Boundary integral methods in high frequency scattering

In this article we review recent progress on the design, analysis and implementation of numerical-asymptotic boundary integral methods for the computation of frequency-domain acoustic scattering in a homogeneous unbounded medium by a bounded obstacle. The main aim of the methods is to allow computation of scattering at arbitrarily high frequency with finite computational resources

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators

Attention deficit hyperactivity disorder (ADHD) and musical behaviour: The significance of context

Recent estimates indicate that attention deficit hyperactivity disorder (ADHD) is prevalent in about 2.5% of adults and 5.9% of young people. Negative impacts of ADHD are often reported in academic performance, emotional and cognitive functioning, and peer relationships, but little is known about ADHD and music. Using a detailed case study approach, structured observations in contrasting settings over a period of several school terms were made of one Primary and one Secondary school-aged boy, each with a formal assessment of ADHD. Analyses of video-based observations every 30 s ( n = 5,961 in total) were related to (1) the particular core ADHD symptoms attributed to inattention, hyperactivity and impulsivity, together with their observed severity; and (2) tutors’ and pupils’ actions during their focus music sessions. These quantitative data enriched the qualitative analyses. The research findings indicate that, notwithstanding their ADHD-related symptoms, the affected individuals could engage successfully in music and acquire musical skills. ADHD was not a static condition, but variable according to pedagogical and musical context. Habitual ADHD symptoms were either reduced or entirely absent when participants were engaged in playing and performing music. Analyses suggest that an effective, context-sensitive and inclusive pedagogy can integrate pupils into successful individual and collective music making

Virtual Data in CMS Analysis

The use of virtual data for enhancing the collaboration between large groups of scientists is explored in several ways: - by defining ``virtual'' parameter spaces which can be searched and shared in an organized way by a collaboration of scientists in the course of their analysis; - by providing a mechanism to log the provenance of results and the ability to trace them back to the various stages in the analysis of real or simulated data; - by creating ``check points'' in the course of an analysis to permit collaborators to explore their own analysis branches by refining selections, improving the signal to background ratio, varying the estimation of parameters, etc.; - by facilitating the audit of an analysis and the reproduction of its results by a different group, or in a peer review context. We describe a prototype for the analysis of data from the CMS experiment based on the virtual data system Chimera and the object-oriented data analysis framework ROOT. The Chimera system is used to chain together several steps in the analysis process including the Monte Carlo generation of data, the simulation of detector response, the reconstruction of physics objects and their subsequent analysis, histogramming and visualization using the ROOT framework.Comment: Talk from the 2003 Computing in High Energy and Nuclear Physics (CHEP03), La Jolla, Ca, USA, March 2003, 9 pages, LaTeX, 7 eps figures. PSN TUAT010. V2 - references adde

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods

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

The clinically extremely vulnerable to COVID: identification and changes in healthcare while self-isolating (shielding) during the coronavirus pandemic.

In March 2020, the government of Scotland identified people deemed clinically extremely vulnerable to COVID due to their pre-existing health conditions. These people were advised to strictly self-isolate (shield) at the start of the pandemic, except for necessary healthcare. We examined who was identified as clinically extremely vulnerable, how their healthcare changed during isolation, and whether this process exacerbated healthcare inequalities. We linked those on the shielding register in NHS Grampian, a health authority in Scotland, to healthcare records from 2015-2020. We described the source of identification, demographics, and clinical history of the cohort. We measured changes in out-patient, in-patient, and emergency healthcare during isolation in the shielding population and compared to the general non-shielding population. The register included 16,092 people (3% of the population), clinically vulnerable primarily due to a respiratory disease, immunosuppression, or cancer. Among them, 42% were not identified by national healthcare record screening but added ad hoc, with these additions including more children and fewer economically-deprived. During isolation, all forms of healthcare use decreased (25%-46%), with larger decreases in scheduled care than in emergency care. However, people shielding had better maintained scheduled care compared to the non-shielding general population: out-patient visits decreased 35% vs 49%; in-patient visits decreased 46% vs 81%. Notably, there was substantial variation in whose scheduled care was maintained during isolation: younger people and those with cancer had significantly higher visit rates, but there was no difference between sexes or socioeconomic levels. Healthcare changed dramatically for the clinically extremely vulnerable population during the pandemic. The increased reliance on emergency care while isolating indicates that continuity of care for existing conditions was not optimal. However, compared to the general population, there was success in maintaining scheduled care, particularly in young people and those with cancer. We suggest that integrating demographic and primary care data would improve identification of the clinically vulnerable and could aid prioritising their care

The clinically extremely vulnerable to COVID : Identification and changes in healthcare while self-isolating (shielding) during the coronavirus pandemic

Peer reviewe

Impact of the June 2018 Saddleworth Moor wildfires on air quality in northern England

The June 2018 Saddleworth Moor fires were some of the largest UK wildfires on record and lasted for approximately three weeks. They emitted large quantities of smoke, trace gases and aerosols which were transported downwind over the highly populated regions of Manchester and Liverpool. Surface observations of PM2.5 indicate that concentrations were 4–5.5 times higher than the recent seasonal average. State-of-the-art satellite measurements of total column carbon monoxide (TCCO) from the TROPOMI instrument on the Sentinel 5—Precursor (S5P) platform, coupled with measurements from a flight of the UK BAe-146–301 research aircraft, are used to quantify the substantial enhancement in emitted trace gases. The aircraft measured plume enhancements with near-fire CO and PM2.5 concentrations >1500 ppbv and >125 μg m−3 (compared to ~100 ppbv and ~5 μg m−3 background concentrations). Downwind fire-plume ozone (O3) values were larger than the near-fire location, indicating O3 production with distance from source. The near-fire O3:CO ratio was (ΔO3/ΔCO) 0.001 ppbv/ppbv, increasing downwind to 0.060–0.105 ppbv/ppbv, suggestive of O3 production enhancement downwind of the fires. Emission rates of CO and CO2 ranged between 1.07 (0.07–4.69) kg s−1 and 13.7 (1.73–50.1) kg s−1, respectively, similar to values expected from a medium sized power station