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.

The utility of survey and administrative data to generate information for research and outcomes-based oral health services development

The aim of this research, which focused on the Irish adult population, was to generate information for policymakers by applying statistical analyses and current technologies to oral health administrative and survey databases. Objectives included identifying socio-demographic influences on oral health and utilisation of dental services, comparing epidemiologically-estimated dental treatment need with treatment provided, and investigating the potential of a dental administrative database to provide information on utilisation of services and the volume and types of treatment provided over time. Information was extracted from the claims databases for the Dental Treatment Benefit Scheme (DTBS) for employed adults and the Dental Treatment Services Scheme (DTSS) for less-well-off adults, the National Surveys of Adult Oral Health, and the 2007 Survey of Lifestyle Attitudes and Nutrition in Ireland. Factors associated with utilisation and retention of natural teeth were analysed using count data models and logistic regression. The chi-square test and the student’s t-test were used to compare epidemiologically-estimated need in a representative sample of adults with treatment provided. Differences were found in dental care utilisation and tooth retention by Socio-Economic Status. An analysis of the five-year utilisation behaviour of a 2003 cohort of DTBS dental attendees revealed that age and being female were positively associated with visiting annually and number of treatments. Number of adults using the DTBS increased, and mean number of treatments per patient decreased, between 1997 and 2008. As a percentage of overall treatments, restorations, dentures, and extractions decreased, while prophylaxis increased. Differences were found between epidemiologically-estimated treatment need and treatment provided for those using the DTBS and DTSS. This research confirms the utility of survey and administrative data to generate knowledge for policymakers. Public administrative databases have not been designed for research purposes, but they have the potential to provide a wealth of knowledge on treatments provided and utilisation patterns.

The design of curved optical waveguides : analytical and numerical analysis

A model for understanding the formation and propagation of modes in curved optical waveguides is developed. A numerical method for the calculation of curved waveguide mode profiles and propagation constants in two dimensional waveguides is developed, implemented and tested. A numerical method for the analysis of propagation of modes in three dimensional curved optical waveguides is developed, implemented and tested. A technique for the design of curved waveguides with reduced transition loss is presented. A scheme for drawing these new waveguides and ensuring that they have constant width is also provided. Claims about the waveguide design technique are substantiated through numerical simulations.