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Modern Econometric Methods for the Analysis of Housing MarketsKesiz Abnousi, Vartan 26 May 2021 (has links)
The increasing availability of richer, high-dimensional, home sales data-sets, as well as spatially geocoded data, allows for the use of new econometric and computational methods to explore novel research questions. This dissertation consists of three separate research papers which aim to leverage this trend to answer empirical inferential questions, propose new computational approaches in environmental valuation, and address future challenges.
The first research chapter estimates the effect on home values of 10 large-scale urban stream restoration projects situated near the project sites. The study area is the Johnson Creek Watershed in Portland, Oregon. The research design incorporates four matching model approaches that vary based on the temporal bands' width, a narrow and a wider band, and two spatial zoning buffers, a smaller and larger that account for the affected homes' distances. Estimated effects tend to be positive for six projects when the restoration projects' distance is smaller, and the temporal bands are narrow, while two restoration projects have positive effects on home values across all four modeling approaches.
The second research chapter focuses on the underlying statistical and computational properties of matching methods for causal treatment effects. The prevailing notion in the literature is that there is a tradeoff between bias and variance linked to the number of matched control observations for each treatment unit. In addition, in the era of Big Data, there is a paucity of research addressing the tradeoffs between inferential accuracy and computational time across different matching methods. Is it worth employing computationally costly matching methods if the gains in bias reduction and efficiency are negligible? We revisit the notion of bias-variance tradeoff and address the subject of computational time considerations. We conduct a simulation study and evaluate 160 models and 320 estimands. The results suggest that the conventional notion of a bias-variance tradeoff, with bias increasing and variance decreasing with the number of matched controls, does not hold under the bias-corrected matching estimator (BCME), developed by Abadie and Imbens (2011). Specifically, for the BCME, the trend of bias decreases as the number of matches per treated unit increases. Moreover, when the pre-matching balance's quality is already good, choosing only one match results in a significantly larger bias under all methods and estimators. In addition, the genetic search matching algorithm, GenMatch, is superior compared to the baseline Greedy Method by achieving a better balance between the observed covariate distributions of the treated and matched control groups. On the down side, GenMatch is 408 times slower compared to a greedy matching method. However, when we employ the BCME on matched data, there is a negligible difference in bias reduction between the two matching methods.
Traditionally, environmental valuation methods using residential property transactions follow two approaches, hedonic price functions and Random Utility sorting models. An alternative approach is the Iterated Bidding Algorithm (IBA), introduced by Kuminoff and Jarrah (2010). This third chapter aims to improve the IBA approach to property and environmental valuation compared to its early applications. We implement this approach in an artificially simulated residential housing market, maintaining full control over the data generating mechanism. We implement the Mesh Adaptive Direct Search Algorithm (MADS) and introduce a convergence criterion that leverages the knowledge of individuals' actual pairing to homes. We proceed to estimate the preference parameters of the distribution of an underlying artificially simulated housing market. We estimate with significantly higher precision than the original baseline Nelder-Mead optimization that relied only on a price discrepancy convergence criterion, as implemented during the IBAs earlier applications. / Doctor of Philosophy / The increasing availability of richer, high-dimensional, home sales data sets enables us to employ new methods to explore novel research questions involving housing markets. This dissertation consists of three separate research papers which leverage this trend.
The first research paper estimates the effects on home values of 10 large-scale urban stream restoration projects in Portland, Oregon. These homes are located near the project sites. The results show that the distance of the homes from the project sites and the duration of the construction cause different effects on home values. However, two restorations have positive effects regardless of the distance and the duration period.
The second research study is focused on the issue of causality. The study demonstrates that a traditional notion concerning causality known as the ``bias-variance tradeoff" is not always valid. In addition, the research shows that sophisticated but time-consuming algorithms have negligible effects in improving the accuracy of estimating the causal effects when we account for the required computational time.
The third research study improves an environmental evaluation method that relies on residential property transactions. The methodology leverages the features of more informative residential data sets in conjunction with a more efficient optimization method, leading to significant improvements. The study concludes that due to these improvements, this alternative method can be employed to elicit the true preferences of homeowners over housing and locational characteristics by avoiding the shortcomings of existing techniques.
