Stress tensor for a scalar field in a spatially varying background potential: Divergences, "renormalization," anomalies, and Casimir forces

Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for $z<0$ and rises like $z^\alpha$, $\alpha>0$, for $z>0$. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, $\alpha=1$ and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).Comment: 20 pages, 6 figure

Investigating the Effects of Finite Resolution on Observed Transverse Jet Profiles

Both the emission properties and evolution of Active Galactic Nuclei (AGN) radio jets are dependent on the magnetic fields that thread them. Faraday Rotation gradients are a very important way of investigating these magnetic fields, and can provide information on the orientation and structure of the magnetic field in the immediate vicinity of the jet; for example, a toroidal or helical field component should give rise to a systematic gradient in the observed Faraday rotation across the jet, as well as characteristic intensity and polarization profiles. However, real observed radio images have finite resolution, usually expressed via convolution with a Gaussian beam whose size corresponds to the central lobe of the point source response function. This will tend to blur transverse structure in the jet profile, raising the question of how well resolved a jet must be in the transverse direction in order to reliably detect transverse structure associated with a helical jet magnetic field. We present results of simulated intensity, polarization and Faraday rotation images designed to directly and empirically investigate the effect of finite resolution on observed transverse jet structures

Developing principles of best practice for art therapists working with children and families

In 2010 the British Association of Art therapists asked art therapists working with specific client groups to produce clear guidelines about current views on best practice in the field. Using the Nominal Group Technique and a modified Delphi process, the special interest group Art Therapists working with Children Adolescents and Families (ATCAF) produced 18 Principles of Best Practice with a range of associated indicators. This paper presents the methods and the results of that process followed by a brief discussio

Neotectonics of the Western Nepal Fault System: Implications for Himalayan strain partitioning

Oblique convergence at the Himalayan margin is hypothesized to be partitioned by orogen-normal thrusting and orogen-parallel strike-slip faulting. We conducted field mapping and remote sensing in the Dhaulagiri Range of Nepal, and the results reveal an active regional fault system termed the Western Nepal Fault System (WNFS). Right and normally offset Quaternary deposits and brittly deformed bedrock demarcate dextral slip along two strike-slip faults striking N40–50°W linked via an extensional right step over striking N10–20°E. The strike-slip attitudes subparallel bedrock foliation, while the step over cuts at a high angle (~70°). Fault slip data along the strike-slip segments trend N70°W with minor dip component, top to north. Fault slip data and observed kinematics along the WNFS support our interpretation that the WNFS formed via arc-parallel stress. On the basis of geometry, kinematics, and structural position we correlate the WNFS to active faults between the Karakoram and Bari Gad faults. This suggests an ~350 km long dextral fault system extending obliquely across the Western Nepal Himalaya which appears to intersect the Main Frontal Thrust (MFT) near 83°30′E, coinciding with a large gradient in the arc-parallel component of GPS velocities. We interpret the WNFS to represent a class of orogen-parallel strike-slip faults working with subduction to accommodate obliquely convergent plate motion. Our observations support the hypothesis that the region lying between the MFT and the WNFS is a continental version of a fore-arc sliver bounded at its base by the Main Himalayan Thrust

Thermochronologic constraints on the late Cenozoic exhumation history of the Gurla Mandhata metamorphic core complex, Southwestern Tibet

This is the publisher's version, also available electronically from http://onlinelibrary.wiley.com/doi/10.1002/2013TC003302/abstractHow the Tibetan plateau is geodynamically linked to the Himalayas is a topic receiving considerable attention. The Karakoram fault plays key roles in describing the structural relationship between southern Tibet and the Himalayas. In particular, considerable debate exists at the southeastern end of the Karakoram fault, where its role is interpreted in two different ways. One interpretation states that slip along the dextral Karakoram fault extends eastward along the Indus-Yalu suture zone, bypassing the Himalayas. The other interprets that fault slip is fed southward into the Himalayan thrust belt along the Gurla Mandhata detachment (GMD). To evaluate these competing models, the late Miocene history of the GMD was reconstructed from thermokinematic modeling of zircon (U-Th)/He data. Three east-west transects reveal rapid cooling of the GMD footwall from 8.0 ± 1.3 Ma to 2.6 ± 0.7 Ma. Model simulations show a southward decrease in slip magnitude and rate along the GMD. In the north, initiation of the GMD range between 14 and 11 Ma with a mean fault slip rate of 5.0 ± 0.9 mm/yr. The central transect shows an initiation age from 14 to 11 Ma with a mean fault slip rate of 3.3 ± 0.6 mm/yr. In the south, initiation began between 15 and 8 Ma with a mean fault slip rate of 3.2 ± 1.6 mm/yr. The initiation ages and slip rates match the Karakoram fault across several timescales, supporting the idea that the two are kinematically linked. Specifically, the data are consistent with the GMD acting as an extensional stepover, with slip transferred southward into the Himalayas of western Nepal

Inducing remission of Type 2 diabetes in the Caribbean: findings from a mixed methods feasibility study of a low-calorie liquid diet-based intervention in Barbados.

