The Positivity of Energy for Asymptotically Anti-de Sitter Spacetimes

We use the formulation of asymptotically anti-de Sitter boundary conditions given by Ashtekar and Magnon to obtain a coordinate expression for the general asymptotically AdeS metric in a neighbourhood of infinity. From this, we are able to compute the time delay of null curves propagating near infinity. If the gravitational mass is negative, so will be the time delay (relative to null geodesics at infinity) for certain null geodesics in the spacetime. Following closely an argument given by Penrose, Sorkin, and Woolgar, who treated the asymptotically flat case, we are then able to argue that a negative time delay is inconsistent with non-negative matter-energies in spacetimes having good causal properties. We thereby obtain a new positive mass theorem for these spacetimes. The theorem may be applied even when the matter flux near the boundary-at-infinity falls off so slowly that the mass changes, provided the theorem is applied in a time-averaged sense. The theorem also applies in certain spacetimes having local matter-energy that is sometimes negative, as can be the case in semi-classical gravity.Comment: (Plain TeX - figures not included

Topology and Signature Changes in Braneworlds

It has been believed that topology and signature change of the universe can only happen accompanied by singularities, in classical, or instantons, in quantum, gravity. In this note, we point out however that in the braneworld context, such an event can be understood as a classical, smooth event. We supply some explicit examples of such cases, starting from the Dirac-Born-Infeld action. Topology change of the brane universe can be realised by allowing self-intersecting branes. Signature change in a braneworld is made possible in an everywhere Lorentzian bulk spacetime. In our examples, the boundary of the signature change is a curvature singularity from the brane point of view, but nevertheless that event can be described in a completely smooth manner from the bulk point of view.Comment: 26 pages, 8 figures, references and comments are added, minor revisions and a number of additional footnotes added, error corrected, minor corrections, to appear in Class. Quant. Gra

The falling chain of Hopkins, Tait, Steele and Cayley

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higher-dimensional versions of it. A home camcorder is used to measure the fall of a three-dimensional version called an $xyz$-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.Comment: 17 pages, 5 figure

Flow in Open Channel with Complex Solid Boundary

yesA two-dimensional steady potential flow theory is applied to calculate the flow in an open channel with complex solid boundaries. The boundary integral equations for the problem under investigation are first derived in an auxiliary plane by taking the Cauchy integral principal values. To overcome the difficulties of a nonlinear curvilinear solid boundary character and free water surface not being known a priori, the boundary integral equations are transformed to the physical plane by substituting the integral variables. As such, the proposed approach has the following advantages: (1) the angle of the curvilinear solid boundary as well as the location of free water surface (initially assumed) is a known function of coordinates in physical plane; and (2) the meshes can be flexibly assigned on the solid and free water surface boundaries along which the integration is performed. This avoids the difficulty of the traditional potential flow theory, which seeks a function to conformally map the geometry in physical plane onto an auxiliary plane. Furthermore, rough bed friction-induced energy loss is estimated using the Darcy-Weisbach equation and is solved together with the boundary integral equations using the proposed iterative method. The method has no stringent requirement for initial free-water surface position, while traditional potential flow methods usually have strict requirement for the initial free-surface profiles to ensure that the numerical computation is stable and convergent. Several typical open-channel flows have been calculated with high accuracy and limited computational time, indicating that the proposed method has general suitability for open-channel flows with complex geometry

Interplay between topography, fog and vegetation in the central South Arabian mountains revealed using a novel Landsat fog detection technique

In the central South Arabian mountains of Yemen and Oman, monsoon fog interception by the endemic cloud forest is essential for ecosystem functions and services. Yet, we know little about the local factors affecting fog distributions and their cumulative effects on vegetation. To examine these relationships, we developed a novel method of high-resolution fog detection using Landsat data, and validated the results using occurrence records of eight moisture-sensitive plant species. Regression tree analysis was then used to examine the topographic factors influencing fog distributions and the topoclimatic factors influencing satellite-derived vegetation greenness. We find that topography affects fog distributions. Specifically, steep windward slopes obstruct the inland movement of fog, resulting in heterogenous fog densities and hotspots of fog interception. We find that fog distributions explain patterns of vegetation greenness, and overall, that greenness increases with fog density. The layer of fog density describes patterns of vegetation greenness more accurately than topographic variables alone, and thus, we propose that regional vegetation patterns more closely follow a fog gradient, than an altitudinal gradient as previously supposed. The layer of fog density will enable an improved understanding of how species and communities, many of which are endemic, range-restricted, and in decline, respond to local variability in topoclimatic conditions

Global economic burden of unmet surgical need for appendicitis

Background: There is a substantial gap in provision of adequate surgical care in many low-and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods: Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results: Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion: For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially

A taxonomic backbone for the global synthesis of species diversity in the angiosperm order Caryophyllales

The Caryophyllales constitute a major lineage of flowering plants with approximately 12500 species in 39 families. A taxonomic backbone at the genus level is provided that reflects the current state of knowledge and accepts 749 genera for the order. A detailed review of the literature of the past two decades shows that enormous progress has been made in understanding overall phylogenetic relationships in Caryophyllales. The process of re-circumscribing families in order to be monophyletic appears to be largely complete and has led to the recognition of eight new families (Anacampserotaceae, Kewaceae, Limeaceae, Lophiocarpaceae, Macarthuriaceae, Microteaceae, Montiaceae and Talinaceae), while the phylogenetic evaluation of generic concepts is still well underway. As a result of this, the number of genera has increased by more than ten percent in comparison to the last complete treatments in the Families and genera of vascular plants” series. A checklist with all currently accepted genus names in Caryophyllales, as well as nomenclatural references, type names and synonymy is presented. Notes indicate how extensively the respective genera have been studied in a phylogenetic context. The most diverse families at the generic level are Cactaceae and Aizoaceae, but 28 families comprise only one to six genera. This synopsis represents a first step towards the aim of creating a global synthesis of the species diversity in the angiosperm order Caryophyllales integrating the work of numerous specialists around the world