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.

Characterization of resistivity of Sb2S3 semiconductor nanowires by conductive AFM and in-situ methods

Conductive AFM and in situ methods were used to determine contact resistance and resistivity of individual Sb2S3 nanowires. Nanowires were deposited on oxidized Si surface for in situ measurements and on Si surface with macroelectrodes for conductive AFM (C-AFM) measurements. Contact resistance was determined by measurement of I(V) characteristics at different distances from the nanowire contact with the macroelectrode and resistivity of nanowires was determined. Sb2S3 is a soft material with low adhesion force to the surface and therefore special precautions were taken during measurements.

Preparation and characterisation of ceria particles

Cerium dioxide (ceria) nanoparticles have been the subject of intense academic and industrial interest. Ceria has a host of applications but academic interest largely stems from their use in the modern automotive catalyst but it is also of interest because of many other application areas notably as the abrasive in chemical-mechanical planarisation of silicon substrates. Recently, ceria has been the focus of research investigating health effects of nanoparticles. Importantly, the role of non-stoichiometry in ceria nanoparticles is implicated in their biochemistry. Ceria has well understood non-stoichiometry based around the ease of formation of anion vacancies and these can form ordered superstructures based around the fluorite lattice structure exhibited by ceria. The anion vacancies are associated with localised or small polaron states formed by the electrons that remain after oxygen desorption. In simple terms these electrons combine with Ce4+ states to form Ce3+ states whose larger ionic radii is associated with a lattice expansion compared to stoichiometric CeO2. This is a very simplistic explanation and greater defect chemistry complexity is suggested by more recent work. Various authors have shown that vacancies are mobile and may result in vacancy clustering. Ceria nanoparticles are of particular interest because of the high activity and surface area of small particulates. The sensitivity of the cerium electronic band structure to environment would suggest that changes in the properties of ceria particles at nanoscale dimensions might be expected. Notably many authors report a lattice expansion with reducing particle size (largely confined to sub-10 nm particles). Most authors assign increased lattice dimensions to the presence of a surface stable Ce2O3 type layer at low nanoparticle dimensions. However, our understanding of oxide nanoparticles is limited and their full and quantitative characterisation offers serious challenges. In a series of chemical preparations by ourselves we see little evidence of a consistent model emerging to explain lattice parameter changes with nanoparticle size. Based on these results and a review of the literature it is worthwhile asking if a model of surface enhanced defect concentration is consistent with known cerium/cerium oxide chemistries, whether this is applicable to a range of different synthesis methods and if a more consistent description is possible. In Chapter one the science of cerium oxide is outlined including the crystal structure, defect chemistry and different oxidation states available. The uses and applications of cerium oxide are also discussed as well as modelling of the lattice parameter and the doping of the ceria lattice. Chapter two describes both the synthesis techniques and the analytical methods employed to execute this research. Chapter three focuses on high surface area ceria nano-particles and how these have been prepared using a citrate sol-gel precipitation method. Changes to the particle size have been made by calcining the ceria powders at different temperatures. X-ray diffraction methods were used to determine their lattice