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Thesis (Master)--İzmir Institute of Technology, İzmir, 2005. / Keywords: Geothermal energy, multi criteria decision method, stochastic methods, Monte Carlo method. Includes bibliographical references (leaves.93-98).

Thesis (M.S.)--West Virginia University, 2006. / Title from document title page. Document formatted into pages; contains viii, 45 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 44-45).

Ship collision accidents are rare events but pose huge threat to human lives, assets, and the environment. Collision resistance of ships is usually assessed in terms of ship structural response such as member displacement, energy dissipation and the extent of damage. Many researchers have sought for effective models that compute ship stochastic response during collisions by considering the variability of collision scenario parameters. However, the models were limited by the capability of the collision computational models and did not completely capture collision scenario, and material and geometric uncertainties. In addition, the simplified models capturing the input-response relationships of the ship structural impact mechanics are in implicit forms which makes them unsuitable for assessing the performance of structural design specifications in collisions. Furthermore, with increasing ship passages in the Arctic region, the probabilities of ship-iceberg interactions are increasing, highlighting the need to focus on risk based ship designs. In this research, a conceptual stochastic modelling framework is developed for performance characterisation and quantitative risk assessment of ship-ship and ship-iceberg collisions. In this direction, an interface for automated stochastic finite element computations was developed to model ship structural resistance in reference collision scenarios. The stochastic structural response was characterised based on the onset of the ship structural failure. The focus was initially on ship-ship collisions to quantify the uncertainties experimentally and to characterise the performance for a variety of striking ships. The framework was then extended to consider probabilistic performance measures in ship-iceberg collisions. The computationally intensive collision response models were captured with efficient surrogate representations so that the performance measures can be obtained with gradient based reliability approaches. The most probable input design sets for the response distribution were sampled with Latin Hypercube models. The probabilistic performance measures were also combined with available collision frequency models from literature for risk computations and to demonstrate the risk tolerance measures. The framework underlines the significance of different risk components, providing valuable guidance for improving risk-based ship designs. Although, a double-hull crude oil carrier is presented as the struck ship, the approach can be readily extended to characterise the performance and risk of other ship structures in collisions.

This thesis is concerned with quantifying the dynamical role of stochasticity in models of recurrent epidemics. Although the simulation of stochastic models can accurately capture the qualitative epidemic patterns of childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns. The novel aspect of this thesis is the use of analytic methods to quantify the results from simulations. All the models are formulated as continuous time Markov processes, the temporal evolutions of which is described by a master equation. This is expanded in the inverse system size, which decomposes the full stochastic dynamics into a macroscopic part, described by deterministic equations, plus a stochastic fluctuating part. The first part examines the inclusion of non-exponential latent and infectious periods into the the standard susceptible-infectious-recovered model. The method of stages is used to formulate the problem as a Markov process and thus derive a power spectrum for the stochastic oscillations. This model is used to understand the dynamics of whooping cough, which we show to be the mixture of an annual limit cycle plus resonant stochastic oscillations. This limit cycle is generated by the time-dependent external forcing, but we show that the spectrum is close to that predicted by the unforced model. It is demonstrated that adding distributed infectious periods only changes the frequency and amplitude of the stochastic oscillations---the basic mechanisms remain the same. In the final part of this thesis, the effect of seasonal forcing is studied with an analysis of the full time-dependent master equation. The comprehensive nature of this approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in measles epidemics. In the pre-vaccination regime the dynamics are dominated by a period doubling bifurcation, which leads to large biennial oscillations in the deterministic dynamics. Vaccination is shown to move the system away from the biennial limit cycle and into a region where there is an annual limit cycle and stochastic oscillations, similar to whooping cough. Finite size effects are investigated and found to be of considerable importance for measles dynamics, especially in the biennial regime.

