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.

Liberation or limitation? Understanding Iyengar Yoga as a practice of the self

This article explores the Foucauldian notions of practices of the self and care of the self, read via Deleuze, in the context of Iyengar yoga (one of the most popular forms of yoga currently). Using ethnographic and interview research data the article outlines the Iyengar yoga techniques which enable a focus upon the self to be developed, and the resources offered by the practice for the creation of ways of knowing, experiencing and forming the self. In particular, the article asks whether Iyengar yoga offers possibilities for freedom and liberation, or whether it is just another practice of control and management. Assessing Iyengar yoga via a ‘critical function’, a function of ‘struggle’ and a ‘curative and therapeutic function’, the article analyses whether the practice might constitute a mode of care of the self, and what it might offer in the context of the contemporary need to live better, as well as longer.

Becoming skilled: The cultural and corporeal geographies of teaching and learning Thai Yoga massage

This paper explores the process of learning an embodied knowledge using the work of Dreyfus and Deleuze. Although geographers have begun to acknowledge the role of embodied knowledges in social life, there have been few in-depth case studies of how these skills are learned. This paper offers a case study of Thai Yoga massage (TYM), a ‘complementary and alternative therapy’ which is growing in popularity in the United Kingdom. Having outlined the case study, the paper explores the cultural geographies of the formalisation, documentation and contestation of the set of techniques that have come to cohere in the UK as TYM. The paper then interrogates the messy corporeal geographies of learning a skill, and briefly considers how more advanced practitioners experience their skilled practice.

Post-phenomenology/post-phenomenological geographies

Post-phenomenological geographies are an emergent (and as yet relatively fragmentary) body of work. This work does not reflect a turn away from phenomenological theories; rather it reflects a critical engagement which rereads them through the post-structuralist theories of such authors as Deleuze, Derrida, and Levinas. This rereading, combined with a disciplinary context of a turn to practice and the ‘more than human’, has resulted in post-phenomenological geographies which extend the boundaries of the phenomenological focus upon the experiencing subject (in place). Thus, the interest is in the ways in which inhuman, nonhuman, and more-than-human forces contribute to processes of subject formation, place making, and inhabiting the world. These geographies have thus far been played out through critical explorations of the realms of the experiencing subject and landscape. This more-than-human focus has tested conventional human geographical methods, requiring innovative use of technologies such as video to document research, the use of experiential research methods, and also experimentation with the form of narrating these experiential methods.

A Cu tolerant population of the earthworm Dendrodrilus rubidus (Savigny, 1862) at Coniston Copper Mines, Cumbria, UK

Dendrodrilus rubidus were sampled from a mine spoil soil at Coniston Copper Mine, an abandoned Cu mine in Cumbria, UK and a Cu-free control site. Earthworms were maintained for 14 d in both Kettering loam and a Moorland soil amended with Cu nitrate. Mortality, condition index, weight change and tissue concentration were determined. In both soils D. rubidus native to the mine site were able to tolerate significantly higher soil Cu concentrations (MWRT, p <= 0.001), and exhibited significantly less change in weight (t-test, p <= 0.001) and a lower loss in condition (t-test, p <= 0.001) than control earthworms. For a given soil Cu concentration tissue Cu concentrations were greater in the mine site earthworms. Low cocoon production and viability from the mine site population prevented the determination of toxicity parameters on the F1 generation and may be an indicator of the cost of tolerance to the population. (c) 2007 Elsevier Ltd. All rights reserved.

Development of a methodology to investigate the importance of chemical speciation on the bioavailability of contaminants to Eisenia andrei

The uptake of metals by earthworms occurs predominantly via the soil pore water, or via an uptake route which is related to the soil pore water metal concentration. However, it has been suggested that the speciation of the metal is also important. A novel technique is described which exposes Eisenia andrei Bouche to contaminant bearing solutions in which the chemical factors affecting its speciation may be individually and systematically manipulated. In a preliminary experiment, the LC50 for copper nitrate was 0.046 mg l(-1) (95 % confidence intervals: 0.03 and 0.07 mg l(-1)). There was a significant positive correlation between earthworm mortality and bulk copper concentration in solution (R-2 = 0.88, P less than or equal to 0.001), and a significant positive increase in earthworm tissue copper concentration with increasing copper concentration in solution (R-2 = 0.97, P less than or equal to 0.001). It is anticipated that quantifying the effect of soil solution chemical speciation on copper bioavailability will provide an excellent aid to understanding the importance of chemical composition and the speciation of metals, in the calculation of toxicological parameters.

Single versus multiple occupancy - Effects on toxicity parameters measured on Eisenia fetida in lead nitrate-treated soil

