Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Howard Barker’s ‘monstrous assaults’: eroticism, death and the antique text

Howard Barker is a writer who has made several notable excursions into what he calls ‘the charnel house…of European drama.’ David Ian Rabey has observed that a compelling property of these classical works lies in what he calls ‘the incompleteness of [their] prescriptions’, and Barker’s Women Beware Women (1986), Seven Lears (1990) and Gertrude: The Cry (2002), are in turn based around the gaps and interstices found in Thomas Middleton’s Women Beware Women (c1627), Shakespeare’s King Lear (c1604) and Hamlet (c1601) respectively. This extends from representing the missing queen from King Lear, who Barker observes, ‘is barely quoted even in the depths of rage or pity’, to his new ending for Middleton’s Jacobean tragedy and the erotic revivification of Hamlet’s mother. This paper will argue that each modern reappropriation accentuates a hidden but powerful feature in these Elizabethan and Jacobean plays – namely their clash between obsessive desire, sexual transgression and death against the imposed restitution of a prescribed morality. This contradiction acts as the basis for Barker’s own explorations of eroticism, death and tragedy. The paper will also discuss Barker’s project for these ‘antique texts’, one that goes beyond what he derisively calls ‘relevance’, but attempts instead to recover ‘smothered genius’, whereby the transgressive is ‘concealed within structures that lend an artificial elegance.’ Together with Barker’s own rediscovery of tragedy, the paper will assert that these rewritings of Elizabethan and Jacobean drama expose their hidden, yet unsettling and provocative ideologies concerning the relationship between political corruption / justice through the power of sexuality (notably through the allure and danger of the mature woman), and an erotics of death that produces tragedy for the contemporary age.

Sarah Kane: Cool Britannia's reluctant feminist

Aleks Sierz in his important survey of mid 1990s drama has identified the plays of Sarah Kane as exemplars of what he terms ‘In-Yer Face’ theatre. Sierz argues that Kane and her contemporaries such as Mark Ravenhill and Judy Upton represent a break with the ideological concerns of the previous generation of playwrights such as Doug Lucie and Stephen Lowe, whose work was shaped through recognizable political concerns, often in direct opposition to Thatcherism. In contrast Sarah Kane and her generation have frequently been seen as literary embodiments of ‘Thatcher’s Children’, whereby following the fall of the Berlin Wall and the inertia of the Major years, their drama eschews a recognizable political position, and seems more preoccupied with the plight of individuals cut adrift from society. In the case of Sarah Kane her frequently quoted statement, ‘I have no responsibility as a woman writer because I don’t believe there’s such a thing’, has compounded this perception. Moreover, its dogmatism also echoes the infamous comments attributed to Mrs Thatcher regarding the role of the individual to society. However, this article seeks to reassess Kane’s position as a woman writer and will argue that her drama is positioned somewhere between the female playwrights who emerged after 1979 such as Sarah Daniels, Timberlake Wertenbaker and Clare McIntyre, whose drama was distinguished by overtly feminist concerns, and its subsequent breakdown, best exemplified by the brief cultural moment associated with the newly elected Blair government known as ‘Cool Britannia’. Drawing on a variety of sources, including Kane’s unpublished monologues, written while she was a student just after Mrs Thatcher left office, this paper will argue that far from being an exponent of post-feminism, Kane’s drama frequently revisits and is influenced by the generation of dramatists whose work was forged out the sharp ideological positions that characterized the 1980s and a direct consequence of Thatcherism.

Modification of cell wall properties in lettuce improves shelf life

It is proposed that post-harvest longevity and appearance of salad crops is closely linked to pre-harvest leaf morphology (cell and leaf size) and biophysical structure (leaf strength). Transgenic lettuce plants (Lactuca sativa cv. Valeria) were produced in which the production of the cell wall-modifying enzyme xyloglucan endotransglucosylase/hydrolase (XTH) was down-regulated by antisense inhibition. Independently transformed lines were shown to have multiple members of the LsXTH gene family down-regulated in mature leaves of 6-week-old plants and during the course of shelf life. Consequently, xyloglucan endotransglucosylase (XET) enzyme activity and action were down-regulated in the cell walls of these leaves and it was established that leaf area and fresh weight were decreased while leaf strength was increased in the transgenic lines. Membrane permeability was reduced towards the end of shelf life in the transgenic lines relative to the controls and bacteria were evident inside the leaves of control plants only. Most importantly, an extended shelf-life of transgenic lines was observed relative to the non-transgenic control plants. These data illustrate the potential for engineering cell wall traits for improving quality and longevity of salad crops using either genetic modification directly, or by using markers associated with XTH genes to inform a commercial breeding programme.

Distributed acceleration of mobile radio network optimisation algorithms

The past decade has witnessed explosive growth of mobile subscribers and services. With the purpose of providing better-swifter-cheaper services, radio network optimisation plays a crucial role but faces enormous challenges. The concept of Dynamic Network Optimisation (DNO), therefore, has been introduced to optimally and continuously adjust network configurations, in response to changes in network conditions and traffic. However, the realization of DNO has been seriously hindered by the bottleneck of optimisation speed performance. An advanced distributed parallel solution is presented in this paper, as to bridge the gap by accelerating the sophisticated proprietary network optimisation algorithm, while maintaining the optimisation quality and numerical consistency. The ariesoACP product from Arieso Ltd serves as the main platform for acceleration. This solution has been prototyped, implemented and tested. Real-project based results exhibit a high scalability and substantial acceleration at an average speed-up of 2.5, 4.9 and 6.1 on a distributed 5-core, 9-core and 16-core system, respectively. This significantly outperforms other parallel solutions such as multi-threading. Furthermore, augmented optimisation outcome, alongside high correctness and self-consistency, have also been fulfilled. Overall, this is a breakthrough towards the realization of DNO.

Acceleration of radio network optimisation algorithms

The increasing demand for cheaper-faster-better services anytime and anywhere has made radio network optimisation much more complex than ever before. In order to dynamically optimise the serving network, Dynamic Network Optimisation (DNO), is proposed as the ultimate solution and future trend. The realization of DNO, however, has been hindered by a significant bottleneck of the optimisation speed as the network complexity grows. This paper presents a multi-threaded parallel solution to accelerate complicated proprietary network optimisation algorithms, under a rigid condition of numerical consistency. ariesoACP product from Arieso Ltd serves as the platform for parallelisation. This parallel solution has been benchmarked and results exhibit a high scalability and a run-time reduction by 11% to 42% based on the technology, subscriber density and blocking rate of a given network in comparison with the original version. Further, it is highly essential that the parallel version produces equivalent optimisation quality in terms of identical optimisation outputs.