This thesis addresses the metal nanocluster growth process on prepatterned substrates, the development of atomistic simulation method with respect to an acceleration of the atomistic transition states, and the continuum model of the ion-beam inducing semiconductor surface pattern formation mechanism. Experimentally, highly ordered Ag nanocluster structures have been grown on pre-patterned amorphous SiO2 surfaces by oblique angle physical vapor deposition at room temperature. Despite the small undulation of the rippled surface, the stripe-like Ag nanoclusters are very pronounced, reproducible and well-separated. The first topic is the investigation of this growth process with a continuum theoretical approach to the surface gas condensation as well as an atomistic cluster growth model. The atomistic simulation model is a lattice-based kinetic Monte-Carlo (KMC) method using a combination of a simplified inter-atomic potential and experimental transition barriers taken from the literature. An effective transition event classification method is introduced which allows a boost factor of several thousand compared to a traditional KMC approach, thus allowing experimental time scales to be modeled. The simulation predicts a low sticking probability for the arriving atoms, millisecond order lifetimes for single Ag monomers and about 1 nm square surface migration ranges of Ag monomers. The simulations give excellent reproduction of the experimentally observed nanocluster growth patterns. The second topic specifies the acceleration scheme utilized in the metallic cluster growth model. Concerning the atomistic movements, a classical harmonic transition state theory is considered and applied in discrete lattice cells with hierarchical transition levels. The model results in an effective reduction of KMC simulation steps by utilizing a classification scheme of transition levels for thermally activated atomistic diffusion processes. Thermally activated atomistic movements are considered as local transition events constrained in potential energy wells over certain local time periods. These processes are represented by Markov chains of multi-dimensional Boolean valued functions in three dimensional lattice space. The events inhibited by the barriers under a certain level are regarded as thermal fluctuations of the canonical ensemble and accepted freely. Consequently, the fluctuating system evolution process is implemented as a Markov chain of equivalence class objects. It is shown that the process can be characterized by the acceptance of metastable local transitions. The method is applied to a problem of Au and Ag cluster growth on a rippled surface. The simulation predicts the existence of a morphology dependent transition time limit from a local metastable to stable state for subsequent cluster growth by accretion. The third topic is the formation of ripple structures on ion bombarded semiconductor surfaces treated in the first topic as the prepatterned substrate of the metallic deposition. This intriguing phenomenon has been known since the 1960s and various theoretical approaches have been explored. These previous models are discussed and a new non-linear model is formulated, based on the local atomic flow and associated density change in the near surface region. Within this framework ripple structures are shown to form without the necessity to invoke surface diffusion or large sputtering as important mechanisms. The model can also be extended to the case where sputtering is important and it is shown that in this case, certain "magic" angles can occur at which the ripple patterns are most clearly defined. The results including some analytic solutions of the nonlinear equation of motions are in very good agreement with experimental observation.:1 Introduction: Atomistic Models 1 1.1 Density Functional Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Schroedinger equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Density functional theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Molecular Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Lagrangian mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 MD algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Lattice Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.1 Thermodynamic variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.2 Metropolis Algorithm and limit theorem . . . . . . . . . . . . . . . . . . . . . 15 1.3.3 Kinetic Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.3.4 Imaginary time reaction diffusion . . . . . . . . . . . . . . . . . . . . . . . . . 24 2 Cluster Growth on Pre-patterned Surfaces 29 2.1 Nanocluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.1 Classical nucleation theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.1.2 Cluster growth on substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.1.3 Experimental motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 Local flux and surface ad-monomer diffusion . . . . . . . . . . . . . . . . . . . . . . 35 2.2.1 Surface topography and local flux . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.2 Surface gas diffusion under inhomogeneous flux . . . . . . . . . . . . . . . . . 37 2.2.3 Surface migration of ad-monomers . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.4 Simulation vs. experimental gauge . . . . . . . . . . . . . . . . . . . . . . . . 45 2.3 Nucleation models: Surface gas condensation . . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.2 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.3 Evolution of sticking probability . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.4 Evolution of Ag cluster growth . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.3.5 Simulation time and system evolution . . . . . . . . . . . . . . . . . . . . . . 