Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version

We consider the two-dimensional Helmholtz equation with constant coefficients on a domain with piecewise analytic boundary, modelling the scattering of acoustic waves at a sound-soft obstacle. Our discretisation relies on the Trefftz-discontinuous Galerkin approach with plane wave basis functions on meshes with very general element shapes, geometrically graded towards domain corners. We prove exponential convergence of the discrete solution in terms of number of unknowns.

Equation for the microwave backscatter cross section of aggregate snowflakes using the self-similar Rayleigh–Gans approximation

In this paper an equation is derived for the mean backscatter cross section of an ensemble of snowflakes at centimeter and millimeter wavelengths. It uses the Rayleigh–Gans approximation, which has previously been found to be applicable at these wavelengths due to the low density of snow aggregates. Although the internal structure of an individual snowflake is random and unpredictable, the authors find from simulations of the aggregation process that their structure is “self-similar” and can be described by a power law. This enables an analytic expression to be derived for the backscatter cross section of an ensemble of particles as a function of their maximum dimension in the direction of propagation of the radiation, the volume of ice they contain, a variable describing their mean shape, and two variables describing the shape of the power spectrum. The exponent of the power law is found to be −. In the case of 1-cm snowflakes observed by a 3.2-mm-wavelength radar, the backscatter is 40–100 times larger than that of a homogeneous ice–air spheroid with the same mass, size, and aspect ratio.

The neoliberal way of war: a critical analysis of contemporary British security in policy and practice.

Dominant paradigms of causal explanation for why and how Western liberal-democracies go to war in the post-Cold War era remain versions of the 'liberal peace' or 'democratic peace' thesis. Yet such explanations have been shown to rest upon deeply problematic epistemological and methodological assumptions. Of equal importance, however, is the failure of these dominant paradigms to account for the 'neoliberal revolution' that has gripped Western liberal-democracies since the 1970s. The transition from liberalism to neoliberalism remains neglected in analyses of the contemporary Western security constellation. Arguing that neoliberalism can be understood simultaneously through the Marxian concept of ideology and the Foucauldian concept of governmentality – that is, as a complementary set of 'ways of seeing' and 'ways of being' – the thesis goes on to analyse British security in policy and practice, considering it as an instantiation of a wider neoliberal way of war. In so doing, the thesis draws upon, but also challenges and develops, established critical discourse analytic methods, incorporating within its purview not only the textual data that is usually considered by discourse analysts, but also material practices of security. This analysis finds that contemporary British security policy is predicated on a neoliberal social ontology, morphology and morality – an ideology or 'way of seeing' – focused on the notion of a globalised 'network-market', and is aimed at rendering circulations through this network-market amenable to neoliberal techniques of government. It is further argued that security practices shaped by this ideology imperfectly and unevenly achieve the realisation of neoliberal 'ways of being' – especially modes of governing self and other or the 'conduct of conduct' – and the re-articulation of subjectivities in line with neoliberal principles of individualism, risk, responsibility and flexibility. The policy and practice of contemporary British 'security' is thus recontextualised as a component of a broader 'neoliberal way of war'.

Letters in cognitive analytic therapy: The patient's experience

Patient perspectives on how therapeutic letters contributed to their experience of cognitive analytic therapy (CAT) were investigated. Eight patients took part in semistructured interviews. A grounded, thematic analysis of their accounts suggested four general processes. First, letters offered a tangible, lasting framework for the assimilation of a new perspective about themselves and their relationships and facilitated coping with a complex range of emotions and risks this awareness required. Second, they demonstrated therapists’ commitment to patients’ growth. Third, they helped to teach participants about the therapy process as an example of an interpersonal exchange. Fourth, they helped participants consider how they wished to share personal information. These data offer a more complex understanding of this standard CAT intervention. Although some findings are consistent with CAT theory, the range of emotional dilemmas associated with letters has not received specific attention. Clinical implications are discussed.

Orientalism and intelligence analysis: deconstructing Anglo-American notions of the ‘Arab’

Despite revived notions of a ‘cultural divide’ between East and West, Edward's Said's ‘Orientalism’ has received little attention from scholars of intelligence and diplomacy. This article brings to light for the first time a number of recently declassified documents of a different nature to usual assessments produced by Anglo-American analytic bodies: those focussed primarily on the issue of ‘national character’. Using and critiquing Said's thesis of Western ‘Orientalism’ it reveals some critical and enduring conceptualizations articulated by the diplomatic and intelligence community about Arab culture such as the role of Islam, rhetoric, political motivation and notions of ‘honour’. Such a critical approach demonstrates how diplomatic and intelligence history can also be a history of culture, ideas and institutional mentalité.

The longitudinal variation of equatorial waves due to propagation on a varying zonal flow

The general 1-D theory of waves propagating on a zonally varying flow is developed from basic wave theory, and equations are derived for the variation of wavenumber and energy along ray paths. Different categories of behaviour are found, depending on the sign of the group velocity (cg) and a wave property, B. For B positive the wave energy and the wave number vary in the same sense, with maxima in relative easterlies or westerlies, depending on the sign of cg. Also the wave accumulation of Webster and Chang (1988) occurs where cg goes to zero. However for B negative they behave in opposite senses and wave accumulation does not occur. The zonal propagation of the gravest equatorial waves is analysed in detail using the theory. For non-dispersive Kelvin waves, B reduces to 2, and analytic solution is possible. B is positive for all the waves considered, except for the westward moving mixed Rossby-gravity (WMRG) wave which can have negative as well as positive B. Comparison is made between the observed climatologies of the individual equatorial waves and the result of pure propagation on the climatological upper tropospheric flow. The Kelvin wave distribution is in remarkable agreement, considering the approximations made. Some aspects of the WMRG and Rossby wave distributions are also in qualitative agreement. However the observed maxima in these waves in the winter westerlies in the eastern Pacific and Atlantic are not consistent with the theory. This is consistent with the importance of the sources of equatorial waves in these westerly duct regions due to higher latitude wave activity.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.