In this thesis we use polynomial chaos expansions to represent the response of criticality calculations when they are subject to large numbers (many hundreds) of correlated nuclear data uncertainties. An adaptive high dimensional model representation (HDMR) is used to decompose the response parameter keff into a superposition of lower dimensional subspaces which are in-turn projected on to a polynomial basis. These projections are evaluated using an adaptive quadrature scheme which is used to infer the polynomial orders of the basis. The combination of adaptive HDMR and adaptive quadrature techniques results in a sparse polynomial expansion which has been optimised to represent the variance of the response with the minimum number of polynomials. The combined application of these techniques is illustrated using UOX and MOX pin cell problems with evaluated nuclear covariance data. We show that this approach to calculating the variance in keff is an order of magnitude more efficient when compared to Latin hypercube sampling with the same number of samples for problems involving up to 988 random dimensions. In the final chapter of this thesis, the adaptive HDMR and quadrature methods combined with polynomial chaos are applied to an industrially relevant problem; the computation of keff uncertainties due to evaluated covariance data. Uncertainties and first order sensitivities are computed from the polynomial chaos expansion which are compared to the results from the first order sensitivity method implemented in the Monte Carlo code MONK. We found that the local sensitivities and uncertainties derived from the PCE compare well with the MONK sensitivity method. These uncertainty quantification approaches were applied to fast spectrum uranium, plutonium and americium-241 critical assemblies. Comparisons between the uranium/plutonium and americium-241 uncertainties were made in the context of the 0.95 sub-critical limit. Suggestions for new sub-critical limits based on differing numbers of standard deviations below the mean values were proposed.

Tensile and compressive tests were carried out on a selection of metals of interest in engineering applications. These metals were tested at a range of strain rates and temperatures with the aim of calibrating material constitutive models for the simulation of full scale structures in industry. In order to validate these models for use under conditions of strain rates exceeding those imposed by the tests which were used for calibration of the models, both tensile and compressive ballistic tests were carried out. A ball on plate experiment was used to compare the deformation predicted under the tensile conditions, including high speed speckle DIC for out of plane displacement measurement. A bespoke gas gun for the purpose of carrying out Taylor impact tests on samples of the same materials was designed and installed at Imperial College. The gas gun was used to carry out Taylor tests which were also lmed at high speed for comparison with tests simulated under compressive loading. Furthermore, post-impact samples were sectioned so that a hardness survey could be carried out across the internal section of a sample. These data were combined to produce a map indicative of plastic strain within the sample and used as another validation tool for the model using the Taylor test. It was found that the Johnson-Cook model was not su cient to represent the materials at the conditions under study. Both the ball on plate and Taylor test comparisons revealed the discrepancy between the model and the actual material response. Furthermore, the hardness map of the post test Taylor cylinders revealed that a volume within the cylinder at the base of the bulge experienced less hardening than the volume around it, consistent with predictions made from the nite element analysis.

The widespread application of electric machines across different industries have a large impact on the operation cost and energy usage. This has driven research to improve the performance of electric machines in terms of the power density, efficiency and reliability. A comprehensive method of thermal management integrating the design, monitoring and control of electric machines is proposed in this research. The method is applied to two permanent magnet motors - a high power axial flux motor and a high precision linear motor. Firstly, a two stage optimization technique is applied to the design of the linear motor. A first stage global search using Genetic Algorithm followed by a second stage Branch and Bound method is a systematic way of searching for the optimal feasible solution. It resulted in an improved design which is more compact in size and produces a higher thrust force (39.9%) while reducing the heat generation (26.2%) when compared to an initial design. The design optimization takes into consideration the multi-physics interactions using a reduced order model. This resulted in a computation time saving of 80% over a commercial software optimization package while modelling accuracy is maintained through an output space mapping technique. During a continuous 5 hour cyclic positioning application, a model based compensation method is applied to the linear motor for real time thermal disturbance rejection. It resulted in improved positioning accuracy with a final mean unidirectional position deviation of −0.2μm and repeatability of ±0.7μm. Effective disturbance rejection is achieved through accurate disturbance modelling while using minimal sensor measurements. The minimal realization of the compensation model is achieved through model identification. In addition, a Modified Kalman Filter is proposed which led to a reduction in the number of temperature sensors required. Lastly, an experimentally determined lumped parameter thermal model is used for condition monitoring of the high power motor. Components of the electromagnetic losses are derived from a parameter estimation method using temperature measurement as input to the model. The method is able to detect input current fluctuations during a drive cycle which makes it possible to identify faults like a short circuit. Moreover, the model is useful for real time temperature monitoring which provides thermal protection against transient overloads. The modelling accuracy is improved by using a model identification technique to determine the thermal parameters.

