A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Annual textural banding in Holocene estuarine silts, Severn Estuary Levels (SW Britain): patterns, cause and implications

A high-resolution textural study has been made of laminated and banded estuarine silts exposed intertidally at representative localities and horizons in the Holocene deposits of the Severn Estuary Levels. The laminae, on a submillimetre to millimetre scale, are sharp-based, graded couplets formed of a lower silty part overlain by a finer-textured clayey element. The centimetre- to decimetre-scale banding is formed of laminae in alternating, gradually intergrading sets of relatively coarse and relative fine-grained examples. At outcrop in the field, the banding is recognizable because the coarse sets prove to be recessive to varying degrees under the influence of weathering and current action. Independent evidence at two localities points toward an annual origin for the banding; at a third it arose during part of what appears to have been a relatively short period. Quantified physical arguments suggest that the textural banding is a response of suspended fine sediment to marked seasonal changes in sea temperature and windiness. The banded silts occur in four distinct stratigraphical contexts and record high deposition rates (order 0.01-0.1 m/yr). Because physical factors determine their textures, the silts potentially afford insights in all contexts into aspects of changing Holocene climatic conditions. In one context, the thickness of the bands points to high (order 0.01-0.1 m/yr) but comparatively short-lived (order 10s-100s yrs) rates of relative water-level rise. In the others, however, the banding has no implications for sea-level behaviour, and simply records gross environmental disequilibrium, for example, the recovery of mudflats/marshes after an erosional episode. Similarly, because on account of their rapid accumulation the banded silts preserve animal and human tracks and trackways especially well, they provide an archive of animal and human behaviour in the area during the Holocene.

Effect of dietary supplementation with selenium-enriched yeast or sodium selenite on selenium tissue distribution and meat quality in beef cattle

The objective was to determine the concentration of total selenium (Se) and the proportion of total Se comprised as selenomethionine (SeMet) and selenocysteine (SeCys) in post mortem tissues of beef cattle offered diets containing graded additions of selenized enriched yeast (SY) [Saccharomyces cerevisae CNCM I-3060]), or sodium selenite (SS). Oxidative stability and tissue glutathione peroxidase (GSH-Px) activity of edible muscle tissue were assessed 10 d post-mortem. Thirty two beef cattle were offered, for a period of 112 d, a total mixed ration which had either been supplemented with SY (0, 0.15 or 0.35 mg Se/kg DM) or SS (0.15 mg Se/kg DM). At enrollment (0 d) and at 28, 56, 84 and 112 d following enrollment, blood samples were taken for Se and Se species determination, as well as whole blood GSH-Px activity. At the end of the study beef cattle were euthanized and samples of heart, liver, kidney, and skeletal muscle (LM and psoas major) were retained for Se and Se species determination. Tissue GSH-Px activity and thiobarbituric acid reactive substances (TBARS) were determined in skeletal muscle tissue (LM only). The incorporation into the diet of ascending concentrations of Se as SY increased whole blood total Se and the proportion of total Se comprised as SeMet, as well as GSH-Px activity. There was also a dose dependant response to the graded addition of SY on total Se and proportion of total Se as SeMet in all tissues and GSH-Px activity in skeletal muscle tissue. Furthermore, total Se concentration of whole blood and tissues was greater in those animals offered SY when compared with those receiving a comparable dose of SS, indicating an improvement in Se availability and tissue Se retention. Likewise, GSH-Px activity in whole blood and LM was greater in those animals offered SY when compared with those receiving a comparable dose of SS. However, these increases in tissue total Se and GSH-Px activity appeared to have little or no effect in meat oxidative stability.