AIM: In a high proportion of people with recently diagnosed Type 2 diabetes, a short (2-3-month) low-calorie diet is able to restore normal glucose and insulin metabolism. The aim of this study was to determine the feasibility of this approach in Barbados. METHODS: Twenty-five individuals with Type 2 diabetes diagnosed within past 6 years, not on insulin, BMI ≥ 27 kg/m2 were recruited. Hypoglycaemic medication was stopped on commencement of the 8-week liquid (760 calorie) diet. Insulin response was assessed in meal tests at baseline, 8 weeks and 8 months. Semi-structured interviews, analysed thematically, explored participants' experiences. 'Responders' were those with fasting plasma glucose (FPG) < 7 mmol/l at 8 weeks. RESULTS: Ten men and 15 women (mean age 48, range 26-68 years) participated. Mean (sd) BMI was 34.2 kg/m2 (6.0); FPG 9.2 mmol/l (2.2). Mean weight loss at 8 weeks and 8 months was 10.1 kg [95% confidence interval (CI) 8.1, 12.0] and 8.2 kg (95% CI 5.8, 10.6); FPG was lower by 2.2 mmol/l (95% CI 1.2, 3.2) and 1.7 mmol/l (95% CI 0.8, 2.7) respectively. Nine of 11 (82%) of those who lost ≥ 10 kg were 'responders' compared with 6 of 14 (43%) who lost < 10 kg (P = 0.048). The 30-min insulin increment was higher in responders at baseline and follow-up (P ≤ 0.01). A food culture based on starchy foods and pressures to eat large amounts at social events were among the challenges identified by participants. CONCLUSIONS: The feasibility of this approach to weight loss and diabetes remission in a predominantly black population in Barbados was demonstrated

A framework for power analysis using a structural equation modelling procedure

BACKGROUND: This paper demonstrates how structural equation modelling (SEM) can be used as a tool to aid in carrying out power analyses. For many complex multivariate designs that are increasingly being employed, power analyses can be difficult to carry out, because the software available lacks sufficient flexibility. Satorra and Saris developed a method for estimating the power of the likelihood ratio test for structural equation models. Whilst the Satorra and Saris approach is familiar to researchers who use the structural equation modelling approach, it is less well known amongst other researchers. The SEM approach can be equivalent to other multivariate statistical tests, and therefore the Satorra and Saris approach to power analysis can be used. METHODS: The covariance matrix, along with a vector of means, relating to the alternative hypothesis is generated. This represents the hypothesised population effects. A model (representing the null hypothesis) is then tested in a structural equation model, using the population parameters as input. An analysis based on the chi-square of this model can provide estimates of the sample size required for different levels of power to reject the null hypothesis. CONCLUSIONS: The SEM based power analysis approach may prove useful for researchers designing research in the health and medical spheres

A Wormhole at the core of an infinite cosmic string

We study a solution of Einstein's equations that describes a straight cosmic string with a variable angular deficit, starting with a $2 \pi$ deficit at the core. We show that the coordinate singularity associated to this defect can be interpreted as a traversible wormhole lodging at the the core of the string. A negative energy density gradually decreases the angular deficit as the distance from the core increases, ending, at radial infinity, in a Minkowski spacetime. The negative energy density can be confined to a small transversal section of the string by gluing to it an exterior Gott's like solution, that freezes the angular deficit existing at the matching border. The equation of state of the string is such that any massive particle may stay at rest anywhere in this spacetime. In this sense this is 2+1 spacetime solution.Comment: 1 tex file and 5 eps files. To be Published in Nov. in Phys.Rev.

Cognitive consequences of perceiving social exclusion

Although a great deal is now known about how people mentally represent individuals and groups, less attention has been paid to the question of how interpersonal relationships are represented in memory. Drawing on principles of categorization, this paper reports an investigation into how we mentally represent the relationships of others. In three experiments, evidence for assimilation effects following social exclusion (and subsequent categorization) is found. Experiment 1 uses a judgment paradigm to demonstrate that social exclusion influences the perception of interpersonal closeness. Experiments 2 and 3 employ a memory confusion paradigm to establish that representations of relationship partners are assimilated following the exclusion of a third party. © 2008 Elsevier Inc. All rights reserved