For systems that are in equilibrium, fluctuations can be understood through interactions with external heat reservoirs. For this reason these fluctuations are known as thermal noise, and they usually become vanishingly small in the thermodynamic limit. However, many systems comprising interacting constituents studied by physicists in recent years are both far from equilibrium, and sufficiently small so that they must be considered finite. The finite number of constituents gives rise to an inherent demographic noise in the system, a source of fluctuations that is always present in the stochastic dynamics. This thesis investigates the role of stochastic fluctuations in the macroscopically observable dynamical behaviour of non-equilibrium, finite systems. To facilitate such a study, we construct microscopic models using an individual based modelling approach, allowing the explicit form of the demographic noise to be identified. In many physical systems and theoretical models, absorbing states are a defining feature. Once a system enters one, it cannot leave. We study the dynamics of a system with two symmetric absorbing states, finding that the amplitude of the multiplicative noise can induce a transition between two universal modes of domain coarsening as the system evolves to one of the absorbing states. In biological and ecological systems, cycles are a ubiquitously observed phenomenon, but are di cult to predict analytically from stochastic models. We examine a potential mechanism for cycling behaviour due to the flow of probability currents, induced by the athermal nature of the demographic noise, in a single patch population comprising two competing species. We find that such a current by itself cannot generate macroscopic cycles, but when combined with deterministic dynamics which constrain the system to a closed circular manifold, gives rise to global quasicycles in the population densities. Finally, we examine a spatially extended system comprising many such patch populations, exploring the emergence of synchronisation between the different cycles. By a stability analysis of the global synchronised state, we probe the relationship between the synchronicity of the metapopulation and the magnitude of the coupling between patches due to species migration. In all cases, we conclude that the nature of the demographic noise can play a pivotal role in the macroscopically observed dynamical behaviour of the system.

Implicit large eddy simulation (ILES) has been shown, in the literature, to have some success for three-dimensional flow (e.g. see [Grinstein, F.F., Margolin, L.G. and Rider, W. Implicit Large Eddy Simulation. Cambridge, 2007]), but it has not previously been examined for two-dimensional flow. This thesis investigates whether ILES can be applied successfully to two-dimensional flow. Modified equation analysis is used to demonstrate the similarities between the truncation errors of certain numerical schemes and the subgrid terms of the barotropic vorticity equation (BVE). This presents a theoretical motivation for the numerical testing. Burgers equation is first used as a model problem to develop the ideas and methodology. Numerical schemes that are known to model Burgers equation well (shock capturing schemes) are shown to be implicitly capturing the subgrid terms of the one-dimensional inviscid Burgers equation through their truncation errors. Numerical tests are performed on three equation sets (BVE, Euler equations and the quasi-geostrophic potential vorticity equation) to assess the application of ILES to two-dimensional flow. The results for each of these equation sets show that the schemes considered for ILES are able to capture some of the subgrid terms through their truncation errors. In terms of accuracy, the ILES schemes are comparable (or outperform) schemes with simple explicit subgrid models when comparing vorticity solutions with a high resolution reference vorticity solution. The results suggest that conservation of vorticity is important to the successful application of ILES to two-dimensional flow, whereas conservation of momentum is not. The schemes considered for ILES are able to successfully model the downscale enstrophy transfer, but none of the schemes considered for ILES (or the schemes with simple subgrid models) can model the correct upscale energy transfer from the subgrid to the resolved scales. Energy backscatter models are considered and are used with the ILES schemes. It is shown that it is possible to create an energy conserving and enstrophy dissipating scheme, composed of an ILES scheme and a backscatter model, that improves the accuracy of the vorticity solution (when compared with the corresponding ILES scheme without backscatter).