Firms' operations management decisions are often complicated by various types of uncertainties, ranging from micro level customer behavior to macro level economic conditions. Operating in the presence of uncertainties and volatilities is a challenging task, one that requires careful mathematical analysis and tailored treatment based on the uncertainty's characteristics. In this thesis we provide three distinct studies on managing stochastic uncertainty in dynamic marketplaces. The first study considers agents' dynamic interactions in a large matching market. A pair needs to inspect for their compatibility in order to form a match. We study a type of market failure called 'information deadlock' that may arise when pairs are only willing to inspect their most preferred prevailing partner. Under information deadlock, a large fraction of agents wait in the market for long (if not forever) in spite of there being opportunities remaining in their consideration sets. Using advanced tools in statistical physics and random graph theory, we derive how the size of the deadlock is affected by the market's primitives. We also show that information deadlock is prevalent in a wide range of markets. Our second study tackles a service firm's problem of choosing between a safe service mode and a risky service mode when serving a customer who might probabilistically churn. One key behavioral feature of the customer that we consider is named recency bias --- his happiness with the firm (that crucially determines his churn risk at the time) depends more heavily on his more recent experience. We show, by solving a stochastic control problem, that the firm should be risk-averse when the customer is marginally satisfied and risk-seeking when the customer is marginally unsatisfied. The optimal sandwich policy can significantly outperform the naive myopic policy in terms of customer lifetime value. Our third study deals with a dual sourcing problem under fluctuating economic conditions. We model this via an underlying Markov modulated state-of-the-world which affects the two suppliers’ cost structures, capacity limits and demands. We develop two approaches to show how the optimal combined ordering strategy from the two suppliers, along with a salvaging policy, can be efficiently computed, and characterize the relatively simple structure of the optimal policies. Interestingly, we find that the firm can, by exploiting the dual sourcing options, benefit from increased environmental volatilities that affect the suppliers’ cost structures or capacity limits.

Non-linearities and dynamic interactions between state variables are characteristic of complex social systems and processes. In this thesis, we present a new methodology to model these non-linearities and interactions from the large panel datasets available for some of these systems. We build macro-level statistical models that can verify theoretical predictions, and use polynomial basis functions so that each term in the model represents a specific mechanism. This bridges the existing gap between macro-level theories supported by statistical models and micro-level mechanistic models supported by behavioural evidence. We apply this methodology to two important problems in the social sciences, the demographic transition and the transition to democracy. The demographic transition is an important problem for economists and development scientists. Research has shown that economic growth reduces mortality and fertility rates, which reduction in turn results in faster economic growth. We build a non-linear dynamic model and show how this data-driven model extends existing mechanistic models. We also show policy applications for our models, especially in setting development targets for the Millennium Development Goals or the Sustainable Development Goals. The transition to democracy is an important problem for political scientists and sociologists. Research has shown that economic growth and overall human development transforms socio-cultural values and drives political institutions towards democracy. We model the interactions between the state variables and find that changes in institutional freedoms precedes changes in socio-cultural values. We show applications of our models in studying development traps. This thesis comprises the comprehensive summary and seven papers. Papers I and II describe two similar but complementary methodologies to build non-linear dynamic models from panel datasets. Papers III and IV deal with the demographic transition and policy applications. Papers V and VI describe the transition to democracy and applications. Paper VII describes an application to sustainable development.

