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.

A lightweight balloon-carried cloud charge sensor

Despite the importance of microphysical cloud processes on the climate system, some topics are under-explored. For example, few measurements of droplet charges in nonthunderstorm clouds exist. Balloon carried charge sensors can be used to provide new measurements. A charge sensor is described for use with meteorological balloons, which has been tested over a range of atmospheric temperatures from -60 to 20 degrees C, in cloudy and clear air. The rapid time response of the sensor (to >10 V s(-1)) permits charge densities from 100 fC m(-3) to 1 nC m(-3) to be determined, which is sufficient for it to act as a cloud edge charge detector at weakly charged horizontal cloud boundaries.

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.

Assessing the sources and magnitude of diurnal nitrate variability in the San Joaquin River (California) with an in-situ optical nitrate sensor and dual nitrate isotopes

We investigated diurnal nitrate (NO3-) concentration variability in the San Joaquin River using an in situ optical NO3- sensor and discrete sampling during a 5-day summer period characterized by high algal productivity. Dual NO3- isotopes (delta N-15(NO3) and delta O-18(NO3)) and dissolved oxygen isotopes (delta O-18(DO)) were measured over 2 days to assess NO3- sources and biogeochemical controls over diurnal time-scales. Concerted temporal patterns of dissolved oxygen (DO) concentrations and delta O-18(DO) were consistent with photosynthesis, respiration and atmospheric O-2 exchange, providing evidence of diurnal biological processes independent of river discharge. Surface water NO3- concentrations varied by up to 22% over a single diurnal cycle and up to 31% over the 5-day study, but did not reveal concerted diurnal patterns at a frequency comparable to DO concentrations. The decoupling of delta N-15(NO3) and delta O-18(NO3) isotopes suggests that algal assimilation and denitrification are not major processes controlling diurnal NO3- variability in the San Joaquin River during the study. The lack of a clear explanation for NO3- variability likely reflects a combination of riverine biological processes and time-varying physical transport of NO3- from upstream agricultural drains to the mainstem San Joaquin River. The application of an in situ optical NO3- sensor along with discrete samples provides a view into the fine temporal structure of hydrochemical data and may allow for greater accuracy in pollution assessment.

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.

Ag dopedWO(3)-based powder sensor for the detection of NO gas in air

WO3-based materials as sensors for the monitor of environmental gases such as NO2 (NO + NO2) have been rapidly developed for various potential applications (stationary and mobile uses). It has been reported that these materials are highly sensitive to NOx with the sensitivity further enhanced by adding precious group metals (PGM such as Pt, Pd, Au, etc.). However, there has been limited work in revealing the sensing mechanism for these gases over the WO3-based sensors. In particular, the role of promoter is not yet clear though speculations on their catalytic, electronic and structural effects have been made in the past. In parallel to these PGM promoters here we report,for the first time, that Ag promotion can also enhance WO3 sensitivity significantly. In addition, this promotion decreases the optimum sensor temperature of 300 degreesC for Most WO3-based sensors, to below 200 degreesC. Characterizations (XRD, TEM, and impedance measurement) reveal that there is no significant bulk structure change nor particle size alteration in the WO3 phases during the NO exposure. However, it is found that the Ag doping creates a high concentration of oxygen vacancies in form of coordinated crystallographic shear (CS) planes onto the underneath WO3. It is thus proposed that the Ag particle facilitates the oxidative conversion of NO to NO2 followed by a subsequent NO2 adsorption on the defective WO, sites created at the Ag-WO3 interface; hence, accounting for the high molecular sensitivity. (C) 2002 Elsevier Science B.V. All rights reserved.

Bis[1,1 '-N,N '-(2-picolyl)aminomethyl]ferrocene as a redox sensor for transition metal ions

The compound bis[1,1'-N,N'-(2-picolyl) aminomethyl] ferrocene, L-1, was synthesized. The protonation constants of this ligand and the stability constants of its complexes with Ni2+, Cu2+, Zn2+, Cd2+ and Pb2+ were determined in aqueous solution by potentiometric methods at 25degreesC and at ionic strength 0.10 mol dm(-3) in KNO3. The compound L-1 forms only 1:1 (M:L) complexes with Pb2+ and Cd2+ while with Ni2+ and Cu2+ species of 2:1 ratio were also found. The complexing behaviour of L-1 is regulated by the constraint imposed by the ferrocene in its backbone, leading to lower values of stability constants for complexes of the divalent first row transition metals when compared with related ligands. However, the differences in stability are smaller for the larger metal ions. The structure of the copper complex with L-1 was determined by single-crystal X-ray diffraction and shows that a species of 2:2 ratio is formed. The two copper centres display distorted octahedral geometries and are linked through the two L1 bridges at a long distance of 8.781(10) Angstrom. The electrochemical behaviour of L-1 was studied in the presence of Ni2+, Cu2+, Zn2+, Cd2+ and Pb2+, showing that upon complexation the ferrocene-ferrocenium half-wave potential shifts anodically in relation to that of the free ligand. The maximum electrochemical shift (DeltaE(1/2)) of 268 mV was found in the presence of Pb2+, followed by Cu2+ (218 mV), Ni2+ (152 mV), Zn2+ (111 mV) and Cd2+ (110 mV). Moreover, L-1 is able to electrochemically and selectively sense Cu2+ in the presence of a large excess of the other transition metal cations studied.