A non-uniform mesh scheme for compressible flow

A non-uniform mesh scheme is presented for the computation of compressible flows governed by the Euler equations of gas dynamics. The scheme is based on flux-difference splitting and represents an extension of a similar scheme designed for uniform meshes. The numerical results demonstrate that little, if any, spurious oscillation occurs as a result of the non-uniformity of the mesh; and importantly, shock speeds are computed correctly.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

Uniform versus discriminatory tariffs

We analyze the non-cooperative interaction between two exporting countries producing differentiated products and one importing country when governments use optimal policies to maximize welfare. The analysis includes product differentiation, asymmetric costs, and Bertrand competition. For identical exporting countries we demonstrate that the importing country always prefers a uniform tariff regime while both exporting countries prefer a discriminatory tariff regime for any degree of product differentiation. If countries are asymmetric in terms of production cost then the higher-cost exporter always prefers the discriminatory regime but the lower-cost exporter prefers the uniform regime if there is a significant cost differential. With cost asymmetry the announcement of a uniform tariff regime by the importer is not a credible strategy since there is an incentive to deviate to discrimination. This implies an international body can play a role in ensuring that tariff agreements are respected.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

Transatlantic spaces: production, location and style in 1960s-1970s action-adventure TV series

This paper argues that transatlantic hybridity connects space, visual style and ideological point of view in British television action-adventure fiction of the 1960s–1970s. It analyses the relationship between the physical location of TV series production at Elstree Studios, UK, the representation of place in programmes, and the international trade in television fiction between the UK and USA. The TV series made at Elstree by the ITC and ABC companies and their affiliates linked Britishness with an international modernity associated with the USA, while also promoting national specificity. To do this, they drew on film production techniques that were already common for TV series production in Hollywood. The British series made at Elstree adapted versions of US industrial organization and television formats, and made programmes expected to be saleable to US networks, on the basis of British experiences in TV co-production with US companies and of the international cinema and TV market.

Thermal comfort assessment in a non-uniform thermal environment

This paper presents results for thermal comfort assessment in non-uniform thermal environments. Three types of displacement ventilation (DV) units that created stratified condition in an environmental test chamber have been selected to carry out the thermal comfort assessment: a flat diffuser (DV1), semi-circular diffuser (DV2), and floor swirl diffuser (DV3). The CBE (Center for the Built Environment at Berkeley) comfort model was implemented in this study to assess the occupant’s thermal comfort for the three DV types. The CBE model predicted the occupant’s mean skin as well as local skin temperatures very well when compared with measurements found in the literature, while it underestimated the occupant’s core temperature. The predicted occupant’s thermal sensation and thermal comfort for the case of (DV2) were the best. Therefore, the semi-circular diffuser (DV2) provided better thermal comfort for the occupant in comparison with the other two DV types.

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.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.

Marks, spaces and boundaries

Dictionary compilers and designers use punctuation to structure and clarify entries and to encode information. Dictionaries with a relatively simple structure can have simple typography, and simple punctuation; as dictionaries grew more complex, and encountered the space constraints of the printed page, complex encoding systems were developed, using punctuation and symbols. Two recent trends have emerged in dictionary design: to eliminate punctuation, and sometimes to use a larger number of fonts, so that the boundaries between elements are indicated by font change, not punctuation.

Community strategies in England: reshaping spaces of governance?

The preparation of Community Strategies (CS) has been required of LSPs and Local Authorities in England since the passing of the Local Government Act 2000. This paper examines the process and content of two Community Strategies in southern England as part of an ongoing project to understand their impact and explore ways that CSs may be carried through in a meaningful and effective manner. The paper concludes that the two CSs studied illustrate the challenge faced by LSPs in producing Strategies that are meaningful, inclusive and which follow the spirit of the government CS guidance. LAs and LSPs are also posed with a difficult challenge of seeing through an implicitly required transition from a traditional representative democratic structure/process with a more fluid participatory model. Thus we detect that at least two forms of conflict may arise – firstly with elected councillors threatened by a loss of power and secondly between communities and the LAs who are encouraged to problematise local policy and service delivery in the context of limited resource availability.