A poly-disperse particle description using a Lagrangian Stochastic (LS) framework coupled to Large Eddy Simulations (LES) of turbulent flows is presented. The aforementioned frameworks are outlined leading to the LES-coupled spray-pdf equation and its equivalent Stochastic Differential Equations (SDE). Three particle processes are investigated: particle dispersion, nucleation and aggregation. The aim of this work is to integrate or extend the models of these processes into the LES-LS framework and evaluate the predictive ability of the developed models. Dispersion in LES is used in conjunction with a stochastic sub-grid model to accurately represent the path of a particle. Such models have a free parameter, the dispersion coefficient, which is not universal. A dynamic model for the evaluation of this coefficient is proposed. The model's predictive ability is investigated in decaying homogeneous isotropic turbulence and a turbulent mixing layer. Nucleation is modelled in a probabilistic manner where the frequency of events is determined from local equilibrium conditions. Two methodologies for the sub-grid influence on nucleation rates are implemented. A turbulent Dibutyl-Phthalate laden Nitrogen jet experiment is used for validation. Aggregation is an inter-particle process which involves a multitude of different physicochemical mechanisms. Particles in the nano-scale are considered, with a concentration which renders their direct simulation as individual real particles intractable. A stochastic aggregation model is presented and its performance is evaluated against analytic solutions, a Planar Jet, and a turbulent jet configuration. It is concluded that the LES-spray pdf framework can be used to develop parameter-free models from phenomenological arguments that accurately describe complex turbulent poly-disperse flows.

This thesis presents the development of a model of the Medical Isotope Production Reactor (MIPR): a conceptual Aqueous Homogeneous Reactor (AHR). The model is a point kinetics model with zero and one-dimensional thermal hydraulic feedbacks. Three versions of the model of increasing complexity are presented and a number of scenarios are modelled with each version. The results of these simulations shows the stability of the reactor against reactivity insertions caused by the strong negative reactivity feedbacks inherent to AHRs. The first version of the model is modified using intrusive polynomial chaos in order to simulate the effects of uncertainty in key parameters. This allows a novel study into which physical parameters and processes are important at each stage of a transient and in determining steady state conditions. The final version of the model is used to model the CRAC-43 experiment and, after modification to include the delay of radiolytic gas production which accompanies the start up of an AHR, good agreement was found between model and experiment. The development of the equations, correlations and parameters used in the model is approached from the point of view of the governing physics. This approach to model development enables a comprehensive exploration of the physical processes underpinning the behaviour of AHRs. As well as being one of the most complete and fundamentally based models of an AHR presented within the literature, the final model is also extremely versatile and general. Given the appropriate input neutronic and thermal-hydraulic data the model presented in this thesis should be able to simulate a very wide range of AHR behaviour.

