A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Flight periodicity and the vertical distribution of high-altitude moth migration over southern Britain

The continuous operation of insect-monitoring radars in the UK has permitted, for the first time, the characterization of various phenomena associated with high-altitude migration of large insects over this part of northern Europe. Previous studies have taken a case-study approach, concentrating on a small number of nights of particular interest. Here, combining data from two radars, and from an extensive suction- and light-trapping network, we have undertaken a more systematic, longer-term study of diel flight periodicity and vertical distribution of macro-insects in the atmosphere. Firstly, we identify general features of insect abundance and stratification, occurring during the 24-hour cycle, which emerge from four years’ aggregated radar data for the summer months in southern Britain. These features include mass emigrations at dusk and to a lesser extent at dawn, and daytime concentrations associated with thermal convection. We then focus our attention on the well-defined layers of large nocturnal migrants that form in the early evening, usually at heights of 200–500 m above ground. We present evidence from both radar and trap data that these nocturnal layers are composed mainly of noctuid moths, with species such as Noctua pronuba, Autographa gamma, Agrotis exclamationis, A. segetum, Xestia c-nigrum and Phlogophora meticulosa predominating.

The high-water mark. The siting of megalithic tombs on the Swedish island of Tjorn

In 1977 Grahame Clark suggested that the siting of megalithic tombs along the west coast of Scandinavia reflected the distribution of productive fishing grounds. Unlike the situation in other parts of Europe, these monuments were not associated with agriculture. Opinions have varied over the last quarter century, but enough is now known about changes of sea-level for his interpretation to be investigated on the ground. There seems to have been considerable diversity. On the large island of Örust some of the tombs located near to the sea appear to be associated with small natural enclosures defined by rock outcrops and may have been associated with grazing land. On the neighbouring island of Tjörn, however, the tombs were associated with small islands and important sea channels. During the Bronze Age the same areas included carvings of ships. Recent fieldwork in western Norway suggests that such locations were especially important in a maritime economy.

Tracking larval insect movement within soil using high resolution X-ray microtomography

1. In contrast to above-ground insects, comparatively little is known about the behaviour of subterranean insects, due largely to the difficulty of studying them in situ. 2. The movement of newly hatched (neonate) clover root weevil (Sitona lepidus L. Coleoptera: Curculinidae) larvae was studied non-invasively using recently developed high resolution X-ray microtomography. 3. The movement and final position of S. lepidus larvae in the soil was reliably established using X-ray microtomography, when compared with larval positions that were determined by destructively sectioning the soil column. 4. Newly hatched S. lepidus larvae were seen to attack the root rhizobial nodules of their host plant, white clover (Trifolium repens L.). Sitona lepidus larvae travelled between 9 and 27 mm in 9 h at a mean speed of 1.8 mm h(-1). 5. Sitona lepidus larvae did not move through the soil in a linear manner, but changed trajectory in both the lateral and vertical planes.

Factors influencing the dissolution of phosphate rock in a range of high P-fixing soils from Cameroon

A laboratory incubation experiment was conducted to evaluate the soil factors that influence the dissolution of two phosphate rocks (PRs) of different reactivity (Gafsa, GPR, reactive PR; and Togo-Hahotoe, HPR, low reactivity PR) in seven agricultural soils from Cameroon having variable phosphorus (P)- sorption capacities, organic carbon (C) contents, and exchangeable acidities. Ground PR was mixed with the soils at a rate of 500 mg P kg 21 soil and incubated at 30 degrees C for 85 days. Dissolution of the PRs was determined at various intervals using the Delta NaOH-P method ( the difference of the amount of P extracted by 0.5 M NaOH between the PR-treated soils and the control). Between 4 and 27% of HPR and 33 and 50% of GPR were dissolved in the soils. Calcium (Ca) saturation of cation exchange sites and proton supply strongly affected PR dissolution in these soils. Acid soils with pH-(H2O), < 5 (NKL, ODJ, NSM, MTF) dissolved more phosphate rock than those with pH-(H2O) > 5 (DSC, FGT, BAF). However, the lack of a sufficient Ca sink in the former constrained the dissolution of both PRs. The dissolution of GPR in the slightly acidic soils was limited by increase in Ca saturation and that of HPR was constrained by limited supply in protons. Generally, the dissolution of GPR was higher than that of HPR for each soil. The kinetics of dissolution of PR in the soils was best described by the power function equation P At B. More efficient use of PR in these soils can be achieved by raising the soil cation exchange capacity, thereby increasing the Ca sink size. This could be done by amending such soils with organic materials.

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.

