A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

HOx observations over West Africa during AMMA: impact of isoprene and NOx

Aircraft OH and HO2 measurements made over West Africa during the AMMA field campaign in summer 2006 have been investigated using a box model constrained to observations of long-lived species and physical parameters. "Good" agreement was found for HO2 (modelled to observed gradient of 1.23 ± 0.11). However, the model significantly overpredicts OH concentrations. The reasons for this are not clear, but may reflect instrumental instabilities affecting the OH measurements. Within the model, HOx concentrations in West Africa are controlled by relatively simple photochemistry, with production dominated by ozone photolysis and reaction of O(1D) with water vapour, and loss processes dominated by HO2 + HO2 and HO2 + RO2. Isoprene chemistry was found to influence forested regions. In contrast to several recent field studies in very low NOx and high isoprene environments, we do not observe any dependence of model success for HO2 on isoprene and attribute this to efficient recycling of HOx through RO2 + NO reactions under the moderate NOx concentrations (5–300 ppt NO in the boundary layer, median 76 ppt) encountered during AMMA. This suggests that some of the problems with understanding the impact of isoprene on atmospheric composition may be limited to the extreme low range of NOx concentrations.

A benchmark method for global optimization problems in structure determination from powder diffraction data

Quasi-Newton-Raphson minimization and conjugate gradient minimization have been used to solve the crystal structures of famotidine form B and capsaicin from X-ray powder diffraction data and characterize the chi(2) agreement surfaces. One million quasi-Newton-Raphson minimizations found the famotidine global minimum with a frequency of ca 1 in 5000 and the capsaicin global minimum with a frequency of ca 1 in 10 000. These results, which are corroborated by conjugate gradient minimization, demonstrate the existence of numerous pathways from some of the highest points on these chi(2) agreement surfaces to the respective global minima, which are passable using only downhill moves. This important observation has significant ramifications for the development of improved structure determination algorithms.

Will rising household incomes solve China's micronutrient deficiency problems?

Rapid economic growth in China has resulted in substantially improved household incomes. Diets have also changed, with a movement away from traditional foods and towards animal products and processed foods. Yet micronutrient deficiencies, particularly for calcium and vitamin A, are still widespread in China. In this research we model the determinants of the intakes of these micronutrients using household panel data, asking particularly whether continuing income increases are likely to cause the deficiencies to be overcome. Nonparametric kernel regressions and random effects panel regression models are employed. The results show a statistically significant but relatively small positive income effect on both nutrient intakes. The local availability of milk is seen to have a strong positive effect on intakes of both micronutrients. Thus, rather than relying on increasing incomes to overcome deficiencies, supplementary government policies, such as school milk programmes, may be warranted.

Mediterranean ecosystems: problems and tools for conservation

Mediterranean ecosystems rival tropical ecosystems in terms of plant biodiversity. The Mediterranean Basin (MB) itself hosts 25 000 plant species, half of which are endemic. This rich biodiversity and the complex biogeographical and political issues make conservation a difficult task in the region. Species, habitat, ecosystem and landscape approaches have been used to identify conservation targets at various scales: ie, European, national, regional and local. Conservation decisions require adequate information at the species, community and habitat level. Nevertheless and despite recent improvements/efforts, this information is still incomplete, fragmented and varies from one country to another. This paper reviews the biogeographic data, the problems arising from current conservation efforts and methods for the conservation assessment and prioritization using GIS. GIS has an important role to play for managing spatial and attribute information on the ecosystems of the MB and to facilitate interactions with existing databases. Where limited information is available it can be used for prediction when directly or indirectly linked to externally built models. As well as being a predictive tool today GIS incorporate spatial techniques which can improve the level of information such as fuzzy logic, geostatistics, or provide insight about landscape changes such as 3D visualization. Where there are limited resources it can assist with identifying sites of conservation priority or the resolution of environmental conflicts (scenario building). Although not a panacea, GIS is an invaluable tool for improving the understanding of Mediterranean ecosystems and their dynamics and for practical management in a region that is under increasing pressure from human impact.

Statistical methods for ordered categorical data based on a constrained odds model

The proportional odds model provides a powerful tool for analysing ordered categorical data and setting sample size, although for many clinical trials its validity is questionable. The purpose of this paper is to present a new class of constrained odds models which includes the proportional odds model. The efficient score and Fisher's information are derived from the profile likelihood for the constrained odds model. These results are new even for the special case of proportional odds where the resulting statistics define the Mann-Whitney test. A strategy is described involving selecting one of these models in advance, requiring assumptions as strong as those underlying proportional odds, but allowing a choice of such models. The accuracy of the new procedure and its power are evaluated.