Epoxies are thermosetting polymers that have uses in a multitude of industrial and consumer applications. The high crosslink density of epoxies gives rise to exceptional mechanical, chemical and heat resistance properties. However, this also results in low toughness, i.e. poor resistance to crack initiation and propagation. The present work discusses the toughening mechanisms of four epoxy polymers modified with several novel modifiers, which create different morphologies. Nanoscale core-shell rubber (CSR) particles are attractive as epoxy tougheners because they remain well dispersed even at high loadings, do not affect the Tg and most importantly, provide good toughness improvement (900% increase in GIC for a low Tg epoxy system). For a given weight percentage of modifiers, the tensile and compressive properties were better maintained for the much smaller CSR particles as these particles have a lower rubber content. However, the fracture performance of the CSR modified epoxies appear to be limited in low Tg epoxies. Examination of the fracture surfaces using high resolution scanning electron microscopy (SEM) show less plastic void growth due to the higher stresses required to initiate cavitation. Amphiphilic triblock copolymers (BCP) represent the next generation of phase separating materials for toughening epoxies. The structure/property relationships of epoxies modified with symmetric and asymmetric triblock copolymers were determined. The complex 3D nanostructures that were created offer greatly increased fracture performance over conventional toughening agents for very tough epoxies, while minimising the decrease in mechanical properties. A measured increase in GIC of 1600% was noted. This increased to 2250% when a further addition of silica nanoparticles was considered. This complex nanostructure allows for more gradual and extensive plastic deformation of the epoxy matrix as shear yielding and plastic void growth initiated by debonding at the BCP/epoxy interface. The morphology was further studied numerically using a phase field model which identified parameters that control the evolution of the microstructure. Graphene nanoplatelets (GNP) vary in size and quality depending on the method of preparation. Thus, a range of GNPs with different platelet sizes, thicknesses and aspect ratios were used to identify the properties that control the mechanical and fracture performance of GNP modified epoxies. The bulk GNP geometry and chemical makeup were first characterised. The optimum dispersion method was determined through systematic experiments using two solvents and an ultrasonic probe, and examined using SEM. Well dispersed GNPs improved the Young's modulus, whereas the fracture energy increased for both well dispersed and poorly dispersed GNPs.

This thesis presents a new system of monitoring human motion and muscle activity concurrently, in pervasive and uncontrolled environments, for prolonged periods of time. Current technologies such as optical based motion tracking and electromyography (EMG) are considered the gold standard, but have limited use outside of a controlled laboratory environment. Restraints on collection durations, due to temporary sensors, as well as a limited collection space in which monitoring is capable, results in a constrained system which is not suitable for prolonged observation. Using a custom made inertial measurement unit (IMU) and mechanomyography (MMG) sensor, information from both motion and muscle activity was combined, in order to better understand human activity by allowing prolonged collection in unrestricted environments. IMU and MMG measurements have been compared to standard optical tracking and EMG measurements, demonstrating the viability of this technology in a clinical setting and particularly in the natural environment. This novel sensor is lightweight, inexpensive, low power, wireless, easy to use, gives results comparable to standard laboratory techniques, and is able to monitor motion and muscle activity over long periods of time. This work shows a strong agreement with the current literature on MMG response to increments of force, and a greater sensitivity to muscular fatigue detection when compared against EMG, all through pervasive studies. Using machine learning and pattern recognition methods, gait analysis and detection of progressive change over time was achieved in typical and atypical conditions, over prolonged periods. Finally, this work has shown applicable use in prosthesis control and gesture switching. Outside of muscle monitoring, alternative uses have been established, with preliminary results showing a suitable use in foetal monitoring. This work establishes a novel method of human motion and muscle monitoring which produces a suitably high accuracy when compared against the gold standard, however, without the limitations which confine the wearer to a finite space or limited duration time. The studies presented here introduce a number of areas in which prolonged and pervasive collection can expand this field, while producing complementary results against laboratory based technology.

