Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

High frequency scattering by convex curvilinear polygons

We consider the scattering of a time-harmonic acoustic incident plane wave by a sound soft convex curvilinear polygon with Lipschitz boundary. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the number of degrees of freedom required to achieve a prescribed level of accuracy grows at least linearly with respect to the frequency of the incident wave. Here we propose a novel Galerkin boundary element method with a hybrid approximation space, consisting of the products of plane wave basis functions with piecewise polynomials supported on several overlapping meshes; a uniform mesh on illuminated sides, and graded meshes refined towards the corners of the polygon on illuminated and shadow sides. Numerical experiments suggest that the number of degrees of freedom required to achieve a prescribed level of accuracy need only grow logarithmically as the frequency of the incident wave increases.

Acute effects of elevated NEFA on vascular function: a comparison of SFA and MUFA

There is emerging evidence to show that high levels of NEFA contribute to endothelial dysfunction and impaired insulin sensitivity. However, the impact of NEFA composition remains unclear. A total of ten healthy men consumed test drinks containing 50 g of palm stearin (rich in SFA) or high-oleic sunflower oil (rich in MUFA) on separate occasions; a third day included no fat as a control. The fats were emulsified into chocolate drinks and given as a bolus (approximately 10 g fat) at baseline followed by smaller amounts (approximately 3 g fat) every 30 min throughout the 6 h study day. An intravenous heparin infusion was initiated 2 h after the bolus, which resulted in a three- to fourfold increase in circulating NEFA level from baseline. Mean arterial stiffness as measured by digital volume pulse was higher during the consumption of SFA (P,0·001) but not MUFA (P¼0·089) compared with the control. Overall insulin and gastric inhibitory peptide response was greater during the consumption of both fats compared with the control (P,0·001); there was a second insulin peak in response to MUFA unlike SFA. Consumption of SFA resulted in higher levels of soluble intercellular adhesion molecule-1 (sI-CAM) at 330 min than that of MUFA or control (P#0·048). There was no effect of the test drinks on glucose, total nitrite, plasminogen activator inhibitor-1 or endothelin-1 concentrations. The present study indicates a potential negative impact of elevated NEFA derived from the consumption of SFA on arterial stiffness and sI-CAM levels. More studies are needed to fully investigate the impact of NEFA composition on risk factors for CVD.

Platonic allusion in Plutarch's Alcibiades 4-7

Plutarch deals with Socrates' relationship with Alcibiades in chs. 4-7 of his Life. He draws heavily here on two Platonic works, the First Alcibiades and the Symposium, but engagement with the Platonic texts is denser and more profound in Alcibiades than a study of just those two texts would suggest. In fact, this part of the Alcibiades contains allusions to several other Platonic texts in which Alcibiades does not occur as a character and in which his name is not mentioned: Republic Books 6 and 8, Charmides, Phaedrus, Apology, and Lysis. These texts function as ‘intertexts’ against which the Alcibiades is to be read.

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Modelling capability and affordance as properties of human/machine resource systems

Understanding how and why the capability of one set of business resources, its structural arrangements and mechanisms compared to another works can provide competitive advantage in terms of new business processes and product and service development. However, most business models of capability are descriptive and lack formal modelling language to qualitatively and quantifiably compare capabilities, Gibson’s theory of affordance, the potential for action, provides a formal basis for a more robust and quantitative model, but most formal affordance models are complex and abstract and lack support for real-world applications. We aim to understand the ‘how’ and ‘why’ of business capability, by developing a quantitative and qualitative model that underpins earlier work on Capability-Affordance Modelling – CAM. This paper integrates an affordance based capability model and the formalism of Coloured Petri Nets to develop a simulation model. Using the model, we show how capability depends on the space time path of interacting resources, the mechanism of transition and specific critical affordance factors relating to the values of the variables for resources, people and physical objects. We show how the model can identify the capabilities of resources to enable the capability to inject a drug and anaesthetise a patient.

