Thesis (M.S.)--University of North Carolina Wilmington, 2009. / Title from PDF title page (February 16, 2010) Includes bibliographical references (p. 30)

Στην παρούσα Διδακτορική Διατριβή παρουσιάζονται τρíα νέα στοχαστικά μοντέλα, τα οποία αναπτύχθηκαν με σκοπό την εξομοίωση της διάδοσης των streamers και των leaders, και της επακόλουθης ηλεκτρικής διάσπασης σε διάκενα αέρα μεγαλύτερα από 5cm υπό ατμοσφαιρική πίεση. Η εξομοίωση της διαδικασίας διάσπασης με την χρήση των στοχαστικών μοντέλων, οδήγησε στην εξαγωγή αποτελεσμάτων που αφορούσαν την τάση διάσπασης U50 καθώς και την τυπική απόκλιση σ, όταν τα διάκενα καταπονούνται από συνεχείς και κρουστικές (1,2/50μsec) τάσεις, θετικής πολικότητας. Εξήχθησαν επίσης αποτελέσματα που αφορούσαν τη μέση και στιγμιαία ταχύτητα διάδοσης των streamers μέσα σε διάκενα αέρα μήκους έως 20cm. / At the present PhD Thesis three new stochastic fractal models were introduced. The stochastic models were developed in order to simulate the propagation of streamers and leaders in air gaps, in a wide range of gap distances, under the application of DC and impulse (1,2/50μsec) voltage of positive polarity. Various results, concerning breakdown voltage U50 and standard deviation σ, were obtained. Results concerning mean and instantaneous propagation velocity of streamers (only for gaps up to 20cm), were also obtained.

This study develops new quantitative thermoelastic stress analysis (TSA) techniques for fracture and fatigue damage analysis of composite materials. The first part deals with the thermo-mechanical derivation of two quantitative TSA techniques applied to orthotropic composites with and without a transversely-isotropic surface coating layer. The new TSA test procedures are derived in order to relate the thermal infrared (IR) images with the sum of in-plane strains multiplied by two newly defined material constants that can be experimentally pre-calibrated. Experiments are performed to verify the TSA methods with finite element (FE) numerical results along with available anisotropic elasticity solution. The second part of this study applies the quantitative TSA techniques together with the Lekhnitskii's general anisotropic elasticity solution to calculate mixed-mode stress intensity factors (SIFs) in cracked composite materials. The cracked composite coupons are subjected to off-axis loadings with respect to four different material angles in order to generate mixed-mode SIFs. A least-squares method is used to correlate the sum of in-plane strains from the elasticity solution with the measured TSA test results. The mode-I and mode-II SIFs are determined from eccentrically loaded single-edge-notch tension (ESE(T)) composite specimens. The FE models and virtual crack closure technique (VCCT) are utilized for comparisons. In the third part, a new stochastic model is proposed to generate S-N curves accounting for the variability of the fatigue process. This cumulative damage Markov chain model (MCM) requires a limited number of fatigue tests for calibrating the probability transition matrix (PTM) in the Markov chain model and mean fatigue cycles to failure from experiments. In order to construct the MCM stochastic S-N curve, an iterative procedure is required to predict the mean cycles to failure. Fatigue tests are conducted in this study to demonstrate the MCM method. Twenty-one open-hole S2-glass laminates are fatigue-cycled at two different stress levels. The coupon overall stiffness and surface-ply TSA damage area have been used as two damage metrics. The MCM can satisfactorily describe the overall fatigue damage evolution for a limited number of coupons (less than 6) subjected to a given specific stress level. The stochastic S-N curve can be constructed using at least two sets of fatigue tests under different stress levels. Three available fatigue tests for different E-glass laminates from the literature are also investigated using the proposed MCM approach. The results show the MCM method can provide the stochastic S-N curves for different composite systems and a wide range of fatigue cycles.

