Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was submitted after responding to a reviewer's comment

Bose-Einstein condensation in variable dimensionality

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali gases (BEC). The perturbation parameter is delta=1/kappa, where kappa depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the N -> infinity Thomas-Fermi ground state approximation (TFA) of the Gross-Pitaevskii equation. The approximation presented here is well-suited for calculating properties of states in three dimensions and in low effective dimensionality, such as vortex states in a highly anisotropic trap

Development of pseudorandom binary arrays for calibration of surface profile metrology tools

Optical Metrology tools, especially for short wavelength (EUV and X-Ray), must cover a wide range of spatial frequencies from the very low, which affects figure, to the important mid-spatial frequencies and the high spatial frequency range, which produces undesirable scattering. A major difficulty in using surface profilometers arises due to the unknown Point-Spread Function (PSF) of the instruments [1] that is responsible for distortion of the measured surface profile. Generally, the distortion due to the PSF is difficult to account because the PSF is a complex function that comes to the measurement via the convolution operation, while the measured profile is described with a real function. Accounting for instrumental PSF becomes significantly simpler if the result of measurement of a profile is presented in a spatial frequency domain as a Power Spectral Density (PSD) distribution [2]. For example, the measured PSD distributions provide a closed set of data necessary for three-dimensional calculations of scattering of light by the optical surfaces [3], [4]. The distortion of the surface PSD distribution due to the PSF can be modeled with the Modulation Transfer Function (MTF), which is defined over the spatial frequency bandwidth of the instrument [1], [2]. The measured PSD distribution can be presented as a product of the squared MTF and the ideal PSD distribution inherent for the System Under Test (SUT). Therefore, the instrumental MTF can be evaluated by comparing a measured PSD distribution of a known test surface with the corresponding ideal numerically simulated PSD. The square root of the ratio of the measured and simulated PSD distributions gives the MTF of the instrument. In previous work [5], [6] the instrumental MTF of a surface profiler was precisely measured using reference test surfaces based on Binary Pseudo-Random (BPR) gratings. Here, we present results of fabricating and using two-dimensional (2D) BPR arrays that allow for a direct 2D calibration of the instrumental MTF. BPR sequences are widely used in engineering and communication applications such as Global Position System, and wireless communication protocols. The ideal BPR pattern has a flat 'white noise' response over the entire range of spatial frequencies of interest. The BPR array used here is based on the Uniformly Redundant Array prescription [7] initially used for x-ray and gamma ray astronomy applications. The URA's superior imaging capability originates from the fact that its cyclical autocorrelation function very closely approximates a delta function, which produces a flat PSD. Three different size BPR array patterns were fabricated by electron beam lithography and ICP etching of silicon. The basic size unit was 200 nm, 400 nm, and 600 nm. Two different etch processes were used, CF{sub 4}/Ar and HBr, which resulted in undercut and vertical sidewall profiles, respectively. The 2D BPR arrays were used as standard test surfaces for MTF calibration of the MicroMap{trademark}-570 interferometric microscope using all available objectives. The HBr etched two-dimensional BPR arrays have proven to be a very effective calibration standard making possible direct calibration corrections without the need of additional calculation considerations, while departures from the ideal vertical sidewall require an additional correction term for the CF{sub 4}/Ar etched samples. [8] Initial surface roughness of low cost 'prime' wafers limits low magnification calibration but should not be a limitation if better polished samples are used

A mechanism for biogenic production and emission of MEK from MVK decoupled from isoprene biosynthesis

Methyl ethyl ketone (MEK) is an important compound in atmospheric chemistry. While attention has been paid mostly to anthropogenic sources of MEK, recently it has been shown that biogenic sources are globally as important as anthropogenic ones. However, the origin of biogenic MEK has yet to be completely elucidated. We present the full mechanism by which within-plant transformation of methyl vinyl ketone (MVK) and, to a minor extent, of 2-butanol and 3-buten-2-ol, is a source of biogenic MEK. Such transformation is observed in red oak for both exogenous MVK, taken up from the atmosphere, and endogenous MVK generated within a plant when it experiences stress (e.g. heat stress). Endogenous MVK emitted by plants is typically explained by within-plant oxidation of isoprene caused by oxidative stress. In this study we show that MVK and MEK emissions caused by heat stress are not related to isoprene in isoprene-emitting plants, implying that the massive carbon investment that plants commit to isoprene production is not explained by a direct antioxidant role. The presented mechanism can be important for inclusion in plant emission and in plant–atmosphere interaction models.</p

Spontaneous DC Current Generation in a Resistively Shunted Semiconductor Superlattice Driven by a TeraHertz Field

We study a resistively shunted semiconductor superlattice subject to a high-frequency electric field. Using a balance equation approach that incorporates the influence of the electric circuit, we determine numerically a range of amplitude and frequency of the ac field for which a dc bias and current are generated spontaneously and show that this region is likely accessible to current experiments. Our simulations reveal that the Bloch frequency corresponding to the spontaneous dc bias is approximately an integer multiple of the ac field frequency.Comment: 8 pages, Revtex, 3 Postscript figure

A case-control study of oesophageal adenocarcinoma in women: a preventable disease

