Game theory is the mathematical study of strategic interaction and decision-making under uncertainty. It is arguably the central tool of microeconomics, and is also widely used in evolutionary biology, cybersecurity and military strategy, among other application areas. Compositionality, one of the most fundamental ideas of software science, is the principle that the behaviour of a system should be understandable in terms of the behaviour of its components. Compositionality allows large, complex systems to be designed, implemented, analysed and tested in a modular way, and allows modules to be reused in different contexts. Without this, modern software engineering would be impossible. Game models, however, are not compositional, and generally must be produced in their entirety rather than by combining standard components. As a result, game-theoretic modelling is a slow process, as small variations in the domain to be modelled can lead to large changes needed in the model. In particular this means that game-theoretic models are currently not well-suited to software implementation. This project concerns a new approach to game theory which is compositional, and therefore promises the possibility of software support for economists and other users of game theory on a scale that is currently impossible. Specifically, it should be possible to specify, simulate, solve and more generally reason about games in a way that allows the reuse of existing work. For example a typical economic system has a hierarchical structure, from agents to households to markets to economies, and it should be possible to gradually build models of each level in a way that directly uses existing models of the lower levels. The mathematical techniques and concepts underlying this approach mostly come from proof theory (part of mathematical logic) and the theory of programming languages (part of theoretical computer science). Fortunately there is no need for users to learn this sophisticated and (to them) unfamiliar theory, because it is also possible to hide the mathematics behind an intuitive graphical language known as string diagrams, which have been widely studied recently due to applications in quantum information theory, linguistics and abstract algebra. This means that game theoretic software can be graphical and intuitive, but still have a strong theoretical underpinning. The purpose of this project is to develop the mathematical theory needed for these economic applications, in a way that exploits the close relationship between theory and applications in this area, while using a worked example (based on modelling of smart energy grids) to provide a continual test of the practical benefits of compositionality. A large part of the theoretical part of this project will involve extending the theory of selection functions with various known concepts in game theory, such as repeated games, imperfect information and different solution concepts, which can be found in any standard text on game theory. This will largely consist of generalising existing theory to the new framework.

Decarbonising heating and cooling, and the wide rollout of thermal storage are some of the greatest remaining challenges to decarbonising our energy system. Heating currently accounts for 45% of UK's energy use. Approximately 25% of the UK population live above abandoned coal mines that host geothermally heated water, which can be upgraded by heat pumps and delivered to homes and businesses through heat networks. If used for thermal energy storage, mines could become a strategic low-carbon vector, storing heat generated from surplus renewable electricity, eliminating wasteful constraint payments. Consideration of minewater thermal resources and district heat in general must occur at the very initial design stages of a project so that demands are balanced with the ability of a minewater resource to supply heating, cooling and thermal storage. This PhD will investigate the potential for mapping the subsurface opportunity against the surface demands and supplies. The project will use the existing mapping of heat demands in Scotland, focussing in on specific case study areas, to develop a truly integrated surface and subsurface approach to developing mine resources. The student will build a coupled surface and subsurface GIS to examine implications for appraisal, optimisation and management of thermal resources, regulation of heat, and energy masterplanning. The student will join the HotScot Network: an academic-industry consortium aiming to transform Scotland's mining legacy from a liability into an asset: providing low cost, low carbon heating, cooling and thermal storage to homes and businesses.

