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Within the dark central umbra of sunspots we can observe localised bright convective features, called umbral dots. It is believed that sunspots, and therefore umbral dots, are formed by the interactions between convection and strong magnetic fields. Numerically, localised convective features have been observed in two-dimensional, and highly truncated three-dimensional, simulations of convection in the presence of an imposed magnetic field. The focus of this dissertation is to consider convection in the presence of a strong magnetic field, as present in the central umbra of a sunspot, to gain an understanding of the formation and structure of localised convective patterns. We begin with a brief survey of solar observational results and previous results from mathematical modelling of the system. We then reconsider the two-dimensional problem through the formation of discrete models that allow very large systems to be considered. Results from the discrete models agree well with results from the full system. In Chapter 3, the numerical methods used to model magnetoconvection are described and full details of the mathematical problem are given. A large study of compressible magnetoconvection in three dimensions is then completed and the results presented. To allow large domains to be investigated a Swift-Hohenberg type model for Boussinesq magnetoconvection is developed in Chapter 5. the thermal conductivity is allowed to vary with depth. This vertical variation breaks the up-down symmetry of Boussinesq convection and allows hexagonal patterns to form. It is found that while localised convective regions can be found in a reasonably generic way for the two-dimensional problem, they typically appear only as transients in the three-dimensional problem. Instead we find relatively weak convection patterns whose amplitude varies on a long length-scale. This is not inconsistent with the solar observations: umbral dots are observed to have a typical lifetime of fifteen minutes to two hours before they decay.

This thesis demonstrates that Clare’s faith is a highly personal and complex negotiation between the reality of the ‘religion’ confronting him in the world, a remarkable knowledge of literature and thought, and a reasoning and intelligent appropriation of influence. It begins by establishing that Clare’s love of certain aspects of Anglican orthodoxy was entirely compatible with his experimentation with alternative denominations. Its survey of ‘religion’ includes the Church of England and its adherents alongside other religious groups, insisting on an understanding of the Christian faith as an implicit presence (although one which was highly politicised, far from unchallenged, and certainly perceived as declining) within the quotidian life of Clare’s society. The thesis examines the importance of ‘alternative beliefs’ as phenomena coexisting with organised religion, assessing the extent of their coincidence, and thus offering a reassessment of what orthodoxy might mean to Clare’s village community. It goes on to acknowledge Clare’s intelligence and idiosyncratic learning (particularly his Bible reading), examining his attitude to ‘science’ and to such concepts as ‘Reason’, ‘Deism’, and ‘Revealed’ and ‘Natural’ religion. The second part of the thesis asserts that Clare’s religious conviction is reinforced by intense subjective spiritual experience. Having explored some ramifications of this, it goes on to reconsider Clare’s thematic treatment of ‘Eden’ and ‘eternity’, Concluding that, within a climate of religious enthusiasm, Clare interprets a sublime rapture repeatedly experienced in the presence of nature as the felt presence of the deity, it suggests that, even when intellectually he doubts his own faith, he is unable fully to relinquish a particular ‘knowledge’ of divinity. The thesis then analyses Clare’s representations of ‘evil’, demanding to know how faith in an omnipotent, benevolent deity is reconciled with a progressive and devastating sense of the predatory cruelty inherent in the natural world (this sense collides with Clare’s fervent love for his environment, coalescing with events emblematic of essentially theological ‘Falls’ which Clare believed, were perpetuated throughout his life). The thesis concludes by attempting to trace the elements of Clare’s creed, and by developing a new understanding of what his conception of ‘God’ might be.