Collapse of Kaluza-Klein Bubbles

Kaluza-Klein theory admits ``bubble" configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of time-symmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) ``Witten bubble" solution. Some of these data have negative total energy. We show here that all the negative energy bubble solutions start out expanding away from the moment of time symmetry, while the positive energy bubbles can start out either expanding or contracting. Thus it is unlikely that the negative energy bubbles would collapse and produce a naked singularity.Comment: 6 pages, plain LaTeX, UMDGR-94-08

The isolation of gravitational instantons: Flat tori V flat R^4

The role of topology in the perturbative solution of the Euclidean Einstein equations about flat instantons is examined.Comment: 15 pages, ICN-UNAM 94-1

Fate of Kaluza-Klein Bubble

We numerically study classical time evolutions of Kaluza-Klein bubble space-time which has negative energy after a decay of vacuum. As the zero energy Witten's bubble space-time, where the bubble expands infinitely, the subsequent evolutions of Brill and Horowitz's momentarily static initial data show that the bubble will expand in terms of the area. At first glance, this result may support Corley and Jacobson's conjecture that the bubble will expand forever as well as the Witten's bubble. The irregular signatures, however, can be seen in the behavior of the lapse function in the maximal slicing gauge and the divergence of the Kretchman invariant. Since there is no appearance of the apparent horizon, we suspect an appearance of a naked singularity as the final fate of this space-time.Comment: 13 pages including 10 figures, RevTeX, epsf.sty. CGPG-99/12-8, RESCEU-6/00 and DAMTP-2000-30. To appear in Phys. Rev.

Black Holes and Wormholes in 2+1 Dimensions

A large variety of spacetimes---including the BTZ black holes---can be obtained by identifying points in 2+1 dimensional anti-de Sitter space by means of a discrete group of isometries. We consider all such spacetimes that can be obtained under a restriction to time symmetric initial data and one asymptotic region only. The resulting spacetimes are non-eternal black holes with collapsing wormhole topologies. Our approach is geometrical, and we discuss in detail: The allowed topologies, the shape of the event horizons, topological censorship and trapped curves.Comment: 23 pages, LaTeX, 11 figure

Asymptotic Behaviour of the Proper Length and Volume of the Schwarzschild Singularity

Though popular presentations give the Schwarzschild singularity as a point it is known that it is spacelike and not timelike. Thus it has a "length" and is not a "point". In fact, its length must necessarily be infinite. It has been proved that the proper length of the Qadir-Wheeler suture model goes to infinity [1], while its proper volume shrinks to zero, and the asymptotic behaviour of the length and volume have been calculated. That model consists of two Friedmann sections connected by a Schwarzschild "suture". The question arises whether a similar analysis could provide the asymptotic behaviour of the Schwarzschild black hole near the singularity. It is proved here that, unlike the behaviour for the suture model, for the Schwarzschild essential singularity $\Delta s$ $\thicksim$ $K^{1/3}\ln K$ and $V\thicksim$ $K^{-1}\ln K$, where $K$ is the mean extrinsic curvature, or the York time.Comment: 13 pages, 1 figur

Phenylketonuria in South Africa - A report on the status quo

During the 1980s a pilot newborn screening programme for the early detection (and treatment) of amino acidopathies, especially phenylketonuria (PKU), was conducted by the Department of National Health and Population Development. The motivation for this pilot programme was the high priority accorded PKU screening in Europe and North America and the presumed similarly high incidence of this condition among South Africans of European origin. From a cohort of 59 600 newborns screened in the Pretoria area over a period of 8 consecutive years (1979 - 1986), only 1 case of PKU (and 1 of tyrosinaemia) was found. Statistically this result is compatible (Poisson distribution, 95% confidence interval) with a 'true' incidence of not more than 3/59 600 (or about 1/20000) newborns. It is concluded from this result and other relevant information that newborn screening for PKU and other amino acidopathies is not cost-effective and justifiable, especially against the background of prevailing demographic conditions and more pressing health priorities in South Africa. This particular screening programme was discontinued in 1986. The results and conclusions are presented here. for the record

Vision therapy manuals for adults and children

This adult Vision Therapy pamphlet is written for patients, parents, and educators. This pamphlet is intended to enhance the public\u27s awareness and understanding of the various aspects of Vision Therapy. We have comprised an in-depth description of Vision Therapy, explained certain visual skills, discussed visual hygiene, and included information about Vision Therapy for children, adults,and athletes. This Children\u27s Red/Green activity book is designed to educate a child from ages three to ten about various techniques and aspects of Vision Therapy. It is a story about a little boy who goes through Vision Therapy successfully. It is to be printed in red and is designed to be a fun anti-suppression activity if used with red/green glasses and a green pen. It is filled with activities such a dot to dots, mazes, coloring, and find it pages

Viscoelastic response of sonic band-gap materials

A brief report is presented on the effect of viscoelastic losses in a high density contrast sonic band-gap material of close-packed rubber spheres in air. The scattering properties of such a material are computed with an on-shell multiple scattering method, properties which are compared with the lossless case. The existence of an appreciable omnidirectional gap in the transmission spectrum, when losses are present, is also reported.Comment: 5 pages, 4 figures, submitted to PR

Methods for generating alternative solutions to water resources planning problems

An optimization model is generally not a perfect representation of a complex water resources planning problem because not all important issues can be captured in a model. Optimization models can be used in a planning process to generate planning alternatives that are good and different so that the analyst and the decision maker can examine a wide range of alternatives t.0 gain insight and understanding. This approach is called modeling to generate alternatives (MGA). Several new MGA methods, a random method, a branch and bound/screening (BBS) method and a Fuzzy BSJ method, are described. This work also provides an assessment of the potential use of these methods as well as the HSJ method for generating good and different alternative solutions; the methods are illustrated using a wastewater treatment system planning problem, which is formulated as a mixed integer programming (MIP) model.U.S. Geological SurveyU.S. Department of the InteriorOpe