Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

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.

The influence of the atmospheric boundary layer on nocturnal layers of noctuids and other moths migrating over southern Britain

Insects migrating at high altitude over southern Britain have been continuously monitored by automatically-operating, vertical-looking radars over a period of several years. During some occasions in the summer months, the migrants were observed to form well-defined layer concentrations, typically at heights of 200-400 m, in the stable night-time atmosphere. Under these conditions, insects are likely to have control over their vertical movements and are selecting flight heights which are favourable for long-range migration. We therefore investigated the factors influencing the formation of these insect layers by comparing radar measurements of the vertical distribution of insect density with meteorological profiles generated by the UK Met. Office’s Unified Model (UM). Radar-derived measurements of mass and displacement speed, along with data from Rothamsted Insect Survey light traps provided information on the identity of the migrants. We present here three case studies where noctuid and pyralid moths contributed substantially to the observed layers. The major meteorological factors influencing the layer concentrations appeared to be: (a) the altitude of the warmest air, (b) heights corresponding to temperature preferences or thresholds for sustained migration and (c), on nights when air temperatures are relatively high, wind-speed maxima associated with the nocturnal jet. Back-trajectories indicated that layer duration may have been determined by the distance to the coast. Overall, the unique combination of meteorological data from the UM and insect data from entomological radar described here show considerable promise for systematic studies of high-altitude insect layering.

The moist boundary layer under a mid-latitude weather system

Mid-latitude weather systems are key contributors to the transport of atmospheric water vapour, but less is known about the role of the boundary layer in this transport. We expand a conceptual model of dry boundary-layer structure under synoptic systems to include moist processes, using idealised simulations of cyclone waves to investigate the three-way interaction between the boundary layer, atmospheric moisture and large-scale dynamics. Forced by large-scale thermal advection, boundary-layer structures develop over large areas, analogous to the daytime convective boundary layer, the nocturnal stable boundary layer and transitional regimes between these extremes.

Reactive Halogens in the Marine Boundary Layer (RHaMBLe): the tropical North Atlantic experiments

The NERC UK SOLAS-funded Reactive Halogens in the Marine Boundary Layer (RHaMBLe) programme comprised three field experiments. This manuscript presents an overview of the measurements made within the two simultaneous remote experiments conducted in the tropical North Atlantic in May and June 2007. Measurements were made from two mobile and one ground-based platforms. The heavily instrumented cruise D319 on the RRS Discovery from Lisbon, Portugal to São Vicente, Cape Verde and back to Falmouth, UK was used to characterise the spatial distribution of boundary layer components likely to play a role in reactive halogen chemistry. Measurements onboard the ARSF Dornier aircraft were used to allow the observations to be interpreted in the context of their vertical distribution and to confirm the interpretation of atmospheric structure in the vicinity of the Cape Verde islands. Long-term ground-based measurements at the Cape Verde Atmospheric Observatory (CVAO) on São Vicente were supplemented by long-term measurements of reactive halogen species and characterisation of additional trace gas and aerosol species during the intensive experimental period. This paper presents a summary of the measurements made within the RHaMBLe remote experiments and discusses them in their meteorological and chemical context as determined from these three platforms and from additional meteorological analyses. Air always arrived at the CVAO from the North East with a range of air mass origins (European, Atlantic and North American continental). Trace gases were present at stable and fairly low concentrations with the exception of a slight increase in some anthropogenic components in air of North American origin, though NOx mixing ratios during this period remained below 20 pptv. Consistency with these air mass classifications is observed in the time series of soluble gas and aerosol composition measurements, with additional identification of periods of slightly elevated dust concentrations consistent with the trajectories passing over the African continent. The CVAO is shown to be broadly representative of the wider North Atlantic marine boundary layer; measurements of NO, O3 and black carbon from the ship are consistent with a clean Northern Hemisphere marine background. Aerosol composition measurements do not indicate elevated organic material associated with clean marine air. Closer to the African coast, black carbon and NO levels start to increase, indicating greater anthropogenic influence. Lower ozone in this region is possibly associated with the increased levels of measured halocarbons, associated with the nutrient rich waters of the Mauritanian upwelling. Bromide and chloride deficits in coarse mode aerosol at both the CVAO and on D319 and the continuous abundance of inorganic gaseous halogen species at CVAO indicate significant reactive cycling of halogens. Aircraft measurements of O3 and CO show that surface measurements are representative of the entire boundary layer in the vicinity both in diurnal variability and absolute levels. Above the inversion layer similar diurnal behaviour in O3 and CO is observed at lower mixing ratios in the air that had originated from south of Cape Verde, possibly from within the ITCZ. ECMWF calculations on two days indicate very different boundary layer depths and aircraft flights over the ship replicate this, giving confidence in the calculated boundary layer depth.