Selenium supplementation of lactating dairy cows: Effect on selenium concentration in blood, milk, urine and feces

The objectives were to determine effects of graded levels of selenized yeast derived from a specific strain of Saccharomyces cerevisiae (CNCM I-3060) on animal performance and in selenium concentrations in the blood, milk, feces, and urine of dairy cows compared with sodium selenite; and to provide preliminary data on the proportion of selenium as selenomethionine in the milk and blood. Twenty Holstein cows were used in a 5 × 5 Latin square design study in which all cows received the same total mixed rations, which varied only in source or concentration of dietary selenium. There were 5 experimental treatments. Total dietary selenium of treatment 1, which received no added selenium, was 0.15 mg/kg of dry matter, whereas values for treatments 2, 3, and 4, derived from selenized yeast, were 0.27, 0.33, and 0.40 mg/kg of dry matter, respectively. Treatment 5 contained 0.25 mg of selenium obtained from sodium selenite/kg of dry matter. There were no significant treatment effects on animal performance, and blood chemistry and hematology showed few treatment effects. Regression analysis noted significant positive linear effects of increasing dietary selenium derived from selenized yeast on selenium concentrations in the milk, blood, urine, and feces. In addition, milk selenium results indicated improved bioavailability of selenium from selenized yeast, compared with sodium selenite. Preliminary analyses showed that compared with sodium selenite, the use of selenized yeast increased the concentration of selenomethionine in the milk and blood. There was no indication of adverse effects on cow health associated with the use of selenized yeast.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

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.

Sustainable building solutions: a review of lessons from the natural world

The realisation that much of conventional. modern architecture is not sustainable over the long term is not new. Typical approaches are aimed at using energy and materials more efficiently. However, by clearly understanding the natural processes and their interactions with human needs in view, designers can create buildings that are delightful. functional productive and regenerative by design. The paper aims to review the biomimetics literature that is relevant to building materials and design. Biomimetics is the abstraction of good design from Nature, an enabling interdisciplinary science. particularly interested in emerging properties of materials and structures as a result of their hierarchical organisation. Biomimetics provides ideas relevant to: graded functionality of materials (nano-scale), adaptive response (nano-, micro-. and macro-scales): integrated intelligence (sensing and actuation at all scales), architecture and additional functionality. There are many examples in biology where emergent response of plants and animals to temperature, humidity and other changes in their physical environments is based on relatively simple physical principles. However, the implementation of design solutions which exploit these principles is where inspiration for man-made structures should be. We analyse specific examples of sustainability from Nature and the benefits or value that these solutions have brought to different creatures. By doing this, we appreciate how the natural world fits into the world of sustainable buildings and how as building engineers we can value its true application in delivering sustainable building.

Making sense of research quality assessment

Purpose – For many academics in UK universities the nature and orientation of their research is overwhelmingly determined by considerations of how that work will be graded in research assessment exercises (RAEs). The grades awarded to work in a particular subject area can have a considerable impact on the individual and their university. There is a need to better understand those factors which may influence these grades. The paper seeks to address this issue. Design/methodology/approach – The paper considers relationships between the grades awarded and the quantitative information provided to the assessment panels for the 1996 and 2001 RAEs for two subject areas, built environment and town and country planning, and for three other subject areas, civil engineering, geography and archaeology, in the 2001 RAE. Findings – A simple model demonstrating strong and consistent relationships is established. RAE performance relates to numbers of research active staff, the production of books and journal papers, numbers of research studentships and graduations, and research income. Important differences between subject areas are identified. Research limitations/implications – Important issues are raised about the extent to which the new assessment methodology to be adopted for the 2008 RAE will capture the essence of good quality research in architecture and built environment. Originality/value – The findings provide a developmental perspective of RAEs and show how, despite a changed methodology, various research activities might be valued in the 2008 RAE. The basis for a methodology for reviewing the credibility of the judgements of panels is proposed.

The effect of a perceptual cognitive task on exercise performance: the dual-task condition after brain injury

