An Einstein-Bianchi system for Smooth Lattice General Relativity. II. 3+1 vacuum spacetimes

We will present a complete set of equations, in the form of an Einstein-Bianchi system, that describe the evolution of generic smooth lattices in spacetime. All 20 independent Riemann curvatures will be evolved in parallel with the leg-lengths of the lattice. We will show that the evolution equations for the curvatures forms a hyperbolic system and that the associated constraints are preserved. This work is a generalisation of our previous paper arXiv:1101.3171 on the Einstein-Bianchi system for the Schwarzschild spacetime to general 3+1 vacuum spacetimes

An Einstein-Bianchi system for Smooth Lattice General Relativity. I. The Schwarzschild spacetime

The second Bianchi identity can be recast as an evolution equation for the Riemann curvatures. Here we will report on such a system for a vacuum static spherically symmetric spacetime. This is the first of two papers. In the following paper we will extend the ideas developed here to general vacuum spacetimes. In this paper we will demonstrate our ideas on a Schwarzschild spacetime and give detailed numerical results. For suitable choices of lapse function we find that the system gives excellent results with long term stability.Comment: minor changes to conform with companion paper, new appendi

An ADM 3+1 formulation for Smooth Lattice General Relativity

A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve three basic steps. First, the coordinate quantities such as the Riemann and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM equations are used to evolve the coordinate data, and finally, the coordinate data is used to update the scalar data on the lattice (such as the leg lengths). The scheme will be presented only for the case of vacuum spacetime though there is no reason why it could not be extended to non-vacuum spacetimes. The scheme allows any choice for the lapse function and shift vectors. An example for the Kasner $T^3$ cosmology will be presented and it will be shown that the method has, for this simple example, zero discretisation error.Comment: 18 pages, plain TeX, 5 epsf figues, gzipped ps file also available at http://newton.maths.monash.edu.au:8000/preprints/3+1-slgr.ps.g

Genomic landscapes and clonality of de novo AML

No abstract available

The need for psychiatric treatment in the general population: the Camberwell Needs for Care Survey

Background, This paper presents the first results of a two-stage psychiatric population survey, which uses a new method of directly evaluating needs for specific psychiatric treatment and the extent to which they have been met.Method, The sample was drawn at random from the population of an area of inner south London with high levels of deprivation. Seven hundred and sixty subjects aged 18-65 completed the GHQ-28. All those scoring > 5 and half of the rest were invited to take part in the second stage, comprising measures of mental state (SCAN), social role performance (SRPS), life events and difficulties (LEDS) and a Treatment Inventory. This information was used to rate the community version of the Needs for Care Assessment (NFCAS-C).Results, In all, 408 subjects were interviewed in the second stage. The weighted 1 month prevalence of hierarchically ordered ICD-10 psychiatric disorders was 9.8 %, the 1 year prevalence 12.3 %. The equivalent prevalences for depressive episode were 3.1 % and 5.3 % respectively, while those for anxiety states were both 2.8 %. At interview nearly 10% of the population were identified as having a need for the treatment of a psychiatric condition. This rose to 10.4 % if the whole of the preceding year was assessed. Less than half of all potentially meetable needs were met. There was only partial overlap between diagnosis and an adjudged need for treatment.Conclusion. A majority of people with mental health problems do not have proper treatment; given more resources and greater public and medical awareness, most could be treated by family doctors

Is the Regge Calculus a consistent approximation to General Relativity?

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.Comment: 27 pages, plain TeX, very belated update to match journal articl