A highly flexible multipart needle is under development in the Mechatronics in Medicine Laboratory at Imperial College, with the aim to achieve multi-curvature trajectories inside biological soft tissue, such as to avoid obstacles during surgery. Currently, there is no dedicated software or analytical methodology for the analysis of the needle's behaviour during the insertion process, which is instead described empirically on the basis of experimental trials on synthetic tissue phantoms. This analysis is crucial for needle and insertion trajectory design purposes. It is proposed that a real-time, progressive, mathematical model of the needle deflection during insertion be developed. This model can serve three purposes, namely, offline needle and trajectory design in a forward solution of the model, when the loads acting on needle from the substrate are known; online, real-time identification of the loads that act on the needle in a reverse solution, when the deflections at discrete points along the needle length are known; and the development of a sensitivity matrix, which enables the calculation of the corrective loads that are required to drive the needle back on track, if any deviations occur away from a predefined trajectory. Previously developed mathematical models of needle deflection inside soft tissue are limited to small deflection and linear strain. In some cases, identical tip path and body shape after full insertion of the needle are assumed. Also, the axial load acting on the needle is either ignored or is calculated from empirical formulae, while its inclusion would render the model nonlinear even for small deflection cases. These nonlinearities are a result of the effects of the axial and transverse forces at the tip being co-dependent, restricting the calculation of the independent effects of each on the needle's deflection. As such, a model with small deflection assumptions incorporating tip axial forces can be called 'quasi-nonlinear' and a methodology is proposed here to tackle the identification of such axial force in the linear range. During large deflection of the needle, discrepancies between the shape of the needle after the insertion and its tip path, computed during the insertion, also significantly increase, causing errors in a model based on the assumption that they are the same. Some of the models developed to date have also been dependent on existing or experimentally derived material models of soft tissue developed offline, which is inefficient for surgical applications, where the biological soft tissue can change radically and experimentation on the patient is limited. Conversely, a model is proposed in this thesis which, when solved inversely, provides an estimate for the contact stiffness of the substrate in a real-time manner. The study and the proposed model and techniques involved are limited to two dimensional projections of the needle movements, but can be easily extended to the 3-dimensional case. Results which demonstrate the accuracy and validity of the models developed are provided on the basis of simulations and via experimental trials of a multi-part 2D steering needle in gelatine.

Interventional MRI requires accurate and fast localization of medical instruments within the imaging volume of the MR scanner. Furthermore, in view of tissue motion and target dislocation, accurate intra-operative imaging is demanded. The research presented in this thesis addresses these issues with reference to a proposed MRI-guided transrectal prostate biopsy system. As the instrument is not visible in the MR images, RF fiducial markers embedded within the instrument are used to determine its pose. A novel localization method to compute the location of N fiducial markers using 1D projections is presented. The method is shown to yield significant improvements over previously proposed methods. Computational complexity was significantly reduced by avoiding cluster analysis, while high accuracy was achieved by using a set of optimally chosen projections and by applying Gaussian interpolation in peak detection. The method was analyzed and validated using a combination of experiments and Monte Carlo simulations. Experiments in 1.5 T and 2.9 T MR scanners involved both water phantoms and volunteer subjects. High robustness and sub-pixel accuracy were demonstrated while the computational time showed an improvement of up to a factor of 100 over existing solutions. This method was employed as the basis for tracking the endorectal probe during the prostate biopsy procedure. The probe was positioned by means of a remotely actuated manipulator. Miniature semiactive markers were embedded within the probe in a rigid known geometrical configuration and tracked by means of the localization method. At each position, Least-Squares fitting of the probe model with the localized one was performed in order to achieve more accurate tracking. Navigation of the probe and biopsy needle was realized through a dedicated graphical user interface. This interface displayed interpolated cross sections through the MR imaging volume and simplified graphical models of the instruments overlaid on the anatomy. Visual guidance was further improved by filtering of the markers' positions, which was enabled by the high tracking rate. In order to improve intra-operative imaging a novel external receiver array was designed and a prototype was built, as an alternative to the more conventional endorectal and pelvic receivers. This new array coil was optimized for imaging of the prostatic area for a patient in the prone position by combining a buttery coil and three single trapezoidal loops. The design is suitable for positioning the endorectal probe and does not introduce any spatial limitation to the range of movements. Experiments in a 1.5 T MR scanner and simulations demonstrated higher receiver sensitivity and homogeneity than conventional coils and also a significantly improved signal-to-noise ratio.

