A frequency-independent boundary element method for scattering by two-dimensional screens and apertures

We propose and analyse a hybrid numerical–asymptotic hp boundary element method (BEM) for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high-frequency asymptotics of the solution. We provide a rigorous frequency-explicit error analysis which proves that the method converges exponentially as the number of degrees of freedom N increases, and that to achieve any desired accuracy it is sufficient to increase N in proportion to the square of the logarithm of the frequency as the frequency increases (standard BEMs require N to increase at least linearly with frequency to retain accuracy). Our numerical results suggest that fixed accuracy can in fact be achieved at arbitrarily high frequencies with a frequency-independent computational cost, when the oscillatory integrals required for implementation are computed using Filon quadrature. We also show how our method can be applied to the complementary ‘breakwater’ problem of propagation through an aperture in an infinite sound-hard screen.

Unpaid work and conformity: why care?

We study the supply of unpaid eldercare (in particular caring for parents) in the UK, focusing on both the division of care and caring tasks by gender and the effect of conformity to social norms in relation to caring. We then investigate the effect of the amount of care on the well-being of caregivers and whether agreeing with the care norm enhances their well-being. Our results suggest that the eldercare reform neglects important aspects underlying the distribution of care hours and care tasks between caregivers and may potentially worsen intrahousehold inequality in earnings and well-being, in particular, between men and women.

Framing fracking: which frames are heard in English planning and environmental policy and practice?

Fracking in England has been the subject of significant controversy and has sparked not only public protest but also an associated framing war with differing social constructions of the technology adopted by different sides. This article explores the frames and counter-frames which have been employed by both the anti-fracking movement and by government and the oil and gas industry. It then considers the way in which the English planning and regulatory permitting systems have provided space for these frames within the relevant machinery for public participation. The article thus enables one to see which frames have been allowed a voice and which have been excluded.

Reticent autobiography: Henry Green and Christopher Isherwood at the Hogarth Press

Christopher Isherwood’s Lions and Shadows (1938) and Henry Green’s Pack My Bag (1940) are accounts of the authors’ educations in the 1920s. Published by Leonard and Virginia Woolf’s Hogarth Press, these works use reticent narrators to test the limits of autobiography. In each case, authorial self-presentation complicates the work’s classification in the literary marketplace: Green paradoxically extends his use of a pseudonym to autobiography and Isherwood assigns his own name to his purportedly fictional protagonist, and yet Hogarth published both as novels. The two texts and their publication histories exemplify modernist autobiography’s blurring of the lines between fiction and personal history.

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Shackle on time, uncertainty and process

This paper is intended both as a contribution to the conceptual work on process in economic thought and as an attempt to connect a non-institutionalist, non-evolutionary thinker to it. The paper has two principal objectives: (i) to delineate a broad, philosophically grounded conception of what an economic process theory (EPT) is; and (ii) to locate the contributions of George Shackle within this broad conception of EPT. In pursuing these two objectives, I hope to draw out the originality and significance of Shackle’s economics with a particular emphasis on what he adds to process conceptions developed within other heterodox traditions such as institutional and evolutionary economics. I will also highlight some of the perceived limitations of Shackle’s approach and link them to the limitations of process philosophy.

Strategic trade policy, competition, and welfare: the case of voluntary export restraints between Britain and Japan (1971–2002)

I evaluate the voluntary export restraint placed on Japanese automobile exports from 1977 to 1999 by the UK. I show that the policy failed to assist the British domestic car industry. Instead, UK-based US multi-nationals and Japanese manufacturers were the primary beneficiaries, at a substantial cost to UK consumers. Whilst there are a number of caveats, the policy was on balance damaging to the UK economy in welfare terms.

Search engine liability for autocomplete suggestions: personality, privacy and the power of the algorithm

This article is concerned with the liability of search engines for algorithmically produced search suggestions, such as through Google’s ‘autocomplete’ function. Liability in this context may arise when automatically generated associations have an offensive or defamatory meaning, or may even induce infringement of intellectual property rights. The increasing number of cases that have been brought before courts all over the world puts forward questions on the conflict of fundamental freedoms of speech and access to information on the one hand, and personality rights of individuals— under a broader right of informational self-determination—on the other. In the light of the recent judgment of the Court of Justice of the European Union (EU) in Google Spain v AEPD, this article concludes that many requests for removal of suggestions including private individuals’ information will be successful on the basis of EU data protection law, even absent prejudice to the person concerned.

How does investing in cheap labour countries affect performance at home? Firm-level evidence from France and Italy

Transferring low tech manufacturing jobs to cheap labour countries is often seen by part of the general public and policy makers as a step into the de-industrialization of the European economies. However, recent contributions have shown that the effects on home economies are rarely negative. Our paper contributes to this literature by examining how outward investments to developing and less developed countries (LDCs) affect home activities of French and Italian firms that turn multinational in the period analysed. The effects of these investments are also compared to the effects of investments to developed economies (DCs). The analysis is carried out by using propensity score matching. We find no evidence of a negative effect of outward investments to LDCs. In Italy they have a positive long term effect on value added and employment. For France we find a positive effect on the size of domestic output and employment.

A priori error analysis of space–time Trefftz discontinuous Galerkin methods for wave problems

We present and analyse a space–time discontinuous Galerkin method for wave propagation problems. The special feature of the scheme is that it is a Trefftz method, namely that trial and test functions are solution of the partial differential equation to be discretised in each element of the (space–time) mesh. The method considered is a modification of the discontinuous Galerkin schemes of Kretzschmar et al. (2014) and of Monk & Richter (2005). For Maxwell’s equations in one space dimension, we prove stability of the method, quasi-optimality, best approximation estimates for polynomial Trefftz spaces and (fully explicit) error bounds with high order in the meshwidth and in the polynomial degree. The analysis framework also applies to scalar wave problems and Maxwell’s equations in higher space dimensions. Some numerical experiments demonstrate the theoretical results proved and the faster convergence compared to the non-Trefftz version of the scheme.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.