Dilute nitride semiconductors : band structure, scattering and high field transport

The substitution of a small fraction x of nitrogen atoms, for the group V elements in conventional III-V semiconductors such as GaAs and GaSb strongly perturbs the conduction band of the host semiconductor. In this thesis we investigate the effects of nitrogen states on the band dispersion, carrier scattering and mobility of dilute nitride alloys. In the supercell model we solve the single particle Hamiltonian for a very large supercell containing randomly placed nitrogen. This model predicts a gap in the density of states of GaNxAs1−x, where this gap is filled in the Green’s function model. Therefore we develop a self-consistent Green’s function (SCGF) approach, which provides excellent agreement with supercell calculations and reveals a gap in the DOS, in contrast with the results of previous non-self-consistent Green’s function calculations. However, including the distribution of N states destroys this gap, as seen in experiment. We then examine the high field transport of carriers by solving the steadystate Boltzmann transport equation and find that it is necessary to include the full distribution of N levels in order to account for the small, low-field mobility and the absence of a negative differential velocity regime observed experimentally with increasing x. Overall the results account well for a wide range of experimental data. We also investigate the band structure, scattering and mobility of carriers by finding the poles of the SCGF, which gives lower carrier mobility for GaNxAs1−x, compared to those already calculated, in better agreement with experiments. The calculated optical absorption spectra for InyGa1−yNxAs1−x and GaNxSb1−x using the SCGF agree well with the experimental data, confirming the validity of this approach to study the band structure of these materials.

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.

Variations in total and differential milk somatic cell counts and plasmin levels and their role in proteolysis and quality of milk and cheese

Increased plasmin and plasminogen levels and elevated somatic cell counts (SCC) and polymorphonuclear leucocyte levels (PMN) were evident in late lactation milk. Compositional changes in these milks were associated with increased SCC. The quality of late lactation milks was related to nutritional status of herds, with milks from herds on a high plane of nutrition having composition and clotting properties similar to, or superior to, early-mid lactation milks. Nutritionally-deficient cows had elevated numbers of polymorphonuclear leucocytes (PMNs) in their milk, elevated plasmin levels and increased overall proteolytic activity. The dominant effect of plasmin on proteolysis in milks of low SCC was established. When present in elevated numbers, somatic cells and PMNs in particular had a more significant influence on the proteolysis of both raw and pasteurised milks than plasmin. PMN protease action on the caseins showed proteolysis products of two specific enzymes, cathepsin B and elastase, which were also shown in high SCC milk. Crude extracts of somatic cells had a high specificity on αs1-casein. Cheeses made from late lactation milks had increased breakdown of αs1-casein, suggestive of the action of somatic cell proteinases, which may be linked to textural defects in cheese. Late lactation cheeses also showed decreased production of small peptides and amino acids, the reason for which is unknown. Plasmin, which is elevated in activity in late lactation milk, accelerated the ripening of Gouda-type cheese, but was not associated with defects of texture or flavour. The retention of somatic cell enzymes in cheese curd was confirmed, and a potential role in production of bitter peptides identified. Cheeses made from milks containing high levels of PMNs had accelerated αs1-casein breakdown relative to cheeses made from low PMN milk of the same total SCC, consistent with the demonstrated action of PMN proteinases. The two types of cheese were determined significantly different by blind triangle testing.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

An exploration of the positive and negative relationships associated with the development of asthma and atopic disorders in primary school children in Cork

Childhood asthma, allergic rhinitis and eczema are complex heterogenic chronic inflammatory allergic disorders which constitute a major burden to children, their families. The prevalence of childhood allergic disorders is increasing worldwide and merely rudimentary understanding exists regarding causality, or the influence of the environment on disease expression. Phase Three of the International Study of Asthma and Allergy in Childhood (ISAAC) reported that Irish adolescents had the 4th highest eczema and rhinoconjunctivitis prevalence and 3rd highest asthma prevalence in the world. There are no ISAAC data pertaining to young Irish children. In 2002, Sturley reported a high prevalence of current asthma in Cork primary school children aged 6-9 years. This thesis comprises of three cross-sectional studies which examined the prevalence of and associations with childhood allergy and a quasi-retrospective cohort study which observed the natural history of allergy from 6-9 until 11-13 years. Although not part of ISAAC, data was attained by parentally completed ISAAC-based questionnaires, using the ISAAC protocol. The prevalence, natural history and risk factors of childhood allergy in Ireland, as described in this thesis, echo those in worldwide allergy research. The variations of prevalence in different populations worldwide and the recurring themes of associations between childhood allergy and microbial exposures, from farming environments and/or gastrointestinal infections, as shown in this thesis, strengthen the mounting evidence that microbial exposure on GALT may hold the key to the mechanisms of allergy development. In this regard, probiotics may be an area of particular interest in allergy modification. Although their effects in relation to allergy, have been investigated now for several years, our knowledge of their diversity, complex functions and interactions with gut microflora, remain rudimentary. Birth cohort studies which include genomic and microbiomic research are recommended in order to examine the underlying mechanisms and the natural course of allergic diseases.