An event-based approach to validating solar wind speed predictions: high-speed enhancements in the Wang-Sheeley-Arge model

One of the primary goals of the Center for Integrated Space Weather Modeling (CISM) effort is to assess and improve prediction of the solar wind conditions in near‐Earth space, arising from both quasi‐steady and transient structures. We compare 8 years of L1 in situ observations to predictions of the solar wind speed made by the Wang‐Sheeley‐Arge (WSA) empirical model. The mean‐square error (MSE) between the observed and model predictions is used to reach a number of useful conclusions: there is no systematic lag in the WSA predictions, the MSE is found to be highest at solar minimum and lowest during the rise to solar maximum, and the optimal lead time for 1 AU solar wind speed predictions is found to be 3 days. However, MSE is shown to frequently be an inadequate “figure of merit” for assessing solar wind speed predictions. A complementary, event‐based analysis technique is developed in which high‐speed enhancements (HSEs) are systematically selected and associated from observed and model time series. WSA model is validated using comparisons of the number of hit, missed, and false HSEs, along with the timing and speed magnitude errors between the forecasted and observed events. Morphological differences between the different HSE populations are investigated to aid interpretation of the results and improvements to the model. Finally, by defining discrete events in the time series, model predictions from above and below the ecliptic plane can be used to estimate an uncertainty in the predicted HSE arrival times.

Synthesis, structure and magnetic characterisation of a new layered ammonium manganese(II) diphosphate hydrate, (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)]

A new layered ammonium manganese(II) diphosphate, (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)], has been synthesised under solvothermal conditions at 433 K in ethylene glycol and the structure determined at 293 K using single-crystal X-ray diffraction data (M-r = 584.82, monoclinic, space group P2(1)/a, a = 9.4610( 8), b = 8.3565( 7), c = 9.477(1) Angstrom, beta = 99.908(9) degrees, V = 738.07 Angstrom(3), Z = 2, R = 0.0351 and R-w = 0.0411 for 1262 observed data (I > 3(sigma(I))). The structure consists of chains of cis- and trans-edge sharing MnO6 octahedra linked via P2O7 units to form layers of formula [Mn3P4O14(H2O)(2)](2-) in the ab plane. Ammonium ions lie between the manganese-diphosphate layers. A network of interlayer and ammonium-layer based hydrogen bonding holds the structure together. Magnetic measurements indicate Curie - Weiss behaviour above 30 K with mu(eff) = 5.74(1) mu(B) and theta = -23(1) K, consistent with the presence of high-spin Mn2+ ions and antiferromagnetic interactions. However, the magnetic data reveal a spontaneous magnetisation at 5 K, indicating a canting of Mn2+ moments in the antiferromagnetic ground state. On heating (NH4)(2)[Mn-3(P2O7)(2)(H2O)(2)] in water at 433 K under hydrothermal conditions, Mn-5(HPO4)(2)(PO4)(2).4H(2)O, synthetic hureaulite, is formed.

Spectroscopy of highly excited vibrational states of HCN in its ground electronic state

An experimental technique based on a scheme of vibrationally mediated photodissociation has been developed and applied to the spectroscopic study of highly excited vibrational states in HCN, with energies between 29 000 and 30 000 cm(-1). The technique consists of four sequential steps: in the first one, a high power laser is used to vibrationally excite the sample to an intermediate state, typically (0,0,4), the nu(3) mode being approximately equivalent to the C-H stretching vibration. Then a second laser is used to search for transitions between this intermediate state and highly vibrationally excited states. When one of these transitions is found, HCN molecules are transferred to a highly excited vibrational state. Third, a ultraviolet laser photodissociates the highly excited molecules to produce H and CN radicals in its A (2)Pi electronic state. Finally, a fourth laser (probe) detects the presence of the CN(A) photofragments by means of an A-->B-->X laser induced fluorescence scheme. The spectra obtained with this technique, consisting of several rotationally resolved vibrational bands, have been analyzed. The positions and rotational parameters of the states observed are presented and compared with the results of a state-of-the-art variational calculation. (C) 2004 American Institute of Physics.

High bandwidth, large workspace haptic interaction: flying phantoms

It is well understood that for haptic interaction: free motion performance and closed-loop constrained motion performance have conflicting requirements. The difficulties for both conditions are compounded when increased workspace is required as most solutions result in a reduction of achievable impedance and bandwidth. A method of chaining devices together to increase workspace without adverse effect on performance is described and analysed. The method is then applied to a prototype, colloquially known as 'The Flying Phantom', and shown to provide high-bandwidth, low impedance interaction over the full range of horizontal movement across the front of a human user.

