Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.

Reduced-order modelling of a high-voltage oscillatory impulse generator

The design of high-voltage equipment encompasses the study of oscillatory surges caused by transients such as those produced by switching. By obtaining a model, the response of which reconstructs that observed in the actual system, simulation studies and critical tests can be carried out on the model rather than on the equipment itself. In this paper, methods for the construction of simplified models are described and it is shown how the use of a complex model does not necessarily result in superior response pattern reconstruction.

Top down influence on visuo-tactile interaction modulates neural oscillatory responses

Multisensory integration involves bottom-up as well as top-down processes. We investigated the influences of top-down control on the neural responses to multisensory stimulation using EEG recording and time-frequency analyses. Participants were stimulated at the index or thumb of the left hand, using tactile vibrators mounted on a foam cube. Simultaneously they received a visual distractor from a light emitting diode adjacent to the active vibrator (spatially congruent trial) or adjacent to the inactive vibrator (spatially incongruent trial). The task was to respond to the elevation of the tactile stimulus (upper or lower), while ignoring the simultaneous visual distractor. To manipulate top-down control on this multisensory stimulation, the proportion of spatially congruent (vs. incongruent) trials was changed across blocks. Our results reveal that the behavioral cost of responding to incongruent than congruent trials (i.e., the crossmodal congruency effect) was modulated by the proportion of congruent trials. Most importantly, the EEG gamma band response and the gamma-theta coupling were also affected by this modulation of top-down control, whereas the late theta band response related to the congruency effect was not. These findings suggest that gamma band response is more than a marker of multisensory binding, being also sensitive to the correspondence between expected and actual multisensory stimulation. By contrast, theta band response was affected by congruency but appears to be largely immune to stimulation expectancy.

Structure and viscoelasticity of an electrorheological fluid in oscillatory shear: computer simulation investigation

The three-dimensional molecular dynamics simulation method has been used to study the dynamic responses of an electrorheological (ER) fluid in oscillatory shear. The structure and related viscoelastic behaviour of the fluid are found to be sensitive to the amplitude of the strain. With the increase of the strain amplitude, the structure formed by the particles changes from isolated columns to sheet-like structures which may be perpendicular or parallel to the oscillating direction. Along with the structure evolution, the field-induced moduli decrease significantly with an increase in strain amplitude. The viscoelastic behaviour of the structures obtained in the cases of different strain amplitudes was examined in the linear response regime and an evident structure dependence of the moduli was found. The reason for this lies in the anisotropy of the arrangement of the particles in these structures. Short-range interactions between the particles cannot be neglected in determining the viscoelastic behaviour of ER fluids at small strain amplitude, especially for parallel sheets. The simulation results were compared with available experimental data and good agreement was reached for most of them.

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.

Further characterization of muscarinic agonist-induced epileptiform bursting activity in immature rat piriform cortex, in vitro

The characteristics of muscarinic acetylcholine receptor agonist-induced epileptiform bursting seen in immature rat piriform cortex slices in vitro were further investigated using intracellular recording, with particular focus on its postnatal age-dependence (P+14-P+30), pharmacology, site(s) of origin and the likely contribution of the muscarinic acetylcholine receptor agonist-induced post-stimulus slow afterdepolarization and gap junction functionality toward its generation. The muscarinic agonist, oxotremorine-M (10 microM), induced rhythmic bursting only in immature piriform cortex slices; however, paroxysmal depolarizing shift amplitude, burst duration and burst incidence were inversely related to postnatal age. No significant age-dependent changes in neuronal membrane properties or postsynaptic muscarinic responsiveness accounted for this decline. Burst incidence was higher when recorded in anterior and posterior regions of the immature piriform cortex. In adult and immature neurones, oxotremorine-M effects were abolished by M1-, but not M2-muscarinic acetylcholine receptor-selective antagonists. Rostrocaudal lesions, between piriform cortex layers I and II, or layer III and endopiriform nucleus in adult or immature slices did not influence oxotremorine-M effects; however, the slow afterdepolarization in adult (but not immature) lesioned slices was abolished. Gap junction blockers (carbenoxolone or octanol) disrupted muscarinic bursting and diminished the slow afterdepolarization in immature slices, suggesting that gap junction connectivity was important for bursting. Our data show that neural networks within layers II-III function as primary oscillatory circuits for burst initiation in immature rat piriform cortex during persistent muscarinic receptor activation. Furthermore, we propose that muscarinic slow afterdepolarization induction and gap junction communication could contribute towards the increased epileptiform susceptibility of this brain area.

Dr John Snow and an early investigation of groundwater contamination

John Snow was a physician but his studies of the way in which cholera is spread have long attracted the interest of hydrogeologists. From his investigation into the epidemiology of the cholera outbreak around the well in Broad Street, London, in 1854, Snow gained valuable evidence that cholera is spread by contamination of drinking water. Subsequent research by others showed that the well was contaminated by sewage. The study therefore represents one of the first, if not the first, study of an incident of groundwater contamination in Britain. Although he had no formal geological training, it is clear that Snow had a much better understanding of groundwater than many modern medical practitioners. At the time of the outbreak Snow was continuing his practice as a physician and anaesthetist. His casebooks for 1854 do not even mention cholera. Yet, nearly 150 years later, he is as well known for his work on cholera as for his pioneering work on anaesthesia, and his discoveries are still the subject of controversy.