O presente trabalho é uma formulação teórica que permite estudar num modelo estocástico, a influência dos erros de classificação na mensuração da prevalência da esquistossomose mansônica. Os erros de classificação são desagregados e identificados como: falhas de leitura por parte do examinador ou preparo inadequado da lâmina; contingências biológicas que possibilitam o aparecimento de ovos não viáveis e a eliminação de ovos contínua por parte dos indivíduos. É apresentada uma solução geral para o problema, bem como soluções para os casos em que se conhece a distribuição de probabilidades do número de ovos de S.mansoni. Uma solução aproximada e independente da forma e dependente dos dois primeiros momentos da distribuição do número de ovos é sugerida. A influência dos erros de classificação pode quantitativamente ser apreciada, através de um conjunto de tabelas elaboradas com diversos valores dos parâmetros intervenientes no problema. / The present paper is a theoretical approach which will, allow studying the influence - in a stochastic model - of errors in classifying the measurement of the prevalence of Schistosomiasis mansoni. The misclassification errors considered are due to: (A) failure of the examiner in either (1) reading or (2) poor technique. (B) biological contingences which will allow for the appearence of (1) sterile eggs, or (2) discontinuity in the elimination of eggs by the carriers. An exact general solution of the problem is presented, as well as solutions for the particular cases in which the probability distribution of S.mansoni eggs counts in known. An approximate solution is suggested, which is independent from the way in which the number of eggs is distributed, but depends upon the first two moments of the probability distribution of the eggs counts. The influence of misclassification errors can be judged in a quantitative way, by means of a set of tables mande up for the different parametric values of the problem.

A novel stochastic earthquake ground motion model is formulated in association with physically interpretable parameters that are capable of efficiently characterizing the complex evolutionary nature of the phenomenon. A multi-modal, analytical, fully non-stationary spectral version of the Kanai-Tajimi (K-T) model is introduced achieving a realistic description of the evolutionary spectral energy distribution of seismic ground motions. The functional forms describing the temporal evolution of the model parameters can efficiently model highly non-stationary power spectral characteristics. The analysis space, where the analytical forms describing the evolution of the model parameters are established, is the energy domain instead of the typical use of the time domain. This space is used in conjunction with a newly defined energy-associated amplitude modulating function. The Spectral Representation Method supports the simulation of sample ground motions realizations. A predictive stochastic model for simulation of earthquake ground motions is developed, using a user-specified earthquake scenario description as input, and resulting in fully nonstationary ground acceleration time-histories at a site of interest. The previously formed analytical non-stationary K-T ground motion model lies at the core of the developed predictive model. An extensive Californian subset of the NGA-West2 earthquake ground motion database is used to develop and calibrate the predictive stochastic model. Sample observations of the model parameters are obtained by fitting the K-T model to the database records, and their resulting marginal distributions are effectively described by simple probability models. Advanced random-effect regression models are established in the normal probabilistic space, capable of linking the stochastic K-T model parameters with the moment magnitude Mw, closest distance Rrup and average shear-wave velocity VS30 at a Californian site of interest. The included random effects take effectively into account the correlation of ground motions pertaining to the same earthquake event, and the fact that each site is expected to have its own effect on the resulting ground motion. The covariance structure of the normal K-T model parameters is next estimated, allowing finally for the complete mathematical description of the predictive stochastic model for a given earthquake scenario. The entirety of the necessary steps for the simulation of the developed predictive stochastic model is provided, resulting in the generation of any number of fully non-stationary ground acceleration time-series that are statistically consistent with the specified earthquake scenario. In an effort to assess the performance and versatility of the developed predictive stochastic model, a list of simple engineering metrics, associated with the characterization of the earthquake ground motion time-series, is studied, and results from simulated earthquake ground acceleration time-series of the developed predictive model are compared with corresponding predictions of pertinent Ground Motion Prediction Equations (GMPEs) for a variety of earthquake and local-site characteristics. The studied set of ground acceleration time-series features includes the Arias intensity IA, the significant duration T5-95 of the strong ground shaking, and the spectral-based mean period of the earthquake record Tm. The predictive stochastic model is next validated against the state-of-the-art NGA-West2 GMPE models. The statistics of elastic response spectra derived by ensembles of synthetic ground motions are compared with the associated response spectra as predicted by the considered NGA-West2 ground motion prediction equations for a wide spectrum of earthquake scenarios. Finally, earthquake non-linear response-history analyses are conducted for a set of representative single- and multi-degree-of-freedom hysteretic structural systems, comparing the seismically induced inelastic structural demand of the considered systems, when subjected to sets of both real strong ground motion records, and associated simulated ground acceleration time-histories as well. The comparisons are performed in terms of seismic structural demand fragility curves.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 172-181).