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.

Alcohol income and health: a complicated but desirable mix

The aim of this thesis is to examine if a difference exists in income for different categories of drinkers in Ireland using the 2007 Slán data set. The possible impact of alcohol consumption on health status and health care utilisation is also examined. Potential endogeneity and selection bias is accounted for throughout. Endogeneity is where an independent variable included in the model is determined within the context of the model (Chenhall and Moers, 2007). An endogenous relationship between income and alcohol and between health and alcohol is accounted for by the use of separate income equations and separate health status equations for each category of drinker similar to what was done in previous studies into the effects of alcohol on earnings (Hamilton and Hamilton, 1997; Barrett, 2002). Sample selection bias arises when a sector selection is non-random due to individuals choosing a particular sector because of their personal characteristics (Heckman, 1979; Zhang, 2004). In relation to alcohol consumption, selection bias may arise as people may select into a particular drinker group due to the fact that they know that by doing so it will not have a negative effect on their income or health (Hamilton and Hamilton, 1997; Di Pietro and Pedace, 2008; Barrett, 2002). Selection bias of alcohol consumption is accounted for by using the Multinomial Logit OLS Two Step Estimate as proposed by Lee (1982), which is an extension of the Heckman Probit OLS Two Step Estimate. Alcohol status as an ordered variable is examined and possible methods of estimation accounting for this ordinality while also accounting for selection bias are looked at. Limited Information Methods and Full Information Methods of estimation of simultaneous equations are assessed and compared. Findings show that in Ireland moderate drinkers have a higher income compared with abstainers or heavy drinkers. Some studies such as Barrett (2002) argue that this is as a consequence of alcohol improving ones health, which in turn can influence ones productivity which may ultimately be reflected in earnings, due to the fact that previous studies have found that moderate levels of alcohol consumption are beneficial towards ones health status. This study goes on to examine the relationship between health status and alcohol consumption and whether the correlation between income and the consumption of alcohol is similar in terms of sign and magnitude to the correlation between health status and the consumption of alcohol. Results indicate that moderate drinkers have a higher income than non or heavy drinkers, with the weekly household income of moderate drinkers being €660.10, non drinkers being €546.75 and heavy drinkers being €449.99. Moderate Drinkers also report having a better health status than non drinkers and a slightly better health status than heavy drinkers. More non-drinkers report poor health than either moderate or heavy drinkers. As part of the analysis into the effect of alcohol consumption on income and on health status, the relationship between other socio economic variables such as gender, age, education among others, with income, health and alcohol status is examined.

Leadership, fairness and gender: a practitioner's perspective

This Portfolio of Exploration outlines the course of learning by a practitioner on a personal leadership journey. It constructs a functional examination of ideas around leadership. It explores the belief system which underpins leadership practice and it also explores to what extent the increased participation of women can lead to a qualitatively different type of leadership. Different models of leadership are explored to find the model which can best fit with the author’s perception of leadership. The Women’s Intercultural Leadership Model is discussed. This model conceptualises leadership as the envisioning of oneself and others as potential leaders. It seeks to promote that recognition whilst at the same time encouraging personal transformation. The promotion of a values based leadership is examined. The value of fairness is examined as an element of functional leadership. The extent to which increasing the number of women in leadership can lead to a qualitatively different type of leadership is explored. Drucker’s assertion that every practice rests on theory is used to unearth the underlying assumptions of this reflective practitioner doctorate. Kegan’s Theory of Adult Mental Development and Subject-Object separation is used to explicitly examine knowledge construction. Myers Briggs Type Indicator (MBTI) and Assumption/Commitment/Behaviour/Outcome (ACBO) template are used to promote practice change.

An investigation into mechanisms of visceral pain in rodents

Visceral pain is a debilitating symptom of irritable bowel syndrome (IBS), a disorder affecting up to 30% of adults. A better understanding of the mechanisms underlying visceral hypersensitivity may facilitate development of more targeted therapies, improving the quality of life of these individuals. The studies performed in this thesis were designed to investigate important factors of visceral pain, including early-life manipulations, genetic predisposition and sex hormones. Maternal separation (MS) consistently reproduces visceral hypersensitivity and altered anxiety-like behaviours in rats, symptoms associated with IBS. It has been found that 5-HT2B receptor antagonism blocks visceral pain but no difference in relative 5-HT2B receptor mRNA expression was found in hippocampus, amygdala and colon. The neuronal activation patterns of prefrontal cortex and amygdala of MS rats were then investigated. MS animals are characterised by differential activation of the prefrontal cortex (anterior cingulate cortex (ACC), infralibic cortex, prelimbic cortex) as well as the central nucleus of the amygdala (CeA). Genetic factors also contribute to pain syndromes such as IBS. We utilised the Wistar Kyoto (WKY) rat, a stress-sensitive strain, as an animal model of brain-gut axis dysfunction. WKY rats have a lower expression of the glutamate transporter EAAT2 and mGlu4 receptor in the ACC. Another early-life factor that can increase susceptibility to functional gastrointestinal symptoms later life is disruption of the gut microbiota, thus early-life antibiotic treatment was used to assess this effect. Antibiotic treatment induced visceral hypersensitivity in adulthood and may be related to observed reductions in spinal cord alpha-2A adrenoreceptor (adra2A) mRNA. Lastly, we investigated sex differences in visceral sensitivity. EAAT1 & 2 mRNA levels are lower in females, potentially increasing glutamatergic concentration at the symaptic level. Moreover, NR1 and NR2B subunits mRNA of NMDA receptor were increased in caudal ACC of females. These findings may account for sex differences in visceral sensitivity.

The Shawlies: A study of early neoliberal ‘gender-fication’. The Street Trading Act, 1926, modern gender-fication, and the implications for Cork’s women street traders

For centuries Cork’s Shawlies, working-class women, survived by trading on public streets. My study explores how the first Irish Free State government, and Cork’s local authority, limited the rights of poor women to earn by subsistence trading with The Street Trading Act, 1926. The government insisted this would regulate street trading. In practice it further marginalised the women economically and socially, containing them outside the privileged, commercial city centre. In Cork the legislation facilitated the gradual disappearance of the Shawlies amid entrenched social processes and relations, contingencies that allowed for the abuse of their rights in the service of amalgamated business interests. This study address the role of discourses in deepening this marginalisation. My theoretical framework is designed to demonstrate how a seemingly innocuous piece of legislation would, in practice, do this. I set out the concepts of ‘Thriving State’, ‘Prosperous State’, and state of ‘Best Intentions’ that uses gentrification to meet these goals. The existing knowledge on women in trade is then examined, highlighting the gaps in what is known about the Shawlies. Chapter 3 details the theory behind my genealogical method. The legislation, debate, and other data produced at the national level is then examined, before moving to the local data. Chapter 6 is devoted to the Shawlies, setting their stories in the larger context of the debates. An examination of studies of contemporary women street traders in poor nations follows, along with a brief history of the decline of street trading in New York city under gentrification. Points of convergence between that process and the one in Cork are identified, along with convergences between contemporary traders and the Shawlies. The conclusion sets out my methodological, theoretical and substantive discoveries, and comments on current nostalgic renderings of the Shawlies in Cork’s newly gentrified Corn Market Street.