A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems

Point Contact Spectroscopy of Superconducting Gap Anisotropy in Nickel Borocarbide Compound LuNi2B2C

Point contacts are used to investigate the anisotropy of the superconducting energy gap in LuNi2B2C in the ab plane and along the c axis. It is shown that the experimental curves should be described assuming that the superconducting gap is non-uniformly distributed over the Fermi surface. The largest and the smallest gaps have been estimated by two-gap fitting models. It is found that the largest contribution to the point-contact conductivity in the c direction is made by a smaller gap and, in the ab plane by a larger gap. The deviation from the one-gap BCS model is pronounced in the temperature dependence of the gap in both directions. The temperature range, where the deviation occurs, is for the c direction approximately 1.5 times more than in the ab plane. The \Gamma parameter, allowing quantitatively estimate the gap anisotropy by one-gap fitting, in c direction is also about 1.5 times greater than in the ab plane. Since it is impossible to describe satisfactorily such gap distribution either by the one- or two-gap models, a continuous, dual-maxima model of gap distribution over the Fermi surface should be used to describe superconductivity in this material.Comment: 10 pages, 14 Figs, accepted in PR

A Path Integral Approach To Noncommutative Superspace

A path integral formula for the associative star-product of two superfields is proposed. It is a generalization of the Kontsevich-Cattaneo-Felder's formula for the star-product of functions of bosonic coordinates. The associativity of the star-product imposes certain conditions on the background of our sigma model. For generic background the action is not supersymmetric. The supersymmetry invariance of the action constrains the background and leads to a simple formula for the star-product.Comment: Latex 13 pages. v2: references and footnotes adde

Effect of transport-induced charge inhomogeneity on point-contact Andreev reflection spectra at ferromagnet-superconductor interfaces

We investigate the transport properties of a ferromagnet-superconductor interface within the framework of a modified three-dimensional Blonder-Tinkham-Klapwijk formalism. In particular, we propose that charge inhomogeneity forms via two unique transport mechanisms, namely, evanescent Andreev reflection and evanescent quasiparticle transmission. Furthermore, we take into account the influence of charge inhomogeneity on the interfacial barrier potential and calculate the conductance as a function of bias voltage. Point-contact Andreev reflection (PCAR) spectra often show dip structures, large zero-bias conductance enhancement, and additional zero-bias conductance peak. Our results indicate that transport-induced charge inhomogeneity could be a source of all these anomalous characteristics of the PCAR spectra.Comment: 9 pages, 6 figure

Endometriosis classification, staging and reporting systems: a review on the road to a universally accepted endometriosis classification,

BACKGROUND: In the field of endometriosis, several classification, staging and reporting systems have been developed. However, endometriosis classification, staging and reporting systems that have been published and validated for use in clinical practice have not been systematically reviewed up to now. OBJECTIVES: The aim of the current review is to provide a historical overview of these different systems based on an assessment of published studies. MATERIALS AND METHODS: A systematic Pubmed literature search was performed. Data were extracted and summarised. RESULTS: Twenty-two endometriosis classification, staging and reporting systems have been published between 1973 and 2021, each developed for specific and different purposes. There is still no international agreement on how to describe the disease. Studies evaluating different systems are summarised showing a discrepancy between the intended and the evaluated purpose, and a general lack of validation data confirming a correlation with pain symptoms or quality of life for any of the current systems. A few studies confirm the value of the Enzian system for surgical description of deep endometriosis. With regards to infertility, the endometriosis fertility index has been confirmed valid for its intended purpose. CONCLUSIONS: Of the 22 endometriosis classification, staging and reporting systems identified in this historical overview, only a few have been evaluated, in 46 studies, for the purpose for which they were developed. It can be concluded that there is no international agreement on how to describe endometriosis or how to classify it, and that most classification/staging systems show no or very little correlation with patient outcomes. WHAT IS NEW? This overview of existing systems is a first step in working towards a universally accepted endometriosis classification

Wavenumber-explicit continuity and coercivity estimates in acoustic scattering by planar screens

We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. We prove continuity and coercivity of the relevant boundary integral operators (the acoustic single-layer and hypersingular operators respectively) in appropriate fractional Sobolev spaces, with wavenumber-explicit bounds on the continuity and coercivity constants. Our analysis is based on spectral representations for the boundary integral operators, and builds on results of Ha-Duong (Jpn J Ind Appl Math 7:489--513 (1990) and Integr Equat Oper Th 15:427--453 (1992)).Comment: v2 has minor corrections compared to v1. arXiv admin note: substantial text overlap with arXiv:1401.280

Towards a Biotic Ligand Model for Green Algae: Surface-bound Copper Predicts the Effect of pH on Copper Toxicity

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A comparison of the recording of 30 common childhood conditions in the Doctor's Independent Network and General Practice Research Databases.

In this article we compare the recording of 30 common childhood conditions in two general practice databases of anonymised computerised medical records based on fundamentally different systems--the Doctor's Independent Network (DIN) database (Torex system) and the General Practice Research Database (GPRD) (In Practice Systems). Analysing the records of all children born 1990-1993 and followed for 5 years we found comparable results for most conditions, but differences between the hierarchical structures of the diagnostic coding systems (Read in DIN, OXMIS in GPRD) led to some differences between the databases. Practice variation was marked, but comparable between databases. Variation was greatest in conditions that are poorly defined clinically

Philanthropy or solidarity? Ethical dilemmas about humanitarianism in crisis afflicted Greece

That philanthropy perpetuates the conditions that cause inequality is an old argument shared by thinkers such as Karl Marx, Oscar Wilde and Slavoj Zizek. I recorded the same argument in conversations regarding a growing humanitarian concern in austerity-ridden Greece. At the local level a number of solidarity initiatives provide the most impoverished families with humanitarian help. Some citizens participate in such initiatives wholeheartedly, while some other citizens criticize solidarity movements drawing primarily from Marxist-inspired arguments, such as, for example, that humanitarianism rationalises state inaction. The local narratives presented in this article bring forward two parallel possibilities engendered by the humanitarian face of social solidarity: first, its empowering potential (where solidarity initiatives enhance local social awareness), and second, the de-politicisation of the crisis and the experience of suffering (a liability that stems from the effectiveness of humanitarianism in ameliorating only temporarily the superficial consequences of the crisis). These two overlapping possibilities can help us problematise the contextual specificity and strategic employment of humanitarian solidarity in times of austerity