Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Interferometric technique for measuring terahertz antenna phase patterns

A quasi-optical interferometric technique capable of measuring antenna phase patterns without the need for a heterodyne receiver is presented. It is particularly suited to the characterization of terahertz antennas feeding power detectors or mixers employing quasi-optical local oscillator injection. Examples of recorded antenna phase patterns at frequencies of 1.4 and 2.5 THz using homodyne detectors are presented. To our knowledge, these are the highest frequency antenna phase patterns ever recovered. Knowledge of both the amplitude and phase patterns in the far field enable a Gauss-Hermite or Gauss-Laguerre beam-mode analysis to be carried out for the antenna, of importance in performance optimization calculations, such as antenna gain and beam efficiency parameters at the design and prototype stage of antenna development. A full description of the beam would also be required if the antenna is to be used to feed a quasi-optical system in the near-field to far-field transition region. This situation could often arise when the device is fitted directly at the back of telescopes in flying observatories. A further benefit of the proposed technique is simplicity for characterizing systems in situ, an advantage of considerable importance as in many situations, the components may not be removable for further characterization once assembled. The proposed methodology is generic and should be useful across the wider sensing community, e.g., in single detector acoustic imaging or in adaptive imaging array applications. Furthermore, it is applicable across other frequencies of the EM spectrum, provided adequate spatial and temporal phase stability of the source can be maintained throughout the measurement process. Phase information retrieval is also of importance to emergent research areas, such as band-gap structure characterization, meta-materials research, electromagnetic cloaking, slow light, super-lens design as well as near-field and virtual imaging applications.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.

Toward vicarious calibration of microwave remote-sensing satellites in arid environments

The Soil Moisture and Ocean Salinity (SMOS) satellite marks the commencement of dedicated global surface soil moisture missions, and the first mission to make passive microwave observations at L-band. On-orbit calibration is an essential part of the instrument calibration strategy, but on-board beam-filling targets are not practical for such large apertures. Therefore, areas to serve as vicarious calibration targets need to be identified. Such sites can only be identified through field experiments including both in situ and airborne measurements. For this purpose, two field experiments were performed in central Australia. Three areas are studied as follows: 1) Lake Eyre, a typically dry salt lake; 2) Wirrangula Hill, with sparse vegetation and a dense cover of surface rock; and 3) Simpson Desert, characterized by dry sand dunes. Of those sites, only Wirrangula Hill and the Simpson Desert are found to be potentially suitable targets, as they have a spatial variation in brightness temperatures of <4 K under normal conditions. However, some limitations are observed for the Simpson Desert, where a bias of 15 K in vertical and 20 K in horizontal polarization exists between model predictions and observations, suggesting a lack of understanding of the underlying physics in this environment. Subsequent comparison with model predictions indicates a SMOS bias of 5 K in vertical and 11 K in horizontal polarization, and an unbiased root mean square difference of 10 K in both polarizations for Wirrangula Hill. Most importantly, the SMOS observations show that the brightness temperature evolution is dominated by regular seasonal patterns and that precipitation events have only little impact.

A methodology for in-situ and remote sensing of microphysical and radiative properties of contrails as they evolve into cirrus

Contrails and especially their evolution into cirrus-like clouds are thought to have very important effects on local and global radiation budgets, though are generally not well represented in global climate models. Lack of contrail parameterisations is due to the limited availability of in situ contrail measurements which are difficult to obtain. Here we present a methodology for successful sampling and interpretation of contrail microphysical and radiative data using both in situ and remote sensing instrumentation on board the FAAM BAe146 UK research aircraft as part of the COntrails Spreading Into Cirrus (COSIC) study.

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

Modelling the time-evolution of phytoplankton size spectra from satellite remote sensing

A dynamic size-structured model is developed for phytoplankton and nutrients in the oceanic mixed layer and applied to extract phytoplankton biomass at discrete size fractions from remotely sensed, ocean-colour data. General relationships between cell size and biophysical processes (such as sinking, grazing, and primary production) of phytoplankton were included in the model through a bottom–up approach. Time-dependent, mixed-layer depth was used as a forcing variable, and a sequential data-assimilation scheme was implemented to derive model trajectories. From a given time-series, the method produces estimates of size-structured biomass at every observation, so estimates seasonal succession of individual phytoplankton size, derived here from remote sensing for the first time. From these estimates, normalized phytoplankton biomass size spectra over a period of 9 years were calculated for one location in the North Atlantic. Further analysis demonstrated that strong relationships exist between the seasonal trends of the estimated size spectra and the mixed-layer depth, nutrient biomass, and total chlorophyll. The results contain useful information on the time-dependent biomass flux in the pelagic ecosystem.