parameters. The particles sizes were also assessed using transmission electron microscopy (TEM), scanning electron microscopy (SEM), and BET, and, the lattice parameter was found to decrease with decreasing particle size. The results are discussed in light of the role played by surface tension effects. Chapter four describes the morphological and structural characterization of crystalline CeO2 nanoparticles prepared by forward and reverse precipitation techniques and compares these by powder x-ray diffraction (PXRD), nitrogen adsorption (BET) and high resolution transmission electron microscopy (HRTEM) analysis. The two routes give quite different materials although in both cases the products are essentially highly crystalline, dense particulates. It was found that the reverse precipitation technique gave the smallest crystallites with the narrowest size dispersion. This route also gave as-synthesised materials with higher surface areas. HRTEM confirmed the observations made from PXRD data and showed that the two methods resulted in quite different morphologies and surface chemistries. The forward route gives products with significantly greater densities of Ce3+ species compared to the reverse route. Data are explained using known precipitation chemistry and kinetic effects. Chapter five centres on the addition of terbia to ceria and has been investigated using XRD, XRF, XPS and TEM. Good solid solutions were formed across the entire composition range and there was no evidence for the formation of mixed phases or surface segregation over either the composition or temperature range investigated. Both Tb3+ and Tb4+ ions exist within the solution and the ratios of these cations are consistent with the addition of Tb8O15 to the fluorite ceria structure across a wide range of compositions. Local regions of anion vacancy ordering may be visible for small crystallites. There is no evidence of significant Ce3+ ion concentrations formed at the surface or in the bulk by the addition of terbia. The lattice parameter of these materials was seen to decrease with decreasing crystallite size. This is consistent with increased surface tension effects at small dimension. Chapter six reviews size related lattice parameter changes and surface defects in ceria nanocrystals. Ceria (CeO2) has many important applications, notably in catalysis. Many of its uses rely on generating nanodimensioned particles. Ceria has important redox chemistry where Ce4+ cations can be reversibly reduced to Ce3+ cations and associated anion vacancies. The significantly larger size of Ce3+ (compared with Ce4+) has been shown to result in lattice expansion. Many authors have observed lattice expansion in nanodimensioned crystals (nanocrystals), and these have been attributed to the presence of stabilized Ce3+ -anion vacancy combinations in these systems. Experimental results presented here show (i) that significant, but complex changes in the lattice parameter with size can occur in 2-500 nm crystallites, (ii) that there is a definitive relationship between defect chemistry and the lattice parameter in ceria nanocrystals, and (iii) that the stabilizing mechanism for the Ce3+ -anion vacancy defects at the surface of ceria nanocrystals is determined by the size, the surface status, and the analysis conditions. In this work, both lattice expansion and a more unusual lattice contraction in ultrafine nanocrystals are observed. The lattice deformations seen can be defined as a function of both the anion vacancy (hydroxyl) concentration in the nanocrystal and the intensity of the additional pressure imposed by the surface tension on the crystal. The expansion of lattice parameters in ceria nanocrystals is attributed to a number of factors, most notably, the presence of any hydroxyl moieties in the materials. Thus, a very careful understanding of the synthesis combined with characterization is required to understand the surface chemistry of ceria nanocrystals.