57 2.4 Extended cluster growth model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4.1 Modified setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.4.2 Simulation result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.4.3 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3 A Markov chain model of transition states 63 3.1 Acceleration of thin film growth simulation . . . . . . . . . . . . . . . . . . . . . . . 63 3.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.3 Transition states of Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.1 Local transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.2 The Monte-Carlo method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.4 Effective transitions of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.1 Convergence of the local fluctuation . . . . . . . . . . . . . . . . . . . . . . . 67 3.4.2 The importance of individual local transitions . . . . . . . . . . . . . . . . . . 68 3.4.3 The modified algorithm for effective transition states . . . . . . . . . . . . . . 69 3.5 Cluster growth simulation models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5.1 The configuration energy and migration barriers . . . . . . . . . . . . . . . . 72 3.5.2 Transition events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.5.3 Comparison with Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5.4 Cluster growth stability evaluation . . . . . . . . . . . . . . . . . . . . . . . . 78 3.6 Stability of modified convergence limit . . . . . . . . . . . . . . . . . . . . . . . . . . 80 3.6.1 Acceleration of convergence to Gibbs field . . . . . . . . . . . . . . . . . . . . 80 3.6.2 Relative convergence speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.6.3 1D Ag models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.6.4 Stability theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4 Ion beam inducing surface pattern formation 89 4.1 Ion-inducing pattern formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.1 Bradley-Harper equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.1.2 Nonlinear continuum models . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.1.3 Other approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.2 Simulation of surface defects induced by ion beams . . . . . . . . . . . . . . . . . . . 94 4.2.1 MD simulation of single ion impact . . . . . . . . . . . . . . . . . . . . . . . . 94 4.2.2 Monte-Carlo simulations of surface modification . . . . . . . . . . . . . . . . 96 4.2.3 Curvature dependent surface diffusion . . . . . . . . . . . . . . . . . . . . . . 102 4.3 Continuum model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.3.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.3.2 A travelling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.3.3 Lyapunov stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.3.4 Comparison with experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.3.5 Approximate solutions for other angles . . . . . . . . . . . . . . . . . . . . . . 110 4.4 Contribution of other effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.1 Surface diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.4.2 Surface Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5 Summary 119 Appendix 123 A The discrete reaction diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . . 123 B The derivation of the solution (2.20) . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 C Contribution of overlapping migration area . . . . . . . . . . . . . . . . . . . . . . . 125 D The RGL potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 E Stability of the traveling wave solution . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Master of Science / Department of Industrial & Manufacturing Systems Engineering / Chih-Hang Wu / The recent economic crisis has been partially blamed on the decline in the housing market. This decline in the housing market resulted in an estimated 87% decline in value of collateralized debt obligations (CDOs) between 2007 and 2008. This drastic decline in home values was sudden and unanticipated, thus it was incomprehensible for many investors how this would affect CDOs. This shows that while analytical techniques can be used to price CDOs, these techniques cannot be used to demonstrate the behavior of CDOs under radically different economic circumstances. To better understand the behavior of CDOs under different economic circumstances, numerical techniques such as Monte Carlo simulation can be used instead of analytical techniques to price CDOs. Andersen et al (2005) proposed a method for calculating the probability of defaults that could then be used in the Monte Carlo simulation to price the collateralized debt obligation. The research proposed by Andersen et al (2005) demonstrates the process of calculating correlated probability of defaults for a group of obligors. This calculation is based on the correlations between the obligors using copulas. Using this probability of default, the price of a collateralized debt obligation can be evaluated using Monte Carlo simulation. Monte Carlo simulation provides a more simple yet effective approach compared to analytical pricing techniques. Simulation also allows investors to have a better understanding of the behaviors of CDOs compared to analytical pricing techniques. By analyzing the various behaviors under uncertainty, it can be observed how a downturn in the economy could affect CDOs. This thesis extends on the use of copulas to simulate the correlation between obligors. Copulas allow for the creation of one joint distribution using a set of independent distributions thus allowing for an efficient way of modeling the correlation between obligors. The research contained within this thesis demonstrates how Monte Carlo simulation can be used to effectively price collateralized debt obligations. It also shows how the use of copulas can be used to accurately characterize the correlation between obligor defaults for pricing collateralized debt obligations. Numerical examples for both the obligor defaults and the price of collateralized debt obligations are presented to demonstrate the results using Monte Carlo simulation.

