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.

Effluent quality and ammonia emissions from out-wintering pads in England, Wales and Ireland

Out-wintering pads offer a reduced cost system for wintering cattle, minimising damage to pasture, providing animal welfare and production benefits, and generate, potentially, a more manageable effluent and lower ammonia emissions. The objectives of the present study were (i) to contribute to improved understanding of the factors impacting on effluent quality, ammonia emissions and animal welfare via observations on four farm-based out-wintering pads (ComOWPs) in England, Wales and Ireland and more detailed studies undertaken on four experimental OWPs (ExpOWPs) constructed at Rothamsted Research North Wyke, Devon, England and (ii) to corroborate the effluent quality data from both the ComOWPs and the ExpOWPs, with findings in the literature. Woodchip size, feeding management and area allowance were the treatment factors applied on the ExpOWPs. These three factors were randomised across the four ExpOWPs, over four 6–7 week periods. Effluent quality from the ExpOWPs was sampled frequently in a flow proportional way and analysed for total N (TN); total P (TP); total solids (TS); ammonium-N (NH4+-N); nitrate-N (NO3−-N). Beef cattle were periodically weighed for determination of live weight gain (LWG). An approximate nitrogen balance was calculated as a means of understanding its partitioning and fate during and after the ExpOWPs use. Effluent quality from the ComOWPs was sampled frequently, also in a flow-proportional way, and analysed for TN, TP, TS, NH4+-N, NO3−-N, total K and COD. Effluent quality data from the ExpOWPs showed no significant differences (P > 0.05) between treatments, with average concentrations of 1095 mg l−1, and 806 mg l−1, for TN and NH4+-N, respectively. Average effluent concentrations from the ComOWPs were 356 mg l−1 TN and 124 mg l−1 NH4+-N. Ammonia emissions from the ExpOWPs showed no significant differences (P > 0.05) between the treatments, with average mean emission rates of 2.5 g m−2 d−1 NH3-N, respectively. A positive correlation was established between NH3-N emission rate and wind speed. Emission rates from the ComOWPs ranged from 0.7 to 1.6 g m−2 d−1 NH3-N. Average daily LWG on the ExpOWPs was 1.33 kg steer−1 d−1. The effluent from both the ComOWPs and ExpOWPs were more similar with dirty water and of consistently lower strength than beef cattle slurry, as supported by findings in the literature, and therefore, it is suggested to be subject to the regulatory requirements of dirty water rather than slurry.

The music instinct: the evolutionary basis of musicality

Why does music pervade our lives and those of all known human beings living today and in the recent past? Why do we feel compelled to engage in musical activity, or at least simply enjoy listening to music even if we choose not to actively participate? I argue that this is because musicality—communication using variations in pitch, rhythm, dynamics and timbre, by a combination of the voice, body (as in dance), and material culture—was essential to the lives of our pre-linguistic hominin ancestors. As a consequence we have inherited a desire to engage with music, even if this has no adaptive benefit for us today as a species whose communication system is dominated by spoken language. In this article I provide a summary of the arguments to support this view.

Cnoc Coig: a Mesolithic shell midden assemblage

Recent work on a sample of the chipped stone from one of the late Mesolithic shell midden sites on the Inner Hebrides island of Oronsay has shown that the assemblage was created using bipolar and platform technologies, with an unexpected element of narrow blade technology shown in cores and core trimming elements, suggesting that there may have been links between this classic ‘Obanian’ assemblage and the more typical Mesolithic narrow blade technology. Findings raise questions about the relationship of settlement on the island to Mesolithic settlement rounds and to the transition to the Neolithic.

Flooding tolerance in four 'Garrigue' landscape plants: implications for their future use in the urban landscapes of north-west Europe?

