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.

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.

Cholinergic modulation of intrinsic fibre-evoked excitatory transmission contains a nicotinic component in immature but not adult rat piriform cortex, in vitro

The piriform cortex (PC) is highly prone to epileptogenesis, particularly in immature animals, where decreased muscarinic modulation of PC intrinsic fibre excitatory neurotransmission is implicated as a likely cause. However, whether higher levels of acetylcholine (ACh) release occur in immature vs. adult PC remains unclear. We investigated this using in vitro extracellular electrophysiological recording techniques. Intrinsic fibre-evoked extracellular field potentials (EFPs) were recorded from layers II to III in PC brain slices prepared from immature (P14-18) and adult (P>40) rats. Adult and immature PC EFPs were suppressed by eserine (1muM) or neostigmine (1muM) application, with a greater suppression in immature ( approximately 40%) than adult ( approximately 30%) slices. Subsequent application of atropine (1muM) reversed EFP suppression, producing supranormal ( approximately 12%) recovery in adult slices, suggesting that suppression was solely muscarinic ACh receptor-mediated and that some 'basal' cholinergic 'tone' was present. Conversely, atropine only partially reversed anticholinesterase effects in immature slices, suggesting the presence of additional non-muscarinic modulation. Accordingly, nicotine (50muM) caused immature field suppression ( approximately 30%) that was further enhanced by neostigmine, whereas it had no effect on adult EFPs. Unlike atropine, nicotinic antagonists, mecamylamine and methyllycaconitine, induced immature supranormal field recovery ( approximately 20%) following anticholinesterase-induced suppression (with no effect on adult slices), confirming that basal cholinergic 'tone' was also present. We suggest that nicotinic inhibitory cholinergic modulation occurs in the immature rat PC intrinsic excitatory fibre system, possibly to complement the existing, weak muscarinic modulation, and could be another important developmentally regulated system governing immature PC susceptibility towards epileptogenesis.

A novel component of cannabis extract potentiates excitatory synaptic transmission in rat olfactory cortex in vitro

Cannabis is a potential treatment for epilepsy, although the few human studies supporting this use have proved inconclusive. Previously, we showed that a standardized cannabis extract (SCE), isolated Delta(9)-tetrahydrocannabinol (Delta(9)-THC), and even Delta(9)-THC-free SCE inhibited muscarinic agonist-induced epileptiform bursting in rat olfactory cortical brain slices, acting via CB1 receptors. The present work demonstrates that although Delta(9)-THC (1microM) significantly depressed evoked depolarizing postsynaptic potentials (PSPs) in rat olfactory cortex neurones, both SCE and Delta(9)-THC-free SCE significantly potentiated evoked PSPs (all results were fully reversed by the CB1 receptor antagonist SR141716A, 1microM); interestingly, the potentiation by Delta(9)-THC-free SCE was greater than that produced by SCE. On comparing the effects of Delta(9)-THC-free SCE upon evoked PSPs and artificial PSPs (aPSPs; evoked electrotonically following brief intracellular current injection), PSPs were enhanced, whereas aPSPs were unaffected, suggesting that the effect was not due to changes in background input resistance. Similar recordings made using CB1 receptor-deficient knockout mice (CB1(-/-)) and wild-type littermate controls revealed cannabinoid or extract-induced changes in membrane resistance, cell excitability and synaptic transmission in wild-type mice that were similar to those seen in rat neurones, but no effect on these properties were seen in CB1(-/-) cells. It appears that the unknown extract constituent(s) effects over-rode the suppressive effects of Delta(9)-THC on excitatory neurotransmitter release, which may explain some patients' preference for herbal cannabis rather than isolated Delta(9)-THC (due to attenuation of some of the central Delta(9)-THC side effects) and possibly account for the rare incidence of seizures in some individuals taking cannabis recreationally