Using continuous ground-based radar and lidar measurements for evaluating the representation of clouds in four operational models

The ability of four operational weather forecast models [ECMWF, Action de Recherche Petite Echelle Grande Echelle model (ARPEGE), Regional Atmospheric Climate Model (RACMO), and Met Office] to generate a cloud at the right location and time (the cloud frequency of occurrence) is assessed in the present paper using a two-year time series of observations collected by profiling ground-based active remote sensors (cloud radar and lidar) located at three different sites in western Europe (Cabauw. Netherlands; Chilbolton, United Kingdom; and Palaiseau, France). Particular attention is given to potential biases that may arise from instrumentation differences (especially sensitivity) from one site to another and intermittent sampling. In a second step the statistical properties of the cloud variables involved in most advanced cloud schemes of numerical weather forecast models (ice water content and cloud fraction) are characterized and compared with their counterparts in the models. The two years of observations are first considered as a whole in order to evaluate the accuracy of the statistical representation of the cloud variables in each model. It is shown that all models tend to produce too many high-level clouds, with too-high cloud fraction and ice water content. The midlevel and low-level cloud occurrence is also generally overestimated, with too-low cloud fraction but a correct ice water content. The dataset is then divided into seasons to evaluate the potential of the models to generate different cloud situations in response to different large-scale forcings. Strong variations in cloud occurrence are found in the observations from one season to the same season the following year as well as in the seasonal cycle. Overall, the model biases observed using the whole dataset are still found at seasonal scale, but the models generally manage to well reproduce the observed seasonal variations in cloud occurrence. Overall, models do not generate the same cloud fraction distributions and these distributions do not agree with the observations. Another general conclusion is that the use of continuous ground-based radar and lidar observations is definitely a powerful tool for evaluating model cloud schemes and for a responsive assessment of the benefit achieved by changing or tuning a model cloud

U.K. HiGEM: Simulations of desert dust and biomass burning aerosols with a high-resolution atmospheric GCM

The atmospheric component of the United Kingdom’s new High-resolution Global Environmental Model (HiGEM) has been run with interactive aerosol schemes that include biomass burning and mineral dust. Dust emission, transport, and deposition are parameterized within the model using six particle size divisions, which are treated independently. The biomass is modeled in three nonindependent modes, and emissions are prescribed from an external dataset. The model is shown to produce realistic horizontal and vertical distributions of these aerosols for each season when compared with available satellite- and ground-based observations and with other models. Combined aerosol optical depths off the coast of North Africa exceed 0.5 both in boreal winter, when biomass is the main contributor, and also in summer, when the dust dominates. The model is capable of resolving smaller-scale features, such as dust storms emanating from the Bode´ le´ and Saharan regions of North Africa and the wintertime Bode´ le´ low-level jet. This is illustrated by February and July case studies, in which the diurnal cycles of model variables in relation to dust emission and transport are examined. The top-of-atmosphere annual mean radiative forcing of the dust is calculated and found to be globally quite small but locally very large, exceeding 20 W m22 over the Sahara, where inclusion of dust aerosol is shown to improve the model radiative balance. This work extends previous aerosol studies by combining complexity with increased global resolution and represents a step toward the next generation of models to investigate aerosol–climate interactions. 1. Introduction Accurate modeling of mineral dust is known to be important because of its radiative impact in both numerical weather prediction models (Milton et al. 2008; Haywood et

3D-Var assimilation of insect-derived Doppler radar radial winds in convective cases using a high resolution model

The assimilation of Doppler radar radial winds for high resolution NWP may improve short term forecasts of convective weather. Using insects as the radar target, it is possible to provide wind observations during convective development. This study aims to explore the potential of these new observations, with three case studies. Radial winds from insects detected by 4 operational weather radars were assimilated using 3D-Var into a 1.5 km resolution version of the Met Office Unified Model, using a southern UK domain and no convective parameterization. The effect on the analysis wind was small, with changes in direction and speed up to 45° and 2 m s−1 respectively. The forecast precipitation was perturbed in space and time but not substantially modified. Radial wind observations from insects show the potential to provide small corrections to the location and timing of showers but not to completely relocate convergence lines. Overall, quantitative analysis indicated the observation impact in the three case studies was small and neutral. However, the small sample size and possible ground clutter contamination issues preclude unequivocal impact estimation. The study shows the potential positive impact of insect winds; future operational systems using dual polarization radars which are better able to discriminate between insects and clutter returns should provided a much greater impact on forecasts.

Infrared filters for space-flight focal plane array applications

Infrared filters and coatings have been employed on many sensing radiometer instruments to measure the thermal emission profiles and concentrations of certian chemical constituents found in planetary atmospheres. The High Resolution Dynamics Limb Sounder ( HIRDLS) is an example of the most recent developments in limb-viewing radiometry by employing a cooled focal plane detector array to provide simultaneous multi-channel monitoring of emission from gas and aerosols over an altitude range between 8 - 70 km. The use of spectrally selective cooled detectors in focal plane arrays has simplified the optical layout of radiometers, greatly reducing the number of components in the optical train. this has inevitably led to increased demands for the enviromnetal durability of the focal plane filters because of the need to cut sub-millimeter sizes, whilst maintaining an optimal spectral performance. Additionally the remaining refractive optical elements require antireflection coatings which must cover the entire spectral range of the focal plane array channels, in this case 6 to 18µm, with a minimum of reflection and absorption. This paper describes the optical layout and spectral design requirements for filteriong in the HIRDLS instrument, and reports progress on the manufacturing and testing of the sub-millimetre sized cooled filters. We also report on the spectral and environmental performance of prototype wideband antireflection coatings which satisfy the requirements above.

High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.