On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Simulating the impacts of global warming on wheat in China using a large area crop model

Temperature is one of the most prominent environmental factors that determine plant growth, devel- opment, and yield. Cool and moist conditions are most favorable for wheat. Wheat is likely to be highly vulnerable to further warming because currently the temperature is already close to or above optimum. In this study, the impacts of warming and extreme high temperature stress on wheat yield over China were investigated by using the general large area model (GLAM) for annual crops. The results showed that each 1±C rise in daily mean temperature would reduce the average wheat yield in China by about 4.6%{5.7% mainly due to the shorter growth duration, except for a small increase in yield at some grid cells. When the maximum temperature exceeded 30.5±C, the simulated grain-set fraction declined from 1 at 30.5±C to close to 0 at about 36±C. When the total grain-set was lower than the critical fractional grain-set (0.575{0.6), harvest index and potential grain yield were reduced. In order to reduce the negative impacts of warming, it is crucial to take serious actions to adapt to the climate change, for example, by shifting sowing date, adjusting crop distribution and structure, breeding heat-resistant varieties, and improving the monitoring, forecasting, and early warning of extreme climate events.

Minimising the latency induced by consistency control, within a large scale multi-user distributed virtual reality system

Where users are interacting in a distributed virtual environment, the actions of each user must be observed by peers with sufficient consistency and within a limited delay so as not to be detrimental to the interaction. The consistency control issue may be split into three parts: update control; consistent enactment and evolution of events; and causal consistency. The delay in the presentation of events, termed latency, is primarily dependent on the network propagation delay and the consistency control algorithms. The latency induced by the consistency control algorithm, in particular causal ordering, is proportional to the number of participants. This paper describes how the effect of network delays may be reduced and introduces a scalable solution that provides sufficient consistency control while minimising its effect on latency. The principles described have been developed at Reading over the past five years. Similar principles are now emerging in the simulation community through the HLA standard. This paper attempts to validate the suggested principles within the schema of distributed simulation and virtual environments and to compare and contrast with those described by the HLA definition documents.

The impact of large scale atmospheric circulation patterns on wind power generation and its potential predictability: a case study over the UK

Over recent years there has been an increasing deployment of renewable energy generation technologies, particularly large-scale wind farms. As wind farm deployment increases, it is vital to gain a good understanding of how the energy produced is affected by climate variations, over a wide range of time-scales, from short (hours to weeks) to long (months to decades) periods. By relating wind speed at specific sites in the UK to a large-scale climate pattern (the North Atlantic Oscillation or "NAO"), the power generated by a modelled wind turbine under three different NAO states is calculated. It was found that the wind conditions under these NAO states may yield a difference in the mean wind power output of up to 10%. A simple model is used to demonstrate that forecasts of future NAO states can potentially be used to improve month-ahead statistical forecasts of monthly-mean wind power generation. The results confirm that the NAO has a significant impact on the hourly-, daily- and monthly-mean power output distributions from the turbine with important implications for (a) the use of meteorological data (e.g. their relationship to large scale climate patterns) in wind farm site assessment and, (b) the utilisation of seasonal-to-decadal climate forecasts to estimate future wind farm power output. This suggests that further research into the links between large-scale climate variability and wind power generation is both necessary and valuable.

Metal-directed assembly of large dinuclear copper(II) dithiocarbamate macrocyclic complexes

The synthesis of a range of dinuclear Cu(II) dithiocarbamate (dtc)-based macrocycles and their characterisation are described. By carefully tuning the size of the aromatic spacer, cavities of different dimensions can be designed. The length and flexibility of the chosen spacer group dictates the intermetallic distance and hence the degree of communication between the two metal centres as evidenced by electrochemical and EPR experiments. This is illustrated by crystallographic evidence that show the macrocycles can host guests (such as CH2Cl2) or can fold and form unexpected Cu(I) dtc clusters.

Lag-time effects on a naturally ventilated large thermometer screen

Systematic natural ventilation effects on measured temperatures within a standard large wooden thermometer screen are investigated under summer conditions, using well-calibrated platinum resistance thermometers. Under low ventilation (2mwind speed u2 < 1.1 m s−1), the screen slightly underestimates daytime air temperature but overestimates air temperature nocturnally by 0.2◦C. The screen’s lag time L lengthens with decreasing wind speed, following an inverse power law relationship between L and u2. For u2 > 2 m s−1, L ∼ 2.5 min, increasing, when calm, to at least 15 min. Spectral response properties of the screen to air temperature fluctuations vary with wind speed because of the lag changes. Ventilation effects are particularly apparent at the higher (>25◦C) temperatures, both through the lag effect and from solar heating. For sites where wind speed decreases with increasing daytime temperature, thermometer screen temperatures may consequently show larger uncertainties at the higher temperatures. Under strong direct beam solar radiation (>850W m−2) the radiation effect is likely to be <0.4◦C. Copyright c 2011 RoyalMeteorological Society

Fast regridding of large, complex geospatial datasets

In the earth sciences, data are commonly cast on complex grids in order to model irregular domains such as coastlines, or to evenly distribute grid points over the globe. It is common for a scientist to wish to re-cast such data onto a grid that is more amenable to manipulation, visualization, or comparison with other data sources. The complexity of the grids presents a significant technical difficulty to the regridding process. In particular, the regridding of complex grids may suffer from severe performance issues, in the worst case scaling with the product of the sizes of the source and destination grids. We present a mechanism for the fast regridding of such datasets, based upon the construction of a spatial index that allows fast searching of the source grid. We discover that the most efficient spatial index under test (in terms of memory usage and query time) is a simple look-up table. A kd-tree implementation was found to be faster to build and to give similar query performance at the expense of a larger memory footprint. Using our approach, we demonstrate that regridding of complex data may proceed at speeds sufficient to permit regridding on-the-fly in an interactive visualization application, or in a Web Map Service implementation. For large datasets with complex grids the new mechanism is shown to significantly outperform algorithms used in many scientific visualization packages.