Applications of finite element computer modelling and thermal infrared remote sensing to the study of geothermal anomalies

Buried heat sources can be investigated by examining thermal infrared images and comparing these with the results of theoretical models which predict the thermal anomaly a given heat source may generate. Key factors influencing surface temperature include the geometry and temperature of the heat source, the surface meteorological environment, and the thermal conductivity and anisotropy of the rock. In general, a geothermal heat flux of greater than 2% of solar insolation is required to produce a detectable thermal anomaly in a thermal infrared image. A heat source of, for example, 2-300K greater than the average surface temperature must be a t depth shallower than 50m for the detection of the anomaly in a thermal infrared image, for typical terrestrial conditions. Atmospheric factors are of critical importance. While the mean atmospheric temperature has little significance, the convection is a dominant factor, and can act to swamp the thermal signature entirely. Given a steady state heat source that produces a detectable thermal anomaly, it is possible to loosely constrain the physical properties of the heat source and surrounding rock, using the surface thermal anomaly as a basis. The success of this technique is highly dependent on the degree to which the physical properties of the host rock are known. Important parameters include the surface thermal properties and thermal conductivity of the rock. Modelling of transient thermal situations was carried out, to assess the effect of time dependant thermal fluxes. One-dimensional finite element models can be readily and accurately applied to the investigation of diurnal heat flow, as with thermal inertia models. Diurnal thermal models of environments on Earth, the Moon and Mars were carried out using finite elements and found to be consistent with published measurements. The heat flow from an injection of hot lava into a near surface lava tube was considered. While this approach was useful for study, and long term monitoring in inhospitable areas, it was found to have little hazard warning utility, as the time taken for the thermal energy to propagate to the surface in dry rock (several months) in very long. The resolution of the thermal infrared imaging system is an important factor. Presently available satellite based systems such as Landsat (resolution of 120m) are inadequate for detailed study of geothermal anomalies. Airborne systems, such as TIMS (variable resolution of 3-6m) are much more useful for discriminating small buried heat sources. Planned improvements in the resolution of satellite based systems will broaden the potential for application of the techniques developed in this thesis. It is important to note, however, that adequate spatial resolution is a necessary but not sufficient condition for successful application of these techniques.

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.

Development of low-cost sensing and separation devices based on macro, micro and nano technology for health applications

The work presented in this thesis described the development of low-cost sensing and separation devices with electrochemical detections for health applications. This research employs macro, micro and nano technology. The first sensing device developed was a tonerbased micro-device. The initial development of microfluidic devices was based on glass or quartz devices that are often expensive to fabricate; however, the introduction of new types of materials, such as plastics, offered a new way for fast prototyping and the development of disposable devices. One such microfluidic device is based on the lamination of laser-printed polyester films using a computer, printer and laminator. The resulting toner-based microchips demonstrated a potential viability for chemical assays, coupled with several detection methods, particularly Chip-Electrophoresis-Chemiluminescence (CE-CL) detection which has never been reported in the literature. Following on from the toner-based microchip, a three-electrode micro-configuration was developed on acetate substrate. This is the first time that a micro-electrode configuration made from gold; silver and platinum have been fabricated onto acetate by means of patterning and deposition techniques using the central fabrication facilities in Tyndall National Institute. These electrodes have been designed to facilitate the integration of a 3- electrode configuration as part of the fabrication process. Since the electrodes are on acetate the dicing step can automatically be eliminated. The stability of these sensors has been investigated using electrochemical techniques with excellent outcomes. Following on from the generalised testing of the electrodes these sensors were then coupled with capillary electrophoresis. The final sensing devices were on a macro scale and involved the modifications of screenprinted electrodes. Screen-printed electrodes (SPE) are generally seen to be far less sensitive than the more expensive electrodes including the gold, boron-doped diamond and glassy carbon electrodes. To enhance the sensitivity of these electrodes they were treated with metal nano-particles, gold and palladium. Following on from this, another modification was introduced. The carbonaceous material carbon monolith was drop-cast onto the SPE and then the metal nano-particles were electrodeposited onto the monolith material

Transitions: From novice participation to expertise, pre-school 'matters' in an Irish pre-school community

This in depth, qualitative, participant observer study tracks children's transition experiences from novice to experienced membership of their pre-school community. It also considers adult roles in mediating this process in the context of the recent introduction of a universal free-pre-school year for children growing up in Ireland. Participation and the space to negotiate a participatory identity is understood in this study as a key element of positive experiences of early years transitions, within pre-school and beyond. The underlying theoretical framework is socio-cultural. This approach shifts from a scientific positivist view of thinking and learning as an individual inside the head process and asserts the historical, social, cultural as well as the situated context of learning and meaning making All participants, including myself as researcher, are recognised, explored and valued as embedded in the cultural context studied. In a sense, this approach tilts the worlds being observed through participation in them and reflects them in new light. The aim is to interpret and reflect the multiple realities constructed in this context rather than seek a truth out there waiting to be found. Special efforts are made to be invited in to and acknowledge children's expertise in the cultural worlds they negotiate with peers and adults in pre-school. The aim is to better understand what children may find motivating, interesting or problematic as they interpret reproduce and transform meaning within their play and learning worlds. My aim is for an honest rendering of the voices of stakeholders in pre-school communities from teachers, parents, and policy makers to children themselves. It makes visible constraints; potentials and possibilities within everyday Irish pre-school practices in the situated context studied as well as the broader societal, legislative and macro policy influences it reflects. Casting light on the taken for granted opens the possibility of adaptation or transformation. Transition itself can act as a tool to meet the changing needs of children on their developmental pathways across the life cycle