Problems with drawing lines: Theo-geographies of the Catholic parish in Ireland

While people in Catholic parishes in Ireland appear keenly aware of parish boundaries, these understandings are more often oral than cartographic. There is no digital map of all of the Catholic parishes in Ireland. However, the institutional Catholic Church insists that no square kilometre can exist outside of a parish boundary. In this paper, I explain a process whereby the Catholic parishes of Ireland were produced digitally. I will outline some of the technical challenges of digitizing such boundaries. In making these maps, it is not only a question of drawing lines but mapping people’s understanding of their locality. Through an example of one part of the digitisation project, I want to talk about how verifying maps with local people often complicates something which may have at first sight seemed simple. The paper ends on a comparison with how other communities of interest are territorialised in Ireland and elsewhere to draw out some broader theoretical and theological issues of concern.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Investigating key decision problems to optimize the operation and maintenance strategy of offshore wind farms

This paper investigates three decision problems with potential to optimize operation and maintenance and logistics strategies for offshore wind farms: the timing of pre-determined jack-up vessel campaigns; selection of crew transfer vessel fleet; and timing of annual services. These problems are compared both in terms of potential cost reduction and the stochastic variability and associated uncertainty of the outcome. Pre-determined jack-up vessel campaigns appear to have a high cost reduction potential but also a higher stochastic variability than the other decision problems. The paper also demonstrates the benefits and difficulties of considering problems together rather than solving them in isolation.

Computing explanations for interactive constraint-based systems

Constraint programming has emerged as a successful paradigm for modelling combinatorial problems arising from practical situations. In many of those situations, we are not provided with an immutable set of constraints. Instead, a user will modify his requirements, in an interactive fashion, until he is satisfied with a solution. Examples of such applications include, amongst others, model-based diagnosis, expert systems, product configurators. The system he interacts with must be able to assist him by showing the consequences of his requirements. Explanations are the ideal tool for providing this assistance. However, existing notions of explanations fail to provide sufficient information. We define new forms of explanations that aim to be more informative. Even if explanation generation is a very hard task, in the applications we consider, we must manage to provide a satisfactory level of interactivity and, therefore, we cannot afford long computational times. We introduce the concept of representative sets of relaxations, a compact set of relaxations that shows the user at least one way to satisfy each of his requirements and at least one way to relax them, and present an algorithm that efficiently computes such sets. We introduce the concept of most soluble relaxations, maximising the number of products they allow. We present algorithms to compute such relaxations in times compatible with interactivity, achieving this by indifferently making use of different types of compiled representations. We propose to generalise the concept of prime implicates to constraint problems with the concept of domain consequences, and suggest to generate them as a compilation strategy. This sets a new approach in compilation, and allows to address explanation-related queries in an efficient way. We define ordered automata to compactly represent large sets of domain consequences, in an orthogonal way from existing compilation techniques that represent large sets of solutions.

Biogas production from novel substrates

Biogas production is the conversion of the organic material into methane (CH4) and carbon dioxide (CO2) under anaerobic conditions. Anaerobic digestion (AD) is widely used in continental and Scandinavian communities as both a waste treatment option and a source of renewable energy. Ireland however lags behind this European movement. Numerous feedstocks exist which could be digested and used to fuel a renewable transport fleet in Ireland. An issue exists with the variety of feedstocks; these need to be assessed and quantified to ascertain their potential resource and application to AD. From literature the ideal C:N ratio is between 25 and 30:1. Low levels of C:N (<15) can lead to problems with ammonia inhibition. Within the digester a plentiful supply of nutrients and a balanced C:N is required for stable performance. Feedstocks were sampled from a range of over 100 different substrates in Ireland including for first, second and third generation feedstocks. The C:N ranged from 81:1 (Winter Oats) to 7:1 (Silage Effluent). The BMP yields were recorded ranging from 38 ± 2.0 L CH4 kg−1 VS for pig slurry (weaning pigs) to 805 ± 57 L CH4 kg−1 VS for used cooking oil (UCO). However the selection of the best preforming feedstock in terms of C:N ratio or BMP yield alone is not sufficiently adequate. A total picture has to be created which includes C:N ratio, BMP yield, harvest yield and availability. Potential feedstocks which best meet these requirements include for Grass silage, Milk processing waste (MPW) and Saccharina latissima. MPW has a potential of meeting over 6 times the required energy for Ireland’s 2020 transport in energy targets. S. Latissima recorded a yield of over 10,000 GJ ha-1 yr-1 which out ranks traditional second generation biofuels by a factor of more than 4.