Communication costs and the boundaries of the firm

Much has been written about where the boundaries of the firm are drawn, but little about what occurs at the boundaries themselves. When a firm subcontracts, does it inform its suppliers fully of what it requires, or is it willing to accept what they have available? In practice firms often engage in a dialogue, or conversation, with their suppliers, in which at first they set out their general requirements, and only when the supplier reports back on how these can be met are their more specific requirements set out. This paper models such conversations as a rational response to communication costs. The model is used to examine the impact of new information technology, such as CAD/CAM, on the conduct of subcontracting. It can also be used to examine its impact on the marketing activities of firms. The technique of analysis, which is based on the economic theory of teams, has more general applications too. It can be used to model all the forms of dialogue involved in the processes of coordination both within and between firms.

Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

Cancer patients taking herbal medicines: a review of clinical purposes, associated factors, and perceptions of benefit or harm

Ethnopharmacological relevance: Cancer patients in all cultures are high consumers of herbal medicines (HMs) usually as part of a regime consisting of several complementary and alternative medicine (CAM) modalities, but the type of patient, the reasons for choosing such HM-CAM regimes, and the benefits they perceive from taking them are poorly understood. There are also concerns that local information may be ignored due to language issues. This study investigates aspects of HM-CAM use in cancer patients using two different abstracting sources: Medline, which contains only peer-reviewed studies from SCI journals, and in order to explore whether further data may be available regionally, the Thai national databases of HM and CAM were searched as an example. Materials and methods: the international and Thai language databases were searched separately to identify relevant studies, using key words chosen to include HM use in all traditions. Analysis of these was undertaken to identify socio-demographic and clinical factors, as well as sources of information, which may inform the decision to use HMs. Results: Medline yielded 5,638 records, with 49 papers fitting the criteria for review. The Thai databases yielded 155, with none relevant for review. Factors associated with HM-CAM usage were: a younger age, higher education or economic status, multiple chemotherapy treatment, late stage of disease. The most common purposes for using HM-CAM cited by patients were to improve physical symptoms, support emotional health, stimulate the immune system, improve quality of life, and relieve side-effects of conventional treatment. Conclusions: Several indicators were identified for cancer patients who are most likely to take HM-CAM. However, interpreting the clinical reasons why patients decide to use HM-CAM is hampered by a lack of standard terminology and thematic coding, because patients' own descriptions are too variable and overlapping for meaningful comparison. Nevertheless, fears that the results of local studies published regionally are being missed, at least in the case of Thailand, appeared to be unfounded.

Why cancer patients choose in-patient complementary therapy in palliative care: a qualitative study at Arokhayasala Hospice in Thailand

Cancer patients often choose complementary and alternative medicine (CAM) in palliative care, often in addition to conventional treatment and without medical advice or approval. Herbal medicines (HM) are the most commonly used type of CAM, but rarely available on an in-patient basis for palliative care. The motivations which lead very ill patients to travel far to receive such therapies are not clear. A qualitative study was therefore carried out to investigate influences on choosing to attend a CAM herbal hospice, to identify cancer patients’ main concerns about end-of-life care. Semi-structured interviews with 32 patients were conducted and analysed using thematic analysis. Patients were recruited from Arokhayasala, a Buddhist cancer hospice in Thailand which provides CAM, in the form of HM, a restricted diet, Thai yoga, deep-breathing exercises, meditation, chanting, Dhamma, laughter and music therapy, free-of-charge. The main factors influencing decision-making were a positive attitude towards HMs and previous use of them, dissatisfaction with conventional treatment, the home environment and their relationships with hospital doctors. Patients’ own perceptions and experiences were more important in making the decision to use CAM, and especially HM, in palliative cancer care than referral by healthcare professionals or scientific evidence of efficacy. Patients were prepared to travel far and live away from home to receive such care, especially as it was cost-free. In view of patients’ previously stated satisfaction with the regime at the Arokhayasala, these findings may be relevant to the provision of in-patient cancer palliative care to other patients.

The risk of water stress

Water resources are under stress in many regions due to increasing demands and, in places, falling quality. Climate change has the potential to change the risks of water stress.1 The focus in this section is on strategic definitions of water stress, which are based on generalized indicators of the amount of water that is available and the demands on that resource. Operational definitions, on the other hand, are typically based on the reliability of the supply of appropriate quality water and are strongly determined by local conditions.

The risk of river flooding

This section of the report outlines the effect of different levels of climate change on exposure to river flood risk, at national and watershed scales.