The purpose of this thesis is to provide a detailed description of recent methods and scientific basis for characterizing earthquake sources within a certain region with distinct tectonic environments. The focus will be on those characteristics that are most significant to the ground-shaking hazard and on how we can incorporate our current knowledge into hazard analyses for engineering design purposes. I treat two particular geographical areas where I think current hazard analysis methods are in need of significant improvement, and suggest some approaches that have proven to be effective in past applications elsewhere. A combined hazard procedure is used to estimate seismicity in northern Central America, where there appear to be four tectonic environments for modeling the seismogenic sources and in Iran, where the large earthquakes usually occur on known faults. A preferred seismic hazard model for northern Central America and the western Caribbean plate based on earthquake catalogs, geodetic measurements, and geological information is presented. I used the widely practiced method of relating seismicity data to geological data to assess the various seismic hazard parameters and test parameter sensitivities. The sensitivity and overall uncertainty in peak ground acceleration (PGA) estimates are calculated for northwestern Iran by using a specific randomized blocks design. A Monte Carlo approach is utilized to evaluate the ground motion hazard and its uncertainties in northern Central America. A set of new seismic hazard maps, exhibiting probabilistic values of peak ground acceleration (PGA) with 50%, 10%, and 5% probabilities of exceedance (PE) in 50 years, is presented for the area of relevance. Disaggregation of seismic hazard is carried out for cities of San Salvador and Guatemala by using a spatial distribution of epicenters around these sites to select design ground motion for seismic risk decisions. In conclusion, consideration of the effect of parameters such as seismic moment, fault rupture, rupture directivity and stress drop are strongly recommended in estimating the near field ground motions. The rupture process of the 2002 Changureh earthquake (Mw = 6.5), Iran, was analyzed by using the empirical Green’s function (EGF) method. This method simulates strong ground motions for future large earthquakes at particular sites where no empirical data are available.

This thesis deals with safety verification analysis of collision avoidance systems for unmanned vehicles. The safety of the vehicle is dependent on collision avoidance algorithms and associated control laws, and it must be proven that the collision avoidance algorithms and controllers are functioning correctly in all nominal conditions, various failure conditions and in the presence of possible variations in the vehicle and operational environment. The current widely used exhaustive search based approaches are not suitable for safety analysis of autonomous vehicles due to the large number of possible variations and the complexity of algorithms and the systems. To address this topic, a new optimisation-based verification method is developed to verify the safety of collision avoidance systems. The proposed verification method formulates the worst case analysis problem arising the verification of collision avoidance systems into an optimisation problem and employs optimisation algorithms to automatically search the worst cases. Minimum distance to the obstacle during the collision avoidance manoeuvre is defined as the objective function of the optimisation problem, and realistic simulation consisting of the detailed vehicle dynamics, the operational environment, the collision avoidance algorithm and low level control laws is embedded in the optimisation process. This enables the verification process to take into account the parameters variations in the vehicle, the change of the environment, the uncertainties in sensors, and in particular the mismatching between model used for developing the collision avoidance algorithms and the real vehicle. It is shown that the resultant simulation based optimisation problem is non-convex and there might be many local optima. To illustrate and investigate the proposed optimisation based verification process, the potential field method and decision making collision avoidance method are chosen as an obstacle avoidance candidate technique for verification study. Five benchmark case studies are investigated in this thesis: static obstacle avoidance system of a simple unicycle robot, moving obstacle avoidance system for a Pioneer 3DX robot, and a 6 Degrees of Freedom fixed wing Unmanned Aerial Vehicle with static and moving collision avoidance algorithms. It is proven that although a local optimisation method for nonlinear optimisation is quite efficient, it is not able to find the most dangerous situation. Results in this thesis show that, among all the global optimisation methods that have been investigated, the DIviding RECTangle method provides most promising performance for verification of collision avoidance functions in terms of guaranteed capability in searching worst scenarios.

