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

The Role of Intrusive Imagery in Hoarding Disorder

Despite the incidence of trauma in the histories of people with Hoarding Disorder (HD), reexperiencing symptoms, namely intrusive images, have not been investigated in the condition. To address this, 27 individuals who met DSM-5 criteria for HD and 28 community controls (CCs) were interviewed about (a) their everyday experiences of intrusive imagery, and (b) the unexpected images they experience when discarding high- and low-value possessions. Compared to CCs, everyday images described by the HD group were more frequent, had a greater negative valence, and were associated with greater interference in everyday life and attempts to avoid the imagery. With regard to discard-related imagery, a MANOVA followed up with mixed ANOVAs showed that HD participants reported more negative experiences of intrusive imagery in comparison with CCs during recent episodes of discarding objects of low subjective value. However, HD and CC participants both experienced positive imagery when discarding high-value objects. CC participants reported greater avoidance of imagery in the high-value object condition, but imagery-avoidance did not change between conditions for HD participants. The findings are discussed, particularly in relation to the potential of imagery-based interventions for HD

Slice Stretching Effects for Maximal Slicing of a Schwarzschild Black Hole

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.Comment: 16 pages, 4 figures, revised version including a study on how slice stretching can be avoided by using excision and/or shift

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 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

Twenty‐year variations in satellite‐derived chlorophyll‐a and phytoplankton size in the Bohai Sea and Yellow Sea

This is the final version. Available from American Geophysical Union (AGU) via the DOI in this record. Phytoplankton cell size is a useful ecological indicator for evaluating the response of phytoplankton community structure to environmental changes. Ocean‐color remote observations and algorithms have allowed us to estimate phytoplankton size classes (PSCs) at decadal scale, helping us to understand their trends under ocean warming. Here a large data set of pigments, derived through high performance liquid chromatography, was collected in the Bohai Sea (BS) and Yellow Sea (YS) between 2014 and 2016. The data set was used to reparametrize the sea surface temperature (SST)‐dependent three‐component model of Brewin et al. (2017) to the region. The model was validated using independent in situ data set and subsequently applied to satellite chlorophyll‐a data from Ocean Colour Climate Change Initiative, spanning from 1997 to 2016, to derive percentages of three PSCs to total chlorophyll‐a. Monthly‐averaged PSCs exhibited spatial‐temporal variations in the study area, linked to topography, temperature, solar radiation, currents, and monsoonal winds. In the surface central south Yellow Sea (SYS), influenced by bottom Yellow Sea Cold Water Mass, tight relationships between PSCs and environmental factors were observed, where high SST, high sea level anomaly, low mixed‐layer depth, and low wind speed resulted in higher proportions of nanoplankton and picoplankton from June to October. Significant interannual anomlies in PSCs were found associated with El Niño events in the central SYS, related to anomalies in SST. The refined model characterized 20‐year variations in chlorophyll‐a concentration and PSCs in complicated optical, hydrodynamic, and biogeochemical environments in the BS and YS.China Scholarship Council (CSC)National Natural Science Foundation of China (NSFC)WLKX

Intrusive Images in Psychological Disorders: Characteristics, Neural Mechanisms, and Treatment Implications

Involuntary images and visual memories are prominent in many types of psychopathology. Patients with posttraumatic stress disorder, other anxiety disorders, depression, eating disorders, and psychosis frequently report repeated visual intrusions corresponding to a small number of real or imaginary events, usually extremely vivid, detailed, and with highly distressing content. Both memory and imagery appear to rely on common networks involving medial prefrontal regions, posterior regions in the medial and lateral parietal cortices, the lateral temporal cortex, and the medial temporal lobe. Evidence from cognitive psychology and neuroscience implies distinct neural bases to abstract, flexible, contextualized representations (C-reps) and to inflexible, sensory-bound representations (S-reps). We revise our previous dual representation theory of posttraumatic stress disorder to place it within a neural systems model of healthy memory and imagery. The revised model is used to explain how the different types of distressing visual intrusions associated with clinical disorders arise, in terms of the need for correct interaction between the neural systems supporting S-reps and C-reps via visuospatial working memory. Finally, we discuss the treatment implications of the new model and relate it to existing forms of psychological therapy

On the convergence of Regge calculus to general relativity

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.Comment: Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

The clinical and cost-effectiveness of a Victim Improvement Package (VIP) for the reduction of chronic symptoms of depression or anxiety in older victims of common crime (the VIP trial): study protocol for a randomised controlled trial.

BACKGROUND: Older people are vulnerable to sustained high levels of psychosocial distress following a crime. A cognitive behavioural therapy (CBT)-informed psychological therapy, the Victim Improvement Package (VIP) may aid recovery. The VIP trial aims to test the clinical and cost-effectiveness of the VIP for alleviating depressive and anxiety symptoms in older victims of crime. METHODS/DESIGN: People aged 65 years or more who report being a victim of crime will be screened by Metropolitan Police Service Safer Neighbourhood Teams within a month of the crime for distress using the Patient Health Questionnaire-2 and the Generalised Anxiety Disorder-2. Those who screen positive will be signposted to their GP for assistance, and re-screened at 3 months. Participants who screen positive for depression and/or anxiety at re-screening are randomised to a CBT informed VIP added to treatment as usual (TAU) compared to TAU alone. The intervention consists of 10 individual 1-h sessions, delivered weekly by therapists from the mental health charity Mind. The primary outcome measure is the Beck Depression Inventory-II (BDI-II) and the Beck Anxiety Inventory (BAI), used as a composite measure, assessed at 6 months after the crime (post therapy) with a 9-month post-crime follow-up. Secondary outcome measures include the EQ-5D, and a modified Client Service Receipt Inventory. A total of 226 participants will be randomised VIP:TAU with a ratio 1:1, in order to detect a standardised difference of at least 0.5 between groups, using a mixed-effects linear-regression model with 90% power and a 5% significance level (adjusting for therapist clustering and potential drop-out). A cost-effectiveness analysis will incorporate intervention costs to compare overall health care costs and quality of life years between treatment arms. An embedded study will examine the impact of past trauma and engagement in safety behaviours and distress on the main outcomes. DISCUSSION: This trial should provide data on the clinical and cost-effectiveness of a CBT-informed psychological therapy for older victims of crime with anxiety and/or depressive symptoms and should demonstrate a model of integrated cross-agency working. Our findings should provide evidence for policy-makers, commissioners and clinicians responding to the needs of older victims of crime. TRIAL REGISTRATION: International Standard Randomised Controlled Trials Number, ID: ISRCTN16929670. Registered on 3 August 2016