Identification of novel innate immune mechanisms regulating inflammation in the gastrointestinal tract

The Gastro-Intestinal (GI) tract is a unique region in the body. Our innate immune system retains a fine homeostatic balance between avoiding inappropriate inflammatory responses against the myriad commensal microbes residing in the gut while also remaining active enough to prevent invasive pathogenic attack. The intestinal epithelium represents the frontline of this interface. It has long been known to act as a physical barrier preventing the lumenal bacteria of the gastro-intestinal tract from activating an inflammatory immune response in the immune cells of the underlying mucosa. However, in recent years, an appreciation has grown surrounding the role played by the intestinal epithelium in regulating innate immune responses, both in the prevention of infection and in maintaining a homeostatic environment through modulation of innate immune signalling systems. The aim of this thesis was to identify novel innate immune mechanisms regulating inflammation in the GI tract. To achieve this aim, we chose several aspects of regulatory mechanisms utilised in this region by the innate immune system. We identified several commensal strains of bacteria expressing proteins containing signalling domains used by Pattern Recognition Receptors (PRRs) of the innate immune system. Three such bacterial proteins were studied for their potentially subversive roles in host innate immune signalling as a means of regulating homeostasis in the GI tract. We also examined differential responses to PRR activation depending on their sub-cellular localisation. This was investigated based on reports that apical Toll-Like Receptor (TLR) 9 activation resulted in abrogation of inflammatory responses mediated by other TLRs in Intestinal Epithelial Cells (IECs) such as basolateral TLR4 activation. Using the well-studied invasive intra-cellular pathogen Listeria monocytogenes as a model for infection, we also used a PRR siRNA library screening technique to identify novel PRRs used by IECs in both inhibition and activation of inflammatory responses. Many of the PRRs identified in this screen were previously believed not to be expressed in IECs. Furthermore, the same study has led to the identification of the previously uncharacterised TLR10 as a functional inflammatory receptor of IECs. Further analysis revealed a similar role in macrophages where it was shown to respond to intracellular and motile pathogens such as Gram-positive L.monocytogenes and Gram negative Salmonella typhimurium. TLR10 expression in IECs was predominantly intracellular. This is likely in order to avoid inappropriate inflammatory activation through the recognition of commensal microbial antigens on the apical cell surface of IECs. Moreover, these results have revealed a more complex network of innate immune signalling mechanisms involved in both activating and inhibiting inflammatory responses in IECs than was previously believed. This contribution to our understanding of innate immune regulation in this region has several direct and indirect benefits. The identification of several novel PRRs involved in activating and inhibiting inflammation in the GI tract may be used as novel therapeutic targets in the treatment of disease; both for inducing tolerance and reducing inflammation, or indeed, as targets for adjuvant activation in the development of oral vaccines against pathogenic attack.

Novel insights into the expression and function of p38δ MAPK in oesophageal squamous cell carcinoma

Oesophageal cancer is an aggressive malignancy which is resistant to conventional therapy and has a poor prognosis. A greater understanding of the underlying molecular biology of oesophageal cancer and the identification of novel targets is necessary for the future treatment of this disease. This thesis focuses specifically on the ill-defined and understudied p38δ mitogen-activated protein kinase (MAPK) and its function(s) in oesophageal squamous cell carcinoma (OESCC). In contrast to the three other p38 isoforms (p38α, -β and –γ which have to-date been relatively well-studied), p38δ MAPK signalling is poorly understood. Thus, this research elucidates some of the role(s) played by p38δ MAPK in cancer progression. This work outlines how loss of p38δ MAPK expression confers greater tumourigenicity in oesophageal cancer. Restoration of p38δ MAPK expression, however, has anti-proliferative and anti-migratory effects and decreases OESCC capacity for anchorageindependent growth. Using a novel application of an enzyme-substrate fusion approach, the effect of phosphorylated p38δ (p-p38δ) MAPK expression is also considered. The work goes onto describe the effect(s) of p38δ MAPK status on the chemosensitivity of OESCC to conventional cisplatin and 5-fluorouracil (CF) versus the effectiveness of doxorubicin, cisplatin and 5-fluorouracil (ACF). ACF treatment of p38δ MAPK-negative OESCC results in decreased proliferation, migration and recovery, and increased apoptosis when compared with CF treatment. This thesis examines the potential mechanisms by which p38δ MAPK expression is lost in OESCC and identifies epigenetic regulation as the probable cause of differential p38δ MAPK expression. Also analysed is the role p38δ MAPK and p-p38δ MAPK play in the cell cycle. In summary, this research identifies p38δ MAPK as a possible molecular target and a potential predictor of response to chemotherapy in OESCC patients.