On the dependence of boundary-layer ventilation on frontal type

Case study simulations with idealized tracers have been used to determine the relationship between the dynamics and conceptual representations of different midlatitude frontal systems and the amount, distribution, and time scale of boundary layer ventilation by these systems. The key features of ventilation by a kata– and ana–cold frontal system are found to be quantitatively and also often qualitatively similar to the main ventilation pathways, which are the conveyor belts, cloud head, and other convection. The conveyor belts and cloud head occur within cloud, implying that they can be identified using satellite imagery. Differences in the transport by the two systems can be related to their conceptual representations and include a sensitive dependence on the diurnal cycle for the kata- but not the ana-cold frontal case.

Observations of changes in marine boundary layer clouds

Recent research outlined by the Intergovernmental Panel on Climate Change (IPCC) highlights the response of marine boundary layer (MBL) clouds to warming associated with increasing greenhouse gases as a major contributor to uncertainties in model projections of climate change. Understanding how MBL clouds respond to increasing temperatures is hampered by the relative scarcity of marine surface observations and the difficulty of retrieving accurate parameters remotely from satellites. In this study we combine data from surface observations with that from the International Satellite Cloud Climatology Project (ISCCP), CloudSat and CALIPSO, with a view to investigating the spatial distribution and variations in MBL cloud fraction and cloud liquid water path (LWP). These results are then compared with the treatment of MBL clouds in the UK Met Office HadGEM models. Future work will assess how variations in LWP impact the top of atmosphere radiative energy balance using data from the Geostationary Earth Radiation Budget (GERB), in order to quantify the response of MBL clouds on interannual timescales to a changing climate

A revision of the Upper Jurassic-Lower Cretaceous dragonfly family Tarsophlebiidae, with a discussion on the phylogenetic positions of the Tarsophlebiidae and Sieblosiidae (Insecta, Odonatoptera, Panodonata)

The Upper Jurassic-Lower Cretaceous dragonfly family Tarsophlebiidae is revised. The type species of the type genus Tarsophlebia Hagen, 1866, T eximia (Hagen, 1862) from the Upper Jurassic Solnhofen Limestones, is redescribed, including important new information on its head, legs, wings, anal appendages and male secondary genital apparatus. The type specimen of Tarsophlebiopsis mayi Tillyard, 1923 is regarded as an aberrant or unusually preserved Tarsophlebia eximia. One new species of Tarsophlebia and three new species of Turanophlebia are described, i.e. Tarsophlebia minor n. sp., Turanophlebia anglicana n. sp., T mongolica n. sp., and T. vitimensis n. sp. A new combination is proposed for Turanophlebia neckini (Martynov, 1927) n. comb. The phylogenetic relationships of the Mesozoic Tarsophlebiidae are discussed on the basis of new body and wing venation characters. The present analysis supports a rather derived position for the Tarsophlebiidae, as sister group of the the Epiproctophora rather than of (Zygoptera + Epiproctophora). Also, through the present discussion, the Oligo-Miocene family Sieblosiidae seems to be more closely related to the Epiproctophora than to the Zygoptera. But the present study and previous analyses suffer of the lack of informations concerning the more inclusive groups of Odonatoptera, viz. Protozygoptera, Triadophlebiomorpha, Protanisoptera, etc. The significance of the tarsophlebiid secondary male genital apparatus for the reconstruction of the evolution of odonate copulation is discussed.

Trace fossils and pseudofossils from the Wealden strata (non-marine Lower Cretaceous) of southern England

The trace fossils of the Wealden (non-marine Lower Cretaceous) of southern England are described. Sixteen invertebrate ichnotaxa include Agrichnium fimbriatus, Beaconites antarcticus, B. barretti, Cochlichnus anguineus, Diplichnites triassicus, Diplocraterion parallelum, Lockeia siliquaria, L. serialis, Monocraterion cf. tentaculum, Palaeophycus striatus, P. tubularis, Planolites montanus, Protovirgularia rugosa, Rhizocorallium isp., Scoyenia cf. gracilis, Unisulcus minutus, insect and root traces. Tetrapod tracks and trackways include tridactyl Iguanodontipus burreyi and other ornithopods, theropod, and tetradactyl sauropod (or possibly ankylosaur), together with extensive dinosaur tramplings. Coprolites are referred to two broad types: spiral, with or without included fish scales (attributable to sharks), and elongate and irregular (possibly produced by reptiles). A skinprint and two types of pseudofossil are also included. Five environmental associations are recognised: (1) lacustrine/lagoonal; (2) brackish incursions (flooding events) into the lacustrine/lagoonal environment; (3) a marginal lacustrine association with fluvial input; (4) a fluvial (lacustrine delta) association; (5) floodplain sediments (seasonal wetlands). These associations are assigned to the fluvial-lacustrine Scoyenia Ichnofacies and the incursions to Glossifungites lchnofacies. (c) 2005 Elsevier Ltd. All rights reserved.

