Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Multivariable cluster analysis for high-speed industrial machinery

The overall operation and internal complexity of a particular production machinery can be depicted in terms of clusters of multidimensional points which describe the process states, the value in each point dimension representing a measured variable from the machinery. The paper describes a new cluster analysis technique for use with manufacturing processes, to illustrate how machine behaviour can be categorised and how regions of good and poor machine behaviour can be identified. The cluster algorithm presented is the novel mean-tracking algorithm, capable of locating N-dimensional clusters in a large data space in which a considerable amount of noise is present. Implementation of the algorithm on a real-world high-speed machinery application is described, with clusters being formed from machinery data to indicate machinery error regions and error-free regions. This analysis is seen to provide a promising step ahead in the field of multivariable control of manufacturing systems.

Modelling the likely impact of healthy eating guidelines on agricultural production and land use in England and Wales

Quadratic programming techniques were applied to household food consumption data in England and Wales to estimate likely changes in diet under healthy eating guidelines, and the consequences this would have on agriculture and land use in England and Wales. The first step entailed imposing nutrient restrictions on food consumption following dietary recommendations suggested by the UK Department of Health. The resulting diet was used, in a second step as a proxy for demand in agricultural commodities, to test the impact of such a scenario on food production and land use in England and Wales and the impacts of this on agricultural landscapes. Results of the diet optimisation indicated a large drop in consumption of foods rich in saturated fats and sugar, essentially cheese and sugar-based products, along with lesser cuts of fat and meat products. Conversely, consumption of fruit and vegetables, cereals, and flour would increase to meet dietary fibre recommendations. Such a shift in demand would dramatically affect production patterns: the financial net margin of England and Wales agriculture would rise, due to increased production of high market value and high economic margin crops. Some regions would, however, be negatively affected, mostly those dependent on beef cattle and sheep production that could not benefit from an increased demand for cereals and horticultural crops. The effects of these changes would also be felt in upstream industries, such as animal feed suppliers. While arable dominated landscapes would be little affected, pastoral landscapes would suffer through loss of grazing management and, possibly, land abandonment, especially in upland areas.

Final report on research project PS2010, proof of concept of automated mapping of weeds in arable fields

Many weeds occur in patches but farmers frequently spray whole fields to control the weeds in these patches. Given a geo-referenced weed map, technology exists to confine spraying to these patches. Adoption of patch spraying by arable farmers has, however, been negligible partly due to the difficulty of constructing weed maps. Building on previous DEFRA and HGCA projects, this proposal aims to develop and evaluate a machine vision system to automate the weed mapping process. The project thereby addresses the principal technical stumbling block to widespread adoption of site specific weed management (SSWM). The accuracy of weed identification by machine vision based on a single field survey may be inadequate to create herbicide application maps. We therefore propose to test the hypothesis that sufficiently accurate weed maps can be constructed by integrating information from geo-referenced images captured automatically at different times of the year during normal field activities. Accuracy of identification will also be increased by utilising a priori knowledge of weeds present in fields. To prove this concept, images will be captured from arable fields on two farms and processed offline to identify and map the weeds, focussing especially on black-grass, wild oats, barren brome, couch grass and cleavers. As advocated by Lutman et al. (2002), the approach uncouples the weed mapping and treatment processes and builds on the observation that patches of these weeds are quite stable in arable fields. There are three main aspects to the project. 1) Machine vision hardware. Hardware component parts of the system are one or more cameras connected to a single board computer (Concurrent Solutions LLC) and interfaced with an accurate Global Positioning System (GPS) supplied by Patchwork Technology. The camera(s) will take separate measurements for each of the three primary colours of visible light (red, green and blue) in each pixel. The basic proof of concept can be achieved in principle using a single camera system, but in practice systems with more than one camera may need to be installed so that larger fractions of each field can be photographed. Hardware will be reviewed regularly during the project in response to feedback from other work packages and updated as required. 2) Image capture and weed identification software. The machine vision system will be attached to toolbars of farm machinery so that images can be collected during different field operations. Images will be captured at different ground speeds, in different directions and at different crop growth stages as well as in different crop backgrounds. Having captured geo-referenced images in the field, image analysis software will be developed to identify weed species by Murray State and Reading Universities with advice from The Arable Group. A wide range of pattern recognition and in particular Bayesian Networks will be used to advance the state of the art in machine vision-based weed identification and mapping. Weed identification algorithms used by others are inadequate for this project as we intend to collect and correlate images collected at different growth stages. Plants grown for this purpose by Herbiseed will be used in the first instance. In addition, our image capture and analysis system will include plant characteristics such as leaf shape, size, vein structure, colour and textural pattern, some of which are not detectable by other machine vision systems or are omitted by their algorithms. Using such a list of features observable using our machine vision system, we will determine those that can be used to distinguish weed species of interest. 3) Weed mapping. Geo-referenced maps of weeds in arable fields (Reading University and Syngenta) will be produced with advice from The Arable Group and Patchwork Technology. Natural infestations will be mapped in the fields but we will also introduce specimen plants in pots to facilitate more rigorous system evaluation and testing. Manual weed maps of the same fields will be generated by Reading University, Syngenta and Peter Lutman so that the accuracy of automated mapping can be assessed. The principal hypothesis and concept to be tested is that by combining maps from several surveys, a weed map with acceptable accuracy for endusers can be produced. If the concept is proved and can be commercialised, systems could be retrofitted at low cost onto existing farm machinery. The outputs of the weed mapping software would then link with the precision farming options already built into many commercial sprayers, allowing their use for targeted, site-specific herbicide applications. Immediate economic benefits would, therefore, arise directly from reducing herbicide costs. SSWM will also reduce the overall pesticide load on the crop and so may reduce pesticide residues in food and drinking water, and reduce adverse impacts of pesticides on non-target species and beneficials. Farmers may even choose to leave unsprayed some non-injurious, environmentally-beneficial, low density weed infestations. These benefits fit very well with the anticipated legislation emerging in the new EU Thematic Strategy for Pesticides which will encourage more targeted use of pesticides and greater uptake of Integrated Crop (Pest) Management approaches, and also with the requirements of the Water Framework Directive to reduce levels of pesticides in water bodies. The greater precision of weed management offered by SSWM is therefore a key element in preparing arable farming systems for the future, where policy makers and consumers want to minimise pesticide use and the carbon footprint of farming while maintaining food production and security. The mapping technology could also be used on organic farms to identify areas of fields needing mechanical weed control thereby reducing both carbon footprints and also damage to crops by, for example, spring tines. Objective i. To develop a prototype machine vision system for automated image capture during agricultural field operations; ii. To prove the concept that images captured by the machine vision system over a series of field operations can be processed to identify and geo-reference specific weeds in the field; iii. To generate weed maps from the geo-referenced, weed plants/patches identified in objective (ii).

