Black Hole in a Model with Dilaton and Monopole Fields

We present an exact black hole solution in a model having besides gravity a dilaton and a monopole field. The solution has three free parameters, one of which can be identified with the monopole charge, and another with the ADM mass. The metric is asymptotically flat and has two horizons and irremovable singularity only at $r=0$. The dilaton field is singular only at $r=0$. The dominant and the strong energy condition are satisfied outside and on the external horizon. According to a formulation of the no hair conjecture the solution is "hairy". Also the well know GHS-GM solution is obtained from our solution for certain values of its parameters.Comment: Selected for Honorable Mention in the Gravity Research Foundation Essay Competition, 2006, 7 page

Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations

We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent if a special ansatz for the dilaton field is used. This choice corresponds to transition to a frame rotated in the $\ln r-t$ plane at a definite angle. We find an infinite countable family of self-similar solutions which can be parametrized by the $N$ - the number of zeros of the relevant Yang-Mills function. According to the performed linear perturbation analysis, the lowest solution with N=0 only occurred to be stable. The Cauchy problem has been solved numerically for a wide range of smooth finite energy initial data. It has been found that if the initial data exceed some threshold, the resulting solutions in a compact region shrinking to the origin, attain the lowest N=0 stable self-similar profile, which can pretend to be a global stable attractor in the Cauchy problem. The solutions live a finite time in a self-similar regime and then the unbounded growth of the second derivative of the YM function at the origin indicates a singularity formation, which is in agreement with the general expectations for the supercritical systems.Comment: 10 pages, 5 figure

New Critical Behavior in Einstein-Yang-Mills Collapse

We extend the investigation of the gravitational collapse of a spherically symmetric Yang-Mills field in Einstein gravity and show that, within the black hole regime, a new kind of critical behavior arises which separates black holes formed via Type I collapse from black holes formed through Type II collapse. Further, we provide evidence that these new attracting critical solutions are in fact the previously discovered colored black holes with a single unstable mode.Comment: 13 pages, 4 figure

Trapped surfaces in spherical expanding open universes

Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic curvature is a constant and that the matter field is at rest at this instant of time. One expects that no trapped surfaces appear in the data if no significant clump of excess matter is to be found. This letter confirms this belief by displaying a necessary condition for the existence of trapped surfaces.This necessary condition, simply stated, says that a relatively large amount of excess matter must be concentrated in a small volume for trapped surfaces to appear.Comment: 8 pages, Late

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

Experimental determination of transient strain in a thermally-cycled simulated turbine blade utilizing a non-contact technique

A type of noncontacting electro-optical extensometer was used to measure the displacement between parallel targets mounted on the leading edge of a simulated turbine blade throughout a complete heating and cooling cycle. The blade was cyclically heated and cooled by moving it into and out of a Mach 1 hot gas stream. The principle of operation and measurement procedure of the electro-optics extensometer are described

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

Comparative thermal fatigue resistances of twenty-six nickel and cobalt base alloys

Thermal fatigue resistances were determined from fluidized bed tests. Cycles to cracking differed by almost three orders of magnitude for these materials with directional solidification and surface protection of definite benefit. The alloy-coating combination with the highest thermal fatigue resistance was directionally solidified NASA TAZ-8A with an RT-XP coating. It oxidation resistance was excellent, showing almost no weight change after 15 000 fluidized bed cycles

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 $\mathbb{R}^2$ into $S^2$.Comment: 14 pages, 5 figures, final version to be published in Nonlinearit

Thermal fatigue resistance of NASA WAZ-20 alloy with three commercial coatings

Screening tests using three commercial coatings (Jocoat, HI-15, and RT-1A) on the nickel-base alloy NASA WAZ-20 were performed by cyclic exposure in a Mach 1 burner facility. These tests showed Jocoated WAZ-20 to have the best cracking resistance. The thermal fatigue resistance of Jocoated WAZ-20 in both the random polycrystalline and directionally solidified polycrystalline forms relative to that of other superalloys was then evaluated in a fluidized-bed facility. This investigation showed that Jocoated random polycrystalline WAZ-20 ranked approximately in midrange in thermal fatigue life. The thermal fatigue life of directionally solidified Jocoated WAZ-20 was shorter than that of other directionally solidified alloys but still longer than that of all alloys in the random polycrystalline form