The phenology of phytoplankton blooms: ecosystems indicators from remote sensing

Remote sensing offers many advantages in the development of ecosystem indicators for the pelagic zone of the ocean. Particularly suitable in this context are the indicators arising from time series that can be constructed from remotely sensed data. For example, using ocean-colour radiometry, the phenology of phytoplankton blooms can be assessed. Metrics defined in this way show promise as informative indicators for the entire pelagic ecosystem. A simple phytoplankton–substrate model, with forcing dependent on latitude and day number is used to explore the qualitative features of bloom phenology for comparison with the results observed in a suite of 10-year time series of chlorophyll concentration, as assessed by remote sensing, from the Northwest Atlantic Ocean. The model reveals features of the dynamics that might otherwise have been overlooked in evaluation of the observational data.

Nutrient sensing and signalling in plants: Potassium and phosphorus

Potassium and phosphorus are important macronutrients for crops but are often deficient in the field. Very little is known about how plants sense fluctuations in K and P and how information about K and P availability is integrated at the whole plant level into physiological and metabolic adaptations. This chapter reviews recent advances in discovering molecular responses of plants to K and P deficiency by microarray experiments. These studies provide us not only with a comprehensive picture of adaptive mechanisms, but also with a large number of transcriptional markers that can be used to identify upstream components of K and P signalling pathways. On the basis of the available information we discuss putative receptors and signals involved in the sensing and integration of K and P status both at the cellular and at the whole plant level. These involve membrane potential, voltage-dependent ion channels, intracellular Ca and pH, and transcription factors, as well as hormones and metabolites for systemic signalling. Genetic screens of reporter lines for transcriptional markers and metabolome analysis of K- and P-deficient plants are likely to further advance our knowledge in this area in the near future.

Electrochemical sensing of 2D condensation in amyloid peptides

The interfacial behavior of the model amyloid peptide octamer YYKLVFFC (peptide 1) and two other amyloid peptides YEVHHQKLVFF (peptide 2) and KKLVFFA (peptide 3) at the metal|aqueous solution interface was studied by voltammetric and constant current chronopotentiometric stripping (CPS). All three peptides are adsorbed in a wide potential range and exhibit different interfacial organizations depending on the electrode potential. At the least negative potentials, chemisorption of peptide 1 occurs through the formation of a metal sulfur bond. This bond is broken close to −0.6 V. The peptide undergoes self-association at more negative potentials, leading to the formation of a “pit” characteristic of a 2D condensed film. Under the same conditions the other peptides do not produce such a pit. Formation of the 2D condensed layer in peptide 1 is supported by the time, potential and temperature dependences of the interfacial capacity and it is shown that presence of the 2D layer is reflected by the peptide CPS signals due to the catalytic hydrogen evolution. The ability of peptide 1 to form the potential-dependent 2D condensed layer has been reported neither for any other peptide nor for any protein molecule. This ability might be related to the well-known oligomerization and aggregation of Alzheimer amyloid peptides.

Comparison of the radiative properties and direct radiative effect of aerosols from a global aerosol model and remote sensing data over ocean

A global aerosol transport model (Oslo CTM2) with main aerosol components included is compared to five satellite retrievals of aerosol optical depth (AOD) and one data set of the satellite-derived radiative effect of aerosols. The model is driven with meteorological data for the period November 1996 to June 1997 which is the time period investigated in this study. The modelled AOD is within the range of the AOD from the various satellite retrievals over oceanic regions. The direct radiative effect of the aerosols as well as the atmospheric absorption by aerosols are in both cases found to be of the order of 20 Wm−2 in certain regions in both the satellite-derived and the modelled estimates as a mean over the period studied. Satellite and model data exhibit similar patterns of aerosol optical depth, radiative effect of aerosols, and atmospheric absorption of the aerosols. Recently published results show that global aerosol models have a tendency to underestimate the magnitude of the clear-sky direct radiative effect of aerosols over ocean compared to satellite-derived estimates. However, this is only to a small extent the case with the Oslo CTM2. The global mean direct radiative effect of aerosols over ocean is modelled with the Oslo CTM2 to be –5.5 Wm−2 and the atmospheric aerosol absorption 1.5 Wm−2.