Plane wave approximation in linear elasticity

We consider the approximation of solutions of the time-harmonic linear elastic wave equation by linear combinations of plane waves. We prove algebraic orders of convergence both with respect to the dimension of the approximating space and to the diameter of the domain. The error is measured in Sobolev norms and the constants in the estimates explicitly depend on the problem wavenumber. The obtained estimates can be used in the h- and p-convergence analysis of wave-based finite element schemes.

Negotiating social identities: the influence of gender, age and ethnicity on young people’s ‘Street Careers’ in Tanzania

This paper explores the diverse ways that children and young people negotiate their social identities and construct their life course trajectories on the street, based on ethnographic research with street children in Tanzania. Drawing on the concept of a ‘street career’, I show how differences of age, gender and ethnicity intersect with the time spent on the street, to influence young people’s livelihood strategies, use of public space, access to services, and adherence to cultural rites of passage. Using the notion of ‘gender performativity’, I analyse how young people actively reconfigure gender norms and the concept of ‘the family’ on the street.

The long-term stability of a possible aqueous ammonium sulfate ocean inside Titan

We model the thermal evolution of a subsurface ocean of aqueous ammonium sulfate inside Titan using a parameterized convection scheme. The cooling and crystallization of such an ocean depends on its heat flux balance, and is governed by the pressure-dependent melting temperatures at the top and bottom of the ocean. Using recent observations and previous experimental data, we present a nominal model which predicts the thickness of the ocean throughout the evolution of Titan; after 4.5 Ga we expect an aqueous ammonium sulfate ocean 56 km thick, overlain by a thick (176 km) heterogeneous crust of methane clathrate, ice I and ammonium sulfate. Underplating of the crust by ice I will give rise to compositional diapirs that are capable of rising through the crust and providing a mechanism for cryovolcanism at the surface. We have conducted a parameter space survey to account for possible variations in the nominal model, and find that for a wide range of plausible conditions, an ocean of aqueous ammonium sulfate can survive to the present day, which is consistent with the recent observations of Titan's spin state from Cassini radar data [Lorenz, R.D., Stiles, B.W., Kirk, R.L., Allison, M.D., del Marmo, P.P., Iess, L., Lunine, J.I., Ostro, S.J., Hensley, S., 2008. Science 319, 1649–1651].

Flying through extratropical cyclone Friedhelm

On 8 December 2011, Cyclone Friedhelm, an explosively deepening cyclone, passed across the UK, causing exceptionally strong winds over Scotland and strong winds over much of the UK. A research flight through this intense cyclone was undertaken as part of the DIAMET project. This article gives an account of the flight as experienced by the authors, who were aboard the aircraft. We describe the objectives of the flight and the measurements obtained, and use photographs taken during the flight to illustrate the cloud structures observed.

Whistler mode wave growth and propagation in the prenoon magnetosphere

Pitch-angle scattering of electrons can limit the stably trapped particle flux in the magnetosphere and precipitate energetic electrons into the ionosphere. Whistler-mode waves generated by a temperature anisotropy can mediate this pitch-angle scattering over a wide range of radial distances and latitudes, but in order to correctly predict the phase-space diffusion, it is important to characterise the whistler-mode wave distributions that result from the instability. We use previously-published observations of number density, pitch-angle anisotropy and phase space density to model the plasma in the quiet pre-noon magnetosphere (defined as periods when AE<100nT). We investigate the global propagation and growth of whistler-mode waves by studying millions of growing ray paths and demonstrate that the wave distribution at any one location is a superposition of many waves at different points along their trajectories and with different histories. We show that for observed electron plasma properties, very few raypaths undergo magnetospheric reflection, most rays grow and decay within 30 degrees of the magnetic equator. The frequency range of the wave distribution at large L can be adequately described by the solutions of the local dispersion relation, but the range of wavenormal angle is different. The wave distribution is asymmetric with respect to the wavenormal angle. The numerical results suggest that it is important to determine the variation of magnetospheric parameters as a function of latitude, as well as local time and L-shell.

18 Nov 2013 In situ detection of electrified aerosols in the upper troposphere and stratosphere

Electrified aerosols have been observed in the lower troposphere and in the mesosphere, but have never been detected in the stratosphere and upper troposphere. We present measurements of aerosols obtained during a balloon flight to an altitude of 24 km. The measurements were per- formed with an improved version of the Stratospheric and Tropospheric Aerosol Counter (STAC) aerosol counter dedi- cated to the search for charged aerosols. It is found that most of the aerosols are charged in the upper troposphere for altitudes below 10 km and in the stratosphere for altitudes above 20 km. Conversely, the aerosols seem to be uncharged between 10 km and 20 km. Model calculations are used to quantify the electrification of the aerosols with a stratospheric aerosol–ion model. The percentages of charged aerosols obtained with model calculations are in excellent agreement with the observations below 10 km and above 20 km. However, the model cannot reproduce the absence of electrification found in the lower stratosphere, as the processes leading to neutralisation in this altitude range are unknown. The presence of sporadic transient layers of electrified aerosol in the upper troposphere and in the stratosphere could have significant implications for sprite formation

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

Evaluation of positioning error-induced pixel shifts on satellite linear push-broom imagery

Georeferencing is one of the major tasks of satellite-borne remote sensing. Compared to traditional indirect methods, direct georeferencing through a Global Positioning System/inertial navigation system requires fewer and simpler steps to obtain exterior orientation parameters of remotely sensed images. However, the pixel shift caused by geographic positioning error, which is generally derived from boresight angle as well as terrain topography variation, can have a great impact on the precision of georeferencing. The distribution of pixel shifts introduced by the positioning error on a satellite linear push-broom image is quantitatively analyzed. We use the variation of the object space coordinate to simulate different kinds of positioning errors and terrain topography. Then a total differential method was applied to establish a rigorous sensor model in order to mathematically obtain the relationship between pixel shift and positioning error. Finally, two simulation experiments are conducted using the imaging parameters of Chang’ E-1 satellite to evaluate two different kinds of positioning errors. The experimental results have shown that with the experimental parameters, the maximum pixel shift could reach 1.74 pixels. The proposed approach can be extended to a generic application for imaging error modeling in remote sensing with terrain variation.