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

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

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

A longitudinal investigation of maternal and child 'anxious cognitions'

Overestimation of threat and underestimation of coping have been frequently reported amongst anxious adults and children. The current study examines the longitudinal relationship between mothers' anxious cognitions and expectations about their child, and children's anxious cognitions. 54 children (aged 10-11 years) and their mothers reported on their interpretation of ambiguous scenarios at two time points. Mothers also reported on their expectations about their child's reaction to ambiguous situations. Significant cross-sectional associations were found between mother and child anticipation of distress. Associations were most consistent between mothers' expectations and children's cognitions. Furthermore, based on regression analyses, mothers' expectations predicted change in children's anxious cognitions over time. Evidence for a reciprocal relationship, that child cognitions predict change in mothers' expectations, was found for girls. The results provide empirical support for potential influences on the development of children's 'anxious cognitive style,' and suggest targets for preventing and reducing maladaptive cognitions in children

General Transformation Formulas for Fermi-Walker Coordinates

We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.Comment: 23 pages. Corrected typos in the last two equations. Accepted for publication in Classical and Quantum Gravit

Regge calculus and Ashtekar variables

Spacetime discretized in simplexes, as proposed in the pioneer work of Regge, is described in terms of selfdual variables. In particular, we elucidate the "kinematic" structure of the initial value problem, in which 3--space is divided into flat tetrahedra, paying particular attention to the role played by the reality condition for the Ashtekar variables. An attempt is made to write down the vector and scalar constraints of the theory in a simple and potentially useful way.Comment: 10 pages, uses harvmac. DFUPG 83/9

A Smooth Lattice construction of the Oppenheimer-Snyder spacetime

We present test results for the smooth lattice method using an Oppenheimer-Snyder spacetime. The results are in excellent agreement with theory and numerical results from other authors.Comment: 60 pages, 28 figure

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2013 Walter de Gruyter GmbH.Non-invasive detection, localization and characterization of an arterial stenosis (a blockage or partial blockage in the artery) continues to be an important problem in medicine. Partial blockage stenoses are known to generate disturbances in blood flow which generate shear waves in the chest cavity. We examine a one-dimensional viscoelastic model that incorporates Kelvin–Voigt damping and internal variables, and develop a proof-of-concept methodology using simulated data. We first develop an estimation procedure for the material parameters. We use this procedure to determine confidence intervals for the estimated parameters, which indicates the efficacy of finding parameter estimates in practice. Confidence intervals are computed using asymptotic error theory as well as bootstrapping. We then develop a model comparison test to be used in determining if a particular data set came from a low input amplitude or a high input amplitude; this we anticipate will aid in determining when stenosis is present. These two thrusts together will serve as the methodological basis for our continuing analysis using experimental data currently being collected.National Institute of Allergy and Infectious Diseases, Air Force Office of Scientific Research, Department of Education, and Engineering and Physical Sciences Research Council

The development of an assessment of freedom for people living with dementia

Within the UK over 850,000 people live with dementia, 650,000 remain in their homes with the support of 600,000 carers. A problem faced by community dwelling PLWD is that of becoming lost when leaving their home. Carers may restrict the freedom of PLWD due to concerns about their safety. Leaving the home unsafely is a significant risk for PLWD with up to a third of people living with the condition becoming lost at some point. This is a frightening and distressing experience which may lead to injury and anxiety. However, when involved in research people living with dementia have identified the benefits of being involved with their local community and environment. For those whose condition is more advanced being able to walk may be calming and reduce agitation and distress. The issue of freedom for people living with the dementia is then a difficult balance between the benefits of risk and safety. This research developed an assessment of freedom for people living with dementia and a theoretical model of freedom. The acronym FREEDEM was used for the assessment. Methods This PhD used an exploratory sequential mixed methods approach to develop FREEDEM. A theoretical model of freedom was initially developed from philosophy. A scoping review collated relevant literature to identify the elements of this assessment. Thirty semi structured interviews were carried out with people living with dementia, carers, and occupational therapists. In these interviews the definition of freedom was explored and how this changed as the condition progressed. This data was used to refine the theoretical model of freedom. Results from the interviews and scoping review were synthesised using triangulation to inform the development of FREEDEM. The assessment components were then subjected to a Delphi study. Results from the Delphi study were used to finalise FREEDEM. Patient and public involvement was integrated into the research process, including study documentation and topic guide design. Results This assessment includes the assessment of risk, early warning systems, carer education, social groups, and telecare technology. The theoretical model identified that elements of the definition of freedom from PLWD included freedom of movement, social integration, choice of activities and relational autonomy. People living with dementia demonstrated an ethic of care towards their carers and the wider community at a point when they had capacity, and insight into the implications of their condition. This was manifested as a concern for both their carers and the wider community if they became lost. This ethic of care changed as the condition progressed. This then led to a situation where freedom may be sought, and carer’s freedom may be compromised as a result. Carers considered their freedom was defended or conceded depending upon their prior relationship with the PLWD and other demands upon their time. Conclusion In the event the freedom of the person living with dementia is restricted they are potentially deprived of their liberty. A legal authorisation may be required for the carer’s actions. Rather than this formal authorisation the assessment aims to facilitate freedom for people living with dementia thereby avoiding the needs for a judicial process. Instead, the person living with condition will be assessed by an occupational therapist who will carry out an assessment that facilitates their freedom and provides support to their carers in facilitating this freedom