Computer programs have been written which allow morphological calculations based on a knowledge of internal crystal structure to he carried out. Details of the programs are presented along with the guidelines developed for their use. The programs were used to compare and contrast the current methods employed for relating crystal shape to structure and to confront specific problems in that field. Calculations on a range of compounds show that the morphologies derived from the simple Donnay-Harker (DHI) model give almost as good a fit to the observed form as the more sophisticated attachment energy (AE) calculations except when strong bonding directions were present. In the first study of its type all the methods currently favoured in the literature including the Ising and PBC approaches as well as DH and AE models were applied to benzophenone. All the models gave the same theoretical morphology. One problem remaining in the field of relating crystal structure and morphology is that of polar morphology. None of the current methods can account for a polar morphology. Surface, bulk, isolated molecule charge distributions were used in a modification of the classical attachment energy model to account for urea exhibiting a polar morphology when growth from the vapour phase. For the disruptive type of tailor made additives an improvement in the current methodology is proposed with the calculation of an additional parameter. This additional parameter accounts for the morphology with an additive present and gives good agreement with the test case of benzamide crystals grown with benzoic acid as an additive. The additive approach also allowed the effects of toluene solvent on the crystal habit of benzophenone to be considered By treating toluene as a tailor made additive it was possible from calculations to identify the likely sites of toluene incorporation and the subsequent effect on crystal growth. The results from the calculation were consistent with experiment.

The thesis focuses on in two vital and interrelated aspects of modelling design support systems, they are: how innovative solutions may arise, and the knowledge-base's extension and maintenance. The dilemma 'reproduction versus creativity' is identified as one of the main deadlocks that the design methods' debate, research in Computer Aided Architectural Design, CAAD, and Artificial Intelligence, AI, have faced in the last thirty years. A hybrid approach is then proposed as a means of overcoming these difficulties, where a rudimentary evolving design support environment is developed. It draws inspiration from three areas of Artificial Intelligence: knowledge-base systems, connectionist models, and case-based reasoning (CBR). However, it differs fundamentally from conventional knowledge-base systems, connectionist models and CBR tools, in its architecture, although strongly inspired by these underlying theories. The main benefits and contributions of this hybrid system are an incremental selfextending feature able to minimise substantially the dependency on knowledge engineer intervention, and an interactive support to innovation by augmenting the designer's creativity.

This project investigates the seismic response to facies variation by modelling facies variation itself, using two different modelling techniques, and then by modelling the seismic response to this variation. This study looks at a new set of attributes, examines their potential both as standard seismic attributes (a qualitative approach), and uses geostatistical analysis to further develop the ability of these attributes to differentiate the seismic response to facies variation. Sedpak, a basin modelling package was used to try to create facies models as a basis for further geophysical modelling. A case study using data from the Beryl area was unsuccessful at trying to create facies models due largely to the limited amount of input data and the scale of the models being attempted. Although an impressive package, Sedpak is most useful when modelling at a basin scale. In order to study the seismic response of sedimentary facies variation simple, deterministic models were set up using the geophysical modelling package, Gxii. An established methodology for analysing seismic data is the study of seismic attributes. The study considers some autocorrelation and power spectrum-derived functions previously described in the literature (Sinvhal and Sinvhal, 1992), and treats them as seismic attributes. Initial analysis of these new attributes in 2D showed them to be successful at detecting the presence of channels within seismic data. On the basis of this, a multivariate study was carried out. Results of this analysis show these attributes to have the potential to detect the presence of channels within seismic data. A suite of computer programs were developed to calculate 3D volumes of the new attributes, and to produce colour sections through the attribute volumes. The volumes were granted using a moving time window and calculating attribute values down through the data volume. Evaluation of the colour sections themselves to illustrate facies changes was disappointing. It is apparent that more work is needed to evaluate the window length over which the attributes are calculated.

This thesis investigates the relationship between discrete event and system dynamics simulation modelling. Each modelling technique has its own strengths and limitations. The choice of using one particular modelling technique often depends on the preference and the knowledge of the modeller rather than on the nature of the problem. The basis of this research has been to address the problem from a different perspective. This has been to look at the nature of the problem first, and then determine the most appropriate modelling technique to apply. The basic method adopted was to compare, contrast and experiment with these two modelling techniques in order to determine a number of common and unrelated concepts between them. This investigation discovered that a system dynamics flow diagram could be used to represent an activity cycle diagram of a discrete event model. The converted flow diagram can provide a different viewpoint from the discrete event model due to the feedback characteristic of system dynamics. This research went on to develop a set of guidelines to convert an activity cycle diagram into a system dynamics flow diagram. Experimentation with many examples demonstrates that these conversion guidelines provide a consistent and systematic method for obtaining a system dynamics flow diagram. The final stage of this research was to develop a prototype computer system (SMCP) to demonstrate these guidelines. SMCP consists of two modules, the ACD module which allows the user to specify a discrete event model through textual descriptions, and the SD module which allows the user to build a system dynamics model by drawing symbols and using text inputs. In addition, SMCP allows users to convert an ACD to a system dynamics flow diagram quickly and easy, and also demonstrates the concept of data sharing.

