Universal behavior of quantum Green's functions

We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = . Recently, in one dimension (1D), the Green's function problem was solved explicitly in inverse form, with diagonal elements of Green's function as prescribed variables. The first aim of this paper is to extract from the 1D inverse solution such information about Green's function which cannot be deduced directly from its definition. Among others, this information involves universal, i.e. u(r)-independent, behavior of Green's function close to the domain boundary. The second aim is to extend the inverse formalism to higher dimensions, especially to 3D, and to derive the universal form of Green's function for various shapes of the confining domain boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy

Global Distribution of Omura’s Whales (Balaenoptera omurai) and Assessment of Range-Wide Threats

When the Omura’s whale (Balaenoptera omurai) was first described in 2003, it was known from only three locations: the southern Sea of Japan, and the vicinities of the Cocos (Keeling) Islands and Solomon Islands. Work over the following decade suggested a range limited to the eastern Indo-Pacific, but more recent discoveries in the western Indian Ocean and Atlantic Ocean suggested a more widespread range than previously thought. Here we use all available sources of information, including published papers, unpublished reports, and internet-based accounts, substantiated through genetic, morphological, photographic and acoustic documentation, to compile accounts of Omura’s whales globally. Reports increased precipitously since 2015 after publication of the first detailed external description of the species, reflecting the impact of the recently elevated awareness of the species. We report 161 accounts from 95 locales in the waters of 21 range states, and found that the species is widely distributed in primarily tropical and warm-temperate locations. Currently it is known from all ocean basins with the exception of the central and eastern Pacific. The majority of accounts remain in the eastern Indo-Pacific suggesting a potentially recent range expansion from this region. There is a strong tendency toward a coastal and neritic distribution, although there are also several pelagic records. A predominantly near-coastal distribution places Omura’s whale at risk from anthropogenic activities throughout its range, and its tropical distribution in often remote and poorly monitored areas makes adequately documenting and assessing threats challenging. We assess documented threats in light of the reported species’ range, and found threats from, at minimum, ship strikes, fisheries bycatch and entanglement, local directed hunting, petroleum exploration (seismic surveys), and coastal industrial development. Current evidence indicates that at least some populations are non-migratory with local, potentially restricted ranges. Furthermore, there is low genetic diversity documented throughout its global distribution. Given the species may be characterized by small local populations, it may be particularly vulnerable to impacts from existing regional anthropogenic threats. We recommend that focused work be conducted to locate and study local populations, assess potential population isolation, and determine conservation status and specific anthropogenic threats across the species’ range

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

BMQ

BMQ: Boston Medical Quarterly was published from 1950-1966 by the Boston University School of Medicine and the Massachusetts Memorial Hospitals. Pages 49-52, v17n2, provided courtesy of Howard Gotlieb Archival Research Center

A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope

A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-linear boundaries. Several results are obtained that relate the coefficients, $b_i$, in the Shephard-Todd polynomial to the geometry of the fundamental domain. For the 3-sphere we show that $b_4$ is given by the ratio of the volume of the fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected

Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Stability of the Autism Diagnostic Interview—Revised from Pre-School to Elementary School Age in Children with Autism Spectrum Disorders

This study examined the stability of scores on the ADI-R from pre-school to elementary school age in children with autism spectrum disorders (ASD). Participants were 35 children who, at T1, all had a clinical diagnosis of ASD. On initial assessment (mean age 3.5 years; SD 0.6), all met ADI-R algorithm criteria for autism. ADI-R assessments were repeated at follow up (FU; mean age 10.5 years; SD 0.8). Changes in ADI-R total, domain and ADI-R algorithm item scores were assessed. Twentyeight children continued to score above the ADI-R cut-off for autism at FU, although significant decreases in ADI-R domain and item scores were also found. In conclusion, while classification of children according to ADI-R criteria, generally remained stable between pre-school and elementary school age, many children demonstrated significant improvements in symptom severity

Randomized community-level HIV prevention intervention trial for men who drink in South African alcohol-serving venues