Sensor networks are an evolving technology that promise numerous applications. The random and dynamic structure of sensor networks has motivated the suggestion of greedy data-routing algorithms. / In this thesis stochastic models are developed to study the advancement of messages under greedy routing in sensor networks. A model framework that is based on homogeneous spatial Poisson processes is formulated and examined to give a better understanding of the stochastic dependencies arising in the system. The effects of the model assumptions and the inherent dependencies are discussed and analyzed. A simple power-saving sleep scheme is included, and its effects on the local node density are addressed to reveal that it reduces one of the dependencies in the model. / Single hop expressions describing the advancement of messages are derived, and asymptotic expressions for the hop length moments are obtained. Expressions for the distribution of the multihop advancement of messages are derived. These expressions involve high-dimensional integrals, which are evaluated with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The subsequent results agree extremely well with those obtained via routing simulations. A renewal process model is proposed to model multihop advancements, and is justified under certain assumptions. / The model framework is extended by incorporating a spatially dependent density, which is inversely proportional to the sink distance. The aim of this extension is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. The final model extension entails including random transmission radii, the effects of which are discussed and analyzed. The thesis is concluded by giving future research tasks and directions.

Sensor networks are an evolving technology that promise numerous applications. The random and dynamic structure of sensor networks has motivated the suggestion of greedy data-routing algorithms. / In this thesis stochastic models are developed to study the advancement of messages under greedy routing in sensor networks. A model framework that is based on homogeneous spatial Poisson processes is formulated and examined to give a better understanding of the stochastic dependencies arising in the system. The effects of the model assumptions and the inherent dependencies are discussed and analyzed. A simple power-saving sleep scheme is included, and its effects on the local node density are addressed to reveal that it reduces one of the dependencies in the model. / Single hop expressions describing the advancement of messages are derived, and asymptotic expressions for the hop length moments are obtained. Expressions for the distribution of the multihop advancement of messages are derived. These expressions involve high-dimensional integrals, which are evaluated with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The subsequent results agree extremely well with those obtained via routing simulations. A renewal process model is proposed to model multihop advancements, and is justified under certain assumptions. / The model framework is extended by incorporating a spatially dependent density, which is inversely proportional to the sink distance. The aim of this extension is to demonstrate that an inhomogeneous Poisson process can be used to model a sensor network with spatially dependent node density. Elliptic integrals and asymptotic approximations are used to describe the random behaviour of hops. The final model extension entails including random transmission radii, the effects of which are discussed and analyzed. The thesis is concluded by giving future research tasks and directions.

L’établissement correspond à la formation d’une population pérenne dans l’aire d’introduction. Les populations introduites ayant des effectifs faibles, elles sont sujettes à plusieurs mécanismes augmentant leurs risques d’extinction. La structure spatiale de l’aire d’introduction, une mosaïque hétérogène de patchs d’habitat appelée « paysage », peut affecter la persistance de la population introduite. L’objectif de cette thèse est d’étudier l’interaction entre cette structure spatiale et ces mécanismes, ainsi que leur impact sur l’établissement. Les recherches entreprises ont été conduites en utilisant des modèles stochastiques afin de simuler des invasions et faire émerger des prédictions, et en testant expérimentalement ces prédictions grâce à des introductions artificielles de Trichogramma chilonis en microcosmes. Ces travaux ont permis d’identifier un effet fort de la connectivité du site d’introduction, qui peut diminuer les chances d’établissement au niveau local en favorisant l’émigration depuis le site d’introduction, et augmenter les chances d’établissement à un niveau plus large en permettant la colonisation d’autres patchs dans l’aire d’introduction. Au niveau du paysage, nous avons identifié l’impact des hubs, des patchs concentrant les flux de dispersion, qui accroissent fortement la vitesse de colonisation mais diminuent le taux d’établissement. L’établissement était également favorisé par l’agrégation de la ressource et la colonisation par sa dissémination à travers le paysage. La nature stochastique des dynamiques de colonisation est telle qu’il est nécessaire de les prendre en compte pour étudier l’établissement. / Establishment is an important stage of biological invasions, which corresponds to the formation of a persistent population in the introduction area. It is not trivial, as introduced populations are often small, and subject to various specific mechanisms, which increase extinction risks. The spatial structure of the introduction area, which is usually a heterogeneous mosaic of habitat patches called a “landscape”, can interact with those mechanisms and impact the introduced population persistence. This thesis objective is to study the interaction between this spatial structure and those mechanisms, as well as their impact on establishment. On the one hand, we used stochastic models to simulate invasions and formulate predictions. On the other hand, we tested these predictions by performing artificial introductions of Trichogramma chilonis in laboratory microcosms. We were able to identify the impact of the introduction site connectivity, which could decrease establishment probabilities at a local level by increasing the emigration rate from the introduction site, and increase establishment at the landscape level by increasing the colonisation rate of other patches in the introduction area. At the landscape level, we identified the impact of hubs, i.e. patches concentrating dispersal fluxes. They strongly increased colonisation speed, but also decreased establishment. The clustering of resources increased establishment, while its scattering increased colonization. Our results show that introduced population dynamics are highly sensitive to their size. The stochastic nature of colonization dynamics is also necessary to study establishment.

