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.

Generation and characterisation of biologically active milk-derived protein and peptide fractions

In recent years, extensive research has been carried out on the health benefits of milk proteins and peptides. Biologically active peptides are defined as specific protein fragments which have a positive impact on the physiological functions of the body; such peptides are produced naturally in vivo, but can also be generated by physical and/or chemical processes, enzymatic hydrolysis and/or microbial fermentation. The aims of this thesis were to investigate not only the traditional methods used for the generation of bioactive peptides, but also novel processes such as heat treatment, and the role of indigenous milk proteases, e.g., in mastitic milk, in the production of such peptides. In addition, colostrum was characterised as a source of bioactive proteins and peptides. Firstly, a comprehensive study was carried out on the composition and physical properties of colostrum throughout the early-lactation period. Marked differences in the physico-chemical properties of colostrum compared with milk were observed. Various fractions of colostrum were also tested for their effect on the secretion of pro- and anti-inflammatory cytokines from a macrophage cell line and bone marrow dendritic cells, as well as insulin secretion from a pancreatic beta cell line. A significant reduction in the secretion of the pro-inflammatory cytokines, TNF-α, IL-6, IL-1β and IL-12, a significant increase in the secretion of the anti-inflammatory cytokine, IL-10, as well as a significant increase in insulin secretion were observed for various colostrum fractions. Another study examined the early proteomic changes in the milk of 8 cows in response to infusion with the endotoxin lipopolysaccharide (LPS) at quarter level in a model mastitic system; marked differences in the protein and peptide profile of milk from LPS challenged cows were observed, and a pH 4.6-soluble fraction of this milk was found to cause a substantial induction in the secretion of IL-10 from a murine macrophage cell line. Heat-induced hydrolysis of sodium caseinate was investigated from the dual viewpoints of protein breakdown and peptide formation, and, a peptide fraction produced in this manner was found to cause a significant increase in the secretion of the anti-inflammatory cytokine, IL-10, from a murine macrophage cell line. The effects of sodium caseinate hydrolysed by chymosin on the gut-derived satiety hormone glucagon-like peptide-1 (GLP-1) were investigated; the resulting casein-derived peptides displayed good in vitro and in vivo secretion of GLP-1. Overall, the studies described in this thesis expand on current knowledge and provide good evidence for the use of novel methods for the isolation, generation and characterisation of bioactive proteins and/or peptides.

Studies on quinoa (Chenopodium quinoa) for novel food and beverage applications

Quinoa (Chenopodium quinoa) is a seed crop native to the Andes, that can be used in a variety of food product in a similar manner to cereals. Unlike most plants, quinoa contains protein with a balanced amino acid profile. This makes it an interesting raw material for e.g. dairy product substitutes, a growing market in Europe and U.S. Quinoa can however have unpleasant off-flavours when processed into formulated products. One means of improving the palatability is seed germination. Also, the increased activities of hydrolytic enzymes can have a beneficial influence in food processing. In this thesis, the germination pattern of quinoa was studied, and the influence of quinoa malt was evaluated in a model product. Additionally, to explore its potential for dairy-type products, quinoa protein was isolated from an embryo-enriched milling fraction of non-germinated quinoa and tested for functional and gelation properties. Quinoa seeds imbibed water very rapidly, and most seeds showed radicle protrusion after 8-9 h. The α-amylase activity was very low, and started to increase only after 24 hours of germination in the starchy perisperm. Proteolytic activity was very high in dry ungerminated seeds, and increased slightly over 24 h. A significant fraction of this activity was located in the micropylar endosperm. The incorporation of germinated quinoa in gluten-free bread had no significant effect on the baking properties due to low α-amylase activity. Upon acidification with glucono-δ-lactone, quinoa milk formed a structured gel. The gelation behaviour was further studied using a quinoa protein isolate (QPI) extracted from an embryoenriched milling fraction. QPI required a heat-denaturation step to form gel structures. The heating pH influenced the properties drastically: heating at pH 10.5 led to a dramatic increase in solubility, emulsifying properties, and a formation of a fine-structured gel with a high storage modulus (G') when acidified. Heating at pH 8.5 varied very little from the unheated protein in terms of functional properties, and only formed a randomly aggregated coagulum with a low G'. Further study of changes over the course of heating showed that the mechanism of heat-denaturation and aggregation indeed varied largely depending on pH. The large difference in gelation behaviour may be related to the nature of aggregates formed during heating. To conclude, germination for increased enzyme activities may not be feasible, but the structure-forming properties of quinoa protein could possibly be exploited in dairy-type products.