Within a changing climate, Mediterranean ‘Garrigue’ xerophytes are increasingly recommended as suitable urban landscape plants in north-west Europe, based on their capacity to tolerate high temperature and reduced water availability during summer. Such species, however, have a poor reputation for tolerating waterlogged soils; paradoxically a phenomenon that may also increase in north-west Europe due to predictions for both higher volumes of winter precipitation, and short, but intensive periods of summer rainfall. This study investigated flooding tolerance in four landscape ‘Garrigue’ species, Stachys byzantina, Cistus × hybridus, Lavandula angustifolia and Salvia officinalis. Despite evolving in a dry habitat, the four species tested proved remarkably resilient to flooding. All species survived 17 days flooding in winter, with Stachys and Lavandula also surviving equivalent flooding duration during summer. Photosynthesis and biomass production, however, were strongly inhibited by flooding although the most tolerant species, Stachys quickly restored its photosynthetic capacity on termination of flooding. Overall, survival rates were comparable to previous studies on other terrestrial (including wetland) species. Subsequent experiments using Salvia (a species we identified as ‘intermediate’ in tolerance) clearly demonstrated adaptations to waterlogging, e.g. acclimation against anoxia when pre-treated with hypoxia. Despite anecdotal information to the contrary, we found no evidence to suggest that these xerophytic species are particularly intolerant of waterlogging. Other climatic and biotic factors may restrict the viability and distribution of these species within the urban conurbations of north-west Europe, but we believe increased incidence of flooding per se should not preclude their consideration.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution 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, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, 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 neighbourhood of wells and away from wells.

The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.

Croig Cave: a late Bronze Age ornament deposition and 3,500 years of coastal foraging in NW Mull, Scotland

Activity within caves provides an important element of the later prehistoric and historic settlement pattern of western Scotland. This contribution reports on a small-scale excavation within Croig Cave, on the coast of north-west Mull, that exposed a 1.95m sequence of midden deposits and cave floors that dated bewteen c 1700 BC and AD 1400. Midden analysis indicated the processing of a .... 950 BC, a penannular copper bracelet a discrete ritual episode within the cycle of otherwise potentially mundane activities. Lead isotope analysis indicates an Irish origin for the copper ore. A piece of iron slag within later midden deposits, dated to c 400 BC, along with high frequencies of wood charcoal, suggest that smithing or smelting may have occurred within the cave. High zinc levels in the historic levels of the midden c AD 1200 might indicate intensive processing of seaweed.

Structural, magnetic, and electronic properties of VxCr2−xS3(0

A new family of vanadium-substituted chromium sulfides (VxCr2-xS3, 0 < x < 2) has been prepared and characterized by powder X-ray and neutron diffraction, SQUID magnetometry, electrical resistivity, and Seebeck coefficient measurements. Vanadium substitution leads to a single-phase region with a rhombohedral Cr2S3 structure over the composition range 0.0 < x e 0.75, while at higher vanadium contents (1.6 e x < 2.0) a second single-phase region, in which materials adopt a cation-deficient Cr3S4 structure, is observed. Materials with the Cr2S3 structure all exhibit semiconducting behavior. However, both transport and magnetic properties indicate an increasing degree of electron delocalization with increasing vanadium content in this compositional region. Materials that adopt a Cr3S4-type structure exhibit metallic behavior. Magnetic susceptibility data reveal that all materials undergo a magnetic ordering transition at temperatures in the range 90–118 K. Low-temperature magnetization data suggest that this involves a transition to a ferrimagnetic state.

Balanced excitation and inhibition: Model based analysis of local field potentials