Vários módulos funcionais de células ou bactérias são controlados por meio de genes que se regulam através da codificação de proteínas repressoras ou indutoras. A compreensão destas redes gênicas é um problema em aberto da biologia. Nesta dissertação procuramos aplicar o modelo estocástico de spins e bósons para o caso da rede mais simples, contiduída de dois genes, o primeiro reprimindo o segundo. Apresentamos a solução exata para a distribuição de probabilidades sobre o número das proteínas dos dois genes no estado estacionário, e a probabilidade dependente do tempo sobre o estado do segundo gene (ativado ou desativado). Discutimos também maneiras de generalizar os resultados para redes maiores. / Several functional modules in cells or bacteria are controlled by genes that regulate each other by coding repressive or inducer proteins. The understanding of these genetic networks is still an open problem in biology. In this work we apply the stochastic spin-boson model to the simplest interacting network, made of two genes, the first repressing the second. We present the exact solution for the stationary probability distribution over their both protein numbers, and the temporal evolution of the second genes state (on or off). We also discuss ways of generalizing these results to larger networks.

A modelagem estocástica sociocultural introduzida por Robert Axelrod é tradicionalmente referida à manutenção das diferenças, pois gera o efeito contra-intuitivo do aparecimento de heterogeneidades ao ser atingido o estado de equilíbrio, apesar de sua interação fundamental homogenizar os interagentes. Devido à sua simplicidade, inúmeras releituras do Modelo de Axelrod foram propostas, como também adendos e pequenas modificações. Um campo externo constante homogenizador, interpretado como a mídia, é um exemplo de uma possível alterações no modelo. Já um exemplo de releitura vem com a alteração funcional da interação bipolar do modelo de Axelrod por uma assimilação cultural, usando o mecanismo de Viés de Frequência. Nesta dissertação analisaremos as simulações propostas por Axelrod, sem e com a mídia externa. Para simularmos a mídia externa usaremos o artifício de adicionar um um vizinho fictício à cada elemento da rede. Além disso, analisaremos o mecanismo de assimilação via Viés de Frequência, mostrando sua relação com o modelo do voto da Maioria da Mecânica Estatística. / The sociocultural stochastic modeling introduced by Robert Axelrod is traditionally referred to as the maintenance of cultural diversity. Since it generates the appearance of heterogeneities on a steady state, even the primordial interaction tends to gauge the interactors. Due to its simplicity, numerous interpretations of this model were studied, as well as additions and minor modifications. One example of a possible change in the model can be a constant external field, interpreted as the media. Another example of a reinterpretation could be changing the Axelrod Model bipolar interaction by a cultural assimilation, using the mechanism of frequency bias. This dissertation aims to study the Axelrod simulation with and without the external media. In order to simulate the external media we will add a virtual neighbor to all elements. Furthermore, we analyze the mechanism of assimilation via Bias frequency, showing its relationship with the model of majority voting in Statistical Mechanics.