This project will research and develop new methods to enable the assessment of risk arising from the bias introduced by alternative interpretational concepts and paradigms to the same geological data set. A crucial task for the petroleum industry is assessing the risk associated with estimates of hydrocarbons. This is of increasing importance for maximising recovery in basins at or past peak production, such as the North Sea. The identification of new reserves in more complex geological situations must also occur within an acceptable commercial risk envelope. Uncertainty in data measurement, collection and processing can be accounted for, at least crudely. A more fundamental difficulty, however, is correctly assigning risk due to interpretational bias. Models of sub-surface geology are created from data sets such as 3D seismic data, well bore geophysical logs, and remote sensing data. These data sample a limited volume of the subsurface and at a limited resolution in time and space, therefore the final model is highly dependent on the interpreter's conceptual framework. It is often the case that interpreters from different educational backgrounds, or with experience in different oil field settings, can come up with very different results for the same data. Models of sub-surface geology are data-under-constrained natural systems and 'diagnostic skill' and statistical uncertainty have significant social and economic impact. This problem will be examined by determining the variability of models derived from synthetic seismic data sets using a number of interpretational concepts. Synthetic seismic data will be created from a fully defined geological model created in Midland Valley's software. The data sets will then be subject to interpretation, and the concepts applied to the data without prior information will be compared to control groups, given prior information. The results will be analysed for variation from the 'real' geology, and for variability between the control and non-control groups. Quantification of the differences will be used to assess the degree of uncertainty due to interpretational bias. The work on synthetic seismic data will be complimented by a field based study, naturally limited in 3D by exposure. Mapped fault networks will be used to create multiple structural models based on different concepts for geometrical fault linkages, in an area that has natural leakage of CO2. Midland Valley's newly developed software 4DMove will be used to validate and assess the uncertainties related to the different interpretational concepts collected, both for the synthetic seismic and the field data. Analysis in 4DMove will be supported by polytomous regression analysis of information captured from participants in questionnaires to assess influences from other factors such as: experience, education and training. Compartmentalisation, and hence hydrocarbon reservoir or CO2 storage potential will be assessed in the software package TrapTester and quantified for different structural models, to highlight the critical impact of sub-surface structural frameworks on reservoir connectivity and hence potential. The current success rate of wells in the North Sea stands at between 35-40%, and with the cost per well c. 10 million dollars, increasing to c.50 million dollars in ultra deep water, erroneous well positioning is a waste of oil company resources. Any tool that reduces geological concept uncertainty will have a large impact within the industry. Similar arguments, for social and economic impact can be made for sub-surface waste disposal and CO2 storage. The projects objectives are: -to develop techniques and methodologies to assess factors influencing conceptual uncertainty -to quantify interpretational error -to quantify the impact on prospectivity of different models (using 4DMove) -to create a process to reduce the uncertainty associated with the structural model in petroleum exploration and waste storage.

Research Summary The primary objective of the research project is to develop an intimate working knowledge of the literary works and theories proposed by the renowned Swiss psychiatrist and psychoanalyst Carl Gustav Jung and then apply this deep learning to contemporary architectural understanding, with a particular focus on built and unbuilt works from the 19th and 20th centuries. This will be undertaken in conjunction with a detailed investigation of the critical influences, intentions and philosophies of influential architectural figures who have been observed to have operated within the frameworks linked to the metaphysical ideas of Architectural Phenomenology and self-embodiment. Research Aim / Hypothesis The research ambition is to explore how the study, exploration and subsequent application of architectural understanding deeply rooted within a Liberal Arts based paradigm can yield prodigious benefits when unwaveringly applied to the education and practice of architecture as a discreet engineering discipline. The central motivation to research the themes detailed is a profoundly held belief that a firmly established appreciation of the Humanities and Social Sciences is critical to the development of deeper knowledge associated with the conception of architecture(s). The comprehensive examination of the theories of Carl Gustav Jung offers a platform to cogently investigate the application of psychological and metaphysical perception within the context of contemporary built and imagined realities, through the lenses of the extraverted and introverted forces that fuel the human desire to continually reshape and redefine the physical dominion. Knowledge Exchange and Transfer The research project will seek to address current identifiable knowledge gaps linking