Independent component analysis of climate data: A new look at EOF rotation

The complexity inherent in climate data makes it necessary to introduce more than one statistical tool to the researcher to gain insight into the climate system. Empirical orthogonal function (EOF) analysis is one of the most widely used methods to analyze weather/climate modes of variability and to reduce the dimensionality of the system. Simple structure rotation of EOFs can enhance interpretability of the obtained patterns but cannot provide anything more than temporal uncorrelatedness. In this paper, an alternative rotation method based on independent component analysis (ICA) is considered. The ICA is viewed here as a method of EOF rotation. Starting from an initial EOF solution rather than rotating the loadings toward simplicity, ICA seeks a rotation matrix that maximizes the independence between the components in the time domain. If the underlying climate signals have an independent forcing, one can expect to find loadings with interpretable patterns whose time coefficients have properties that go beyond simple noncorrelation observed in EOFs. The methodology is presented and an application to monthly means sea level pressure (SLP) field is discussed. Among the rotated (to independence) EOFs, the North Atlantic Oscillation (NAO) pattern, an Arctic Oscillation–like pattern, and a Scandinavian-like pattern have been identified. There is the suggestion that the NAO is an intrinsic mode of variability independent of the Pacific.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low-shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional-wave velocity is strongly correlated with the shear-wave velocity in this suite of rocks. The ratio V-P/V-S varies significantly with change of both pore-fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot-flow and squirt-flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt-flow of fluid between the pores of various geometries. The contribution of the Biot-flow loss mechanism to the total loss is negligible. The compressional-wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low-shale, high-porosity sandstone reservoirs.

Isolating the 'farmer' effect as a component of the advantage of growing genetically modified varieties in developing countries: a Bt cotton case study from Jalgaon, India

The present paper explores the 'farmer' effect in economic advantages often claimed for Bt cotton varieties (those with the endotoxin gene from Bacillus thuringiensis conferring resistance to some insect pests) compared to non-Bt varieties. Critics claim that much of the yield advantage of Bt cotton could be due to the fact that farmers adopting the technology are in a better position to provide inputs and management and so much of any claimed Bt advantage is an artefact rather than reflecting a real advantage of the variety per se. The present paper provides an in-depth analysis of 63 non-adopting and 94 adopting households of Bt cotton in Jalgaon, Maharashtra State, India, spanning the seasons 2002 and 2003. Results suggest that Bt adopters are indeed different from non-adopters in a number of ways. Adopters appear to specialize more on cotton (at least in terms of the land area they devote to the crop), spend more money on irrigation and grow well-performing non-Bt varieties of cotton (Bunny). Taking gross margin as the basis for comparison, Bt plots had 2.5 times the gross margin of non-Bt plots in both seasons. If only adopters are considered then the gross margin advantage of Bt plots reduces to 1.6 times that of non-Bt plots. This is still a significant advantage and could well explain the popularity of Bt in Maharashtra. However, it is clear that great care needs to be taken with such comparative studies.

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.

Acoustic scattering by mildly rough unbounded surfaces in three dimensions

For a nonlocally perturbed half- space we consider the scattering of time-harmonic acoustic waves. A second kind boundary integral equation formulation is proposed for the sound-soft case, based on a standard ansatz as a combined single-and double-layer potential but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half- space Green's function. Due to the unboundedness of the surface, the integral operators are noncompact. In contrast to the two-dimensional case, the integral operators are also strongly singular, due to the slow decay at infinity of the fundamental solution of the three-dimensional Helmholtz equation. In the case when the surface is sufficiently smooth ( Lyapunov) we show that the integral operators are nevertheless bounded as operators on L-2(Gamma) and on L-2(Gamma G) boolean AND BC(Gamma) and that the operators depend continuously in norm on the wave number and on G. We further show that for mild roughness, i.e., a surface G which does not differ too much from a plane, the boundary integral equation is uniquely solvable in the space L-2(Gamma) boolean AND BC(Gamma) and the scattering problem has a unique solution which satisfies a limiting absorption principle in the case of real wave number.

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.