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Understanding the behavior of complex, large-scale, interconnected systems in a rigorous and structured manner is one of the most pressing scientific and technological challenges of current times. These systems include, among many others, transportation and communications systems, smart grids and power grids, financial markets etc. Failures of these systems have potentially enormous social, environmental and financial costs. In this work, we investigate the failure mechanisms of load-sharing complex systems. The systems are composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand respectively) as well as the ability of a component to share its load with its neighbors when needed. Each component possesses a specific strength (capacity) and can be in one of three states: failed, damaged or functioning normally. The states are determined based on the load (demand) on the component. We focus on two distinct mechanisms to model the interaction between components strengths and loads. The first, a Loss of Strength (LOS) model and the second, a Customer Service (CS) model. We implement both models on lattice and scale-free graph network topologies. The failure mechanisms of these two models demonstrate temporal scaling phenomena, phase transitions and multiple distinct failure modes excited by extremal dynamics. We find that the resiliency of these models is sensitive to the underlying network topology. For critical ranges of parameters the models demonstrate power law and exponential failure patterns. We find that the failure mechanisms of these models have parallels to failure mechanisms of critical infrastructure systems such as congestion in transportation networks, cascading failure in electrical power grids, creep-rupture in composite structures, and draw-downs in financial markets. Based on the different variants of failure, strategies for mitigating and postponing failure in these critical infrastructure systems can be formulated.

The dynamics around managing urban infrastructure are changing dramatically. Today???s infrastructure management challenges ??? in the wake of shrinking coffers and stricter stakeholders??? requirements ??? include finding better condition assessment tools and prediction models, and effective and intelligent use of hard-earn data to ensure the sustainability of urban infrastructure systems. Wastewater collection networks ??? an important and critical component of urban infrastructure ??? have been neglected, and as a result, municipalities in North America and other parts of the world have accrued significant liabilities and infrastructure deficits. To reduce cost of ownership, to cope with heighten accountability, and to provide reliable and sustainable service, these systems need to be managed in an effective and intelligent manner. The overall objective of this research is to present a new strategic management framework and related tools to support multi-perspective maintenance, rehabilitation and replacement (M, R&R) planning for wastewater collection networks. The principal objectives of this research include: (1) Developing a comprehensive wastewater collection network asset database consisting of high quality condition assessment data to support the work presented in this thesis, as well as, the future research in this area. (2) Proposing a framework and related system to aggregate heterogeneous data from municipal wastewater collection networks to develop better understanding of their historical and future performance. (3) Developing statistical models to understand the deterioration of wastewater pipelines. (4) To investigate how strategic management principles and theories can be applied to effectively manage wastewater collection networks, and propose a new management framework and related system. (5) Demonstrating the application of strategic management framework and economic principles along with the proposed deterioration model to develop long-term financial sustainability plans for wastewater collection networks. A relational database application, WatBAMS (Waterloo Buried Asset Management System), consisting of high quality data from the City of Niagara Falls wastewater collection system is developed. The wastewater pipelines??? inspections were completed using a relatively new Side Scanner and Evaluation Technology camera that has advantages over the traditional Closed Circuit Television cameras. Appropriate quality assurance and quality control procedures were developed and adopted to capture, store and analyze the condition assessment data. To aggregate heterogeneous data from municipal wastewater collection systems, a data integration framework based on data warehousing approach is proposed. A prototype application, BAMS (Buried Asset Management System), based on XML technologies and specifications shows implementation of the proposed framework. Using wastewater pipelines condition assessment data from the City of Niagara Falls wastewater collection network, the limitations of ordinary and binary logistic regression methodologies for deterioration modeling of wastewater pipelines are demonstrated. Two new empirical models based on ordinal regression modeling technique are proposed. A new multi-perspective ??? that is, operational/technical, social/political, regulatory, and finance ??? strategic management framework based on modified balanced-scorecard model is developed. The proposed framework is based on the findings of the first Canadian National Asset Management workshop held in Hamilton, Ontario in 2007. The application of balanced-scorecard model along with additional management tools, such as strategy maps, dashboard reports and business intelligence applications, is presented using data from the City of Niagara Falls. Using economic principles and example management scenarios, application of Monte Carlo simulation technique along with the proposed deterioration model is presented to forecast financial requirements for long-term M, R&R plans for wastewater collection networks. A myriad of asset management systems and frameworks were found for transportation infrastructure. However, to date few efforts have been concentrated on understanding the performance behaviour of wastewater collection systems, and developing effective and intelligent M, R&R strategies. Incomplete inventories, and scarcity and poor quality of existing datasets on wastewater collection systems were found to be critical and limiting issues in conducting research in this field. It was found that the existing deterioration models either violated model assumptions or assumptions could not be verified due to limited and questionable quality data. The degradation of Reinforced Concrete pipes was found to be affected by age, whereas, for Vitrified Clay pipes, the degradation was not age dependent. The results of financial simulation model show that the City of Niagara Falls can save millions of dollars, in the long-term, by following a pro-active M, R&R strategy. The work presented in this thesis provides an insight into how an effective and intelligent management system can be developed for wastewater collection networks. The proposed framework and related system will lead to the sustainability of wastewater collection networks and assist municipal public works departments to proactively manage their wastewater collection networks.

