454 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
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
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
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
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
Structure of solutions of the Skyrme model on three-sphere. Numerical results
The hedgehog Skyrme model on three-sphere admits very rich spectrum of
solitonic solutions which can be encompassed by a strikingly simple scheme. The
main result of this paper is the statement of the tripartite structure of
solutions of the model and the discovery in what configurations these solutions
appear. The model contains features of more complicated models in General
Relativity and as such can give insight into them.Comment: 20 pages, 13 figures in, with emai
Saddle point solutions in Yang-Mills-dilaton theory
The coupling of a dilaton to the -Yang-Mills field leads to
interesting non-perturbative static spherically symmetric solutions which are
studied by mixed analitical and numerical methods. In the abelian sector of the
theory there are finite-energy magnetic and electric monopole solutions which
saturate the Bogomol'nyi bound. In the nonabelian sector there exist a
countable family of globally regular solutions which are purely magnetic but
have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is
bounded from above by the energy of the abelian magnetic monopole with unit
magnetic charge. The stability analysis demonstrates that the solutions are
saddle points of the energy functional with increasing number of unstable
modes. The existence and instability of these solutions are "explained" by the
Morse-theory argument recently proposed by Sudarsky and Wald.Comment: 11 page
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