Certain types of long, axially compressed structures have the potential to buckle locally in one or more regions rather than uniformly along their length. Here, the potential for localized buckle patterns in an elastic layer embedded in a visco-elastic medium is investigated using a strut-on-foundation model. Applications of this model include the growth of geological folds and other time-dependent instability processes. The model consists of an elastic strut of uniform flexural stiffness supported by a Winkler-type foundation made up of discrete Maxwell elements. Mathematically, this model corresponds to a nonlinear partial differential equation which is fourth-order in space and first-order in time. The nature of the buckling process is characterized by an initial period of elastic deformation followed by an evolutionary phase in which both elasticity and viscosity have a role to play. Two different formulations are studied: the first combines linear strut theory with a nonlinear foundation and is valid for small, but finite, deflections; the other incorporates the exact expression for curvature of the strut resulting in geometrical nonlinearities and is capable of modelling large deflections. The evolution of non-periodic buckle patterns in each system is examined under the constraint of controlled end displacement. Two independent methods are used to approximate the solution of the governing equations. Modal solutions, based on the method of weighted residuals, complement accurate numerical solutions obtained with a boundary-value solver. In either case, the results suggest that for the perfect system, localized solutions follow naturally from the inclusion of nonlinear elasticity with softening characteristics. Emphasis throughout is on the qualitative features displayed by the phenomenon of localization rather than specific applications. Nevertheless, the ideas and results are a step towards accounting for the rich variety of deformed shapes exhibited by nature.

Nitride fuels have always been considered a good candidate for GENIV reactors, as well as space reactors, due to their high fissile density, highthermal conductivity and high melting point. In these concepts, not beingcompatible with water is not a significant problem. However, in recent years,nitride fuels started to raise an interest for application in thermal reactors,as accident tolerant or high performance fuels. However, oxide fuels havebenefited from decades of intensive research, and thousands of reactor-years.As such, a large effort has to be made on qualifying the fuel and developingtools to help assess their performances.In this thesis, the modeling side of this task is chosen. The effort istwo-fold: determining fundamental properties using atomistic models andputting together all the properties to predict the performances under irradi-ation using a fuel performance code. The first part is done combining manyframeworks. The density functional theory is the basis to compute the elec-tronic structure of the materials, to which a Hubbard correction is added tohandle the strong correlation effects. Negative side effects of the Hubbardcorrection are tackled using the so-called occupation matrix control method.This combined framework is first tested, and then used to find electronic andmechanic properties of the bulk material as well as the thermomechanicalbehavior of foreign atoms. Then, another method, the self-consistent meanfield (SCMF) one, is used to reach the dynamics properties of these foreignatoms. In the SCMF theory, the data that were obtained performing the abinitio simulations are treated to provide diffusion and kinetic flux couplingproperties.In the second step of the work, the fuel performance code TRANSURA-NUS is used to model complete fuel pins. An athermal fission gas releasemodel based on the open porosity is developed and tested on oxide fuels.A model for nitride fuels is introduced, and some correlations are bench-marked. Major issues remaining are pointed out and recommendations asto how to solve them are made. / <p>QC 20170227</p>