Dairy-Met: compositional metagenomic analysis of milk and cheeses

Unpasteurised milk and many cheeses contain a diverse microbiological population. These microorganisms play important roles in dairy foods and can, for example, contribute to the development of flavours and aromas, determine safety, cause spoilage or enhance the health of the consumer. It is thus important to understand thoroughly the microorganisms present in these food types. Traditional culture dependent and culture-independent methods have provided much detail regarding the microbial content of dairy foods. However, the development of next-generation DNA sequencing technologies has revolutionised our knowledge of complex microbial environments. Throughout this thesis we observe the benefits of applying these technologies to provide a detailed understanding of the bacterial content of dairy foods, including those present in milk pre- and post-pasteurisation, Irish farmhouse cheeses and commercially produced cheeses which encounter a discolouration defect, as well as to study genomic changes in microbes associated with dairy foods. Through the application of these state-of-the-art technologies we identified the presence of microorganisms not previously associated with dairy foods.

Application of signal detection methods to fisheries management

The abundance of many commercially important fish stocks are declining and this has led to widespread concern on the performance of traditional approach in fisheries management. Quantitative models are used for obtaining estimates of population abundance and the management advice is based on annual harvest levels (TAC), where only a certain amount of catch is allowed from specific fish stocks. However, these models are data intensive and less useful when stocks have limited historical information. This study examined whether empirical stock indicators can be used to manage fisheries. The relationship between indicators and the underlying stock abundance is not direct and hence can be affected by disturbances that may account for both transient and persistent effects. Methods from Statistical Process Control (SPC) theory such as the Cumulative Sum (CUSUM) control charts are useful in classifying these effects and hence they can be used to trigger management response only when a significant impact occurs to the stock biomass. This thesis explores how empirical indicators along with CUSUM can be used for monitoring, assessment and management of fish stocks. I begin my thesis by exploring various age based catch indicators, to identify those which are potentially useful in tracking the state of fish stocks. The sensitivity and response of these indicators towards changes in Spawning Stock Biomass (SSB) showed that indicators based on age groups that are fully selected to the fishing gear or Large Fish Indicators (LFIs) are most useful and robust across the range of scenarios considered. The Decision-Interval (DI-CUSUM) and Self-Starting (SS-CUSUM) forms are the two types of control charts used in this study. In contrast to the DI-CUSUM, the SS-CUSUM can be initiated without specifying a target reference point (‘control mean’) to detect out-of-control (significant impact) situations. The sensitivity and specificity of SS-CUSUM showed that the performances are robust when LFIs are used. Once an out-of-control situation is detected, the next step is to determine how much shift has occurred in the underlying stock biomass. If an estimate of this shift is available, they can be used to update TAC by incorporation into Harvest Control Rules (HCRs). Various methods from Engineering Process Control (EPC) theory were tested to determine which method can measure the shift size in stock biomass with the highest accuracy. Results showed that methods based on Grubb’s harmonic rule gave reliable shift size estimates. The accuracy of these estimates can be improved by monitoring a combined indicator metric of stock-recruitment and LFI because this may account for impacts independent of fishing. The procedure of integrating both SPC and EPC is known as Statistical Process Adjustment (SPA). A HCR based on SPA was designed for DI-CUSUM and the scheme was successful in bringing out-of-control fish stocks back to its in-control state. The HCR was also tested using SS-CUSUM in the context of data poor fish stocks. Results showed that the scheme will be useful for sustaining the initial in-control state of the fish stock until more observations become available for quantitative assessments.

Self-neglect: development and evaluation of a self-neglect (SN-37) measurement instrument

Aim: To develop and evaluate the psychometric properties of an instrument for the measurement of self-neglect (SN).Conceptual Framework: An elder self-neglect (ESN) conceptual framework guided the literature review and scale development. The framework has two key dimensions physical/psycho-social and environmental and seven sub dimensions which are representative of the factors that can contribute to intentional and unintentional SN. Methods: A descriptive cross-sectional design was adopted to achieve the research aim. The study was conducted in two phases. Phase 1 involved the development of the questionnaire content and structure. Phase 2 focused on establishing the psychometric properties of the instrument. Content validity was established by a panel of 8 experts and piloted with 9 health and social care professionals. The instrument was subsequently posted with a stamped addressed envelope to 566 health and social care professionals who met specific eligibility criteria across the four HSE areas. A total of 341 questionnaires were returned, a response rate of 60% and 305 (50%) completed responses were included in exploratory factor analysis (EFA). Item and factor analyses were performed to elicit the instruments underlying factor structure and establish preliminary construct validity. Findings: Item and factor analyses resulted in a logically coherent, 37 items, five factor solution, explaining 55.6% of the cumulative variance. The factors were labelled: ‘Environment’, ‘Social Networks’, ‘Emotional and Behavioural Liability’, ‘Health Avoidance’ and ‘Self-Determinism’. The factor loadings were >0.40 for all items on each of the five subscales. Preliminary construct validity was supported by findings. Conclusion: The main outcome of this research is a 37 item Self-Neglect (SN-37) measurement instrument that was developed by EFA and underpinned by an ESN conceptual framework. Preliminary psychometric evaluation of the instrument is promising. Future work should be directed at establishing the construct and criterion related validity of the instrument.

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.

Synthesis and reactivity of pyridine substituted α-diazocarbonyl compounds and exploration of rhodium carboxylates as asymmetric catalysts