Grasshoppers and crickets (Insecta : Orthoptera) from the lower cretaceous of southern England

This is a synoptic monograph of fossil Orthoptera from the English Lower Cretaceous (Purbeck and Wealden groups). The previously described taxa of these insects are revised on the basis of type specimens and examination of extensive new material. Eight new genera and 30 new species are proposed: Probaisselcana cretacea sp. nov., Minelcana membranacea gen. et sp. nov., Panorpidium proximum sp. nov., P. bimacillatum sp. nov., ?P. parvum sp. nov. (Elcanidae); ?Cyrtophyllites cretaceus sp. nov. (Haglidae); Aenigmodus minutus gen. et sp. nov., Pseudaboilus wealdensis gen. et sp. nov., P. purbeckensis sp. nov., Tettigoilus sonorus gen. et sp. nov., ?Agrionidium obscurum sp. nov. (Prophalangopsidae); Notocearagryllus britannicus sp. nov., N. grandispeculum sp. nov., N. cordispeculum sp. nov., Anglogryllus lyristes gen. et sp. nov., A. rotundispeculum sp. nov.. Speculogryllus acutispeculum gen. et sp. nov., Sharategia davisi sp. nov., S. batchelorae sp. nov., S. baldocki sp. nov. (Baissogryllidae); ?Araripegryllus orientalis sp. nov. (Gryllidae); Deinovitimia occidentalis sp. nov. (Ensifera: infraorder incertae sedis); Cretoxya rasnitsyni gen. et sp. nov. (Tridactylidae); Locustopsis posterior sp. nov., Zeunerella prior sp. nov., Zessinia borealis sp. nov., Mesolocustopsis anglica sp. nov., M. angusta sp. nov., M. problematica sp. nov., and Britannacrida distincta gen. et sp. nov (Locustopsidae). The subfamily Baisselcaninae is synonymized with Elcaninae, and a new subfamily (Archelcaninae subfam. nov.) is proposed for a segregate of Elcaninae. A preliminary comparison of the Purbeck/Wealden with other Early Cretaceous orthopteran faunas is given. (c) 2006 Published by Elsevier Ltd.

The Upper Valanginian (Early Cretaceous) positive carbon-isotope event recorded in terrestrial plants

Our understanding of the ancient ocean-atmosphere system has focused on oceanic proxies. However, the study of terrestrial proxies is equally necessary to constrain our understanding of ancient climates and linkages between the terrestrial and oceanic carbon reservoirs. We have analyzed carbon-isotope ratios from fossil plant material through the Valanginian and Lower Hauterivian from a shallow-marine, ammonite-constrained succession in the Crimean Peninsula of the southern Ukraine in order to determine if the Upper Valanginian positive carbon-isotope excursion is expressed in the atmosphere. delta(13)C(plant) values fluctuate around -23% to -22% for the Valanginian-Hauterivian, except during the Upper Valanginian where delta(13)C(plant) values record a positive excursion to similar to-18%. Based upon ammonite biostratigraphy from Crimea, and in conjunction with a composite Tethyan marine delta(13)C(carb) curve, several conclusions can be drawn: (1) the delta(13)C(plant) record indicates that the atmospheric carbon reservoir was affected; (2) the defined ammonite correlations between Europe and Crimea are synchronous; and (3) a change in photosynthetic carbon-isotope fractionation, caused by a decrease in atmospheric PCO2, occurred during the Upper Valanginian Positive delta(13)C excursion. Our new data, combined with other paleoenvironmental and paleoclimatic information, indicate that the Upper Valanginian was a cool period (icehouse) and highlights that the Cretaceous period was interrupted by periods of cooling and was not an equable climate as previously thought. (C) 2005 Elsevier B.V. All rights reserved.

Horseflies and athericids (Diptera: Tabanidae, Athericidae) from the Lower Cretaceous of England and Transbaikalia

New taxa of tabanids and athericids are described from the Lower Cretaceous deposits of England and Transbaikalia. The relationships of new genera to the Recent Athericidae and Recent and fossil Rhagionidae are discussed. Atherix sauneri Theobald, 1937 from the Oligocene of France is removed from the family Athericidae.

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.