Boundary integral equations on unbounded rough surfaces: Fredholmness and the finite section method

We consider a class of boundary integral equations that arise in the study of strongly elliptic BVPs in unbounded domains of the form $D = \{(x, z)\in \mathbb{R}^{n+1} : x\in \mathbb{R}^n, z > f(x)\}$ where $f : \mathbb{R}^n \to\mathbb{R}$ is a sufficiently smooth bounded and continuous function. A number of specific problems of this type, for example acoustic scattering problems, problems involving elastic waves, and problems in potential theory, have been reformulated as second kind integral equations $u+Ku = v$ in the space $BC$ of bounded, continuous functions. Having recourse to the so-called limit operator method, we address two questions for the operator $A = I + K$ under consideration, with an emphasis on the function space setting $BC$. Firstly, under which conditions is $A$ a Fredholm operator, and, secondly, when is the finite section method applicable to $A$?

20th century intraseasonal Asian monsoon dynamics viewed from Isomap

The Asian summer monsoon is a high dimensional and highly nonlinear phenomenon involving considerable moisture transport towards land from the ocean, and is critical for the whole region. We have used daily ECMWF reanalysis (ERA-40) sea-level pressure (SLP) anomalies to the seasonal cycle, over the region 50-145°E, 20°S-35°N to study the nonlinearity of the Asian monsoon using Isomap. We have focused on the two-dimensional embedding of the SLP anomalies for ease of interpretation. Unlike the unimodality obtained from tests performed in empirical orthogonal function space, the probability density function, within the two-dimensional Isomap space, turns out to be bimodal. But a clustering procedure applied to the SLP data reveals support for three clusters, which are identified using a three-component bivariate Gaussian mixture model. The modes are found to appear similar to active and break phases of the monsoon over South Asia in addition to a third phase, which shows active conditions over the Western North Pacific. Using the low-level wind field anomalies the active phase over South Asia is found to be characterised by a strengthening and an eastward extension of the Somali jet whereas during the break phase the Somali jet is weakened near southern India, while the monsoon trough in northern India also weakens. Interpretation is aided using the APHRODITE gridded land precipitation product for monsoon Asia. The effect of large-scale seasonal mean monsoon and lower boundary forcing, in the form of ENSO, is also investigated and discussed. The outcome here is that ENSO is shown to perturb the intraseasonal regimes, in agreement with conceptual ideas.

Realism and politics in alienated space: Trevor Griffiths's plays of the 1970s in the television studio

The television studio play is often perceived as a somewhat compromised, problematic mode in which spatial and technological constraints inhibit the signifying and aesthetic capacity of dramatic texts. Leah Panos examines the function of the studio in the 1970s television dramas of socialist playwright Trevor Griffiths, and argues that the established verbal and visual conventions of the studio play, in its confined and ‘alienated’ space, connect with and reinforce various aspects of Griffiths's particular approach and agenda. As well as suggesting ways in which the idealist, theoretical focus of the intellectual New Left is reflexively replicated within the studio, Panos explores how the ‘intimate’ visual language of the television studio allows Griffiths to create a ‘humanized’ Marxist discourse through which he examines dialectically his dramatic characters' experiences, ideas, morality, and political objectives. Leah Panos recently completed her doctoral thesis, ‘Dramatizing New Left Contradictions: Television Texts of Ken Loach, Jim Allen, and Trevor Griffiths’, at the University of Reading and is now a Postdoctoral Researcher on the AHRC funded project, ‘Spaces of Television: Production, Site and Style’, which runs from July 2010 to March 2014.

Historicizing counterurbanization: in-migration and the reconstruction of rural space in Berkshire (UK), 1901-51

This article uses census data for Berkshire to argue that large-scale counterurbanization began much earlier than is generally recognized in some parts of southern England. This was not just movement down the urban hierarchy, which as Pooley and Turnbull have demonstrated was a long-term feature of England’s settlement system, but in some cases at least amenity-driven migration to rural areas of the kind increasingly recognized as a core component of recent counterurbanization. Despite a reduction of acreage Berkshire’s rural districts saw a 54% rise in population between 1901 and 1951. The sub-regional pattern of growth is assessed to gauge whether ‘clean break’ migration to the remote west of the county (which remained effectively out of commuting range from London throughout the period) was taking place, or whether counterurbanization was confined to the more accessible eastern districts. However, whilst population did increase in both west and east, it was in fact the central districts that grew most impressively. Three case study parishes are investigated in order to gauge the nature and consequences of counterurbanization at a local level. Professional and business migrants figure prominently, seeking to preserve and promote the rural attributes of their new communities, without however cutting their ties to urban centres. It is argued that migration to rural Berkshire in the first half of the twentieth century cannot adequately be described either as a form of extended suburbanization or an anti-metropolitan ‘clean break’. Rather, early counterurbanization marks the first stage on the long road to a post-productivist countryside, in which countryside becomes detached from agriculture, there is socio-economic convergence between town and country, and the ‘rural’ increasingly becomes defined by landscape and identity rather than economic function.

Aircraft routing with minimal climate impact: the REACT4C climate cost function modelling approach (V1.0)

In addition to CO2, the climate impact of aviation is strongly influenced by non-CO2 emissions, such as nitrogen oxides, influencing ozone and methane, and water vapour, which can lead to the formation of persistent contrails in ice-supersaturated regions. Because these non-CO2 emission effects are characterised by a short lifetime, their climate impact largely depends on emission location and time; that is to say, emissions in certain locations (or times) can lead to a greater climate impact (even on the global average) than the same emission in other locations (or times). Avoiding these climate-sensitive regions might thus be beneficial to climate. Here, we describe a modelling chain for investigating this climate impact mitigation option. This modelling chain forms a multi-step modelling approach, starting with the simulation of the fate of emissions released at a certain location and time (time-region grid points). This is performed with the chemistry–climate model EMAC, extended via the two submodels AIRTRAC (V1.0) and CONTRAIL (V1.0), which describe the contribution of emissions to the composition of the atmosphere and to contrail formation, respectively. The impact of emissions from the large number of time-region grid points is efficiently calculated by applying a Lagrangian scheme. EMAC also includes the calculation of radiative impacts, which are, in a second step, the input to climate metric formulas describing the global climate impact of the emission at each time-region grid point. The result of the modelling chain comprises a four-dimensional data set in space and time, which we call climate cost functions and which describes the global climate impact of an emission at each grid point and each point in time. In a third step, these climate cost functions are used in an air traffic simulator (SAAM) coupled to an emission tool (AEM) to optimise aircraft trajectories for the North Atlantic region. Here, we describe the details of this new modelling approach and show some example results. A number of sensitivity analyses are performed to motivate the settings of individual parameters. A stepwise sanity check of the results of the modelling chain is undertaken to demonstrate the plausibility of the climate cost functions.