The primary objective of this thesis was the preparation of a series of pyridine-containing α-diazocarbonyl compounds and subsequent investigation of the reactivity of these compounds on exposure to transition metal catalysts. In particular, the reactivity of the pyridyl α-diazocarbonyls was compared to that of the analogous phenyl α-diazocarbonyl compounds to ascertain the impact of replacement of the phenyl ring with pyridine. The first chapter initially provides a brief introduction into α-diazocarbonyl chemistry, comprising a compendium of well-established and recently developed methods in the preparation of these compounds, as well as an outline of the reactivity of these versatile substrates. The substantive element of this introductory chapter comprises a detailed review focused on transition metal-catalysed transformations of heterocyclic α-diazocarbonyl compounds, highlighting the extraordinary diversity of reaction products which can be accessed. This review is undertaken to set the work of this thesis in context. The results of this research are discussed in the second and third chapters together with the associated experimental details, including spectroscopic and analytical data obtained in the synthesis of all compounds during this research. The second chapter describes the preparation of a range of novel pyridine-containing α-diazocarbonyl compounds via a number of synthetic strategies including both acylation and diazo transfer methodologies. In contrast to the phenyl analogues, the generation of the pyridine α-diazocarbonyl substrates was complicated by a number of factors including the inherent basicity of the pyridine ring, tautomerism and existence of rotamers. Rhodium- and copper-mediated transformations of the pyridine-containing α-diazocarbonyl compounds is discussed in detail displaying very different reactivity patterns to those seen with the phenyl analogues; oxidation to 2,3- diketones, 1,2-hydride shift to form enones and oxonium and sulfonium ylide formation/rearrangement are prominent in the pyridyl series, with no evidence of aromatic addition to the pyridine ring. The third chapter focuses on exploration of novel chiral rhodium(II) catalysts, developed in the Maguire team, in both intermolecular cyclopropanations and intramolecular C–H insertion reactions. In this chapter, the studies are focused on standard α-diazocarbonyl compounds without heteroaryl substituents. The most notable outcome was the achievement of high enantiopurities for intramolecular C–H insertions, which were competitive with, and even surpassed, established catalyst systems in some cases. This work has provided insight into solvent and temperature effects on yields as well as enantio- and diastereoselectivity, thereby providing guidance for future development and design of chiral rhodium carboxylate catalysts. While this is a preliminary study, the significance of the results lie in the fact that these are the first reactions to give substantial asymmetric induction with these novel rhodium carboxylates. While the majority of the α-diazocarbonyl compounds explored in this work were α-diazoketones, a number of α-diazoesters are also described. Details of chiral stationary phase HPLC analysis, single crystal analysis and 2D NMR experiments are included in the Appendix (Appendix III-V).

Childhood obesity in Ireland: recent trends and modifiable determinants

Background: Childhood obesity is a global epidemic posing a significant threat to the health and wellbeing of children. To reverse this epidemic, it is essential that we gain a deeper understanding of the complex array of driving factors at an individual, family and wider ecological level. Using a social-ecological framework, this thesis investigates the direction, magnitude and contribution of risk factors for childhood overweight and obesity at multiple levels of influence, with a particular focus on diet and physical activity. Methods: A systematic review was conducted to describe recent trends (from 2002-2012) in childhood overweight and obesity prevalence in Irish school children from the Republic of Ireland. Two datasets (Cork Children’s Lifestyle [CCLaS] Study and the Growing Up in Ireland [GUI] Study) were used to explore determinants of childhood overweight and obesity. Individual lifestyle factors examined were diet, physical activity and sedentary behaviour. The determinants of physical activity were also explored. Family factors examined were parental weight status and household socio-economic status. The impact of food access in the local area on diet quality and body mass index (BMI) was investigated as an environmental level risk factor. Results: Between 2002 and 2012, the prevalence of childhood overweight and obesity in Ireland remained stable. There was some evidence to suggest that childhood obesity rates may have decreased slightly though one in four Irish children remained either overweight or obese. In the CCLaS study, overweight and obese children consumed more unhealthy foods than normal weight children. A diet quality score was constructed based on a previously validated adult diet score. Each one unit increase in diet quality was significantly associated with a decreased risk of childhood overweight and obesity. Individual level factors (including gender, being a member of a sports team, weight status) were more strongly associated with physical activity levels than family or environmental factors. Overweight and obese children were more sedentary and less active than normal weight children. There was a dose response relationship between time spent at moderate to vigorous physical activity (MVPA) and the risk of childhood obesity independent of sedentary time. In contrast, total sedentary time was not associated with the risk of childhood obesity independent of MVPA though screen time was associated with childhood overweight and obesity. In the GUI Study, only one in five children had 2 normal weight parents (or one normal weight parent in the case of single parent families). Having overweight and obese parents was a significant risk factor for overweight and obesity regardless of socio-economic characteristics of the household. Family income was not associated with the odds of childhood obesity but social class and parental education were important risk factors for childhood obesity. Access to food stores in the local environment did not impact dietary quality or the BMI of Irish children. However, there was some evidence to suggest that the economic resources of the family influenced diet and BMI. Discussion: Though childhood overweight and obesity rates appear to have stabilised over the previous decade, prevalence rates are unacceptably high. As expected, overweight and obesity were associated with a high energy intake and poor dietary quality. The findings also highlight strong associations between physical inactivity and the risk of overweight and obesity, with effect sizes greater than what have been typically found in adults. Important family level determinants of childhood overweight and obesity were also identified. The findings highlight the need for a multifaceted approach, targeting a range of modifiable determinants to tackle the problem. In particular, policies and interventions at the shared family environment or community level may be an effective mean of tackling this current epidemic.

