A well-posed integral equation formulation for three-dimensional rough surface scattering

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space L-2 (Gamma) when the scattering surface G does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, kappa, for kappa > 0, if the coupling parameter h is chosen proportional to the wave number. In the case when G is a plane, we show that the choice eta = kappa/2 is nearly optimal in terms of minimizing the condition number.

Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces

We consider the problem of scattering of time harmonic acoustic waves by an unbounded sound soft surface which is assumed to lie within a finite distance of some plane. The paper is concerned with the study of an equivalent variational formulation of this problem set in a scale of weighted Sobolev spaces. We prove well-posedness of this variational formulation in an energy space with weights which extends previous results in the unweighted setting [S. Chandler-Wilde and P. Monk, SIAM J. Math. Anal., 37 (2005), pp. 598–618] to more general inhomogeneous terms in the Helmholtz equation. In particular, in the two-dimensional case, our approach covers the problem of plane wave incidence, whereas in the three-dimensional case, incident spherical and cylindrical waves can be treated. As a further application of our results, we analyze a finite section type approximation, whereby the variational problem posed on an infinite layer is approximated by a variational problem on a bounded region.

Changing state disruption of lip-reading by irrelevant sound in perceptual and memory tasks

Three experiments investigated irrelevant sound interference of lip-read lists. In Experiment 1, an acoustically changing sequence of nine irrelevant utterances was more disruptive to spoken immediate identification of lists of nine lip-read digits than nine repetitions of the same utterances (the changing-state effect; Jones, Madden, & Miles, 1992). Experiment 2 replicated this finding when lip-read items were sampled with replacement from the nine digits to form the lip-read lists. In Experiment 3, when the irrelevant sound was confined to the retention interval of a delayed recall task, a changing-state pattern of disruption also occurred. Results confirm a changing-state effect in memory for lip-read items but also point to the possibility that, for lip-reading, changing-state effects may occur at an earlier, perceptual stage.

Auditory memory and the irrelevant sound effect: further evidence for changing state disruption

Four experiments investigate the hypothesis that irrelevant sound interferes with serial recall of auditory items in the same fashion as with visually presented items. In Experiment 1 an acoustically changing sequence of 30 irrelevant utterances was more disruptive than 30 repetitions of the same utterance (the changing-state effect; Jones, Madden, & Miles, 1992) whether the to-be-remembered items were visually or auditorily presented. Experiment 2 showed that two different utterances spoken once (a heterogeneous compound suffix; LeCompte & Watkins, 1995) produced less disruption to serial recall than 15 repetitions of the same sequence. Disruption thus depends on the number of sounds in the irrelevant sequence. In Experiments 3a and 3b the number of different sounds, the "token-set" size (Tremblay & Jones, 1998), in an irrelevant sequence also influenced the magnitude of disruption in both irrelevant sound and compound suffix conditions. The results support the view that the disruption of memory for auditory items, like memory for visually presented items, is dependent on the number of different irrelevant sounds presented and the size of the set from which these sounds are taken. Theoretical implications are discussed.

A left-ear disadvantage for the presentation of irrelevant sound: manipulations of task requirements and changing state

Three experiments attempted to clarify the effect of altering the spatial presentation of irrelevant auditory information. Previous research using serial recall tasks demonstrated a left-ear disadvantage for the presentation of irrelevant sounds (Hadlington, Bridges, & Darby, 2004). Experiments 1 and 2 examined the effects of manipulating the location of irrelevant sound on either a mental arithmetic task (Banbury & Berry, 1998) or a missing-item task (Jones & Macken, 1993; Experiment 4). Experiment 3 altered the amount of change in the irrelevant stream to assess how this affected the level of interference elicited. Two prerequisites appear necessary to produce the left-ear disadvantage; the presence of ordered structural changes in the irrelevant sound and the requirement for serial order processing of the attended information. The existence of a left-ear disadvantage highlights the role of the right hemisphere in the obligatory processing of auditory information. (c) 2006 Published by Elsevier Inc.

Pulse shaping using state space algorithms

We discuss the use of pulse shaping for optimal excitation of samples in time-domain THz spectroscopy. Pulse shaping can be performed in a 4f optical system to specifications from state space models of the system's dynamics. Subspace algorithms may be used for the identification of the state space models.

State-space model identification of a wireless THz network

We model the large scale fading of wireless THz communications links deployed in a metropolitan area taking into account reception through direct line of sight, ground or wall reflection and diffraction. The movement of the receiver in the three dimensions is modelled by an autonomous dynamic linear system in state-space whereas the geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a Wiener model from time-domain measurements of the field intensity.