In recent years, metal-organic frameworks (MOFs) have been identified as promising adsorbents in a number of industrially relevant, yet challenging, separations, including the removal of propane from propane/propylene mixtures and the separation of mixtures of xylene isomers. The highly tuneable nature of MOFs - wherein structures may be constructed from a variety of diverse building blocks – has resulted in the publication of a staggering number of frameworks incorporating a wide range of network topologies, pore shapes and pore diameters. As a result, there are a huge number of candidate adsorbents to consider for a given separation. Molecular simulation techniques allow the identification of those structural features and characteristics of a MOF which exert the greatest influence on the adsorption and separation of the compounds of interest, providing insights which can both guide the selection and accelerate the development of adsorbents for a specific application. The separation of propane/propylene mixtures via adsorption has typically focused on selective adsorption of the olefin, propylene, via specific olefin-adsorbent interactions. These propylene-selective MOFs result in processes which selectively remove the most abundant species in the process stream and are typically characterised by high heats of adsorption, resulting in large adsorption units and adsorbents which are difficult to regenerate. In this work, the capability of MOFs to selectively adsorb propane over propylene is explored, potentially allowing for the design of smaller and more energy-efficient adsorption units. By studying a range of different MOFs as well as carbon-based model pores, it was found that the low-pressure selectivity of the structure is determined by the strength of the electrostatic interaction between propylene and the framework, while the adsorptive preference at industrially-relevant pressures is dominated by the enhanced packing efficiency of propylene over propane. The confinement of C3 molecules, however, may be employed to negate this entropic advantage and guide the development of materials which selectively adsorb propane over propylene. It has recently been reported that the adsorptive preference of a MOF for one xylene isomer over another may be predicted based solely on the pore size distribution of the structure. In this work, the impact of pore size on selectivity was studied systematically in both one-dimensional model pore systems of varying geometries and analogous published MOF structures. The ability of the framework to discriminate between xylene molecules in these systems was found to be determined primarily by the different packing arrangements available to the different isomers – while small pores were found to favour the slimmest of the isomers, larger pores were found to favour the more compact ortho- isomer. Finally, the adsorption and diffusion of xylene isomers in a more complex MOF, UiO-66(Zr), was studied in depth. Simulations were able to correctly predict the previously-reported preference of the MOF for ortho-xylene (oX). The smaller volume of the oX molecule compared to the other isomers was found to be responsible both for an enhanced entropic contribution and higher guest-host interaction energies. The importance of framework flexibility in the diffusion of xylene isomers in UiO-66(Zr) was also explored, with distortion of the structure in response to interaction with adsorbed molecules found to be essential in allowing xylenes to diffuse through the pore space.

The backbone of our industrialised society and economy is electricity. To avoid a catastrophic situation, a plan for how to act during a power shortage is crucial. Previous research shows that decision models provide support to decision makers providing efficient energy rationing during power shortages in the Netherlands, United States and Canada. The existing research needs to be expanded with a group decision model to enable group decisions. This study is conducted with a case study approach where the Swedish emergency preparedness plan in case of power shortage, named Styrel, is explored and used to evaluate properties of a proposed group decision model. The study consist of a qualitative phase and a quantitative phase including a Monte Carlo simulation of group decisions in Styrel evaluated with correlation analysis. The qualitative results show that participants in Styrel experience the group decisions as time-consuming and unstructured. The current decision support is not used in neither of the two counties included in the study, with the motivation that the preferences provided by the decision support are misleading. The proposed group decision model include a measurable value function assigning values to priority classes for electricity users, an additive model to represent preferences of individual decision makers and an additive group decision model to aggregate preferences of several individual decision makers into a group decision. The conducted simulation indicate that the proposed group decision model evaluated in Styrel is sensitive to significant changes and more robust to moderate changes in preference differences between priority classes.