Detailed characterization of size and shape of polymers, and development of methods to elucidate the mechanisms behind shape transitions are central issues in this thesis. In particular we characterize grafted polymer chains under confinement in terms of the chain entanglement complexity and mean molecular size. Confinement of polymers into small regions can drastically affect the structural and mechanical properties, and make these systems convenient for a large number of applications, including the design of lubricants, coatings, and various biotechnical applications. Using Monte Carlo simulations with a model including both persistence length and intramolecular non-bonded interaction, we find two regimes of polymer behaviour: i) soft mushrooms, where confinement successively flattens the chains with accompanying change in the folding complexity, and ii) hard mushrooms where the compact structures appear to resist confinement and the only way to reorganize the entanglements is by flattening under strong confinement. We also show that a simultaneous use of mean molecular size and chain entanglement complexity renders the possibility to create configurational "phase" diagrams for a wide range of polymers. We have further introduced a new descriptor of folding complexity, the path-space ratio, ζα which captures essential features of molecular shape beyond those conveyed by mean size and asphericity. This thesis also contains results of light scattering measurements on supramolecular complexes formed when mixing an adamantane end-capped star polymer with a β-cyclodextrin polymer. The specific interactions result in an interplay between the association of the end-caps and a strong inclusion interaction between adamantane and β-cyclodextrin.

This thesis consists of two different parts, related to two different fields in mathematical physics: wave propagation and kinetic theory of gases. Various mathematical and computational problems for equations from these areas are treated.   The first part is devoted to high order finite difference methods for the Helmholtz equation and the wave equation. Compact schemes with high order accuracy are obtained from an investigation of the function derivatives in the truncation error. With the help of the equation itself, it is possible to transfer high order derivatives to lower order or to transfer time derivatives to space derivatives. For the Helmholtz equation, a compact scheme based on this principle is compared to standard schemes and to deferred correction schemes, and the characteristics of the errors for the different methods are demonstrated and discussed. For the wave equation, a finite difference scheme with fourth order accuracy in both space and time is constructed and applied to a problem in discontinuous media.   The second part addresses some problems related to kinetic equations. A direct simulation Monte-Carlo method is constructed for the Landau-Fokker-Planck equation, and numerical tests are performed to verify the accuracy of the algorithm. A formal derivation of the method from the Boltzmann equation with grazing collisions is performed. The linear and linearized Boltzmann collision operators for the hard sphere molecular model are studied using exact reduction of integral equations to ordinary differential equations. It is demonstrated how the eigenvalues of the operators are found from these equations, and numerical values are computed. A proof of existence of non-zero discrete eigenvalues is given. The ordinary diffential equations are also used for investigation of the Chapman-Enskog distribution function with respect to its asymptotic behavior.

