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.

Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Preventing carbon contamination of optical devices for X-rays: the effect of oxygen on photon-induced dissociation of CO on platinum

Platinum is one of the most common coatings used to optimize mirror reflectivity in soft X-ray beamlines. Normal operation results in optics contamination by carbon-based molecules present in the residual vacuum of the beamlines. The reflectivity reduction induced by a carbon layer at the mirror surface is a major problem in synchrotron radiation sources. A time-dependent photoelectron spectroscopy study of the chemical reactions which take place at the Pt(111) surface under operating conditions is presented. It is shown that the carbon contamination layer growth can be stopped and reversed by low partial pressures of oxygen for optics operated in intense photon beams at liquidnitrogen temperature. For mirrors operated at room temperature the carbon contamination observed for equivalent partial pressures of CO is reduced and the effects of oxygen are observed on a long time scale.

Wernicke’s aphasia reflects a combination of acoustic-phonological and semantic control deficits: A case-series comparison of Wernicke’s aphasia, semantic dementia and semantic aphasia

Wernicke’s aphasia (WA) is the classical neurological model of comprehension impairment and, as a result, the posterior temporal lobe is assumed to be critical to semantic cognition. This conclusion is potentially confused by (a) the existence of patient groups with semantic impairment following damage to other brain regions (semantic dementia and semantic aphasia) and (b) an ongoing debate about the underlying causes of comprehension impairment in WA. By directly comparing these three patient groups for the first time, we demonstrate that the comprehension impairment in Wernicke’s aphasia is best accounted for by dual deficits in acoustic-phonological analysis (associated with pSTG) and semantic cognition (associated with pMTG and angular gyrus). The WA group were impaired on both nonverbal and verbal comprehension assessments consistent with a generalised semantic impairment. This semantic deficit was most similar in nature to that of the semantic aphasia group suggestive of a disruption to semantic control processes. In addition, only the WA group showed a strong effect of input modality on comprehension, with accuracy decreasing considerably as acoustic-phonological requirements increased. These results deviate from traditional accounts which emphasise a single impairment and, instead, implicate two deficits underlying the comprehension disorder in WA.

Reading is now 'cool': a study of English teachers' perspectives on e-reading devices as a challenge and an opportunity

E-reading devices such as The Kindle have rapidly secured a significant place in a number of societies as at least one major platform for reading. To some extent they are part of the overarching move towards a fully digitised world but they have a distinctiveness in being deliberately “book-like”. Teachers generally have some suspicion towards “New Media”, especially when it challenges their established practice and nothing dominates the school more than the physical book. What may be the challenges but also the benefits of e-readers to teachers and students? What may be the particular challenges to those teachers who are, traditionally, the guardians of the book, that is the teachers of mother tongue literature? This article reports on a survey of English teachers in England to gauge their reactions to e-readers, both personally and professionally and describes their speculations about the place of e-readers in schools in the future. There is a mixed reaction with some teachers concerned about the demise of the book and the potential negative impact on reading. However, the majority welcome e-readers as a dynamic element within the reading environment with particular potential to enthuse reluctant readers and those with special or linguistic needs. They also, some grudgingly, view the fact that reading using this form of technology appeals to the “e-generation” and may succeed in making reading “cool”. This form of technology is, ironically (given that it appears to threaten traditional books) likely to be rapidly adopted in classrooms.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

Infotainment across access devices: the perceptual impact of multimedia QoS

The introduction of multimedia on pervasive and mobile communication devices raises a number of perceptual quality issues. However, limited work has been done examining the 3-way interaction between use of equipment, user perceptual quality and quality of service. Our work measures user perceptual quality with the quality of perception (QoP) metrics which comprises levels of informational transfer (objective) and user satisfaction (subjective) when users are presented with multimedia video clips at three different frame rates, using four different display devices. Finally, our results will show that variation in frame-rate does not impact a user’s level of information assimilation (IA), however, does impact a users’ perception of multimedia video ‘quality’.

A conceptual valuation framework (VF) for home telecare system devices

Purpose – The aim of this paper is to present a conceptual valuation framework to allow telecare service stakeholders to assess telecare devices in the home in terms of their social, psychological and practical effects. The framework enables telecare service operators to more effectively engage with the social and psychological issues resulting from telecare technology deployment in the home and to design and develop appropriate responses as a result. Design/methodology/approach – The paper provides a contextual background for the need for sociologically pitched tools that engage with the social and cultural feelings of telecare service users before presenting the valuation framework and how it could be used. Findings – A conceptual valuation framework is presented for potential development/use. Research limitations/implications – The valuation framework has yet to be extensively tested or verified. Practical implications – The valuation framework needs to be tested and deployed by a telecare service operator but the core messages of the paper are valid and interesting for readership. Social implications – In addressing the social and cultural perspectives of telecare service stakeholders, the paper makes a link between the technologies in the home, the feelings and orientations of service users (e.g. residents, emergency services, wardens, etc.) and the telecare service operator. Originality/value – The paper is an original contribution to the field as it details how the sociological orientations of telecare technology service users should be valued and addressed by service operators. It has a value through the conceptual arguments made and through valuation framework presented.

Efficient calculation of two-dimensional periodic and waveguide acoustic Green’s functions

New representations and efficient calculation methods are derived for the problem of propagation from an infinite regularly spaced array of coherent line sources above a homogeneous impedance plane, and for the Green's function for sound propagation in the canyon formed by two infinitely high, parallel rigid or sound soft walls and an impedance ground surface. The infinite sum of source contributions is replaced by a finite sum and the remainder is expressed as a Laplace-type integral. A pole subtraction technique is used to remove poles in the integrand which lie near the path of integration, obtaining a smooth integrand, more suitable for numerical integration, and a specific numerical integration method is proposed. Numerical experiments show highly accurate results across the frequency spectrum for a range of ground surface types. It is expected that the methods proposed will prove useful in boundary element modeling of noise propagation in canyon streets and in ducts, and for problems of scattering by periodic surfaces.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

Acoustic scattering by an inhomogeneous layer on a rigid plate

The problem of scattering of time-harmonic acoustic waves by an inhomogeneous fluid layer on a rigid plate in R2 is considered. The density is assumed to be unity in the media: within the layer the sound speed is assumed to be an arbitrary bounded measurable function. The problem is modelled by the reduced wave equation with variable wavenumber in the layer and a Neumann condition on the plate. To formulate the problem and prove uniqueness of solution a radiation condition appropriate for scattering by infinite rough surfaces is introduced, a generalization of the Rayleigh expansion condition for diffraction gratings. With the help of the radiation condition the problem is reformulated as a system of two second kind integral equations over the layer and the plate. Under additional assumptions on the wavenumber in the layer, uniqueness of solution is proved and the nonexistence of guided wave solutions of the homogeneous problem established. General results on the solvability of systems of integral equations on unbounded domains are used to establish existence and continuous dependence in a weighted norm of the solution on the given data.

Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane

This paper is concerned with the problem of propagation from a monofrequency coherent line source above a plane of homogeneous surface impedance. The solution of this problem occurs in the kernel of certain boundary integral equation formulations of acoustic propagation above an impedance boundary, and the discussion of the paper is motivated by this application. The paper starts by deriving representations, as Laplace-type integrals, of the solution and its first partial derivatives. The evaluation of these integral representations by Gauss-Laguerre quadrature is discussed, and theoretical bounds on the truncation error are obtained. Specific approximations are proposed which are shown to be accurate except in the very near field, for all angles of incidence and a wide range of values of surface impedance. The paper finishes with derivations of partial results and analogous Laplace-type integral representations for the case of a point source.