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Introduction: The techniques of electron paramagnetic resonance (E.P.R.) have been used to investigate the interaction of rare earth ions with (a) their crystalline environment, by measuring their effective g tensor, and, (b) each other, by observing their pair spectra. The experiments have been carried out in host lattices which, when magnetically concentrated, show interesting ordering properties. The Apparatus: Measurements have been made at both X and K Band frequencies. The X Band spectrometer, originally constructed by Drs. A.H. Cooke and J.G. Park, was modified by the addition of a 115 Ke/s, and 50 c/s, phase sensitive detection system to give greater sensitivity. The K Band spectrometer was designed with a tuneable cylindrical H011 transmission cavity, and incorporated an improved system of cryogenics. E.P.R. of rare earth ions in diamagnetic garnets: The investigation of the properties or rare earth ions la diamagnetic garnets is of importance in connection with their profound influence on the ferrimagnetism of the iron garnets (for example see Dillon et al. 1960). The results of Ryan (1960) on the E.P.R. of rare earth lone in yttrium aluminium garnet (YAG) and yttrium gallium garnet (YGG) have shown a considerable difference of their g tensor in the two lattices, particularly for the case of Kr3+. In order to investigate further this variation, in particular the dependence on the host ion in the rare earth site, measurements have been made of the g tensors in the lutetium garnets LAG and LGG. The results, obtained mainly at X Band and 4.2°K, are given in Table 1 together with that for Dy3+ in YAG where no resonance had previously been observed. They indicate that the variation between lutetium and yttrium lattices is not so great as that between the aluminium and gallium lattices.

Recent developments in network theory have provided new avenues for studying the spread of disease within populations. However, there is a need to develop dynamic generative models of networks that can capture the dynamic nature of many real-world systems that typical models cannot account for. Models of the spread of livestock disease have frequently employed traditional network approaches, but with the availability of highly detailed animal movement datasets, there is unprecedented scope to develop generative models of livestock trade parameterised by these data and exploring the spread of disease modulated by trade. Livestock diseases incur significant financial burdens on farms and governments, and the presence of disease remains a constant issue, so developing new insights and novel control strategies is vital. Analytically tractable generative models of livestock trade, parameterised to the Scottish cattle trading system, are developed, incorporating dynamics such as time-varying trading partnerships that, to date, have not been accounted for. Expressions for the basic reproduction number R0 are obtained and manipulations to trading behaviour are shown to reduce $R_0$ while maintaining farm business requirements. Extended models, accounting for time-varying trading behaviours, are developed. Individual-based adaptation in response to changes in trading propensities is shown to mitigate the prevalence reducing potential of such changes, highlighting the need to account for behavioural responses when modelling disease spread. Typical disease control measures, such as post-movement testing and risk aversion are shown to be effective in controlling disease, but can perturb the trading system. When parameterised to the Scottish cattle trade system, the impact of these control measures on prevalence is explored. The models presented here are a first attempt at analysing trade and its effect on disease spread at a national scale for a highly heterogeneous system using a generative network modelling approach, and can be extended to other real-world systems.

Infectious diseases are a major threat to the wellbeing of humans, livestock, and wildlife. However, there is often a paucity of information for responding to these threats, and thus a need to make efficient use of existing data. This thesis shows how to use Bayesian analysis to maximise the information gained from already collected diagnostic test data. First, the commonly used latent class analysis of multiple binary diagnostic tests is ex- tended to account for vaccinated individuals, and used to estimate the effect of study size on sensitivity and specificity estimates of DIVA (”Distinguishing Infected and Vaccinated Animals”) tests for bovine Tuberculosis. It is then shown how quantitative test responses can be used as clocks indicating the time since infection to “hindcast” historic trends of disease incidence using cross-sectional data. This is used to determine whether an endemic disease is increasing or decreasing up to the time of sampling, enabling the tracking of trends in populations where routine surveillance data is not available. It is further demonstrated how to hindcast the rise and fall of disease outbreaks. Using the 2007 UK Bluetongue virus outbreak and a whooping cough outbreak as examples, it is shown that hindcasting can be used to determine whether an outbreak is increasing or past its peak at the time of sampling, thus informing potential outbreak responses. In the light of these methods for analysing quantitative test data, the challenges of generating data on test kinetics are discussed. Suggestions are given for how to improve on current methods by modelling the development of paired diagnostic tests as a dynamic host-pathogen system. This thesis demonstrates that multiple quantitative tests can be used to recover disease trends in a population. These methods have far-reaching consequences for the design and practice of disease surveillance in all contexts.

