An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

In this paper we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying `bulge', symmetric in the longitudinal direction. Extending the work in Biggs (2012), we first employ a WKBJ-type ansatz to identify the possible quasi-mode solutions which propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-on regions. We note that the expansions are nonuniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-on regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x = 0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

Noise propagation from a cutting of arbitrary cross-section and impedance

A boundary integral equation is described for the prediction of acoustic propagation from a monofrequency coherent line source in a cutting with impedance boundary conditions onto surrounding flat impedance ground. The problem is stated as a boundary value problem for the Helmholtz equation and is subsequently reformulated as a system of boundary integral equations via Green's theorem. It is shown that the integral equation formulation has a unique solution at all wavenumbers. The numerical solution of the coupled boundary integral equations by a simple boundary element method is then described. The convergence of the numerical scheme is demonstrated experimentally. Predictions of A-weighted excess attenuation for a traffic noise spectrum are made illustrating the effects of varying the depth of the cutting and the absorbency of the surrounding ground surface.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

Commodity risks and the cross-section of equity returns

The article examines whether commodity risk is priced in the cross-section of global equity returns. We employ a long-only equally-weighted portfolio of commodity futures and a term structure portfolio that captures phases of backwardation and contango as mimicking portfolios for commodity risk. We find that equity-sorted portfolios with greater sensitivities to the excess returns of the backwardation and contango portfolio command higher average excess returns, suggesting that when measured appropriately, commodity risk is pervasive in stocks. Our conclusions are robust to the addition to the pricing model of financial, macroeconomic and business cycle-based risk factors.

A study by high energy transfer inelastic neutron scattering spectroscopy of the mineral fraction of ox femur bone

We have used high energy transfer (HET) inelastic neutron scattering spectroscopy to measure the vibrational modes in the spectra of hydroxyapatite, bone and brushite to confirm our earlier work that only a fraction of the hydroxyl groups in bone mineral are substituted. The HET spectra are better observed due to the higher scattering cross section of hydrogen compared with the other elements in the calcium phosphate compounds. (C) 2003 Elsevier Science B.V. All rights reserved.

A study by high energy transfer inelastic neutron scattering spectroscopy of the mineral fraction of ox femur bone

We have used high energy transfer (HET) inelastic neutron scattering spectroscopy to measure the vibrational modes in the spectra of hydroxyapatite, bone and brushite to confirm our earlier work that only a fraction of the hydroxyl groups in bone mineral are substituted. The HET spectra are better observed due to the higher scattering cross section of hydrogen compared with the other elements in the calcium phosphate compounds. (C) 2003 Elsevier Science B.V. All rights reserved.

A study of the atmospherically relevant reaction between molecular chlorine and dimethylsulfide (DMS): establishing the reaction intermediate and measurement of absolute photoionization cross-sections

In a study using UV photoelectron spectroscopy (PES) of the atmospherically relevant reaction CH3SCH3 + Cl2 → CH3SCH2Cl + HCl bands associated with a reaction intermediate have been observed. These have been assigned to ionization of the covalently bound molecule (CH3)2SCl2 on the basis of the intensity of the observed bands as a function of reaction time, molecular orbital calculations of vertical ionization energies and evidence from infrared spectroscopy. A method has also been developed, with the flow-tube/PE spectrometer combination used, to measure photoionization cross-sections of the reagents and products at the photon energy utilized and this has allowed the photoionization cross-section of the intermediate to be estimated. This work augments an earlier study in which the rate constant of the reaction between CH3SCH3 (DMS) and Cl2 has been measured at room temperature.

Wild bird feeding in a large UK urban area: characteristics and estimates of energy input and individuals supported

Wild bird feeding is popular in domestic gardens across the world. Nevertheless, there is surprisingly little empirical information on certain aspects of the activity and no year-round quantitative records of the amounts and nature of the different foods provided in individual gardens. We sought to characterise garden bird feeding in a large UK urban area in two ways. First, we conducted face-to-face questionnaires with a representative cross-section of residents. Just over half fed birds, the majority doing so year round and at least weekly. Second, a two-year study recorded all foodstuffs put out by households on every provisioning occasion. A median of 628 kcal/garden/day was given. Provisioning level was not significantly influenced by weather or season. Comparisons between the data sets revealed significantly less frequent feeding amongst these ‘keen’ feeders than the face-to-face questionnaire respondents, suggesting that one-off questionnaires may overestimate provisioning frequency. Assuming 100% uptake, the median provisioning level equates to sufficient supplementary resources across the UK to support 196 million individuals of a hypothetical average garden-feeding bird species (based on 10 common UK garden-feeding birds’ energy requirements). Taking the lowest provisioning level recorded (101 kcal/day) as a conservative measure, 31 million of these average individuals could theoretically be supported.