The incidence of adenocarcinoma of the oesophagus in British women is among the highest in the world. To investigate its aetiology, we conducted a multi-centre, population based case–control study in four regions in England and Scotland. We included 74 incident cases in women with histologically confirmed diagnoses of adenocarcinoma of the oesophagus, and 74 female controls matched by age and general practice. High body mass index (BMI) around the age of 20 years (highest vs lowest quartile, adjusted odds ratio (OR) = 6.04, 95% confidence interval (CI) 1.28–28.52) and low consumption of fruit (highest vs lowest quartile, adjusted OR = 0.08, 95% Cl 0.01–0.49) were associated with increases in risk. Breastfeeding by women was associated with reduced risk of their subsequently developing this cancer (ever vs never, adjusted OR = 0.41, 95% CI 0.20–0.82) and there was a significant dose–response effect with total duration of breastfeeding. The summary population attributable risk from these three factors was 96% (90% if breastfeeding is excluded). We conclude that high BMI in early adulthood and low consumption of fruit are important risk factors for adenocarcinoma of the oesophagus. Breastfeeding may confer a protective effect but this needs confirmation. This cancer is a largely preventable disease in women. © 2000 Cancer Research Campaig

Collaboration between Science and Religious Education teachers in Scottish Secondary schools

The article reports on quantitative research that examines: (1) the current practice in collaboration; and (2) potential for collaboration between Science and Religious Education teachers in a large sample of Scottish secondary schools. The authors adopt and adapt three models (conflict; concordat and consonance) to interrogate the relationship between science and religion (and the perceived relation between these two subjects in schools) (Astley and Francis 2010). The findings indicate that there is evidence of limited collaboration and, in a few cases, a dismissive attitude towards collaboration (conflict and concordat and very weak consonance). There is, however, evidence of a genuine aspiration for greater collaboration among many teachers (moving towards a more robust consonance model). The article concludes by discussing a number of key factors that must be realised for this greater collaboration to be enacted

Highly anisotropic Bose-Einstein condensates: crossover to lower dimensionality

We develop a simple analytical model based on a variational method to explain the properties of trapped cylindrically symmetric Bose-Einstein condensates (BEC) of varying degrees of anisotropy well into regimes of effective one dimension (1D) and effective two dimension (2D). Our results are accurate in regimes where the Thomas-Fermi approximation breaks down and they are shown to be in agreement with recent experimental data.Comment: 4 pages, 2 figures; significantly more new material added; title and author-list changed due to changes in conten

High Levels of Education Are Associated With an Increased Risk of Latent Autoimmune Diabetes in Adults: Results from the Nord-Trøndelag Health Study

Although autoimmune diabetes in adults is a common form of diabetes, knowledge on risk factors and long term consequences of the disease is limited. The aims of this thesis were to investigate the influence of socioeconomic factors (education and occupation), sleep disturbances and psychological well-being on the risk of developing autoimmune diabetes in adults, to investigate whether genetic variation in the melatonin receptor 1B (MTNR1B) contributes to the association between poor sleep and type 2 diabetes which has been previously suggested, and finally to investigate the risk of mortality from all causes, cardiovascular disease and ischemic heart disease in adult-onset autoimmune diabetes, with consideration of the possible influence of metabolic risk factors, glycaemic control, lifestyle factors and socioeconomic position. These studies are based on data from the Norwegian HUNT Study, to date the largest population-based study where incident cases of autoimmune diabetes in adults can be separated from cases of type 2 diabetes. The HUNT Study consists of three separate surveys performed on three occasions in 1984-2008 and contains information from questionnaires, clinical examinations and blood samples. Information on mortality was obtained by linkage to the national Cause of Death Registry. Individuals who were positive for antibodies against glutamic acid decarboxylase and with onset of diabetes at ≥35 years were classified as having autoimmune diabetes in adults. The main finding of Study I was that high educational levels (university versus primary school) were associated with an increased risk of autoimmune diabetes in adults (HR 1.98, 95% CI 1.21-3.26) after adjustment for BMI, physical activity, smoking, alcohol consumption, and family history of diabetes, whereas type 2 diabetes was more common in those with low education. An increased risk of autoimmune diabetes in adults was also seen in individuals who reported having sleep disturbances and low psychological well-being (HR 1.84, 95% CI 1.10-3.09), a risk similar to that seen in type 2 diabetes (HR 1.31, 95% CI 1.13-1.50) (Study II). The results from Study III indicated that there was no influence of the MTNR1B genetic variant on the association between poor sleep and type 2 diabetes. The association remained after adjustment for genotype and was seen in non-carriers as well as in carriers of the risk allele. Mortality from all causes (HR 1.55, 95% CI 1.25-1.92), cardiovascular disease (HR 1.87, 95% CI 1.40-2.48) and ischemic heart disease (HR 2.39, 95% CI 1.57-3.64) was increased in autoimmune diabetes in adults compared to individuals without diabetes. Importantly, mortality risk was as high as in type 2 diabetes, despite a more favourable metabolic risk profile in patients with autoimmune diabetes. In these patients, excess mortality appeared to be primarily associated with poor glycaemic control. These findings suggest, for the first time, that socioeconomic and psychosocial factors contribute to the development of autoimmune diabetes in adults. The results are in line with previous data indicating that the aetiology of autoimmune diabetes is partly similar to that of type 2 diabetes but suggest, also, that there are other, currently unidentified, environmental risk factors for autoimmune diabetes that remain to be explored. Finally, the results indicate that survival in individuals with autoimmune diabetes with adult onset would be improved by a more effective treatment