We have developed a model of the local field potential (LFP) based on the conservation of charge, the independence principle of ionic flows and the classical Hodgkin–Huxley (HH) type intracellular model of synaptic activity. Insights were gained through the simulation of the HH intracellular model on the nonlinear relationship between the balance of synaptic conductances and that of post-synaptic currents. The latter is dependent not only on the former, but also on the temporal lag between the excitatory and inhibitory conductances, as well as the strength of the afferent signal. The proposed LFP model provides a method for decomposing the LFP recordings near the soma of layer IV pyramidal neurons in the barrel cortex of anaesthetised rats into two highly correlated components with opposite polarity. The temporal dynamics and the proportional balance of the two components are comparable to the excitatory and inhibitory post-synaptic currents computed from the HH model. This suggests that the two components of the LFP reflect the underlying excitatory and inhibitory post-synaptic currents of the local neural population. We further used the model to decompose a sequence of evoked LFP responses under repetitive electrical stimulation (5 Hz) of the whisker pad. We found that as neural responses adapted, the excitatory and inhibitory components also adapted proportionately, while the temporal lag between the onsets of the two components increased during frequency adaptation. Our results demonstrated that the balance between neural excitation and inhibition can be investigated using extracellular recordings. Extension of the model to incorporate multiple compartments should allow more quantitative interpretations of surface Electroencephalography (EEG) recordings into components reflecting the excitatory, inhibitory and passive ionic current flows generated by local neural populations.

A dynamic model of neurovascular coupling: Implications for blood vessel dilation and constriction

Neurovascular coupling in response to stimulation of the rat barrel cortex was investigated using concurrent multichannel electrophysiology and laser Doppler flowmetry. The data were used to build a linear dynamic model relating neural activity to blood flow. Local field potential time series were subject to current source density analysis, and the time series of a layer IV sink of the barrel cortex was used as the input to the model. The model output was the time series of the changes in regional cerebral blood flow (CBF). We show that this model can provide excellent fit of the CBF responses for stimulus durations of up to 16 s. The structure of the model consisted of two coupled components representing vascular dilation and constriction. The complex temporal characteristics of the CBF time series were reproduced by the relatively simple balance of these two components. We show that the impulse response obtained under the 16-s duration stimulation condition generalised to provide a good prediction to the data from the shorter duration stimulation conditions. Furthermore, by optimising three out of the total of nine model parameters, the variability in the data can be well accounted for over a wide range of stimulus conditions. By establishing linearity, classic system analysis methods can be used to generate and explore a range of equivalent model structures (e.g., feed-forward or feedback) to guide the experimental investigation of the control of vascular dilation and constriction following stimulation.

A three-compartment model of the hemodynamic response and oxygen delivery to brain

We describe a mathematical model linking changes in cerebral blood flow, blood volume and the blood oxygenation state in response to stimulation. The model has three compartments to take into account the fact that the cerebral blood flow and volume as measured concurrently using laser Doppler flowmetry and optical imaging spectroscopy have contributions from the arterial, capillary as well as the venous compartments of the vasculature. It is an extension to previous one-compartment hemodynamic models which assume that the measured blood volume changes are from the venous compartment only. An important assumption of the model is that the tissue oxygen concentration is a time varying state variable of the system and is driven by the changes in metabolic demand resulting from changes in neural activity. The model takes into account the pre-capillary oxygen diffusion by flexibly allowing the saturation of the arterial compartment to be less than unity. Simulations are used to explore the sensitivity of the model and to optimise the parameters for experimental data. We conclude that the three-compartment model was better than the one-compartment model at capturing the hemodynamics of the response to changes in neural activation following stimulation.

A model of the dynamic relationship between blood flow and volume changes during brain activation

The temporal relationship between changes in cerebral blood flow (CBF) and cerebral blood volume (CBV) is important in the biophysical modeling and interpretation of the hemodynamic response to activation, particularly in the context of magnetic resonance imaging and the blood oxygen level-dependent signal. Grubb et al. (1974) measured the steady state relationship between changes in CBV and CBF after hypercapnic challenge. The relationship CBV proportional to CBFPhi has been used extensively in the literature. Two similar models, the Balloon (Buxton et al., 1998) and the Windkessel (Mandeville et al., 1999), have been proposed to describe the temporal dynamics of changes in CBV with respect to changes in CBF. In this study, a dynamic model extending the Windkessel model by incorporating delayed compliance is presented. The extended model is better able to capture the dynamics of CBV changes after changes in CBF, particularly in the return-to-baseline stages of the response.