Originating from a disenfranchisement with the contemporary definition and realisation of Westernised architecture as a commodity and product, this thesis seeks to explore alternative examples of positive socio-spatial practice and agency. These alternative spatial practices and methodologies are drawn from participatory and grass-roots development agency in informal settlements and contexts of economic absence, most notably in the global South. This thesis explores whether such examples can be interpreted as practical realisations of key theoretical advocacies for positive social space that have emerged in the context of post-Second World-War capitalism. The principal methodological framework utilises two differing trajectories of spatial discourse. Firstly, Henri Lefebvre and Doreen Massey as formative protagonists of Western spatial critique, and secondly, John F. C. Turner and Nabeel Hamdi as key advocates of participatory development practice in informal settlements. These two research trajectories are notably separated by geographical, economic and political differentiations, as well as conventional disciplinary boundaries. However by undertaking a close textual reading of these discourses this thesis critically re-contextualises the socio-spatial methodologies of participatory development practice, observing multiple theoretical convergences and provocative commonalities. This research proposes that by critically comparing these previously unconnected disciplinary trajectories certain similarities, resonances and equivalences become apparent. These resonances reveal comparable critiques of choice, value, and identity which transcend the gap between such differing theoretical and practical engagements with space. Subsequently, these thematic resonances allow this research to critically engage with further appropriate surrounding discourses, including Marxist theory, orientalism, post- structural pluralism, development anthropology, post-colonial theory and subaltern theory. 5 In summary, this thesis explores aspects of Henri Lefebvre's and Doreen Massey's urban and spatial theory through a close textual reading of key texts from their respective discourses. This methodology provides a layered analysis of post-Marxist urban space, and an exploration of an explicit connection between Lefebvre and Massey in terms of the social production and multiplicity of space. Subsequently, this examination provides a theoretical framework from which to reinterpret and revalue the approaches to participatory development practice found in the writings and projects of John Turner and Nabeel Hamdi. The resulting comparative framework generates interconnected thematic trajectories of enquiry that facilitate the re-reading and critical reflection of Turner and Hamdi's development practices. Thus, selected Western spatial discourse acts as a critical lens through which to re-value the social, political and economical achievements of participatory development. Reciprocally, development practice methodologies are recognised as invaluable and provocative realisations of the socio-spatial qualities that Western spatial discourse has long advocated for, and yet have remained predominantly unrealised in the global North.

This thesis deals with cohomologies on the symplectic quotient of a Frölicher space which is locally diffeomorphic to a Euclidean Frölicher subspace of Rn of constant dimension equal to n. The symplectic reduction under consideration in this thesis is an extension of the Marsden-Weinstein quotient (also called, the reduced space) well-known from the finite-dimensional smooth manifold case. That is, starting with a proper and free action of a Frölicher-Lie-group on a locally Euclidean Frölicher space of finite constant dimension, we study the smooth structure and the topology induced on a small subspace of the orbit space. It is on this topological space that we will construct selected cohomologies such as : sheaf cohomology, Alexander-Spanier cohomology, singular cohomology, ~Cech cohomology and de Rham cohomology. Some natural questions that will be investigated are for instance: the impact of the symplectic structure on these di erent cohomologies; the cohomology that will give a good description of the topology on the objects of category of Frölicher spaces; the extension of the de Rham cohomology theorem in order to establish an isomorphism between the five cohomologies. Beside the algebraic, topological and geometric study of these new objects, the thesis contains a modern formalism of Hamiltonian mechanics on the reduced space under symplectic and Poisson structures. / Mathematical Sciences / D. Phil. (Mathematics)

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

<p dir="ltr">Additive manufacturing (AM) of gun propellants is an emerging and promising field which addresses the limitations of conventional manufacturing techniques. Overall, this thesis is a body of work which serves to bridge the gap between fundamental research and application of additively manufactured gun propellants.</p>