When banks lend capital to counterparties they take on a risk, known as credit risk which traditionally has been the largest risk exposure for banks. To be protected against potential default losses when lending capital, banks must hold a regulatory capital that is based on a regulatory formula for calculating risk weighted assets (RWA). This formula is part of the Basel Accords and it is implemented in the legal system of all European Union member states. The key parameters of the RWA formula are probability of default, loss given default and asset correlation. Banks today have the option to estimate the probability of default and loss given default by internal models however the asset correlation must be determined by a formula provided by the legal framework. This project is a first approach for Handelsbanken to study what would happen if banks were allowed to estimate asset correlation by internal models. We assess two models for estimating the asset correlation of a portfolio of Small and Medium Enterprices (SME). The estimates are compared with the asset correlation given by the regulatory formula and with estimates for another parameter called default correlation. The models are validated using predicted historical data and Monte-Carlo Simulations. For the studied SME portfolio, the models give similar estimates for the asset correlations and the estimates are lower than those given by the regulatory formula. This would imply a lower capital requirement if banks were allowed to use internal models to estimate the asset correlation used in the RWA formula. Default correlation, if not used synonymously with asset correlation, is shown to be another measure and should not be used in the RWA formula. / När banker lånar ut kapital till motparter tar de en risk, mer känt som kreditrisk som traditionellt har varit den största risken för banker. För att skydda sig mot potentiella förluster vid utlåning måste banker ha ett reglerat kapital som bygger på en formel för beräkning av riskvägda tillgångar (RWA). Denna formel ingår i Basels regelverk och är implementerad i rättssystemet i alla EU-länder. De viktigaste parametrarna för RWA-formeln är sannolikheten att fallera, förlustgivet fallissemang och tillgångskorrelation. Bankerna har idag möjlighet att beräkna de två variablerna sannolikheten att fallera och förlustgivet fallissemang med interna modeller men tillgångskorrelation måste bestämmas med hjälp av en standardformel givet från regelverket. Detta projekt är ett första tillvägagångssätt för Handelsbanken att studera vad som skulle hända om banker fick beräkna tillgångskorrelation med interna modeller. Vi analyserar två modeller för att skatta tillgångskorrelation i en portfölj av Små och Medelstora Företag (SME). Uppskattningarna jämförs sedan med den tillgångskorrelation som ges av regelverket och jämförs även mot en parameter som kallas fallissemangskorrelation. Modellerna som används för att beräkna korrelationerna valideras med hjälp av estimerat data och Monte-Carlo Simuleringar. För den studerade SME portföljen ges liknande uppskattningar för de båda tillgångskorrelationsmodellerna, samt visar det sig att de är lägre än den korrelationen som ges av regelverket. Detta skulle innebära ett lägre kapitalkrav om bankerna fick använda sig av interna modeller för att estimera tillgångskorrelation som används i RWA-formeln. Om fallissemangskorrelation inte används synonymt till tillgångskorrelation, visar det sig att fallisemangskorrelation är en annan mätning än tillgångskorrelation och bör inte användas i RWA-formeln.

Alzheimer's disease (AD), as one of the most common neurodegenerative diseases, is characterized by the loss of neuronal dysfunction and death resulting in progressive cognitive impairment. The main histopathological hallmark of AD is the accumulation and deposition of misfolded Aβ peptide as amyloid plaques, however the precise role of Aβ toxicity in the disease pathogenesis is still unclear. Moreover, at early stages of the disease the important clinical features of the disorder, in addition to memory loss, are the disruptions of circadian rhythms and spatial disorientation. In the present work I first studied the role of Aβ toxicity by comparing the findings of genome-wide association studies in sporadic AD with the results of an RNAi screen in a transgenic C. elegans model of Aβ toxicity. The initial finding was that none of the human orthologues of these worm genes are associated with risk for sporadic Alzheimer’s disease, indicating that Aβ toxicity in the worm model may not be equivalent to sporadic AD. Nevertheless, comparing the first degree physical interactors (+1 interactome) of the GWAS and worm screen-derived gene products have uncovered 4 worm genes that have a +1 interactome overlap with the GWAS genes that is larger than one would expect by chance. Three of these genes form a chaperonin complex and the fourth gene codes for actin, a major substrate of the same chaperonin. Next I have evaluated the circadian disruptions in AD by developing a new system to simultaneously monitor the oscillations of the peripheral molecular clock and behavioural rhythms in single Drosophila. Experiments were undertaken on wild- type and Aβ-expressing flies. The results indicate the robustness of the peripheral clock is not correlated with the robustness of the circadian sleep and locomotor behaviours, indicating that the molecular clock does not directly drive behaviour. This is despite period length correlations that indicate that the underlying molecular mechanisms that generate both molecular and behavioural rhythms are the same. Rhythmicity in Aβ-expressing flies is worse than in controls. I further investigated the mechanism of spatial orientation in Drosophila. It was established that in the absence of visual stimuli the flies use self-motion cues to orientate themselves within the tubes and that in a Drosophila model of Aβ toxicity this control function is disrupted.