A solid-state noise source for millimetre wave spectrometry

A novel wide-band noise source for millimetre-wave spectrometry is described. It uses power combined Schottky diodes, reverse biased to avalanche breakdown, mounted in a wide-band tapered slot antenna. Power has been produced from 15 to 200 GHz with an equivalent temperature of 28200 K at 40 GHz.

The British state and the Irish rebellion of 1916: an intelligence failure or an failure of response

The teleological narrative that has dominated the handling of intelligence by the British state in the events that led up to the 1916 Irish Rebellion in Dublin has been characterised as a cocktail of incompetence and mendacity. Using new and existing archive material this article argues that both the cabinet in London and key members of the Irish Executive in Dublin were supplied with accurate and timely intelligence by the Admiralty's signals intelligence unit, the Royal Irish Constabulary and the Dublin Metropolitan Police with respect to this event. Far from being a failure of intelligence here is evidence to show that there occurred a failure of response on behalf of key decision-makers. The warnings that were given by intelligence organisations were filtered through the existing policy preferences and assumptions. As a result of these factors accurate evaluations and sound judgement were not exercised by key officials, such as Sir Matthew Nathan, in Dublin Castle.

Wave trapping in a two-dimensional sound-soft or sound-hard acoustic waveguide of slowly-varying width

In this paper we derive novel approximations to trapped waves in a two-dimensional acoustic waveguide whose walls vary slowly along the guide, and at which either Dirichlet (sound-soft) or Neumann (sound-hard) conditions are imposed. The guide contains a single smoothly bulging region of arbitrary amplitude, but is otherwise straight, and the modes are trapped within this localised increase in width. Using a similar approach to that in Rienstra (2003), a WKBJ-type expansion yields an approximate expression for the modes which can be present, which display either propagating or evanescent behaviour; matched asymptotic expansions are then used to derive connection formulae which bridge the gap across the cut-off between propagating and evanescent solutions in a tapering waveguide. A uniform expansion is then determined, and it is shown that appropriate zeros of this expansion correspond to trapped mode wavenumbers; the trapped modes themselves are then approximated by the uniform expansion. Numerical results determined via a standard iterative method are then compared to results of the full linear problem calculated using a spectral method, and the two are shown to be in excellent agreement, even when $\epsilon$, the parameter characterising the slow variations of the guide’s walls, is relatively large.

Relaxing the Tropics to an ‘observed’ state: analysis using a simple baroclinic model

The technique of relaxation of the tropical atmosphere towards an analysis in a month-season forecast model has previously been successfully exploited in a number of contexts. Here it is shown that when tropical relaxation is used to investigate the possible origin of the observed anomalies in June–July 2007, a simple dynamical model is able to reproduce the observed component of the pattern of anomalies given by an ensemble of ECMWF forecast runs. Following this result, the simple model is used for a range of experiments on time-scales of relaxation, variables and regions relaxed based on a control model run with equatorial heating in a zonal flow. A theory based on scale analysis for the large-scale tropics is used to interpret the results. Typical relationships between scales are determined from the basic equations, and for a specified diabatic heating a chain of deductions for determining the dependent variables is derived. Different critical time-scales are found for tropical relaxation of different dependent variables to be effective. Vorticity has the longest critical time-scale, typically 1.2 days. For temperature and divergence, the time-scales are 10 hours and 3 hours, respectively. However not all the tropical fields, in particular the vertical motion, are reproduced correctly by the model unless divergence is heavily damped. To obtain the correct extra-tropical fields, it is crucial to have the correct rotational flow in the subtropics to initiate the Rossby wave propagation from there. It is sufficient to relax vorticity or temperature on a time-scale comparable or less than their critical time-scales to obtain this. However if the divergent advection of vorticity is important in the Rossby Wave Source then strong relaxation of divergence is required to accurately represent the tropical forcing of Rossby waves.

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.

On the detection and attribution of gravity waves generated by the 20 March 2015 solar eclipse

Internal gravity waves are generated as adjustment radiation whenever a sudden change in forcing causes the atmosphere to depart from its large-scale balanced state. Such a forcing anomaly occurs during a solar eclipse, when the Moon’s shadow cools part of the Earth’s surface. The resulting atmospheric gravity waves are associated with pressure and temperature perturbations, which in principle are detectable both at the surface and aloft. In this study, surface pressure and temperature data from two UK sites at Reading and Lerwick are analysed for eclipse-driven gravity-wave perturbations during the 20 March 2015 solar eclipse over north-west Europe. Radiosonde wind data from the same two sites are also analysed using a moving parcel analysis method, to determine the periodicities of the waves aloft. On this occasion, the perturbations both at the surface and aloft are found not to be confidently attributable to eclipse-driven gravity waves. We conclude that the complex synoptic weather conditions over the UK at the time of this particular eclipse helped to mask any eclipse-driven gravity waves.