South African alcohol-serving establishments (i.e., shebeens) offer unique opportunities to reduce HIV risks among men who drink. Purpose: To test an individual- and a social structural-level HIV prevention intervention for men who drink in shebeens. Methods: Twelve matched pairs of township neighbourhoods were randomized to receive either (i) an HIV prevention intervention (guided by Social Action Theory) to reduce sexual risk and increase risk reduction communication in social networks, or (ii) an attention-matched control intervention that focused on the prevention of relationship violence. At the individual level, the interventions delivered skills building workshops focused on sexual risk reduction. At the social structural level, the intervention aimed to increase conversations about safer sex among men in the shebeens, distributed small media and implemented community educational events. Individual-level outcomes were assessed by following the workshop cohorts for 1 year (N = 984), and community-level outcomes were examined through cross-sectional community surveys conducted for 1 year in the shebeens (N = 9,678). Results: Men in the HIV prevention workshops demonstrated greater condom use, more HIV prevention-oriented conversations and greater perceptions of safer sex norms than men in the comparison workshops. Changes at the community level demonstrated significant differences in condom use, although the pattern was not consistent over time. Conclusions: Multi-level interventions that target men who drink in South African shebeens may help reduce risks for HIV and other sexually transmitted infections.Web of Scienc

Maternal age and offspring developmental vulnerability at age five: A population-based cohort study of Australian children

Published: April 24, 2018Background: In recent decades, there has been a shift to later childbearing in high-income countries. There is limited large-scale evidence of the relationship between maternal age and child outcomes beyond the perinatal period. The objective of this study is to quantify a child’s risk of developmental vulnerability at age five, according to their mother’s age at childbirth. Methods and findings: Linkage of population-level perinatal, hospital, and birth registration datasets to data from the Australian Early Development Census (AEDC) and school enrolments in Australia’s most populous state, New South Wales (NSW), enabled us to follow a cohort of 99,530 children from birth to their first year of school in 2009 or 2012. The study outcome was teacher-reported child development on five domains measured by the AEDC, including physical health and well-being, emotional maturity, social competence, language and cognitive skills, and communication skills and general knowledge. Developmental vulnerability was defined as domain scores below the 2009 AEDC 10th percentile cut point. The mean maternal age at childbirth was 29.6 years (standard deviation [SD], 5.7), with 4,382 children (4.4%) born to mothers aged <20 years and 20,026 children (20.1%) born to mothers aged ≥35 years. The proportion vulnerable on ≥1 domains was 21% overall and followed a reverse J-shaped distribution according to maternal age: it was highest in children born to mothers aged ≤15 years, at 40% (95% CI, 32–49), and was lowest in children born to mothers aged between 30 years and ≤35 years, at 17%–18%. For maternal ages 36 years to ≥45 years, the proportion vulnerable on ≥1 domains increased to 17%–24%. Adjustment for sociodemographic characteristics significantly attenuated vulnerability risk in children born to younger mothers, while adjustment for potentially modifiable factors, such as antenatal visits, had little additional impact across all ages. Although the multi-agency linkage yielded a broad range of sociodemographic, perinatal, health, and developmental variables at the child’s birth and school entry, the study was necessarily limited to variables available in the source data, which were mostly recorded for administrative purposes. Conclusions: Increasing maternal age was associated with a lesser risk of developmental vulnerability for children born to mothers aged 15 years to about 30 years. In contrast, increasing maternal age beyond 35 years was generally associated with increasing vulnerability, broadly equivalent to the risk for children born to mothers in their early twenties, which is highly relevant in the international context of later childbearing. That socioeconomic disadvantage explained approximately half of the increased risk of developmental vulnerability associated with younger motherhood suggests there may be scope to improve population-level child development through policies and programs that support disadvantaged mothers and children.Kathleen Falster, Mark Hanly, Emily Banks, John Lynch, Georgina Chambers, Marni Brownell, Sandra Eades, Louisa Jor

On electrostatic and Casimir force measurements between conducting surfaces in a sphere-plane configuration

We report on measurements of forces acting between two conducting surfaces in a spherical-plane configuration in the 35 nm-1 micrometer separation range. The measurements are obtained by performing electrostatic calibrations followed by a residual analysis after subtracting the electrostatic-dependent component. We find in all runs optimal fitting of the calibrations for exponents smaller than the one predicted by electrostatics for an ideal sphere-plane geometry. We also find that the external bias potential necessary to minimize the electrostatic contribution depends on the sphere-plane distance. In spite of these anomalies, by implementing a parametrixation-dependent subtraction of the electrostatic contribution we have found evidence for short-distance attractive forces of magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss the relevance of our findings in the more general context of Casimir-Lifshitz force measurements, with particular regard to the critical issues of the electrical and geometrical characterization of the involved surfaces.Comment: 22 pages, 15 figure