Wormlike micelle formation and flow alignment of a pluronic block copolymer in aqueous solution

The self-assembly into wormlike micelles of a poly(ethylene oxide)-b-poly(propylene oxide)-b-poly(ethylene oxide) triblock copolymer Pluronic P84 in aqueous salt solution (2 M NaCl) has been studied by rheology, small-angle X-ray and neutron scattering (SAXS/SANS), and light scattering. Measurements of the flow curves by controlled stress rheometry indicated phase separation under flow. SAXS on solutions subjected to capillary flow showed alignment of micelles at intermediate shear rates, although loss of alignment was observed for high shear rates. For dilute solutions, SAXS and static light scattering data on unaligned samples could be superposed over three decades in scattering vector, providing unique information on the wormlike micelle structure over several length scales. SANS data provided information on even shorter length scales, in particular, concerning "blob" scattering from the micelle corona. The data could be modeled based on a system of semiflexible self-avoiding cylinders with a circular cross-section, as described by the wormlike chain model with excluded volume interactions. The micelle structure was compared at two temperatures close to the cloud point (47 degrees C). The micellar radius was found not to vary with temperature in this region, although the contour length increased with increasing temperature, whereas the Kuhn length decreased. These variations result in an increase of the low-concentration radius of gyration with increasing temperature. This was consistent with dynamic light scattering results, and, applying theoretical results from the literature, this is in agreement with an increase in endcap energy due to changes in hydration of the poly(ethylene oxide) blocks as the temperature is increased.

A 3D cloud-construction algorithm for the EarthCARE satellite mission

This article presents and assesses an algorithm that constructs 3D distributions of cloud from passive satellite imagery and collocated 2D nadir profiles of cloud properties inferred synergistically from lidar, cloud radar and imager data. It effectively widens the active–passive retrieved cross-section (RXS) of cloud properties, thereby enabling computation of radiative fluxes and radiances that can be compared with measured values in an attempt to perform radiative closure experiments that aim to assess the RXS. For this introductory study, A-train data were used to verify the scene-construction algorithm and only 1D radiative transfer calculations were performed. The construction algorithm fills off-RXS recipient pixels by computing sums of squared differences (a cost function F) between their spectral radiances and those of potential donor pixels/columns on the RXS. Of the RXS pixels with F lower than a certain value, the one with the smallest Euclidean distance to the recipient pixel is designated as the donor, and its retrieved cloud properties and other attributes such as 1D radiative heating rates are consigned to the recipient. It is shown that both the RXS itself and Moderate Resolution Imaging Spectroradiometer (MODIS) imagery can be reconstructed extremely well using just visible and thermal infrared channels. Suitable donors usually lie within 10 km of the recipient. RXSs and their associated radiative heating profiles are reconstructed best for extensive planar clouds and less reliably for broken convective clouds. Domain-average 1D broadband radiative fluxes at the top of theatmosphere(TOA)for (21 km)2 domains constructed from MODIS, CloudSat andCloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) data agree well with coincidental values derived from Clouds and the Earth’s Radiant Energy System (CERES) radiances: differences betweenmodelled and measured reflected shortwave fluxes are within±10Wm−2 for∼35% of the several hundred domains constructed for eight orbits. Correspondingly, for outgoing longwave radiation∼65% are within ±10Wm−2.

Measurement of the salinity and freezing tolerance of Crataegus genotypes using chlorophyll fluorescence

The effect of increasing salinity and freezing stress singly and in combination on a range of chlorophyll fluorescence parameters in foliar tissue of six Crataegus genotypes was examined. In general, increased stress reduced fluorescence values and absorption, trapping and electron transport energy fluxes per leaf reaction center and cross section, with decreased sigmoidicity of OJIP curves as a measure of the plastoquinone pool, reflecting decreased energy fluxes. Based on percentage reduction in a performance index from controls compared to stress-treated values, plants were ranked in order of tolerant > intermediate > sensitive. Use of this PIp ranking criteria enabled the distinguishing of marked differences in foliar salt/freezing hardiness between the Crataegus species used. Interpretation of the photochemical data showed that salinity and freezing affects both the acceptor and donor side of Photosystem II, while OJIP observations provided information regarding structural and functional changes in the leaf photosynthetic apparatus of the test species. It is concluded that chlorophyll fluorescence offers a rapid screening technique for assessing foliar salinity and freezing tolerance of woody perennials

Further investigations of the quartz optically stimulated luminescence components using linear modulation

The optically stimulated luminescence (OSL) from quartz is known to be the sum of several components with different rates of charge loss, originating from different trap types. The OSL components are clearly distinguished using the linear modulation (LM OSL) technique. A variety of pre-treatment and measurement conditions have been used on sedimentary samples in conjunction with linearly modulated optical stimulation to study in detail the behaviour of the OSL components of quartz. Single aliquots of different quartz samples have been found to contain typically five or six common LM OSL components when stimulated at View the MathML source. The components have been parameterised in terms of thermal stability (i.e. E and s), photoionisation cross-section energy dependence and dose response. The results of studies concerning applications of component-resolved LM OSL measurements on quartz are also presented. These include the detection of partial bleaching in young samples, use of ‘stepped wavelength’ stimulation to observe OSL from single components and attempts to extend the age range of quartz OSL dating.