An efficient and flexible modelling and simulation toolset for solving spatially-resolved models of photovoltaic (PV) devices is developed, and its application towards a quantitative description of localised electrical behaviour is given. A method for the extraction of local electrical device parameters is developed as a complementary approach to the conventional characterisation techniques based on lumped models to meet the emerging demands of quantitative spatially-resolved characterisation in the PV community. It allows better understanding of the effects of inhomogeneities on performance of PV devices. The simulation tool is named PV-Oriented Nodal Analysis (PVONA). This is achieved by integrating a specifically designed sparse data structure and a graphics processing unit (GPU)-based parallel conjugate gradient algorithm into a PV-oriented numerical solver. It allows more efficient high-resolution spatially-resolved modelling and simulations of PV devices than conventional approaches based on SPICE (Simulation Program with Integrated Circuit Emphasis) tools in terms of computation time and memory usage. In tests, mega-sub-cell level test cases failed in the latest LTSpice version (v4.22) and a PSpice version (v16.6) on desktop PCs with mainstream hardware due to a memory shortage. PVONA efficiently managed to solve the models. Moreover, it required up to only 5% of the time comparing the two SPICE counterparts. This allows the investigation of inhomogeneities and fault mechanisms in PV devices with high resolution on common computing platforms. The PVONA-based spatially-resolved modelling and simulation is used in various purposes. As an example, it is utilised to evaluate the impacts of nonuniform illumination profiles in a concentrator PV unit. A joint optical and electrical modelling framework is presented. Simulation results suggest that uncertainties introduced during the manufacturing and assembly of the optical components can significantly affect the performance of the system in terms of local voltage and current distribution and global current-voltage characteristics. Significant series resistance and shunt resistance effects are found to be caused by non-uniformity irradiance profiles and design parameters of PV cells. The potential of utilising PVONA as a quality assessment tool for system design is discussed. To achieve quantitative characterisation, the PVONA toolset is then used for developing a 2-D iterative method for the extraction of local electrical parameters of spatially-resolved models of thin-film devices. The method employs PVONA to implement 2-D fitting to reproduce the lateral variations in electroluminescence (EL) images, and to match the dark current-voltage characteristic simultaneously to compensate the calibration factor in EL characterisations. It managed to separate the lateral resistance from the overall series resistance effects. The method is verified by simulations. Experimental results show that pixellation of EL images can be achieved. Effects of local shunts are accurately reproduced by a fitting algorithm. The outcomes of this thesis provide valuable tools that can be used as a complementary means of performance evaluation of PV devices. After proper optimisation, these tools can be used to assist various analysis tasks during the whole lifecycle of PV products.

Objective assessment of the neonatal outcome of labour is important, but it is a difficult and challenging problem. It is an invaluable source of information which can be used to provide feedback to clinicians, to audit a unit's overall performance, and can guide subsequent neonatal care. Current methods are inadequate as they fail to distinguish damage that occurred during labour from damage that occurred before or after labour. Analysis of the chemical acid-base status of blood taken from the umbilical cord of an infant immediately after delivery provides information on any damage suffered by the infant due to lack of oxygen during labour. However, this process is complex and error prone, and requires expertise which is not always available on labour wards. A model of clinical expertise required for the accurate interpretation of umbilical acid-base status was developed, and encapsulated in a rule-based expert system. This expert system checks results to ensure their consistency, identifies whether the results come from arterial or venous vessels, and then produces an interpretation of their meaning. This 'crisp' expert system was validated, verified and commercially released, and has since been installed at twenty two hospitals all around the United Kingdom. The assessment of umbilical acid-base status is characterised by uncertainty in both the basic data and the knowledge required for its interpretation. Fuzzy logic provides a technique for representing both these forms of uncertainty in a single framework. A 'preliminary' fuzzy-logic based expert system to interpret error-free results was developed, based on the knowledge embedded in the crisp expert system. Its performance was compared against clinicians in a validation test, but initially its performance was found to be poor in comparison with the clinicians and inferior to the crisp expert system. An automatic tuning algorithm was developed to modify the behaviour of the fuzzy model utilised in the expert system. Sub-normal membership functions were used to weight terms in the fuzzy expert system in a novel manner. This resulted in an improvement in the performance of the fuzzy expert system to a level comparable to the clinicians, and superior to the crisp expert system. Experimental work was carried out to evaluate the imprecision in umbilical cord acid-base parameters. This information, in conjunction with fresh knowledge elicitation sessions, allowed the creation of a more comprehensive fuzzy expert system, to validate and interpret all acid-base data. This 'integrated' fuzzy expert system was tuned using the comparison data obtained previously, and incorporated vessel identification rules and interpretation rules, with numeric and linguistic outputs for each. The performance of each of the outputs was evaluated in a rigorous validation study. This demonstrated excellent agreement with the experts for the numeric outputs, and agreement on a par with the experts for the linguistic outputs. The numeric interpretation produced by the fuzzy expert system is a novel single dimensional measure that accurately represents the severity of acid-base results. The development of the crisp and fuzzy expert systems represents a major achievement and constitutes a significant contribution to the assessment of neonatal outcome.