<p>Three methods of sensitivity and unceartainty analysis have been applied to the operative stormwater- and recipient model StormTac. The study area is the watershed of lake Flaten in the municipality Salem. StormTac’s submodels for stormwater, pollutant transport and the recipient are cosidired. In the sensitivity assessment, the model parametres and inputs were varied one at a time by a constant percentage according to the “one at a time” (OAAT) method and the response of the outputs were calculated. It was found that the stormwater- and baseflow were most sensitive to perturbations in the perciptation. Unceartainty analysis using Monte Carlo simulation was performed in two different ways. (1) All model parametres and inputs were included with defined unceartainties and the resulting unceartainty for the target variable was quantified. Thereafter, whith the purpose to estimate the contribution of all the parametres and inputs, the cumulative uncertainty for the target variable, each parameters/inputs unceartainty was omitted one at the time. The most crucial uncertainty for the storm water flow was the runoff coefficient for forestland and the perciptation (i.e the differens between the 90- and 10-percentile for the storm water flow was reduced whith 44 % and 33 % respectively). (2) To identify optimal parameter intervals, the probability for an acceptable value of the target variable was plotted against each parameters value range. The result suggests that for some of the parametres i StormTac, the ranges should be changed.</p> / <p>Den operativa dagvatten- och recipientmodellen StormTac har applicerats på sjön Flatens avrinningsområde i Salems kommun. StormTac:s delmodeller för dagvatten, föroreningstransport och recipienten studerades. Tre olika metoder för att undersöka osäkerheten och känsligheten hos parametrar och indata i delmodellerna tillämpades. I känslighetsanalysen (OAAT-metoden) behäftades parametervärdena och indata med systematiska fel och responsen hos utdata beräknades. Dag- och basvattenflödet var känsligast mot fel i nederbördsdata, medan kväve-, fosfor- och kopparbelastningen till recipienten var känsligast mot respektive förorenings dagvattenkoncentration från områden med bebyggelse. Varje parameter och indatas bidrag till den kumulativa osäkerheten hos utdata uppskattades med hjälp av Montecarlosimulering. Genom att för varje effektvariabel studera differensen mellan 90- och 10-percentilen när osäkerheten hos en parameter/indata i taget utelämnades, kunde varje parameters/indatas bidrag till modellresultatets osäkerhet kvantifieras. För dagvattenflödet bidrog avrinningskoefficienten för skogmark med 44 % av osäkerheten och nederbörden med 33 %. Montecarloanlys praktiserades även för att identifiera optimala intervall för parametrarna i modellen. Sannolikheten för ett accepterat värde på den simulerade effektvariabeln plottades mot varje parameters värdemängd. För vissa parametrar indikerade resultatet att intervallen kan förändras mot hur de i nuläget ser ut i StormTac. Uniforma sannolikhetsfördelningar, begränsade av StormTac:s min- och maxvärden för parametrarna och ± 50% av orginalvärdet för indata, användes i båda osäkerhetsanalyserna.</p>

Electron beam therapy planning and custom electron bolus design were identified as areas in which improvements in equipment and techniques could lead to significant improvements in treatment delivery and patient outcomes. The electron pencil beam algorithms used in conventional Treatment Planning Systems do not accurately model the dose distribution in irregularly shaped objects, near oblique surfaces or in inhomogeneous media. For this reason, at Christchurch Oncology Centre the TPS is not relied on for planning electron beam treatments. This project is an initial study of ways to improve the design of custom electron bolus, the planning of electron beam therapy, and other radiation therapy simulation tasks, by developing a system for the accurate assessment of dose distributions under irregular contours in clinically relevant situations. A shaped water phantom system and a diode array have been developed and tested. The design and construction of this water phantom dosimetry system are described, and its capabilities and limitations discussed. An EGS/BEAM Monte Carlo simulation system has been installed, and models of the Christchurch Oncology Centre linacs in 6MeV and 9MeV electron beam modes have been built and commissioned. A test was run comparing the EGS/BEAM Monte Carlo system and the CMS Xio conventional treatment planning system with the experimental measurement technique using the water phantom and the diode array. This test was successful as a proof of the concept of the experimental technique. At the conclusion of this project, the main limitation of the diode array system was the lack of data processing software. The array produces a large volume of raw data, but not enough processed data was produced during this project to match the spatial resolution of the computer models. An automated data processing system will be needed for clinical use of the array. It has been confirmed that Monte Carlo and pencil-beam algorithms predict significantly different dose distributions for an irregularly shaped object irradiated with megavoltage electron beams. The results from the diode array were consistent with the theoretical models. This project was an initial investigation. At the time of writing, the diode array and the water phantom systems were still at an early stage of development. The work reported here was performed to build, test and commission the equipment. Additional work will be needed to produce an instrument for clinical use. Research into electron beam therapy could be continued, or the equipment used to expand research into new areas.