>Magister Scientiae - MSc / We present various methods of pricing Asian options. The methods include Monte Carlo simulations designed using control and antithetic variates, numerical solution of partial differential equation and using lower bounds.The price of the Asian option is known to be a certain risk-neutral expectation. Using the Feynman-Kac theorem, we deduce that the problem of determining the expectation implies solving a linear parabolic partial differential equation. This partial differential equation does not admit explicit solutions due to the fact that the distribution of a sum of lognormal variables is not explicit. We then solve the partial differential equation numerically using finite difference and Monte Carlo methods.Our Monte Carlo approach is based on the pseudo random numbers and not deterministic sequence of numbers on which Quasi-Monte Carlo methods are designed. To make the Monte Carlo method more effective, two variance reduction techniques are discussed.Under the finite difference method, we consider explicit and the Crank-Nicholson’s schemes. We demonstrate that the explicit method gives rise to extraneous solutions because the stability conditions are difficult to satisfy. On the other hand, the Crank-Nicholson method is unconditionally stable and provides correct solutions. Finally, we apply the pricing methods to a similar problem of determining the price of a European-style arithmetic basket option under the Black-Scholes framework. We find the optimal lower bound, calculate it numerically and compare this with those obtained by the Monte Carlo and Moment Matching methods.Our presentation here includes some of the most recent advances on Asian options, and we contribute in particular by adding detail to the proofs and explanations. We also contribute some novel numerical methods. Most significantly, we include an original contribution on the use of very sharp lower bounds towards pricing European basket options.

Les avancées technologiques et l'intégration massive de dispositifs électroniques nanométriques dans les objets de notre vie quotidienne ont généré une explosion des coûts de R&D, de conception et de production, ainsi que des inquiétudes sociétales quant à l'impact environnemental des déchets électroniques. En raison de procédés de production moins coûteux et à faible impact environnemental, de leur souplesse d’utilisation et de la possibilité de moduler leurs propriétés à l’infini, les molécules et polymères organiques constituent une classe de matériaux prometteuse pour la mise au point de nouveaux dispositifs électroniques. L’électronique organique couvre ainsi un vaste domaine d’applications, parmi lesquelles se trouvent les diodes électroluminescentes, les transistors à effet de champ ou les cellules photovoltaïques. Bien que la plupart de ces dispositifs soient déjà commercialisés, les processus gouvernant leur efficacité à l’échelle atomique sont loin d’être entièrement compris et maîtrisés. C’est en particulier le cas des processus de transport de charge, qui interviennent dans tous ces dispositifs.L'objectif de cette thèse est d’apporter une compréhension fondamentale des processus de transport de charge dans les semiconducteurs organiques, à partir d'approches théoriques combinant dynamique moléculaire, calculs quantiques et simulations Monte Carlo. Ce travail est développé suivant trois axes principaux:(I) Etude des relations liant l'organisation structurale et les propriétés de transport de cristaux moléculaires, et du rôle des fluctuations énergétiques dans des matériaux polymères amorphes. Des simulations Monte Carlo Cinétique (KMC) couplés au formalisme de Marcus-Levich-Jortner pour le calcul des taux de transfert ont été effectués afin de déterminer les mobilités des électrons et des trous au sein de dix structures cristallines de dérivés phtalocyanines. Dans une deuxième étude, une approche similaire a été employée afin de décrire les propriétés de transport de charge au sein d'un copolymère amorphe de fluorène-triphénylamine, ainsi que l'impact des fluctuations énergétiques sur ces dernières. La méthodologie développée permet d'obtenir, pour un faible coût calculatoire, une estimation semi-quantitative des mobilités des porteurs de charge dans ce type de système.(II) Etude de l'impact de contraintes mécaniques sur les propriétés de transport de matériaux organiques cristallins. La réponse électronique et les propriétés de transport de matériaux organiques soumis à une contrainte mécanique ont été étudiés à l'aide de simulations de dynamique moléculaire et de calculs DFT. Le rubrène cristallin et ses polymorphes, ainsi que les dérivés du BTBT, ont été considérés pour cette étude, qui révèle un couplage électromécanique inhabituel entre les différents axes cristallographiques. Les résultats démontrent en particulier que l'anisotropie structurale des monocristaux organiques conduit à une anisotropie du couplage électromécanique.