Materials need to be designed under certain conditions to withstand high thermal gradients to operate at high temperature environments. Many advanced gas cooled reactor (AGR) power plant components with operating temperatures in the range of 500-650 °C undergo creep-fatigue loading conditions. These components may be subject to isothermal low cycle fatigue (LCF) and thermo mechanical fatigue (TMF) damages due to the cyclic operation of power plant caused by the start-up and shutdown processes and due to the fluctuation of energy demand in daily operation. Hence, the influence of these cyclic loads induced mechanically and thermally, on the different structural components need to be carefully monitored and analysed in order to prevent failure and ensure safe operating conditions of critical units. The material Type 316 SS with cast number S7646, widely used in this type of components, is investigated in this project. The aim of this research is to conduct experimental tests to obtain quality stress-strain data for the material under investigation under cyclic plasticity in isothermal and an-isothermal tests using the available testing machine systems in the University of Imperial College London. The data obtained from experimental results are then utilised to develop advanced novel finite element damage models in a creep/fatigue loading environment in order to predict the cyclic behaviour under LCF conditions. Finally, the results of cyclic data derived from isothermal tests were used to predict the thermo mechanical fatigue behaviour for this alloy. The LCF-TMF testing unit, Instron 8801 with a temperature uniformity of less than ±10°C within the gauge section of the specimens were employed to conduct the experimental tests. Fully-reversed, strain-controlled isothermal tests were conducted at 500°C and 650°C for the strain ranges of ∆ɛ=±0.4%, ±0.8%, ±1.0% and ±01.2%. Strain-controlled in-phase (IP) thermo-mechanical fatigue tests were conducted on the same material and the temperature was cycled between 500°C and 650°C. Additionally, the creep-fatigue interactions were investigated with the introduction of symmetrical hold time at maximum strains in tension and compression under both LCF-TMF tests. From the investigation and the analysis of the experimental stress-strain data, three phases are observed when the cyclic stress responses are plotted; cyclic hardening, stabilisation and damage evolution. In the final stage of the behaviour of the material, a nonlinear decrease of the peak stress level was observed which was initiated by the presence of micro-crack and the failure occurred as the crack propagated. The evolution of inelastic strain energy density, ∆w, against the number of cycles, N, was used to determine the number of cycles at which the material stabilised, N_sta , the damage initiated, N_i and the failure occurred,N_f. The introduction of the hold time in both tension and compression strains in the LCF and TMF tests, produced an increase in the plastic strain range which subsequently increased the inelastic strain energy density and slightly reduced the peak flow stress when compared with the continues cyclic tests. The stress relaxation was observed when the hold time was introduced. The amount of stress relaxation was dependent on the test temperature and the imposed strain amplitude and the same trend was found when different strain ranges were examined. The cyclic behaviour of the Type 316 steel was further studied by analysing and performing microstructural investigations using the scanning electron microscope (SEM). The metallographic and the fractographic studies revealed that in all LCF-TMF tests the cracks mostly initiated in transgranular mode and propagated in either transgranular (under continuous cyclic loading) or in a mixed mode (under symmetric dwell period). The comparison of the metallographic and the fractographic studies of the LCF and TMF tests under both conditions (i.e. with and without dwell period) highlighted that the proportion of intergranular cracking increases with decrease in frequency, i.e. from 0.01Hz to 0.001Hz. Furthermore, the transgranular fatigue process dominates at high frequencies whereas the intergranular time dependent mechanism governs at low frequencies, low imposed mechanical strain amplitude and they both act together at intermediate frequencies and imposed mechanical strain amplitude. A constitutive model based on isotropic and nonlinear kinematic hardening rules was used to replicate numerically the cyclic structural behaviour of the material. A user-defined subroutine was developed and implemented in the finite element software, ABAQUS to predict the cyclic hardening, the stress relaxation during hold time and finally to demonstrate the damage evolution once the damage initiated. The final stage of the material behaviour (i.e. failure) was simulated numerically for both LCF and TMF tests conducted with and without hold time where for the tests with continuous cyclic loading (without hold time) a hysteresis energy-based phenomenological model was implemented in a USDFLD subroutine. Further, this model in combination with the creep damage model based on the time-fraction law were employed simultaneously to replicate the experimental results in which the hold time was introduced. In the end, the FE results were compared with the experimental results and the minor deviations observed in e.g. the first and stabilised hysteresis loops under TMF conditions or in the FE hysteresis damages, could be minimised by conducting further isothermal tests to define additional material properties at intermediate temperatures and performing tests at various strain ranges respectively.