The mortality (7 and 14 d), weight change (7 and 14 d), and metal uptake of Eisenia fetida (Savigny, 1826) kept in Pb(NO3)(2)-treated Kettering loam soil in single- and multiple-occupancy (10 earthworms) test containers were determined. The number of earthworms to dry mass (g) ratio of soil was 1:50 in both sets of test containers. Lead concentrations were in the nominal range of 0 to 10,000 mg Pb/kg soil (mg/kg hereafter). Levels of mortality at a given concentration were statistically identical between the single- and multiple-occupancy tests, except at 1,800 mg/kg, at which significantly (p less than or equal to 0.05) more mortality occurred in the multiple-occupancy tests. Death of individual earthworms in the multiple-occupancy tests did not trigger death of the other earthworms in that soil. The LC50 values (concentration statistically likely to kill 50% of the population) were identical between the multiple- and single-occupancy soils: 2,662 mg/kg (2,598-2,984, 7 d) and 2,589 mg/kg (2,251-3,013, 14 d) for the multiple-occupancy soils and 2,827 mg/kg (2,443-3,168, both 7 and 14 d) for the single-occupancy soils (values in brackets represent the 95% confidence intervals). Data were insufficient to calculate the concentration statistically likely to reduce individual earthworm mass by 50% (EC50), but after 14 d, the decrease in earthworm weight in the 1,800 and 3,000 mg/kg tests was significantly greater in the multiple- than in the single-occupancy soils. At 1,000, 1,800, and 3,000 mg/kg tests, earthworm Pb tissue concentration was significantly (p less than or equal to 0.05) greater in earthworms from the multiple-occupancy soils. The presence of earthworms increased the NH3 content of the soil; earthworm mortality increased NH3 concentrations further but not to toxic levels.

Survival, Pb-uptake and behaviour of three species of earthworm in Pb treated soils determined using an OECD-style toxicity test and a soil avoidance test

Mature (clitellate) Eisenia andrei Bouche (ultra epigeic), Lumbricus rubellus Hoffmeister (epigeic), and Aporrectodea caliginosa (Savigny) (endogeic) earthworms were placed in soils treated with Pb(NO3)(2) to have concentrations in the range 1000 to 10 000 mg Pb kg(-1). After 28 days LC50(-95%confidence limit) (+95%confidence limit) values were E. andrei 5824(-361)(+898) mg Pb kg(-1), L. rubellus 2867(-193)(+145) mg Pb kg(-1) and A. caliginosa 2747(-304)(+239) mg Pb kg(-1) and EC50s for weight change were E. andrei 2841(-68)(+150) Pb kg(-1), L. rubellus 1303(-201)(+204) mg Pb kg(-1) and A. caliginosa 1208(-206)(+212) Mg Pb kg(-1). At any given soil Pb concentration, Pb tissue concentrations after 28 days were the same for all three earthworm species. In a soil avoidance test there was no difference between the behaviour of the different species. The lower sensitivity to Pb exhibited by E. andrei is most likely due to physiological adaptations associated with the modes of life of the earthworms, and could have serious implications for the use of this earthworm as the species of choice in standard toxicological testing. (c) 2005 Elsevier Ltd. All rights reserved.

Inherited resistance to arsenate toxicity in two populations of Lumbricus rubellus

No unequivocal evidence exists of genetically inherited resistance to metals/metalloids in field populations of earthworms. We studied cocoon production in adult Lumbricus rubellus Hoffmeister collected from an abandoned arsenic and copper mine (Devon Great Consols, Devon, UK), and abandoned tungsten mine (Carrock Fell, Cumbria, UK) and an uncontaminated cultured population. The earthworms were kept in uncontaminated soil for nine weeks. From a total of 42 L. rubellus from each site, Devon Great Consols adults produced 301 cocoons, of which 42 were viable; Carrock Fell 60 cocoons, of which 11 were viable; and the reference population 101 cocoons, of which 62 were viable. The hatchlings were collected and stored at 4degreesC at weekly intervals. After 12 weeks, all hatchlings were transferred to clean soil and maintained at 15degreesC for 20 weeks until they showed evidence of a clitellum. In toxicity trials, F1 generation L. rubellus were exposed to 2,000 mg As/kg as sodium arsenate or 300 mg Cu/kg as copper chloride for 28 d. The F1 generation L. rubellus from Devon Great Consols mine demonstrated resistance to arsenate but not copper. All L. rubellus from Devon Great Consols kept in soil treated with sodium arsenate remained in good condition over the 28-d period but lost condition rapidly and suffered high mortality in soil treated with copper chloride. The control population suffered high mortality in soil treated with sodium arsenate and copper chloride. Previous work has shown that field-collected adults demonstrate resistance to both arsenate and Cu toxicity under these conditions. Thus, while arsenate resistance may be demonstrated in F1 generation L. rubellus from one of the contaminated sites, Cu resistance is not. The F1 adults and F2 cocoons did not have significantly higher levels of As than the control population, with no residual As tissue burden, suggesting that resistance to As in these populations may be inherited.

Interactions between earthworms and arsenic in the soil environment: a review

Chemical pollution of the environment has become a major source of concern. In particular, many studies have investigated the impact of pollution on biota in the environment. Studies on metalliferous contaminated mine spoil wastes have shown that some soil organisms have the capability to become resistant to metal/metalloid toxicity. Earthworms are known to inhabit arsenic-rich metalliferous soils and, due to their intimate contact with the soil, in both the solid and aqueous phases, are likely to accumulate contaminants present in mine spoil. Earthworms that inhabit metalliferous contaminated soils must have developed mechanisms of resistance to the toxins found in these soils. The mechanisms of resistance are not fully understood; they may involve physiological adaptation (acclimation) or be genetic. This review discusses the relationships between earthworms and arsenic-rich mine spoil wastes, looking critically at resistance and possible mechanisms of resistance, in relation to soil edaphic factors and possible trophic transfer routes. (C) 2003 Elsevier Science Ltd. All rights reserved.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

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.