Stress intensity factors in two bonded elastic layers containing cracks perpendicular to and on the interface. Part 1: Analysis

The basic crack problem which is essential for the study of subcritical crack propagation and fracture of layered structural materials is considered. Because of the apparent analytical difficulties, the problem is idealized as one of plane strain or plane stress. An additional simplifying assumption is made by restricting the formulation of the problem to crack geometries and loading conditions which have a plane of symmetry perpendicular to the interface. The general problem is formulated in terms of a coupled system of four integral equations. For each relevant crack configuration of practical interest, the singular behavior of the solution near and at the ends and points of intersection of the cracks is investigated and the related characteristic equations are obtained. The edge crack terminating at and crossing the interface, the T-shaped crack consisting of a broken layer and a delamination crack, the cross-shaped crack which consists of a delamination crack intersecting a crack which is perpendicular to the interface, and a delamination crack initiating from a stress-free boundary of the bonded layers are some of the practical crack geometries considered

Non-Abelian Black Holes in D=5 Maximal Gauged Supergravity

We investigate static non-abelian black hole solutions of anti-de Sitter Einstein-Yang-Mills-Dilaton gravity, which is obtained as a consistent truncation of five-dimensional maximal gauged supergravity. If the dilaton is (consistently) set to zero, the remaining equations of motion, with a spherically-symmetric ansatz, may be derived from a superpotential. The associated first-order equations admit an explicit solution supported by a non-abelian SU(2) gauge potential, which has a logarithmically growing mass term. In an extremal limit the horizon geometry becomes AdS$_2\times S^3$. If the dilaton is also excited, the equations of motion cannot easily be solved explicitly, but we obtain the asymptotic form of the more general non-abelian black holes in this case. An alternative consistent truncation, in which the Yang-Mills fields are set to zero, also admits a description in terms of a superpotential. This allows us to construct explicit wormhole solutions (neutral spherically-symmetric domain walls). These solutions may be generalised to dimensions other than five.Comment: Author's address, and a reference, adde

Domain Walls and Massive Gauged Supergravity Potentials

We point out that massive gauged supergravity potentials, for example those arising due to the massive breathing mode of sphere reductions in M-theory or string theory, allow for supersymmetric (static) domain wall solutions which are a hybrid of a Randall-Sundrum domain wall on one side, and a dilatonic domain wall with a run-away dilaton on the other side. On the anti-de Sitter (AdS) side, these walls have a repulsive gravity with an asymptotic region corresponding to the Cauchy horizon, while on the other side the runaway dilaton approaches the weak coupling regime and a non-singular attractive gravity, with the asymptotic region corresponding to the boundary of spacetime. We contrast these results with the situation for gauged supergravity potentials for massless scalar modes, whose supersymmetric AdS extrema are generically maxima, and there the asymptotic regime transverse to the wall corresponds to the boundary of the AdS spacetime. We also comment on the possibility that the massive breathing mode may, in the case of fundamental domain-wall sources, stabilize such walls via a Goldberger-Wise mechanism.Comment: latex file, 11 pages, 3 figure

Consistent Kaluza-Klein Sphere Reductions

We study the circumstances under which a Kaluza-Klein reduction on an n-sphere, with a massless truncation that includes all the Yang-Mills fields of SO(n+1), can be consistent at the full non-linear level. We take as the starting point a theory comprising a p-form field strength and (possibly) a dilaton, coupled to gravity in the higher dimension D. We show that aside from the previously-studied cases with (D,p)=(11,4) and (10,5) (associated with the S^4 and S^7 reductions of D=11 supergravity, and the S^5 reduction of type IIB supergravity), the only other possibilities that allow consistent reductions are for p=2, reduced on S^2, and for p=3, reduced on S^3 or S^{D-3}. We construct the fully non-linear Kaluza-Klein Ansatze in all these cases. In particular, we obtain D=3, N=8, SO(8) and D=7, N=2, SO(4) gauged supergravities from S^7 and S^3 reductions of N=1 supergravity in D=10.Comment: 27 pages, Latex, typo correcte

Entropy-Product Rules for Charged Rotating Black Holes

We study the universal nature of the product of the entropies of all horizons of charged rotating black holes. We argue, by examining further explicit examples, that when the maximum number of rotations and/or charges are turned on, the entropy product is expressed in terms of angular momentum and/or charges only, which are quantized. (In the case of gauged supergravities, the entropy product depends on the gauge-coupling constant also.) In two-derivative gravities, the notion of the "maximum number" of charges can be defined as being sufficiently many non-zero charges that the Reissner-Nordstrom black hole arises under an appropriate specialisation of the charges. (The definition can be relaxed somewhat in charged AdS black holes in $D\ge 6$.) In higher-derivative gravity, we use the charged rotating black hole in Weyl-Maxwell gravity as an example for which the entropy product is still quantized, but it is expressed in terms of the angular momentum only, with no dependence on the charge. This suggests that the notion of maximum charges in higher-derivative gravities requires further understanding.Comment: References added. 24 page

Decoupling Limit, Lens Spaces and Taub-NUT: D=4 Black Hole Microscopics from D=5 Black Holes

We study the space-times of non-extremal intersecting p-brane configurations in M-theory, where one of the components in the intersection is a ``NUT,'' i.e. a configuration of the Taub-NUT type. Such a Taub-NUT configuration corresponds, upon compactification to D=4, to a Gross-Perry-Sorkin (GPS) monopole. We show that in the decoupling limit of the CFT/AdS correspondence, the 4-dimensional transverse space of the NUT configuration in D=5 is foliated by surfaces that are cyclic lens spaces S^3/Z_N, where N is the quantised monopole charge. By contrast, in D=4 the 3-dimensional transverse space of the GPS monopole is foliated by 2-spheres. This observation provides a straightforward interpretation of the microscopics of a D=4 string-theory black hole, with a GPS monopole as one of its constituents, in terms of the corresponding D=5 black hole with no monopole. Using the fact that the near-horizon region of the NUT solution is a lens space, we show that if the effect of the Kaluza-Klein massive modes is neglected, p-brane configurations can be obtained from flat space-time by means of a sequence of dimensional reductions and oxidations, and U-duality transformations.Comment: 22 pages, Late

An MDL approach to the climate segmentation problem

This paper proposes an information theory approach to estimate the number of changepoints and their locations in a climatic time series. A model is introduced that has an unknown number of changepoints and allows for series autocorrelations, periodic dynamics, and a mean shift at each changepoint time. An objective function gauging the number of changepoints and their locations, based on a minimum description length (MDL) information criterion, is derived. A genetic algorithm is then developed to optimize the objective function. The methods are applied in the analysis of a century of monthly temperatures from Tuscaloosa, Alabama.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS289 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org