall flow is readily understood once this novel feature is taken into
account.Comment: 4 pages, 6 figures, submitte
Transport Coefficients for Granular Media from Molecular Dynamics Simulations
Under many conditions, macroscopic grains flow like a fluid; kinetic theory
pred icts continuum equations of motion for this granular fluid. In order to
test the theory, we perform event driven molecular simulations of a
two-dimensional gas of inelastic hard disks, driven by contact with a heat
bath. Even for strong dissipation, high densities, and small numbers of
particles, we find that continuum theory describes the system well. With a bath
that heats the gas homogeneously, strong velocity correlations produce a
slightly smaller energy loss due to inelastic collisions than that predicted by
kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients
are induced. Determination of the resulting fluxes allows calculation of the
thermal conductivity and shear viscosity, which are compared to the predictions
of granular kinetic theory, and which can be used in continuum modeling of
granular flows. The shear viscosity is close to the prediction of kinetic
theory, while the thermal conductivity can be overestimated by a factor of 2;
in each case, transport is lowered with increasing inelasticity.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199
Odd-parity perturbations of self-similar Vaidya spacetime
We carry out an analytic study of odd-parity perturbations of the
self-similar Vaidya space-times that admit a naked singularity. It is found
that an initially finite perturbation remains finite at the Cauchy horizon.
This holds not only for the gauge invariant metric and matter perturbation, but
also for all the gauge invariant perturbed Weyl curvature scalars, including
the gravitational radiation scalars. In each case, `finiteness' refers to
Sobolev norms of scalar quantities on naturally occurring spacelike
hypersurfaces, as well as pointwise values of these quantities.Comment: 28 page
Cosmology and Static Spherically Symmetric solutions in D-dimensional Scalar Tensor Theories: Some Novel Features
We consider scalar tensor theories in D-dimensional spacetime, D \ge 4. They
consist of metric and a non minimally coupled scalar field, with its non
minimal coupling characterised by a function. The probes couple minimally to
the metric only. We obtain vacuum solutions - both cosmological and static
spherically symmetric ones - and study their properties. We find that, as seen
by the probes, there is no singularity in the cosmological solutions for a
class of functions which obey certain constraints. It turns out that for the
same class of functions, there are static spherically symmetric solutions which
exhibit novel properties: {\em e.g.} near the ``horizon'', the gravitational
force as seen by the probe becomes repulsive.Comment: Revtex. 21 pages. Version 2: More references added. Version 3: Issues
raised by the referee are addressed. Results unchanged. Title modified; a new
subsection and more references added. Verison to appear in Physical Review
Continuum-type stability balloon in oscillated granular layers
The stability of convection rolls in a fluid heated from below is limited by
secondary instabilities, including the skew-varicose and crossroll
instabilities. We observe a stability boundary defined by the same
instabilities in stripe patterns in a vertically oscillated granular layer.
Molecular dynamics simulations show that the mechanism of the skew-varicose
instability in granular patterns is similar to that in convection. These
results suggest that pattern formation in granular media can be described by
continuum models analogous to those used in fluid systems.Comment: 4 pages, 6 ps figs, submitted to PR
Effect of boundary conditions on diffusion in two-dimensional granular gases
We analyze the influence of boundary conditions on numerical simulations of
the diffusive properties of a two dimensional granular gas. We show in
particular that periodic boundary conditions introduce unphysical correlations
in time which cause the coefficient of diffusion to be strongly dependent on
the system size. On the other hand, in large enough systems with hard walls at
the boundaries, diffusion is found to be independent of the system size. We
compare the results obtained in this case with Langevin theory for an elastic
gas. Good agreement is found. We then calculate the relaxation time and the
influence of the mass for a particle of radius in a sea of particles of
radius . As granular gases are dissipative, we also study the influence of
an external random force on the diffusion process in a forced dissipative
system. In particular, we analyze differences in the mean square velocity and
displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include
Einstein-Yang-Mills Isolated Horizons: Phase Space, Mechanics, Hair and Conjectures
The concept of "Isolated Horizon" has been recently used to provide a full
Hamiltonian treatment of black holes. It has been applied successfully to the
cases of {\it non-rotating}, {\it non-distorted} black holes in Einstein
Vacuum, Einstein-Maxwell and Einstein-Maxwell-Dilaton Theories. In this note,
it is investigated the extent to which the framework can be generalized to the
case of non-Abelian gauge theories where `hairy black holes' are known to
exist. It is found that this extension is indeed possible, despite the fact
that in general, there is no `canonical normalization' yielding a preferred
Horizon Mass. In particular the zeroth and first laws are established for all
normalizations. Colored static spherically symmetric black hole solutions to
the Einstein-Yang-Mills equations are considered from this perspective. A
canonical formula for the Horizon Mass of such black holes is found. This
analysis is used to obtain nontrivial relations between the masses of the
colored black holes and the regular solitonic solutions in Einstein-Yang-Mills
theory. A general testing bed for the instability of hairy black holes in
general non-linear theories is suggested. As an example, the embedded Abelian
magnetic solutions are considered. It is shown that, within this framework, the
total energy is also positive and thus, the solutions are potentially unstable.
Finally, it is discussed which elements would be needed to place the Isolated
Horizons framework for Einstein-Yang-Mills theory in the same footing as the
previously analyzed cases. Motivated by these considerations and using the fact
that the Isolated Horizons framework seems to be the appropriate language to
state uniqueness and completeness conjectures for the EYM equations --in terms
of the horizon charges--, two such conjectures are put forward.Comment: 24 pages, 3 figures, Revtex fil
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