[pt] As novas tecnologias no setor sucroalcooleiro permitem flexibilidade no que diz respeito a produzir etanol ou açúcar, podendo em qualquer momento concentrar a produção na commodity que gere maior rentabilidade. Ao longo da pesquisa foi identificado que o Imposto sobre Operações relativas à Circulação de Mercadorias e Prestação de Serviços de Transporte Interestadual e Intermunicipal e de Comunicação (ICMS), gera uma variação importante no preço destas duas commodities nas diferentes regiões do Brasil. Como exemplo, podemos citar o fato de São Paulo em 2013 ter um ICMS de 12 porcento, enquanto no estado do Pará foi observada uma taxa de 30 porcento para a mesma data. Neste estudo trabalha-se com duas regiões do Brasil, a sudeste representada pelo estado de São Paulo e a região Nordeste representada pelos estados de Alagoas e Pernambuco. Para conseguir avaliar a flexibilidade gerencial, nesta dissertação é utilizada a teoria das Opções Reais (OR) que enfatiza o valor da flexibilidade que o tomador de decisões possui ao possibilitar a alteração dos rumos de um projeto especialmente em condições de incerteza. Neste estudo foram feitos testes que determinaram que os preços das commodities seguem um Movimento de Reversão à Média Aritmética, com o qual determinou-se os parâmetros que descrevem este tipo de comportamento. Utilizou-se as abordagens de árvores recombinantes de Nelson e Ramaswamy (1990) e de arvores bivariáveis de Hahn e Dyer (2011) é construído para estas teorias um algoritmo programado em Matlab. Esta pesquisa revela que para as duas regiões estudadas a flexibilidade de produção gera rentabilidade maior que nas usinas cuja produção não é flexível, além disso mostra que a capacidade de produção maior e um imposto ICMS menor, proporcionam às empresas flexíveis da região sudeste um maior valor quando comparadas com as usinas da região nordeste. / [en] New technologies in the Sugar-Alcohol sector allow flexibility with regard to produce ethanol or sugar, it may at any time concentrate production in the commodity that generates higher benefits. During the research, it was identified that tax over operations related to Circulation of Goods and Supply of Services of Interstate and Intermunicipal Transportation and Communication (ICMS) generates a significant variation in the price of these two commodities in different regions of Brazil. As an example, we can mention the fact that Sao Paulo in 2013 had a ICMS of 12 percent, while in the state of Pará a rate of 30 percent was observed for the same date. In this study we work with two regions of Brazil, the southeast region represented by the state of São Paulo and the Northeast region represented by the states of Alagoas and Pernambuco. To be able to assess the managerial flexibility, this dissertation is to the theory of real options (OR) that emphasizes the value of flexibility that the decision maker has to enable the change of the direction of a project especially under conditions of uncertainty. This study made tests that determined that commodity prices follow a Reversal Movement to the Arithmetic Mean, with which it was determined the parameters that describe this behavior. We used the approach of recombinant tree Nelson and Ramaswamy (1990) and Hahn bivariate trees and Dyer (2011) is constructed for these theories an algorithm programmed in Matlab. This research reveals that for both regions studied the production flexibility generates higher profitability than in plants whose production is not flexible, also shows that the increased production capacity and a smaller ICMS tax, provide flexible companies from the Southeast greater value when compared with the plants in the northeastern.

