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.

Reading 'The Truman Show' inside out

This essay explores how The Truman Show, Peter Weir’s film about a television show, deserves more sustained analysis than it has received since its release in 1998. I will argue that The Truman Show problematizes the binary oppositions of cinema/television, disruption/stability, reality/simulation and outside/inside that structure it. The Truman Show proposes that binary oppositions such as outside/inside exist in a mutually implicating relationship. This deconstructionist strategy not only questions the film’s critical position, but also enables a reflection on the very status of film analysis itself.

Letterforms for handwriting and reading: print script and sanserifs in early twentieth-century England

This essay is about letterforms and typography in reading books for young children and how they were influenced by the teaching of handwriting in the early decades of the twentieth century. I examine the contributions made by infant teachers to typography and book design and draw particular attention to the print script movement and the gradual introduction of sanserif typefaces in reading books. I suggest that the use of sanserifs in reading books for young children is one of their first appearances for continuous text. Although the influence of print script on the teaching of handwriting may have had some undesirable effects, I suggest that it indirectly contributed to some innovations in book design.

Replication enhancer elements within the open reading frame of tick-borne encephalitis virus and their evolution within the Flavivirus genus

We provide experimental evidence of a replication enhancer element (REE) within the capsid gene of tick-borne encephalitis virus (TBEV, genus Flavivirus). Thermodynamic and phylogenetic analyses predicted that the REE folds as a long stable stem–loop (designated SL6), conserved among all tick-borne flaviviruses (TBFV). Homologous sequences and potential base pairing were found in the corresponding regions of mosquito-borne flaviviruses, but not in more genetically distant flaviviruses. To investigate the role of SL6, nucleotide substitutions were introduced which changed a conserved hexanucleotide motif, the conformation of the terminal loop and the base-paired dsRNA stacking. Substitutions were made within a TBEV reverse genetic system and recovered mutants were compared for plaque morphology, single-step replication kinetics and cytopathic effect. The greatest phenotypic changes were observed in mutants with a destabilized stem. Point mutations in the conserved hexanucleotide motif of the terminal loop caused moderate virus attenuation. However, all mutants eventually reached the titre of wild-type virus late post-infection. Thus, although not essential for growth in tissue culture, the SL6 REE acts to up-regulate virus replication. We hypothesize that this modulatory role may be important for TBEV survival in nature, where the virus circulates by non-viraemic transmission between infected and non-infected ticks, during co-feeding on local rodents.

Reading Derrida on mathematics

This article engages with the claims of Anne Brubaker that “[n]ow that the dust has settled after the so-called ‘Science Wars’ […] it is an opportune time to reassess the ways in which poststructural theory both argues persuasively for mathematics as a culturally embedded practice – a method as opposed to a metaphysics – and, at the same time, reinscribes realist notions of mathematics as a noise-free description of a mind independent reality.” Through a close re-reading of Jacques Derrida’s work I argue, in alliance with Vicki Kirby’s critique of the work of Brian Rotman, not only that Brubaker misunderstands Derrida’s “writing” but also that her argument constitutes a typical instance of much wider misreadings of Derrida and “poststructuralism” across a range of disciplines in terms of the ways in which her text re-institutes the very stabilities it itself attributes to Derrida’s texts.