Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

Regge Calculus as a Fourth Order Method in Numerical Relativity

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show that these averages actually converge to zero as the fourth power of the lattice spacing.Comment: 14 pages, LaTeX, 8 figures mailed in separate file or email author directl

Discrete structures in gravity

Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalising these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalisations are explored for the original formulation of discrete gravity using edge-length variables.Comment: 30 pages, 4 figure

Prediction of posttraumatic stress disorder among adults in flood district

<p>Abstract</p> <p>Background</p> <p>Flood is one of the most common and severe forms of natural disasters. Posttraumatic stress disorder (PTSD) is a common disorder among victims of various disasters including flood. Early prediction for PTSD could benefit the prevention and treatment of PTSD. This study aimed to establish a prediction model for the occurrence of PTSD among adults in flood districts.</p> <p>Methods</p> <p>A cross-sectional survey was carried out in 2000 among individuals who were affected by the 1998 floods in Hunan, China. Multi-stage sampling was used to select subjects from the flood-affected areas. Data was collected through face-to-face interviews using a questionnaire. PTSD was diagnosed according to DSM-IV criteria. Study subjects were randomly divided into two groups: group 1 was used to establish the prediction model and group 2 was used to validate the model. We first used the logistic regression analysis to select predictive variables and then established a risk score predictive model. The validity of model was evaluated by using the model in group 2 and in all subjects. The area under the receiver operation characteristic (ROC) curve was calculated to evaluate the accuracy of the prediction model.</p> <p>Results</p> <p>A total of 2336 (9.2%) subjects were diagnosed as probable PTSD-positive individuals among a total of 25,478 study subjects. Seven independent predictive factors (age, gender, education, type of flood, severity of flood, flood experience, and the mental status before flood) were identified as key variables in a risk score model. The area under the ROC curve for the model was 0.853 in the validation data. The sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) of this risk score model were 84.0%, 72.2%, 23.4%, and 97.8%, respectively, at a cut-off value of 67.5 in the validation data.</p> <p>Conclusions</p> <p>A simple risk score model can be used to predict PTSD among victims of flood.</p

Area-angle variables for general relativity

We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.Comment: 7 pages, 1 figure. v2 small changes to match published versio

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

Model validation for a noninvasive arterial stenosis detection problem

Copyright @ 2013 American Institute of Mathematical SciencesA current thrust in medical research is the development of a non-invasive method for detection, localization, and characterization of an arterial stenosis (a blockage or partial blockage in an artery). A method has been proposed to detect shear waves in the chest cavity which have been generated by disturbances in the blood flow resulting from a stenosis. In order to develop this methodology further, we use both one-dimensional pressure and shear wave experimental data from novel acoustic phantoms to validate corresponding viscoelastic mathematical models, which were developed in a concept paper [8] and refined herein. We estimate model parameters which give a good fit (in a sense to be precisely defined) to the experimental data, and use asymptotic error theory to provide confidence intervals for parameter estimates. Finally, since a robust error model is necessary for accurate parameter estimates and confidence analysis, we include a comparison of absolute and relative models for measurement error.The National Institute of Allergy and Infectious Diseases, the Air Force Office of Scientific Research, the Deopartment of Education and the Engineering and Physical Sciences Research Council (EPSRC)

Marine plastics threaten giant Atlantic Marine Protected Areas.

There has been a recent shift in global perception of plastics in the environment, resulting in a call for greater action. Science and the popular media have highlighted plastic as an increasing stressor [1,2]. Efforts have been made to confer protected status to some remote locations, forming some of the world's largest Marine Protected Areas, including several UK overseas territories. We assessed plastic at these remote Atlantic Marine Protected Areas, surveying the shore, sea surface, water column and seabed, and found drastic changes from 2013-2018. Working from the RRS James Clark Ross at Ascension, St. Helena, Tristan da Cunha, Gough and the Falkland Islands (Figure 1A), we showed that marine debris on beaches has increased more than 10 fold in the past decade. Sea surface plastics have also increased, with in-water plastics occurring at densities of 0.1 items m-3; plastics on seabeds were observed at ≤ 0.01 items m-2. For the first time, beach densities of plastics at remote South Atlantic sites approached those at industrialised North Atlantic sites. This increase even occurs hundreds of meters down on seamounts. We also investigated plastic incidence in 2,243 animals (comprising 26 species) across remote South Atlantic oceanic food webs, ranging from plankton to seabirds. We found that plastics had been ingested by primary consumers (zooplankton) to top predators (seabirds) at high rates. These findings suggest that MPA status will not mitigate the threat of plastic proliferation to this rich, unique and threatened biodiversity

Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion