A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ot

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

Ground deformation at Soufriere Hills Volcano, Montserrat during 1998-2000 measured by radar interferometry and GPS

We examine the motion of the ground surface on the Soufriere Hills Volcano, Montserrat between 1998 and 2000 using radar interferometry (InSAR). To minimise the effects of variable atmospheric water vapour on the InSAR measurements we use independently-derived measurements of the radar path delay from six continuous GPS receivers. The surfaces providing a measurable inter-ferometric signal are those on pyroclastic flow deposits, mainly emplaced in 1997. Three types of surface motion can be discriminated. Firstly, the surfaces of thick, valley-filling deposits subsided at rates of 150-120 mm/year in the year after emplacement to 50-30 mm/year two years later. This must be due to contraction and settling effects during cooling. The second type is the near-field motion localised within about one kilometre of the dome. Both subsidence and uplift events are seen and though the former could be due to surface gravitational effects, the latter may reflect shallow (< 1 km) pressurisation effects within the conduit/dome. Far-field motions of the surface away from the deeply buried valleys are interpreted as crustal strains. Because the flux of magma to the surface stopped from March 1998 to November 1999 and then resumed from November 1999 through 2000, we use InSAR data from these two periods to test the crustal strain behaviour of three models of magma supply: open, depleting and unbalanced. The InSAR observations of strain gradients of 75-80 mm/year/krn uplift during the period of quiescence on the western side of the volcano are consistent with an unbalanced model in which magma supply into a crustal magma chamber continues during quiescence, raising chamber pressure that is then released upon resumption of effusion. GPS motion vectors agree qualitatively with the InSAR displacements but are of smaller magnitude. The discrepancy may be due to inaccurate compensation for atmospheric delays in the InSAR data. (c) 2005 Elsevier B.V. All rights reserved.

The point-source method for 3D reconstructions for the Helmholtz and Maxwell equations

We use the point-source method (PSM) to reconstruct a scattered field from its associated far field pattern. The reconstruction scheme is described and numerical results are presented for three-dimensional acoustic and electromagnetic scattering problems. We give new proofs of the algorithms, based on the Green and Stratton-Chu formulae, which are more general than with the former use of the reciprocity relation. This allows us to handle the case of limited aperture data and arbitrary incident fields. Both for 3D acoustics and electromagnetics, numerical reconstructions of the field for different settings and with noisy data are shown. For shape reconstruction in acoustics, we develop an appropriate strategy to identify areas with good reconstruction quality and combine different such regions into one joint function. Then, we show how shapes of unknown sound-soft scatterers are found as level curves of the total reconstructed field.

Airborne measurements of the spatial distribution of aerosol chemical composition across Europe and evolution of the organic fraction

The spatial distribution of aerosol chemical composition and the evolution of the Organic Aerosol (OA) fraction is investigated based upon airborne measurements of aerosol chemical composition in the planetary boundary layer across Europe. Sub-micron aerosol chemical composition was measured using a compact Time-of-Flight Aerosol Mass Spectrometer (cToF-AMS). A range of sampling conditions were evaluated, including relatively clean background conditions, polluted conditions in North-Western Europe and the near-field to far-field outflow from such conditions. Ammonium nitrate and OA were found to be the dominant chemical components of the sub-micron aerosol burden, with mass fractions ranging from 20--50% each. Ammonium nitrate was found to dominate in North-Western Europe during episodes of high pollution, reflecting the enhanced NO_x and ammonia sources in this region. OA was ubiquitous across Europe and concentrations generally exceeded sulphate by 30--160%. A factor analysis of the OA burden was performed in order to probe the evolution across this large range of spatial and temporal scales. Two separate Oxygenated Organic Aerosol (OOA) components were identified; one representing an aged-OOA, termed Low Volatility-OOA and another representing fresher-OOA, termed Semi Volatile-OOA on the basis of their mass spectral similarity to previous studies. The factors derived from different flights were not chemically the same but rather reflect the range of OA composition sampled during a particular flight. Significant chemical processing of the OA was observed downwind of major sources in North-Western Europe, with the LV-OOA component becoming increasingly dominant as the distance from source and photochemical processing increased. The measurements suggest that the aging of OA can be viewed as a continuum, with a progression from a less oxidised, semi-volatile component to a highly oxidised, less-volatile component. Substantial amounts of pollution were observed far downwind of continental Europe, with OA and ammonium nitrate being the major constituents of the sub-micron aerosol burden. Such anthropogenically perturbed air masses can significantly perturb regional climate far downwind of major source regions.

Fabrication and characterization of micromachined rectangular waveguide components for use at millimeter-wave and terahertz frequencies

The fabrication and characterization of micromachined reduced-height air-filled rectangular waveguide components suitable for integration is reported in this paper. The lithographic technique used permits structures with heights of up to 100 μm to be successfully constructed in a repeatable manner. Waveguide S-parameter measurements at frequencies between 75-110 GHz using a vector network analyzer demonstrate low loss propagation in the TE10 mode reaching 0.2 dB per wavelength. Scanning electron microscope photographs of conventional and micromachined waveguides show that the fabrication technique can provide a superior surface finish than possible with commercially available components. In order to circumvent problems in efficiently coupling free-space propagating beams to the reduced-height G-band waveguides, as well as to characterize them using quasi-optical techniques, a novel integrated micromachined slotted horn antenna has been designed and fabricated, E-, H-, and D-plane far-field antenna pattern measurements at different frequencies using a quasi-optical setup show that the fabricated structures are optimized for 180-GHz operation with an E-plane half-power beamwidth of 32° elevated 35° above the substrate, a symmetrical H-plane pattern with a half-power beamwidth of 23° and a maximum D-plane cross-polar level of -33 dB. Far-field pattern simulations using HFSS show good agreement with experimental results.

A study on orthogonality sampling.

The goal of this paper is to study and further develop the orthogonality sampling or stationary waves algorithm for the detection of the location and shape of objects from the far field pattern of scattered waves in electromagnetics or acoustics. Orthogonality sampling can be seen as a special beam forming algorithm with some links to the point source method and to the linear sampling method. The basic idea of orthogonality sampling is to sample the space under consideration by calculating scalar products of the measured far field pattern , with a test function for all y in a subset Q of the space , m = 2, 3. The way in which this is carried out is important to extract the information which the scattered fields contain. The theoretical foundation of orthogonality sampling is only partly resolved, and the goal of this work is to initiate further research by numerical demonstration of the high potential of the approach. We implement the method for a two-dimensional setting for the Helmholtz equation, which represents electromagnetic scattering when the setup is independent of the third coordinate. We show reconstructions of the location and shape of objects from measurements of the scattered field for one or several directions of incidence and one or many frequencies or wave numbers, respectively. In particular, we visualize the indicator function both with the Dirichlet and Neumann boundary condition and for complicated inhomogeneous media.

An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples.

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.

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Transmission of wireless power by magnetic resonance

The work involves investigation of a type of wireless power system wherein its analysis will yield the construction of a prototype modeled as a singular technological artifact. It is through exploration of the artifact that forms the intellectual basis for not only its prototypical forms, but suggestive of variant forms not yet discovered. Through the process it is greatly clarified the role of the artifact, its most suitable application given the constraints on the delivery problem, and optimization strategies to improve it. In order to improve maturity and contribute to a body of knowledge, this document proposes research utilizing mid-field region, efficient inductive-transfer for the purposes of removing wired connections and electrical contacts. While the description seems enough to state the purpose of this work, it does not convey the compromises of having to redraw the lines of demarcation between near and far-field in the traditional method of broadcasting. Two striking scenarios are addressed in this thesis: Firstly, the mathematical explanation of wireless power is due to J.C. Maxwell's original equations, secondly, the behavior of wireless power in the circuit is due to Joseph Larmor's fundamental works on the dynamics of the field concept. A model of propagation will be presented which matches observations in experiments. A modified model of the dipole will be presented to address the phenomena observed in the theory and experiments. Two distinct sets of experiments will test the concept of single and two coupled-modes. In a more esoteric context of the zero and first-order magnetic field, the suggestion of a third coupled-mode is presented. Through the remaking of wireless power in this context, it is the intention of the author to show the reader that those things lost to history, bound to a path of complete obscurity, are once again innovative and useful ideas.