Constrained models of evolution lead to improved prediction of functional linkage from correlated gain and loss of genes

Motivation: We compare phylogenetic approaches for inferring functional gene links. The approaches detect independent instances of the correlated gain and loss of pairs of genes from species' genomes. We investigate the effect on results of basing evidence of correlations on two phylogenetic approaches, Dollo parsminony and maximum likelihood (ML). We further examine the effect of constraining the ML model by fixing the rate of gene gain at a low value, rather than estimating it from the data. Results: We detect correlated evolution among a test set of pairs of yeast (Saccharomyces cerevisiae) genes, with a case study of 21 eukaryotic genomes and test data derived from known yeast protein complexes. If the rate at which genes are gained is constrained to be low, ML achieves by far the best results at detecting known functional links. The model then has fewer parameters but it is more realistic by preventing genes from being gained more than once. Availability: BayesTraits by M. Pagel and A. Meade, and a script to configure and repeatedly launch it by D. Barker and M. Pagel, are available at http://www.evolution.reading.ac.uk .

Plant conservation: old problems, new perspectives

A review is given of the major conceptual changes that have taken place during the last 50 years in our understanding of the nature of plant conservation and of the principal methodological advances in undertaking conservation assessments and actions, largely through the incorporation of tools and techniques from other disciplines. The interrelationships between conservation and sustainable use are considered as well as the impact of the development of the discipline of conservation biology, the effects of the general acceptance of the concept of biodiversity and the practical implications of the implementation of the Convention on Biological diversity. The effect on conservation policy and management of the accelerating loss or conversion of habitats throughout the world and approaches for combating this are discussed.

Recognition of sequence-information in synthetic copolymer chains by a conformationally-constrained tweezer molecule

A novel type of tweezer molecule containing electron-rich 2-pyrenyloxy arms has been designed to exploit intramolecular hydrogen bonding in stabilising a preferred conformation for supramolecular complexation to complementary sequences in aromatic copolyimides. This tweezer-conformation is demonstrated by single-crystal X-ray analyses of the tweezer molecule itself and of its complex with an aromatic diimide model-compound. In terms of its ability to bind selectively to polyimide chains, the new tweezer molecule shows very high sensitivity to sequence effects. Thus, even low concentrations of tweezer relative to diimide units (<2.5 mol%) are sufficient to produce dramatic, sequence-related splittings of the pyromellitimide proton NMR resonances. These induced resonance-shifts arise from ring-current shielding of pyromellitimide protons by the pyrenyloxy arms of the tweezer-molecule, and the magnitude of such shielding is a function of the tweezer-binding constant for any particular monomer sequence. Recognition of both short-range and long-range sequences is observed, the latter arising from cumulative ring-current shielding of diimide protons by tweezer molecules binding at multiple adjacent sites on the copolymer chain.

Application of olefin metathesis for the synthesis of constrained beta-amino esters from norbornenes

Synthesis of a number of novel, conformationally rigid beta-amino esters has been achieved via a tandem olefin metathesis reaction. The starting materials are readily accessible from the Diels-Alder adduct between cyclopentadiene and maleic anhydride.

Modelling metal cutting using modern ductile fracture mechanics: Quantitative explanations for some longstanding problems

The assumption that negligible work is involved in the formation of new surfaces in the machining of ductile metals, is re-examined in the light of both current Finite Element Method (FEM) simulations of cutting and modern ductile fracture mechanics. The work associated with separation criteria in FEM models is shown to be in the kJ/m2 range rather than the few J/m2 of the surface energy (surface tension) employed by Shaw in his pioneering study of 1954 following which consideration of surface work has been omitted from analyses of metal cutting. The much greater values of surface specific work are not surprising in terms of ductile fracture mechanics where kJ/m2 values of fracture toughness are typical of the ductile metals involved in machining studies. This paper shows that when even the simple Ernst–Merchant analysis is generalised to include significant surface work, many of the experimental observations for which traditional ‘plasticity and friction only’ analyses seem to have no quantitative explanation, are now given meaning. In particular, the primary shear plane angle φ becomes material-dependent. The experimental increase of φ up to a saturated level, as the uncut chip thickness is increased, is predicted. The positive intercepts found in plots of cutting force vs. depth of cut, and in plots of force resolved along the primary shear plane vs. area of shear plane, are shown to be measures of the specific surface work. It is demonstrated that neglect of these intercepts in cutting analyses is the reason why anomalously high values of shear yield stress are derived at those very small uncut chip thicknesses at which the so-called size effect becomes evident. The material toughness/strength ratio, combined with the depth of cut to form a non-dimensional parameter, is shown to control ductile cutting mechanics. The toughness/strength ratio of a given material will change with rate, temperature, and thermomechanical treatment and the influence of such changes, together with changes in depth of cut, on the character of machining is discussed. Strength or hardness alone is insufficient to describe machining. The failure of the Ernst–Merchant theory seems less to do with problems of uniqueness and the validity of minimum work, and more to do with the problem not being properly posed. The new analysis compares favourably and consistently with the wide body of experimental results available in the literature. Why considerable progress in the understanding of metal cutting has been achieved without reference to significant surface work is also discussed.