<p>Highway infrastructure, including roads/pavements, contributes significantly to a country’s economic growth, quality of life improvement, and negative environmental impacts. Hence, highway agencies strive to make efficient and effective use of their limited funding to maintain their pavement infrastructure in good structural and functional conditions. This necessitates predicting pavement performance and scheduling maintenance interventions accurately and reliably by using appropriate performance modeling and maintenance optimization methodologies, while considering the impact of influential variables and the uncertainty inherent in pavement condition data.</p> <p> </p> <p>Despite the enormous research efforts toward stochastic pavement performance modeling and maintenance optimization, several research gaps still exist. Prior research has not provided a synthesis of Markovian models and their associated methodologies that could assist researchers and highway agencies in selecting the Markov methodology that is appropriate for use with the data available to the agency. In addition, past Markovian pavement performance models did not adequately account for the marginal effects of the preventive maintenance (PM) treatments due to the lack of historical PM data, resulting in potentially unreliable models. The primary components of a Markov model are the transition probability matrix, number of condition states (NCS), and length of duty cycle (LDC). Previous Markovian pavement performance models were developed using NCS and LDC based on data availability, pavement condition indicator and data collection frequency. However, the selection of NCS and LDC should also be based on producing pavement performance models with high levels of prediction accuracy. Prior stochastic pavement maintenance optimization models account for the uncertainty of the budget allocated to pavement preservation at the network level. Nevertheless, variables such as pavement condition deterioration and improvement that are also associated with uncertainty, were not included in stochastic optimization models due to the expected large size of the optimization problem.</p><p>The overarching goal of this dissertation is to contribute to filling these research gaps with a view to improving pavement management systems, helping to predict probabilistic pavement performance and schedule pavement preventive maintenance accurately and reliably. This study reviews Markovian pavement performance models using various Markov methodologies and transition probabilities estimation methods, presents a critical analysis of the different aspects of Markovian models as applied in the literature, reveals gaps in knowledge, and offers suggestions for bridging those gaps. This dissertation develops a decision tree which could be used by researchers and highway agencies to select appropriate Markov methodologies to model pavement performance under different conditions of data availability. The lack of consideration of pavement PM impacts into probabilistic pavement performance models due to absence of historical PM data may result in erroneous and often biased pavement condition predictions, leading to non-optimal pavement maintenance decisions. Hence, this research introduces and validates a hybrid approach to incorporate the impact of PM into probabilistic pavement performance models when historical PM data are limited or absent. The types of PM treatments and their times of application are estimated using two approaches: (1) Analysis of the state of practice of pavement maintenance through literature and expert surveys, and (2) Detection of PM times from probabilistic pavement performance curves. Using a newly developed optimization algorithm, the estimated times and types of PM treatments are integrated into pavement condition data. A non-homogeneous Markovian pavement performance model is developed by estimating the transition probabilities of pavement condition using the ordered-probit method. The developed hybrid approach and performance models are validated using cross-validation with out-of-sample data and through surveys of subject matter experts in pavement engineering and management. The results show that the hybrid approach and models developed can predict probabilistic pavement condition incorporating PM effects with an accuracy of 87%.</p><p>The key Markov chain methodologies, namely, homogeneous, staged-homogeneous, non-homogeneous, semi- and hidden Markov, have been used to develop stochastic pavement performance models. This dissertation hypothesizes that the NCS and LDC significantly influence the prediction accuracy of Markov models and that the nature of such influence varies across the different Markov methodologies. As such, this study develops and compares the Markovian pavement performance models using empirical data and investigates the sensitivity of Markovian model prediction accuracy to the NCS and LDC. The results indicate that the semi-Markov is generally statistically superior to the homogeneous and staged-homogeneous Markov (except in a few cases of NCS and LDC combinations) and that Markovian model prediction accuracy is significantly sensitive to the NCS and LDC: an increase in NCS improves the prediction accuracy until a certain NCS threshold after which the accuracy decreases, plausibly due to data overfitting. In addition, an increase in LDC improves the prediction accuracy when the NCS is small.</p><p>Scheduling pavement maintenance at road network level without considering the uncertainty of pavement condition deterioration and improvement over the long-term (typically, pavement design life) likely results in mistiming maintenance applications and less optimal decisions. Hence, this dissertation develops stochastic pavement maintenance optimization models that account for the uncertainty of pavement condition deterioration and improvement as well as the budget constraint. The objectives of the stochastic optimization models are to minimize the overall deterioration of road network condition while minimizing the total maintenance cost of the road network over a 20-year planning horizon (typical pavement design life). Multi-objective Genetic Algorithm (MOGA) is used because of its robust search capabilities, which lead to global optimal solutions. In order to reduce the number of combinations of solutions of stochastic MOGA models, three approaches are proposed and applied: (1) using PM treatments that are most commonly used by highway agencies, (2) clustering pavement sections based on their ages, and (3) creating a filtering constraint that applies a rest period after treatment applications. The results of the stochastic MOGA models show that the Pareto optimal solutions change significantly when the uncertainty of pavement condition deterioration and improvement is included.</p>