Wave spectra assimilation in typhoon wave modeling for the East China Sea

The East China Sea is a hot area for typhoon waves to occur. A wave spectra assimilation model has been developed to predict the typhoon wave more accurately and operationally. This is the first time where wave data from Taiwan have been used to predict typhoon wave along the mainland China coast. The two-dimensional spectra observed in Taiwan northeast coast modify the wave field output by SWAN model through the technology of optimal interpolation (OI) scheme. The wind field correction is not involved as it contributes less than a quarter of the correction achieved by assimilation of waves. The initialization issue for assimilation is discussed. A linear evolution law for noise in the wave field is derived from the SWAN governing equations. A two-dimensional digital low-pass filter is used to obtain the initialized wave fields. The data assimilation model is optimized during the typhoon Sinlaku. During typhoons Krosa and Morakot, data assimilation significantly improves the low frequency wave energy and wave propagation direction in Taiwan coast. For the far-field region, the assimilation model shows an expected ability of improving typhoon wave forecast as well, as data assimilation enhances the low frequency wave energy. The proportion of positive assimilation indexes is over 81% for all the periods of comparison. The paper also finds that the impact of data assimilation on the far-field region depends on the state of the typhoon developing and the swell propagation direction.

How is the balance of a forecast ensemble affected by adaptive and non-adaptive localization schemes?

This paper investigates the effect on balance of a number of Schur product-type localization schemes which have been designed with the primary function of reducing spurious far-field correlations in forecast error statistics. The localization schemes studied comprise a non-adaptive scheme (where the moderation matrix is decomposed in a spectral basis), and two adaptive schemes, namely a simplified version of SENCORP (Smoothed ENsemble COrrelations Raised to a Power) and ECO-RAP (Ensemble COrrelations Raised to A Power). The paper shows, we believe for the first time, how the degree of balance (geostrophic and hydrostatic) implied by the error covariance matrices localized by these schemes can be diagnosed. Here it is considered that an effective localization scheme is one that reduces spurious correlations adequately but also minimizes disruption of balance (where the 'correct' degree of balance or imbalance is assumed to be possessed by the unlocalized ensemble). By varying free parameters that describe each scheme (e.g. the degree of truncation in the schemes that use the spectral basis, the 'order' of each scheme, and the degree of ensemble smoothing), it is found that a particular configuration of the ECO-RAP scheme is best suited to the convective-scale system studied. According to our diagnostics this ECO-RAP configuration still weakens geostrophic and hydrostatic balance, but overall this is less so than for other schemes.

Stress field control of eruption dynamics at a rift volcano: Nyamuragira, D.R.Congo

Using the record of 30 flank eruptions over the last 110 years at Nyamuragira, we have tested the relationship between the eruption dynamics and the local stress field. There are two groups of eruptions based on their duration (< 80days >) that are also clustered in space and time. We find that the eruptions fed by dykes parallel to the East African Rift Valley have longer durations (and larger volumes) than those eruptions fed by dykes with other orientations. This is compatible with a model for compressible magma transported through an elastic-walled dyke in a differential stress field from an over-pressured reservoir (Woods et al., 2006). The observed pattern of eruptive fissures is consistent with a local stress field modified by a northwest-trending, right lateral slip fault that is part of the northern transfer zone of the Kivu Basin rift segment. We have also re-tested with new data the stochastic eruption models for Nyamuragira of Burt et al. (1994). The time-predictable, pressure-threshold model remains the best fit and is consistent with the typically observed declining rate of sulphur dioxide emission during the first few days of eruption with lava emission from a depressurising, closed, crustal reservoir. The 2.4-fold increase in long-term eruption rate that occurred after 1977 is confirmed in the new analysis. Since that change, the record has been dominated by short-duration eruptions fed by dykes perpendicular to the Rift. We suggest that the intrusion of a major dyke during the 1977 volcano-tectonic event at neighbouring Nyiragongo volcano inhibited subsequent dyke formation on the southern flanks of Nyamuragira and this may also have resulted in more dykes reaching the surface elsewhere. Thus that sudden change in output was a result of a changed stress field that forced more of the deep magma supply to the surface. Another volcano-tectonic event in 2002 may also have changed the magma output rate at Nyamuragira.

The effect of electric field direction on the-shear stress of ER fluids

The effect of the direction of external electric field on the shear stress of an ER fluid has been studied by molecular-dynamics simulation. Due to the formation of inclined chains, the shear stress strongly depends on the direction of the field, and it may be very large under some special field direction. And theoretical model of ideal microstructure of ER fluids has proved this result. Thus the ER effect may be greatly enhanced just by choosing an optimum direction for the field without any additional requirement, suggesting a promising way to the practical application of ER fluids.