Explaining the 'health check' of the Common Agricultural Policy: budgetary politics, globalisation and paradigm change revisited

Three potential explanations of past reforms of the Common Agricultural Policy (CAP) can be identified in the literature: a budget constraint, pressure from General Agreement on Tariffs and Trade/World Trade Organization (GATT/WTO) negotiations or commitments and a paradigm shift emphasising agriculture’s provision of public goods. This discussion on the driving forces of CAP reform links to broader theoretical questions on the role of budgetary politics, globalisation of public policy and paradigm shift in explaining policy change. In this article, the Health Check reforms of 2007/2008 are assessed. They were probably more ambitious than first supposed, although it was a watered-down package agreed by ministers in November 2008. We conclude that the Health Check was not primarily driven by budget concerns or by the supposed switch from the state-assisted to the multifunctional policy paradigm. The European Commission’s wish to adopt an offensive negotiating stance in the closing phases of the Doha Round was a more likely explanatory factor. The shape and purpose of the CAP post-2013 is contested with divergent views among the Member States.

The Finance Acts 1998 and 2000: can the owners of agricultural land continue to gain from their capital disposals?

This paper seeks to analyse and discuss, from the perspective of the owners of agricultural land, the main changes to the Capital Gains Tax regime introduced in the Finance Act 1998 and subsequently amended in the Finance Act 2000. The replacement of indexation with a new Taper relief is examined, along with the phasing out of Retirement relief, and the interaction of Taper relief with Rollover relief. The opportunity for tax mitigation by the owners of agricultural land is critically examined.

The impact of an insecticide on insect flower visitation and pollination in an agricultural landscape

1 Pesticides are considered a threat to pollinators but little is known about the potential impacts of their widespread use on pollinators. Less still is known about the impacts on pollination, comprising the ecosystem service that pollinators provide to wildflowers and crops. 2 The present study measured flower visitation and pollination in an agricultural landscape, by placing potted flowering plants (Petunia sp.) in vine fields sprayed with a highly toxic insecticide (fenitrothion). During two sampling rounds, insect visitors to the petunias were observed and measures of pollination were recorded by counting and weighing seeds. 3 In the earlier sampling round, a lower species richness of insect visitors was observed in fields that had received an early application of insecticide. No negative impacts were found from later applications. The results obtained suggest a greater potential harm to insect pollinators and flower visitation as a result of insecticide application early in the season. 4 No reduction in pollination was found in fields that received an early insecticide application. Pollination was greater with two insecticide applications between sampling rounds rather than one application. 5 In the present study system, insecticide application had a negative effect on pollinators but a possible positive effect on pollination services. In some cases, it may be that actions for conserving biodiversity will not benefit pollination services to all plants.

Contributing understanding of mitigation options for phosphorus and sediment to a review of the efficacy of contemporary agricultural stewardship measures

Experiences from the Mitigation Options for Phosphorus and Sediment (MOPS) projects, which aim to determine the effectiveness of measures to reduce pollutant loading from agricultural land to surface waters, have been used to contribute to the findings of a recent paper (Kay et al., 2009, Agricultural Systems, 99, 67–75), which reviewed the efficacy of contemporary agricultural stewardship measures for ameliorating the water pollution problems of key concern to the UK water industry. MOPS1 is a recently completed 3-year research project on three different soil types in the UK, which focused on mitigation options for winter cereals. MOPS1 demonstrated that tramlines can be the major pathway for sediment and nutrient transfer from arable hillslopes, and that although minimum tillage, crop residue incorporation, contour cultivation, and beetle banks also have potential to be cost-effective mitigation options, tramline management is the one of the most promising treatments for mitigating diffuse pollution losses, as it was able to reduce sediment and nutrient losses by 72–99% in four out of five site years trialled. Using information from the MOPS projects, this paper builds on the findings of Kay et al. to provide an updated picture of the evidence available and the immediate needs for research in this area.