(III) Etude du rôle du polyélectrolyte dans la conductivité des complexes conducteurs. Le polystyrène substitué par du bis(sulfonyl)imide est utilisé comme un contre-ion et un dopant dans les complexes conducteurs PEDOT-polyélectrolytes. En complément des analyses expérimentales, des simulations de dynamique moléculaire couplées à des calculs DFT ont été effectuées dans ces systèmes afin d'analyser l'impact de la conformation et de l'état de protonation du polyélectrolyte sur la conductivité du complexe formé avec le PEDOT.Les études décrites ci-dessus, réalisées sur différents types de matériaux en couplant différents types d'approches théoriques, ont permis d'apporter une compréhension fondamentale des propriétés de transport dans les semiconducteurs organiques. Elles mettent en particulier en évidence l'impact de l'organisation structurale, des interactions intermoléculaires et de l'application de contraintes mécaniques sur la mobilité des porteurs de charges dans ces matériaux. / With the advancement of technology, miniaturized electronic devices are progressively integrated into our everyday lives, generating concerns about cost, efficiency and environmental impact of electronic waste. Organic electronics offers a tangible solution paving the way for low-cost, flexible, transparent and environment friendly devices. However, improving the functionalities of organic (opto) electronic devices such as light emitting diodes and photovoltaics still poses technological challenges due to factors like low efficiencies, performance stability, flexibility etc. Although more and more organic materials are being developed to meet these challenges, one of the fundamental concerns still arises from the lack of established protocols that correlate the inherent properties of organic materials like the chemical structure, molecular conformation, supra-molecular arrangement to their resulting charge-transport characteristics.In this context, this thesis addresses the prediction of charge transport properties of organic semiconductors through theoretical and computational studies at the atomistic scale, developed along three main axes :(I) Structure-charge transport relationships of crystalline organic materials and the role of energetic fluctuations in amorphous polymeric organic semiconductors. Kinetic Monte-Carlo (KMC) studies employing the Marcus-Levich-Jortner rate formalism are performed on ten crystalline Group IV phthalocyanine derivatives and trends linking the crystalline arrangement to the anisotropic mobility of electrons and holes are obtained. Subsequently, KMC simulations based on the simpler Marcus formalism are performed on an amorphous semiconducting fluorene-triphenylamine (TFB) copolymer, to highlight the impact of energetic fluctuations on charge transport characteristics. A methodology is proposed to include these fluctuations towards providing a semi-quantitative estimate of charge-carrier mobilities at reduced computational cost.(II) Impact of a mechanical strain on the electronic and charge transport properties of crystalline organic materials. Crystalline rubrene and its polymorphs, as well as BTBT derivatives (well studied high mobility organic materials) are subjected to mechanical strain and their electronic response is analyzed. Employing tools like Molecular Dynamic (MD) simulations and plane wave DFT (PW-DFT) calculations, unusual electro-mechanical coupling between different crystallographic axes is demonstrated, highlighting the role of inherent anisotropy that is present in the organic single crystals which translates in an anisotropy of their electro-mechanical coupling.(III) Protonation-dependent conformation of polyelectrolyte and its role in governing the conductivity of polymeric conducting complexes. Polymeric bis(sulfonyl)imide substituted polystyrenes are currently employed as counter-ions and dopants for conducting poly(3,4-ethylenedioxythiophene) (PEDOT), resulting in PEDOT-polyelectrolyte conducting complexes. Employing MD simulations and DFT calculations, inherent characteristics of the polyelectrolyte like its acid-base behavior, protonation state and conformation, are analyzed in conjunction with available experimental data and the role of these characteristics in modulating the conductivity of resulting PEDOT-polyelectrolyte conducting complexes is highlighted.The above studies, performed on different organic electronic systems, emphasize the importance of inherent characteristics of organic materials in governing the charge transport behavior in these materials. By considering the inherent characteristics of organic electronic materials and systematically incorporating them into simulation models, accuracy of simulation predictions can be greatly improved, thereby serving not only as a tool to design new, stable and high performance organic materials but also for optimizing device performances.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação são apresentados resultados de simulações Monte Carlo de fluorescência de raios X (XRF), utilizando o programa GEANT4, para medidas de espessura de revestimento metálico (Ni e Zn) em base metálica (Fe). As simulações foram feitas para dois tamanhos de espessura para cada metal de revestimento, (5μm e 10μm), com passos de 0,1 μm e 0,001 μm e com 106 histórias. No cálculo da espessura do revestimento foram feitas as aproximações de feixe de raios X monoenegético, com a análise da transmissão apenas da energia do K-alfa e para uma geometria compatível com um sistema real de medição (ARTAX-200). Os resultados mostraram a eficiência da metodologia de simulação e do cálculo da espessura do revestimento, o que permitirá futuros cálculos, inclusive para multirevestimentos metálicos em base metálica. / This dissertation is presented results of x-ray fluorescence (XRF) Monte Carlo simulations) using GEANT4 for metallic coating (Ni and Zn) thickness determination on metallic base (Fe). The simulations were made for two values of coating thickness for each covering (5 μm and 10 μm), with steps of 0.1 μm and 0.001 μm, and with 106 stories. The monoenergetic x-ray approach was used assuming the transmission of only K-alpha line. The experiment and geometry was similar to the real system of measurement (ARTAX-200 ). The results showed the efficiency of the simulation methodology, as well as the ability to measure the thickness of coating by XRF. Thus, a continuation of this study for multilayer metal coating could be promising.