Objective: To examine the effect of additional cognitive demand on cycling performance in individuals with acquired brain injury (ABI). Design: Prospective observational study. Setting: Rivermead Rehabilitation Centre. Participants: Ten individuals with ABI ( 7 men, 3 women) ( traumatic brain injury 7, tumour 1, stroke 2) and 10 healthy controls ( 6 men, 4 women). Intervention: Individuals were asked to maintain a set cadence during a three-stage incremental cycling test in both single-task ( no additional task) and dual-task ( whilst performing an additional cognitive task) conditions. Results: The ABI group showed a slight slowing in cadence in stages 1 and 3 of the graded exercise test from the single-to the dual-task condition, although this was not significant ( p less than or equal to 0.05). The control group showed no slowing of cadence at any incremental stage. When directly comparing the ABI with the control group, the change in cadence observed in dual-task conditions was only significantly different in stage 3 ( p less than or equal to 0.05). Conclusions: Clinicians should be aware of the possibility that giving additional cognitive tasks ( such as monitoring exercise intensity) while individuals with acquired brain injury are performing exercises may detrimentally affect performance. The effect may be more marked when the individuals are performing exercise at higher intensities.

A model for self-directed problem-based learning for renal therapeutics

Objective To introduce a new approach to problem-based learning (PBL) for self-directed learning in renal therapeutics. Design This 5-week course, designed for large student cohorts using minimal teaching resources, was based on a series of case studies and subsequent pharmaceutical care plans, followed by intensive and regular feedback from the instructor. Assessment Assessment of achievement of the learning outcomes was based on weekly-graded care plans and peer review assessment, allowing each student to judge the contributions of each group member and their own, along with a written case-study based examination. The pharmaceutical care plan template, designed using a “tick-box” system, significantly reduced staff time for feedback and scoring. Conclusion The proposed instructional model achieved the desired learning outcomes with appropriate student feedback, while promoting skills that are essential for the students' future careers as health care professionals.

A high frequency boundary element method for scattering by convex polygons with impedance boundary conditions

We consider scattering of a time harmonic incident plane wave by a convex polygon with piecewise constant impedance boundary conditions. Standard finite or boundary element methods require the number of degrees of freedom to grow at least linearly with respect to the frequency of the incident wave in order to maintain accuracy. Extending earlier work by Chandler-Wilde and Langdon for the sound soft problem, we propose a novel Galerkin boundary element method, with the approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh with smaller elements closer to the corners of the polygon. Theoretical analysis and numerical results suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency of the incident wave.

High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Effect of dietary supplementation with selenium-enriched yeast or sodium selenite on selenium tissue distribution and meat quality in commercial-line turkeys

The objective of this study was to determine the concentration of total selenium (Se) and proportions of total Se comprised as selenomethionine (SeMet) and selenocysteine (SeCys) in the tissues of female turkeys offered diets containing graded additions of selenized-enriched yeast (SY), or sodium selenite (SS). Oxidative stability and tissue glutathione peroxidase (GSH-Px) activity of breast and thigh muscle were assessed at 0 and 10 days post mortem. A total of 216 female turkey poults were enrolled in the study. A total of 24 birds were euthanized at the start of the study and samples of blood, breast, thigh, heart, liver, kidney and gizzard were collected for determination of total Se. Remaining birds were blocked by live weight and randomly allocated to one of four dietary treatments(n548 birds/treatment) that differed either in Se source (SY v. SS) or dose (Con [0.2 mg/kg total Se], SY-L and SS-L [0.3mg/kg total Se as SY and SS, respectively] and SY-H [0.45mg total Se/kg]). Following 42 and 84 days of treatment 24 birds per treatment were euthanized and samples of blood, breast, thigh, heart, liver, kidney and gizzard were retained for determination of total Se and the proportion of total Se comprised as SeMet or SeCys. Whole blood GSH-Px activity was determined at each time point. Tissue GSH-Px activity and thiobarbituric acid reactive substances were determined in breast and thigh tissue at the end of the study. There were responses (P,0.001) in all tissues to the graded addition of dietary Se, although rates of accumulation were highest in birds offered SY. There were notable differences between tissue types and treatments in the distribution of SeMet and SeCys, and the activity of tissue and erythrocyte GSH-Px (P,0.05). SeCys was the predominant form of Se in visceral tissue and SeMet the predominant form in breast tissue. SeCys contents were greater in thigh when compared with breast tissue. Muscle tissue GSH-Px activities mirrored SeCys contents. Despite treatment differences in tissue GSH-Px activity, there were no effects of treatment on any meat quality parameter.