The homogenisation of Maxwell's equations with applications to photonic crystals and localised waveforms on metafilms

An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions; potentially highly-oscillatory short-scale detail is encapsulated through integrated quantities. The theory we develop is then applied to two topical examples, the first being the case of aligned dielectric cylinders, which has great importance in the modelling of photonic crystal fibres. We then consider the propagation of waves in a structured metafilm, here chosen to be a planar array of dielectric spheres. At certain frequencies strongly directional dynamic anisotropy is observed, and the asymptotic theory is shown to capture the effect, giving highly accurate qualitative and quantitative results as well as providing interpretation for the underlying change from elliptic to hyperbolic behaviour

High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure

Parabolic Metamaterials and Dirac Bridges

A new class of multi-scale structures, referred to as `parabolic metamaterials' is introduced and studied in this paper. For an elastic two-dimensional triangular lattice, we identify dynamic regimes, which corresponds to so-called `Dirac Bridges' on the dispersion surfaces. Such regimes lead to a highly localised and focussed unidirectional beam when the lattice is excited. We also show that the flexural rigidities of elastic ligaments are essential in establishing the `parabolic metamaterial' regimes.Comment: 14 pages, 4 figure

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

Thinking territory historically.

BACKGROUND: While the randomised controlled trial (RCT) is generally regarded as the design of choice for assessing the effects of health care, within the social sciences there is considerable debate about the relative suitability of RCTs and non-randomised studies (NRSs) for evaluating public policy interventions. // OBJECTIVES: To determine whether RCTs lead to the same effect size and variance as NRSs of similar policy interventions; and whether these findings can be explained by other factors associated with the interventions or their evaluation. // METHODS: Analyses of methodological studies, empirical reviews, and individual health and social services studies investigated the relationship between randomisation and effect size of policy interventions by: 1) Comparing controlled trials that are identical in all respects other than the use of randomisation by 'breaking' the randomisation in a trial to create non-randomised trials (re-sampling studies). 2) Comparing randomised and non-randomised arms of controlled trials mounted simultaneously in the field (replication studies). 3) Comparing similar controlled trials drawn from systematic reviews that include both randomised and non-randomised studies (structured narrative reviews and sensitivity analyses within meta-analyses). 4) Investigating associations between randomisation and effect size using a pool of more diverse RCTs and NRSs within broadly similar areas (meta-epidemiology). // RESULTS: Prior methodological reviews and meta-analyses of existing reviews comparing effects from RCTs and nRCTs suggested that effect sizes from RCTs and nRCTs may indeed differ in some circumstances and that these differences may well be associated with factors confounded with design. Re-sampling studies offer no evidence that the absence of randomisation directly influences the effect size of policy interventions in a systematic way. No consistent explanations were found for randomisation being associated with changes in effect sizes of policy interventions in field trials

The engineering design integration (EDIN) system

A digital computer program complex for the evaluation of aerospace vehicle preliminary designs is described. The system consists of a Univac 1100 series computer and peripherals using the Exec 8 operating system, a set of demand access terminals of the alphanumeric and graphics types, and a library of independent computer programs. Modification of the partial run streams, data base maintenance and construction, and control of program sequencing are provided by a data manipulation program called the DLG processor. The executive control of library program execution is performed by the Univac Exec 8 operating system through a user established run stream. A combination of demand and batch operations is employed in the evaluation of preliminary designs. Applications accomplished with the EDIN system are described

Geometry Technology Module (GTM). Volume 2: Programmers' manual

For abstract, see N75-17120

The clinical effectiveness and cost-effectiveness of ablative therapies in the management of liver metastases: systematic review and economic evaluation

Background: Many deaths from cancer are caused by metastatic burden. Prognosis and survival rates vary, but survival beyond 5 years of patients with untreated metastatic disease in the liver is rare. Treatment for liver metastases has largely been surgical resection, but this is feasible in only approximately 20–30% of people. Non-surgical alternatives to treat some liver metastases can include various forms of ablative therapies and other targeted treatments.Objectives: To evaluate the clinical effectiveness and cost-effectiveness of the different ablative and minimally invasive therapies for treating liver metastases.Data sources: Electronic databases including MEDLINE, EMBASE and The Cochrane Library were searched from 1990 to September 2011. Experts were consulted and bibliographies checked.Review methods: Systematic reviews of the literature were undertaken to appraise the clinical effectiveness and cost-effectiveness of ablative therapies and minimally invasive therapies used for people with liver metastases. Studies were any prospective study with sample size greater than 100 participants. A probabilistic model was developed for the economic evaluation of the technologies where data permitted.Results: The evidence assessing the clinical effectiveness and cost-effectiveness of ablative and other minimally invasive therapies was limited. Nine studies of ablative therapies were included in the review; each had methodological shortcomings and few had a comparator group. One randomised controlled trial (RCT) of microwave ablation versus surgical resection was identified and showed no improvement in outcomes compared with resection. In two prospective case series studies that investigated the use of laser ablation, mean survival ranged from 41 to 58 months. One cohort study compared radiofrequency ablation with surgical resection and five case series studies also investigated the use of radiofrequency ablation. Across these studies the median survival ranged from 44 to 52 months. Seven studies of minimally invasive therapies were included in the review. Two RCTs compared chemoembolisation with chemotherapy only. Overall survival was not compared between groups and methodological shortcomings mean that conclusions are difficult to make. Two case series studies of laser ablation following chemoembolisation were also included; however, these provide little evidence of the use of these technologies in combination. Three RCTs of radioembolisation were included. Significant improvements in tumour response and time to disease progression were demonstrated; however, benefits in terms of survival were equivocal. An exploratory survival model was developed using data from the review of clinical effectiveness. The model includes separate analyses of microwave ablation compared with surgery and radiofrequency ablation compared with surgery and one of radioembolisation in conjunction with hepatic artery chemotherapy compared with hepatic artery chemotherapy alone. Microwave ablation was associated with an incremental cost-effectiveness ratio (ICER) of £3664 per quality-adjusted life-year (QALY) gained, with microwave ablation being associated with reduced cost but also with poorer outcome than surgery. Radiofrequency ablation compared with surgical resection for solitary metastases < 3 cm was associated with an ICER of –£266,767 per QALY gained, indicating that radiofrequency ablation dominates surgical resection. Radiofrequency ablation compared with surgical resection for solitary metastases ? 3 cm resulted in poorer outcomes at lower costs and a resultant ICER of £2538 per QALY gained. Radioembolisation plus hepatic artery chemotherapy compared with hepatic artery chemotherapy was associated with an ICER of £37,303 per QALY gained.Conclusions: There is currently limited high-quality research evidence upon which to base any firm decisions regarding ablative therapies for liver metastases. Further trials should compare ablative therapies with surgery, in particular. A RCT would provide the most appropriate design for undertaking any further evaluation and should include a full economic evaluation, but the group to be randomised needs careful selection.Source of funding: Funding for this study was provided by the Health Technology Assessment programme of the National Institute for Health Research