Investigation of numerical atomic orbitals for first-principles calculations of the electronic and transport properties of silicon nanowire structures

This thesis is focused on the application of numerical atomic basis sets in studies of the structural, electronic and transport properties of silicon nanowire structures from first-principles within the framework of Density Functional Theory. First we critically examine the applied methodology and then offer predictions regarding the transport properties and realisation of silicon nanowire devices. The performance of numerical atomic orbitals is benchmarked against calculations performed with plane waves basis sets. After establishing the convergence of total energy and electronic structure calculations with increasing basis size we have shown that their quality greatly improves with the optimisation of the contraction for a fixed basis size. The double zeta polarised basis offers a reasonable approximation to study structural and electronic properties and transferability exists between various nanowire structures. This is most important to reduce the computational cost. The impact of basis sets on transport properties in silicon nanowires with oxygen and dopant impurities have also been studied. It is found that whilst transmission features quantitatively converge with increasing contraction there is a weaker dependence on basis set for the mean free path; the double zeta polarised basis offers a good compromise whereas the single zeta basis set yields qualitatively reasonable results. Studying the transport properties of nanowire-based transistor setups with p+-n-p+ and p+-i-p+ doping profiles it is shown that charge self-consistency affects the I-V characteristics more significantly than the basis set choice. It is predicted that such ultrascaled (3 nm length) transistors would show degraded performance due to relatively high source-drain tunnelling currents. Finally, it is shown the hole mobility of Si nanowires nominally doped with boron decreases monotonically with decreasing width at fixed doping density and increasing dopant concentration. Significant mobility variations are identified which can explain experimental observations.

Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

From respect for nature to agency as realisation in response to the ecological emergency

'The ecological emergency’ describes both our emergence into, and the way we relate within, a set of globally urgent circumstances, brought about through anthropogenic impact. I identify two phases to this emergency. Firstly, there is the anthropogenic impact itself, interpreted through various conceptual models. Secondly, however, is the increasingly entrenched commitment to divergent conceptual positions, that leads to a growing disparateness in attitudes, and a concurrent difficulty with finding any grounds for convergence in response. I begin by reviewing the environmental ethics literature in order to clarify which components of the implicit narratives and beliefs of different positions create the foundations for such disparateness of views. I identify the conceptual frameworks through which moral agency and human responsibility are viewed, and that justify an ethical response to the ecological emergency. In particular, I focus on Paul Taylor's thesis of 'respect for nature' as a framework for revising both the idea that we are ‘moral’ and the idea that we are ‘agents’ in this unique way, and I open to question the idea that any response to the ecological emergency need be couched in ethical terms. This revision leads me to formulate an alternative conceptual model that makes use of Timothy Morton’s idea of enmeshment. I propose that we dramatically revise our idea of moral agency using the idea of enmeshment as a starting point. I develop an alternative framework that locates our capacity for responsibility within our capacity for realisation, both in the sense of understanding, and of making real, sets of conditions within our enmeshment. I draw parallels between this idea of ‘realisation as agency’ and the work of Dōgen and other non-dualists. I then propose a revised understanding of ‘the good’ of systems from a biophysical perspective, and compare this with certain features of Asian traditions of thought. I consider the practical implications of these revisions, and I conclude that the act of paying close attention, or realising, contains our agency, as does the attitude, or manner, with which we focus. This gives us the basis for a convergent response to the ecological emergency: the way of our engagement that is the key to responding to the ecological emergency

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.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