Oxidation-reduction potential and its influence on Cheddar cheese quality

Oxidation-reduction (redox) potential is a fundamental physicochemical parameter that affects the growth of microorganisms in dairy products and contributes to a balanced flavour development in cheese. Even though redox potential has an important impact on the quality of dairy products, it is not usually monitored in dairy industry. The aims of this thesis were to develop practical methods for measuring redox potential in cheese, to provide detailed information on changes in redox potential during the cheesemaking and cheese ripening and how this parameter is influenced by starter systems and to understand the relationship between redox potential and cheese quality. Methods were developed for monitoring redox potential during cheesemaking and early in ripening. Changes in redox potential during laboratory scale manufacture of Cheddar, Gouda, Emmental, and Camembert cheeses were determined. Distinctive kinetics of reduction in redox potential during cheesemakings were observed, and depended on the cheese technology and starter culture utilised. Redox potential was also measured early in ripening by embedding electrodes into Cheddar cheese at moulding together with the salted curd pieces. Using this approach it was possible to monitor redox potential during the pressing stage. The redox potential of Emmental cheese was also monitored during ripening. Moreover, since bacterial growth drives the reduction in redox potential during cheese manufacture and ripening, the ability of Lactococcus lactis strains to affect redox potential was studied. Redox potential of a Cheddar cheese extract was altered by bacterial growth and there were strain-specific differences in the nature of the redox potential/time curves obtained. Besides, strategies to control redox potential during cheesemaking and ripening were developed. Oxidizing or reducing agents were added to the salted curd before pressing and results confirmed that a negative redox potential is essential for the development of sulfur compounds in Cheddar cheese. Overall, the studies described in this thesis gave an evidence of the importance of the redox potential on the quality of dairy products. Redox potential could become an additional parameter used to select microorganisms candidate as starters in fermented dairy products. Moreover, it has been demonstrated that the redox potential influences the development of flavour component. Thus, measuring continuously changes in redox potential of a product and controlling, and adjusting if necessary, the redox potential values during manufacture and ripening could be important in the future of the dairy industry.

Artificial opal photonic crystals and inverse opal structures - fundamentals and applications from optics to energy storage

Photonic crystals (PhCs) influence the propagation of light by their periodic variation in dielectric contrast or refractive index. This review outlines the attractive optical qualities inherent to most PhCs namely the presence of full or partial photonic band gaps and the possibilities they present towards the inhibition of spontaneous emission and the localization of light. Colloidal self-assembly of polymer or silica spheres is one of the most favoured and low cost methods for the formation of PhCs as artificial opals. The state of the art in growth methods currently used for colloidal self-assembly are discussed and the use of these structures for the formation of inverse opal architectures is then presented. Inverse opal structures with their porous and interconnected architecture span several technological arenas - optics and optoelectronics, energy storage, communications, sensor and biological applications. This review presents several of these applications and an accessible overview of the physics of photonic crystal optics that may be useful for opal and inverse opal researchers in general, with a particular emphasis on the recent use of these three-dimensional porous structures in electrochemical energy storage technology. Progress towards all-optical integrated circuits may lie with the concepts of the photonic crystal, but the unique optical and structural properties of these materials and the convergence of PhC and energy storage disciplines may facilitate further developments and non-destructive optical analysis capabilities for (electro)chemical processes that occur within a wide variety of materials in energy storage research.