The changing abundance and distribution of parasitic helminths has been identified as one of the greatest threats to animal health in the UK under climate change. This is due to the strong influence of abiotic conditions on parasites’ free-living stages. Planning adaptation and mitigation strategies requires predictions of parasite risk, and understanding of subtle interactions between abiotic conditions and parasite transmission. This requires development and application of a range of different modelling approaches. This thesis includes the first long-term forecast showing potential impacts of climate change on a parasitic helminth in the UK. By combining a correlative parasite risk model with UKCP09 climate projections, risk maps are generated identifying which areas of the UK are predicted to experience unprecedented levels of fasciolosis (liver fluke) risk in the future. Correlative models provide warnings of future risk, indicating where resources for monitoring and control should be targeted. To address more complex issues, and foresee consequences of subtle interactions between various components of a system under climate influence, a drive towards process-based mechanistic models is required. Consequently, a spatially explicit mechanistic model is developed, for the transmission of gastro-intestinal nematodes in a controlled grazing system. This allows investigation into how climate impacts on different elements of transmission. A non-linear relationship between climate change and parasite risk is revealed, with a distinct ‘tipping point’ in outbreaks when temperature driven processes exceed critical rates. This indicates that climate change could lead to sudden and dramatic changes in parasite risk. Through combining the models developed here with improved empirical data and a broader view of livestock systems, our understanding of future risks and opportunities can be increased. This will allow improved control of these physically and economically damaging parasites, reducing deleterious impacts on production efficiency and animal welfare.

Population reduction is often used as a control strategy when managing infectious diseases in wildlife populations, however it disrupts existing social structures and increases movement of infectives due to the vacuum effect, which may lead to enhanced disease transmission. Using a generic non-spatial model, key characteristics of disease systems are identified for which such effects reduce or even reverse the disease control benefits of population reduction. If population reduction is not sufficiently severe, then enhanced transmission can lead to the perturbation effect, whereby disease levels increase or disease can be stabilised where it would otherwise be unstable. Perturbation effects are enhanced for systems with low levels of disease, e.g. low levels of endemicity or emerging disease. Mechanisms observed in real systems are examined for their role in the perturbation effect. If population reduction is non-random and fails to target infected individuals, then vertical transmission (an important mechanism in many diseases including tuberculosis and paratuberculosis) can lead to the perturbation effect if horizontal transmission is low. The perturbation effect can also arise when population reduction preferentially targets resistant individuals, or mature individuals with low susceptibility, a factor implicated in wild boar and classical swine fever. In a stochastic spatial model of demography and disease dynamics with density dependent dispersal (implicated in the spread of rabies in foxes, and tuberculosis in badgers and wild boar due to the vacuum effect), enhanced transmission is found to arise implicitly as an emergent property of the disease-system, even when population reduction is entirely random. Culling strategies are examined, and the spatial heterogeneity of distribution of culling resources and timing of culling intervals are shown to influence the perturbation effect. Whilst the perturbation effect may not always be apparent, the various effects modelled are likely present in many disease systems, mitigating the results of population reduction.

The high temperature behaviour of the fluorite oxides UO2, THO2 and Y2O3-stabilised ZrO 2 have been investigated using a variety of neutron scattering techniques. Interest has centred on the cause of the anomalously large enthalpy of UO2 at temperatures above 15OOK, an understanding of which is important in view of its use as a fission reactor fuel. High temperature techniques have been developed which enable the performance of neutron scattering at temperatures up to 3OOOK. Bragg diffraction measurements have shown that a growing fraction of anions vacate their regular sites above 21OOK in UO2 and above 23OOK in ThO2 attaining vacancy concentrations of ~2O% at 29OOK in both materials. Quasielastic scattering investigations have confirmed the occurrence of anion Frenkel disorder in UO2 at high temperatures and have shown that the disorder is of a dynamic nature. Both sets of results may be interpreted in terms of fluctuating, dynamic clusters of vacancies and inter stitials, having lifetimes of a few phonon periods. The elastic constants of UO2, which have been determined up to 293OK from measurements of the long wavelength acoustic phonons, show an increased rate of softening above 24OOK. The zone-centre optic phonons broaden rapidly above 2OOOK in UO2- The full phonon dispersion relation of ThO2, measured at 293K, resembles closely that of UO2. The results provide the first direct, unambiguous evidence of thermally-induced Frenkel disorder in UO2, which is analogous to the disorder observed in the fast-ion phase of the fluorite halides, such as CaF2. Quasielastic scattering techniques have also been used to study the defect structure of Y 2O 3 -stabilised ZrO 2 between 293K and 2OOOK. Many general features of the scattering observed at room temperature may be explained in terms of nearest neighbour relaxations around oxygen vacancies. The diffuse scattering broadens in energy above 1OOOK, signifying that these clusters of relaxed ions have a finite lifetime of ~5ps at 15OOK. The results have been interpreted in terms of a vacancy hopping model which is consistent with the enhanced conductivity observed in this temperature range.