An examination of the construction of meanings for obesity in Ireland

Obesity has been defined as a consequence of energy imbalance, where energy intake exceeds energy expenditure and results in a build-up of adipose tissue. However, this scientific definition masks the complicated social meanings associated with the condition. This research investigated the construction of meaning around obesity at various levels of inquiry to inform how obesity is portrayed and understood in Ireland. A multi-paradigmatic approach was adopted, drawing on theory and methods from psychology and sociology and an analytical framework combining the Common Sense Model and framing theory was employed. In order to examine the exo-level meanings of obesity, content analysis was performed on two media data sets (n=479, n=346) and a thematic analysis was also performed on the multiple newspaper sample (n=346). At the micro-level, obesity discourses were investigated via the thematic analysis of comments sampled from an online message board. Finally, an online survey assessed individual-level beliefs and understandings of obesity. The media analysis revealed that individual blame for obesity was pervasive and the behavioural frame was dominant. A significant increase in attention to obesity over time was observed, manifestations of weight stigma were common, and there was an emotive discourse of blame directed towards the parents of obese children. The micro-level analysis provided insight into the weight-based stigma in society and a clear set of negative ‘default’ judgements accompanied the obese label. The survey analysis confirmed that the behavioural frame was the dominant means of understanding obesity. One of the strengths of this thesis is the link created between framing and the Common Sense Model in the development of an analytical framework for application in the examination of health/illness representations. This approach helped to ascertain the extent of the pervasive biomedical and individual blame discourse on obesity, which establishes the basis for the stigmatisation of obese persons.

Novel insights into the inflammatory basis of gastrointestinal disease

It has become clear that inflammation is beneficial to man, there are situations though that the inflammatory response causes damage to the host that is harmful to health. When the inflammatory response fails or is too strong, the health of the host is damaged and disease can occur. The implication of intestinal disease caused by an ineffective immune response is of great social and economic burden to society. The overarching purpose of this thesis is to assess inflammatory signalling targets associated with immune mediated disorders such as IBD, IBS and inflammatory liver disease. By assessing these targets and modifying their function I hope to contribute and expand further the pre-existing information on these disorders and improve the therapeutic interventions available in these debilitating conditions. I will assess the role of inflammation in disorders of the GI tract and liver IBD, IBS, hepatic inflammatory injury and furthermore, I will use pharmaceutical agents to activate and suppress components of the immune system. I will examine the inflammatory response in experimental models of disease for IBD and liver injury, I will attempt to alter these pathways using pharmaceutical intervention to delineate the disease causing mechanism that may lead to clinically relevant therapeutic interventions. In regards to IBS, I will attempt to improve the existing knowledge that exists in relation to the pathogenesis of this functional bowel disorder. I will attempt to define a mechanism by which the low grade mucosal inflammation that has been demonstrated by others arises and what this inflammation is induced by. The overall aim of this thesis is to attempt to further understand the mechanisms behind GI and liver disease. Looking at the inflammatory response in these specific conditions and how they can be altered may lead to exciting new therapies for inflammatory conditions in the gastrointestinal tract.

Exploring the physicochemical basis of cheese texture, rheology and functionality, with emphasis on cation-casein interactions

The physicochemical properties of cheese and milk gels are greatly influenced by molecular interactions between the casein proteins involving calcium. Novel experiments were designed to investigate the relationship between insoluble caseinbound cations and rheological properties of Cheddar cheese and rennet-induced milk gels. Cheddar cheese and rennet-induced milk gels were supplemented with Mg2+ or Sr2+ to compare their effects on their rheological properties to those previously reported in literature for Ca2+ supplementation. Sr2+ displayed behaviour similar to Ca2+ as observed by its ability to increase the rigidity of cheese and rennet milk gels and also decrease cheese meltability. Mg+2 had no influence on cheese rheological properties and was greatly inferior to Ca2+ and Sr2+ in its ability to increase rennet milk gel elasticity. Cheddar cheese was supplemented with the calcium-chelating salts trisodium citrate, disodium hydrogen phosphate or disodium EDTA, in an attempt to reduce the CCP content of cheese and thereby modify its rheological and functional properties. TSC and EDTA were successful in decreasing cheese CCP, whereas DSP caused an initial increase in CCP content. Cheddar cheese was supplemented with chlorides of iron, copper and zinc at salting to investigate the effects of concentrations of these elements in excess of those found innately or commonly in fortification studies, with emphasis on mineral equilibria changes and resultant alteration of rheological properties. Zinc addition was the only added metal that significantly influenced cheese rheological properties, leading to an increase in cheese rigidity and decreased cheese melt at elevated temperatures. Gum tragacanth was used as a fat-replacer in the manufacture of reduced-fat Cheddar cheese, in an attempt to improve the rheological, functional and sensory properties of reduced-fat Cheddar. Overall, the experimental work reported in this thesis generated new knowledge and theories about how casein-mineral interactions influence rheological properties of casein systems.