Soliton Solutions to the Einstein Equations in Five Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson--(anti)-de Sitter ((A)dS) metrics, with the added feature of having Lorentzian signatures. They provide an affirmative answer to the open question as to whether or not there exist solutions with negative cosmological constant that asymptotically approach AdS$_{5}/\Gamma$, but have less energy than AdS$_{5}/\Gamma$. We present evidence that these solutions are the lowest-energy states within their asymptotic class.Comment: 9 pages, Latex; Final version that appeared in Phys. Rev. Lett; title changed by journal from original title "Eguchi-Hanson Solitons

Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

Locally extracting scalar, vector and tensor modes in cosmological perturbation theory

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedom. A similar local differential operation will return a pure vector mode. This means that scalar and vector degrees of freedom have local descriptions. The corresponding local extraction of the tensor mode is unknown however. We give it here. The operators we define are useful for defining gauge-invariant quantities at second-order. We perform much of our analysis using an index-free `vector-calculus' approach which makes manipulating tensor equations considerably simpler.Comment: 13 pages. Final version to appear in CQ

M-Branes on k-center Instantons

We present analytic solutions for membrane metric function based on transverse $k$-center instanton geometries. The membrane metric functions depend on more than two transverse coordinates and the solutions provide realizations of fully localized type IIA D2/D6 and NS5/D6 brane intersections. All solutions have partial preserved supersymmetries.Comment: 22 pages, 5 figure

A generalized linear Hubble law for an inhomogeneous barotropic Universe

In this work, I present a generalized linear Hubble law for a barotropic spherically symmetric inhomogeneous spacetime, which is in principle compatible with the acceleration of the cosmic expansion obtained as a result of high redshift Supernovae data. The new Hubble function, defined by this law, has two additional terms besides an expansion one, similar to the usual volume expansion one of the FLRW models, but now due to an angular expansion. The first additional term is dipolar and is a consequence of the existence of a kinematic acceleration of the observer, generated by a negative gradient of pressure or of mass-energy density. The second one is quadrupolar and due to the shear. Both additional terms are anisotropic for off-centre observers, because of to their dependence on a telescopic angle of observation. This generalized linear Hubble law could explain, in a cosmological setting, the observed large scale flow of matter, without to have recourse to peculiar velocity-type newtonian models. It is pointed out also, that the matter dipole direction should coincide with the CBR dipole one.Comment: 9 pages, LaTeX, to be published in Class. Quantum Gra

Modification of cell wall properties in lettuce improves shelf life

It is proposed that post-harvest longevity and appearance of salad crops is closely linked to pre-harvest leaf morphology (cell and leaf size) and biophysical structure (leaf strength). Transgenic lettuce plants (Lactuca sativa cv. Valeria) were produced in which the production of the cell wall-modifying enzyme xyloglucan endotransglucosylase/hydrolase (XTH) was down-regulated by antisense inhibition. Independently transformed lines were shown to have multiple members of the LsXTH gene family down-regulated in mature leaves of 6-week-old plants and during the course of shelf life. Consequently, xyloglucan endotransglucosylase (XET) enzyme activity and action were down-regulated in the cell walls of these leaves and it was established that leaf area and fresh weight were decreased while leaf strength was increased in the transgenic lines. Membrane permeability was reduced towards the end of shelf life in the transgenic lines relative to the controls and bacteria were evident inside the leaves of control plants only. Most importantly, an extended shelf-life of transgenic lines was observed relative to the non-transgenic control plants. These data illustrate the potential for engineering cell wall traits for improving quality and longevity of salad crops using either genetic modification directly, or by using markers associated with XTH genes to inform a commercial breeding programme

Combined Reconstruction and Registration of Digital Breast Tomosynthesis

Digital breast tomosynthesis (DBT) has the potential to en- hance breast cancer detection by reducing the confounding e ect of su- perimposed tissue associated with conventional mammography. In addi- tion the increased volumetric information should enable temporal datasets to be more accurately compared, a task that radiologists routinely apply to conventional mammograms to detect the changes associated with ma- lignancy. In this paper we address the problem of comparing DBT data by combining reconstruction of a pair of temporal volumes with their reg- istration. Using a simple test object, and DBT simulations from in vivo breast compressions imaged using MRI, we demonstrate that this com- bined reconstruction and registration approach produces improvements in both the reconstructed volumes and the estimated transformation pa- rameters when compared to performing the tasks sequentially

The application of reliability methods in the design of stiffened FRP composite panels for marine vessels

The use of composite laminate materials has increased rapidly in recent years due to their excellent strength to weight ratio and resistance to corrosion. In the construction of marine vessels, stiffened plates are the most commonly used structural elements, forming the deck, bottom hull, side shells and bulkheads. This paper presents the use of a stochastic approach to the design of stiffened marine composite panels as part of a current research programme into developing stochastic methods for composite ship structures, accounting for variations in material properties, geometric indices and processing techniques, from the component level to the full system level. An analytical model for the solution of a stiffened isotropic plate using a grillage analogy is extended by the use of equivalent elastic properties for composite modelling. This methodology is applied in a reliability analysis of an isotropic (steel) stiffened plate before the final application for a reliability analysis for a FRP composite stiffened plate

Eguchi-Hanson Solitons in Odd Dimensions

We present a new class of solutions in odd dimensions to Einstein's equations containing either a positive or negative cosmological constant. These solutions resemble the even-dimensional Eguchi-Hanson-(A)dS metrics, with the added feature of having Lorentzian signatures. They are asymptotic to (A)dS$_{d+1}/Z_p$. In the AdS case their energy is negative relative to that of pure AdS. We present perturbative evidence in 5 dimensions that such metrics are the states of lowest energy in their asymptotic class, and present a conjecture that this is generally true for all such metrics. In the dS case these solutions have a cosmological horizon. We show that their mass at future infinity is less than that of pure dS.Comment: 26 pages, Late