455 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
Thermal-fatigue and oxidation resistance of cobalt-modified Udimet 700 alloy
Comparative thermal-fatigue and oxidation resistances of cobalt-modified wrought Udimet 700 alloy (obtained by reducing the cobalt level by direct substitution of nickel) were determined from fluidized-bed tests. Bed temperatures were 1010 and 288 C (1850 and 550 C) for the first 5500 symmetrical 6-min cycles. From cycle 5501 to the 14000-cycle limit of testing, the heating bed temperature was increased to 1050 C (1922 F). Cobalt levels between 0 and 17 wt% were studied in both the bare and NiCrAlY overlay coated conditions. A cobalt level of about 8 wt% gave the best thermal-fatigue life. The conventional alloy specification is for 18.5% cobalt, and hence, a factor of 2 in savings of cobalt could be achieved by using the modified alloy. After 13500 cycles, all bare cobalt-modified alloys lost 10 to 13 percent of their initial weight. Application of the NiCrAlY overlay coating resulted in weight losses of 1/20 to 1/100 of that of the corresponding bare alloy
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
Three-dimensional finite-element elastic analysis of a thermally cycled single-edge wedge geometry specimen
An elastic stress analysis was performed on a wedge specimen (prismatic bar with single-wedge cross section) subjected to thermal cycles in fluidized beds. Seven different combinations consisting of three alloys (NASA TAZ-8A, 316 stainless steel, and A-286) and four thermal cycling conditions were analyzed. The analyses were performed as a joint effort of two laboratories using different models and computer programs (NASTRAN and ISO3DQ). Stress, strain, and temperature results are presented
Renormalization and blow up for charge one equivariant critical wave maps
We prove the existence of equivariant finite time blow up solutions for the
wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the
sum of a dynamically rescaled ground-state harmonic map plus a radiation term.
The local energy of the latter tends to zero as time approaches blow up time.
This is accomplished by first "renormalizing" the rescaled ground state
harmonic map profile by solving an elliptic equation, followed by a
perturbative analysis
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
Hairy Black Holes, Horizon Mass and Solitons
Properties of the horizon mass of hairy black holes are discussed with
emphasis on certain subtle and initially unexpected features. A key property
suggests that hairy black holes may be regarded as `bound states' of ordinary
black holes without hair and colored solitons. This model is then used to
predict the qualitative behavior of the horizon properties of hairy black
holes, to provide a physical `explanation' of their instability and to put
qualitative constraints on the end point configurations that result from this
instability. The available numerical calculations support these predictions.
Furthermore, the physical arguments are robust and should be applicable also in
more complicated situations where detailed numerical work is yet to be carried
out.Comment: 25 pages, 5 (new) figures. Revtex file. Final version to appear in
CQ
Dirty blackholes: Thermodynamics and horizon structure
Considerable interest has recently been expressed in (static spherically
symmetric) blackholes in interaction with various classical matter fields (such
as electromagnetic fields, dilaton fields, axion fields, Abelian Higgs fields,
non--Abelian gauge fields, {\sl etc}). A common feature of these investigations
that has not previously been remarked upon is that the Hawking temperature of
such systems appears to be suppressed relative to that of a vacuum blackhole of
equal horizon area. That is: . This paper will argue that this suppression is generic.
Specifically, it will be shown that
Here is an integral quantity, depending on the distribution of
matter, that is guaranteed to be positive if the Weak Energy Condition is
satisfied. Several examples of this behaviour will be discussed.
Generalizations of this behaviour to non--symmetric non--static blackholes are
conjectured.Comment: [minor revisions] 22 pages, RevTe
On the stability of soliton and hairy black hole solutions of SU(N) Einstein-Yang-Mills theory with a negative cosmological constant
We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional su(N) Einstein-Yang-Mills theory with a
negative cosmological constant Λ. These solutions are described by N − 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N − 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded su(2) solutions, provided the magnitude of the cosmological constant |Λ| is sufficiently large.
Kewywords : Stability, hairy black hole, soliton, Einstein-Yang-Mills, anti de-Sitte
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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