architectural practice and education within the context of theoretical methodologies popularised by Carl Jung in relation to archetypal images. A fundamental component related to the successful evidencing and recording of a discernible KE will necessitate the delineation and delivery of a sequence of theoretically concentrated workshops aimed at incorporating the research findings within the framework of professional architectural practice. A critical aspect of the dissertation will be to study the effects of setting(s) on the architectural design procedure. Preparatory exploration has revealed the dynamic links that exist between the generation of real world and imagined space and the social and environmental experienced by the designer. The study will analyse the essential characteristics of a Liberal Arts education delivered within an architectural curriculum/setting and how this learning can be transformed into a tangible shift in the manner in which the domain of the built environment is both taught and understood. Public Engagement and Impact(s) The research findings resulting from the investigation of the detectable gaps in knowledge will be disseminated principally through the delivery of a structured series of pedagogical workshops involving both professionals and students. A pivotal characteristic of the research proposal will be to discourse the requirement for a far-reaching understanding between the vital roles played by Architecture and Psychology in shaping the discernments and cultural engagements that populate both realities and un-realities. The central impact of the Postgraduate Research degree will be to enrich relationships connecting the spheres of Architecture, the Liberal Arts and the Social Sciences by adopting and testing an assortment of both traditional and innovative research methodologies. A crucial component associated with the completion of the Postgraduate Research degree is the desire to imbed Jung's philosophical frameworks within the design of real and imagined worlds to the benefit of not only the academic community but a wider diversity of societal contexts, via the adoption of a multidisciplinary approach.

Crystallisation is widely used for purification of commodity and speciality chemicals and pharmaceuticals and for making advanced materials for catalysis, separations and sensing applications. One of main challenges in developing robust and efficient crystallisation processes is to control nucleation of desired crystalline phases as many systems tend to crystallise in multiple structural forms of the same composition called polymorphs. For example, polymorphism is extremely important in the development of pharmaceutical products as polymorphs have different properties, such as solubility, dissolution rate and thus bioavailability in resulting dosage forms. Control of polymorph nucleation is a particular challenge for the development of continuous crystallisation processes when nucleation in bulk solution is not forthcoming or undesirable polymorphs tend to nucleate spontaneously. Crystallisation of competing polymorhps is strongly dependent on kinetic effects and is highly pathway dependent. A variety of heuristic approaches are commonly used to control the kinetic pathway, such as solvent effects, quenching and heterogeneous nucleation approaches through various interfaces deliberately introduced into supersaturated solutions. Interfaces that are designed to induce nucleation are commonly called nucleants and numerous strategies have been proposed for their design under three broad areas: epitaxy, surface chemistry and surface topology. While epitaxy matching is suitable for some specific systems, its general use is limited. Using surface chemistry is typically based on trial and error and there is a lack of general underlying principles. However, previous approaches tend to overlook the role of electrostatic effects at crystal/nucleant interfaces. This aim of this project is to develop a new approach to designing heterogeneous nucleants based on tunable interfacial electrostatics using surfaces functionalised with monolayers of molecules with a range of dipole moments and functional end groups. This will allow us to independently vary both surface chemistry and surface electrostatics in order to direct formation of desired polymorphs. In particular, the surface electrostatics (adjustable through monolayer dipole moment) will be crucial in controlling solid forms with unit cells with a net dipole moment. There are many such systems, ranging from the smallest amino acid (glycine) to pharmaceuticals to functional polymers. This project will take a combined experimental and simulation approach to understand how to manipulate surface chemistry and surface electrostatics in tandem to direct formation of a particular polymorph. In the experimental part, we will systematically investigate the effect of tunable monolayers on heterogeneous nucleation of representative organic compounds relevant to the pharmaceutical and fine chemical industries in order to explore the design space of novel heterogeneous nucleants. Characterisation of functionalised surfaces and crystals grown on them will be performed with a suite of advanced characterisation techniques available in the CMAC National Facility housed in TIC, including AFM, SEM, Raman microscopy and GI-SAXS. In the simulation part, we will gain a molecular level insight using a combination of quantum mechanical calculations and classical molecular dynamics simulations, which will enable calculation of relative energetics of competing polymorphs on functionalised surfaces spanning the range of surface chemistry and surface electrostatics corresponding to systems investigated experimentally.