In 1996, a concept was proposed by the UK Ministry of Defence with the intention of making the field of reliability more useful to the end user, particularly within the field of military aerospace. This idea was the Maintenance Free Operating Period (MFOP), a duration of time in which the overall system can complete all of its required missions without the need to undergo emergency repairs or maintenance, with a defined probability of success. The system can encounter component or subsystem failures, but these must be carried with no effect to the overall mission, until such time as repair takes place. It is thought that advanced technologies such as redundant systems, prognostics and diagnostics will play a major role in the successful use of MFOP in practical applications. Many types of system operate missions that are made up of several sequential phases. For a mission to be successful, the system must satisfactorily complete each of the objectives in each of the phases. If the system fails or cannot complete its goals in any one phase, the mission has failed. Each phase will require the system to use different items, and so the failure logic changes from phase to phase. Mission unreliability is defined as the probability that the system fails to function successfully during at least one phase of the mission. An important problem is the efficient calculation of the value of mission unreliability. This thesis investigates the creation of a modelling method to consider as many features of systems undergoing both MFOPs and phased missions as possible. This uses Petri nets, a type of digraph allowing storage and transit of tokens which represent system states. A simple model is presented, following which, a more complex model is developed and explained, encompassing those ideas which are believed to be important in delivering a long MFOP with a high degree of confidence. A demonstration of the process by which the modelling method could be used to improve the reliability performance of a large system is then shown. The complex model is employed in the form of a Monte-Carlo simulation program, which is applied to a life-size system such as may be encountered in the real world. Improvements are suggested and results from their implementation analysed.

Growth mechanism of electroplated copper columns has been systematically studied by simulations and characterizations. A two-dimensional cross-sectional kinetic Monte Carlo (2DCS-KMC) model has been developed to simulate the electrodeposition of single crystal copper. The evolution of the microstructure has been visualized. The cluster density, average cluster size, variance of the cluster size and average aspect ratio were obtained from the simulations. The growth history of the deposition from the first atom to an equivalent of 100 monolayers was reconstructed. Following the single-lattice 2DCS-KMC model for a single crystal, a two-dimensional cross-sectional poly-lattice kinetic Monte Carlo (2DCSP-KMC) model has been developed for simulation of the electrodeposition of polycrystalline copper on both a copper and a gold substrate. With this model, the early-stage nucleation and the grain growth after impingement of nuclei can be simulated; as such the entire growth history is reconstructed in terms of the evolution of microstructure, grain statistics and grain boundary misorientation. The model is capable of capturing some key aspects of nucleation and growth mechanisms including the nucleation type (e.g. homogeneous or heterogeneous), texture development, the growth of grains and higher energetic state of grain boundaries. The model has also proven capable of capturing the effects of deposition parameters including applied electrode potential, concentration of cupric ions and temperature. Their effects are largely dependent on the substrates. The early-stage electrocrystallization of Cu on polycrystalline Au has been studied by ex-situ AFM observations. The evolution of surface morphology of the electrodeposited copper on a sputtered Au seed layer from 16ms to 1000s was observed and their formation mechanism discussed. The heterogeneous nucleation phenomenon, the competitive growth both longitudinally and laterally, and the dominant growth of some nuclei were experimentally observed, which are also visualized by the relevant KMC simulation results at a smaller size scale and a shorter time scale. A heuristic model is therefore proposed to describe the mechanism of the early-stage electrocrystallization of Cu on a polycrystalline Au seed layer. Electroplated copper columns plated for different times have been characterized in terms of the evolution of their external morphology, cross-sectional microstructure and crystal structure. The microstructure of electroplated copper columns is characteristic of bi-modal or tri-modal grain size distribution. The results indicate that recrystallization has occurred during or after the plating, top-down and laterally. Slight changes of the crystal structure were observed by in-situ XRD and it was found that the changes of the (111) and (200) planes occurred at different stages of self-annealing. Finally, the results indicate the presence of organic additives is not essential for self-annealing of a copper column to occur.