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NETWORK ALIGNMENT USING TOPOLOGICAL AND NODE EMBEDDING FEATURESAljohara Fahad Almulhim (19200211) 03 September 2024 (has links)
<p dir="ltr">In today's big data environment, development of robust knowledge discovery solutions depends on integration of data from various sources. For example, intelligence agencies fuse data from multiple sources to identify criminal activities; e-commerce platforms consolidate user activities on various platforms and devices to build better user profile; scientists connect data from various modality to develop new drugs, and treatments. In all such activities, entities from different data sources need to be aligned---first, to ensure accurate analysis and more importantly, to discover novel knowledge regarding these entities. If the data sources are networks, aligning entities from different sources leads to the task of network alignment, which is the focus of this thesis. The main objective of this task is to find an optimal one-to-one correspondence among nodes in two or more networks utilizing graph topology and nodes/edges attributes. </p><p dir="ltr">In existing works, diverse computational schemes have been adopted for solving the network alignment task; these schemes include finding eigen-decomposition of similarity matrices, solving quadratic assignment problems via sub-gradient optimization, and designing iterative greedy matching techniques. Contemporary works approach this problem using a deep learning framework by learning node representations to identify matches. Node matching's key challenges include computational complexity and scalability. However, privacy concerns or unavailability often prevent the utilization of node attributes in real-world scenarios. In light of this, we aim to solve this problem by relying solely on the graph structure, without the need for prior knowledge, external attributes, or guidance from landmark nodes. Clearly, topology-based matching emerges as a hard problem when compared to other network matching tasks.</p><p dir="ltr">In this thesis, I propose two original works to solve network topology-based alignment task. The first work, Graphlet-based Alignment (Graphlet-Align), employs a topological approach to network alignment. Graphlet-Align represents each node with a local graphlet count based signature and use that as feature for deriving node to node similarity across a pair of networks. By using these similarity values in a bipartite matching algorithm Graphlet-Align obtains a preliminary alignment. It then uses high-order information extending to k-hop neighborhood of a node to further refine the alignment, achieving better accuracy. We validated Graphlet-Align's efficacy by applying it to various large real-world networks, achieving accuracy improvements ranging from $20\%$ to $72\%$ over state-of-the-art methods on both duplicated and noisy graphs.</p><p dir="ltr">Expanding on this paradigm that focuses solely on topology for solving graph alignment, in my second work, I develop a self-supervised learning framework known as Self-Supervised Topological Alignment (SST-Align). SST-Align uses graphlet-based signature for creating self-supervised node alignment labels, and then use those labels to generate node embedding vectors of both the networks in a joint space from which node alignment task can be effectively and accurately solved. It starts with an optimization process that applies average pooling on top of the extracted graphlet signature to construct an initial node assignment. Next, a self-supervised Siamese network architecture utilizes both the initial node assignment and graph convolutional networks to generate node embeddings through a contrastive loss. By applying kd-tree similarity to the two networks' embeddings, we achieve the final node mapping. Extensive testing on real-world graph alignment datasets shows that our developed methodology has competitive results compared to seven existing competing models in terms of node mapping accuracy. Additionally, we establish the Ablation Study to evaluate the two-stage accuracy, excluding the learning representation part and comparing the mapping accuracy accordingly.</p><p dir="ltr">This thesis enhances the theoretical understanding of topological features in the analysis of graph data for network alignment task, hence facilitating future advancements toward the field.</p>
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Essays on the evaluation of land use policy: the effects of regulatory protection on land use and social welfareAndam, Kwaw Senyi 28 March 2008 (has links)
Societies frequently implement land use policies to regulate resource extraction or to regulate development. However, two important policy questions remain unresolved. First, how effective are land use regulations? Second, how do land use regulations affect socioeconomic conditions? Three issues complicate the evaluation of land use policies: (1) overt bias may lead to incorrect estimates of policy effects if implementation is nonrandom; (2) the policy may affect outcomes in neighboring unregulated lands; and (3) unobservable differences between regulated and unregulated lands may lead to biased assessments. Previous evaluations of land use policies fail to address these sources of bias simultaneously.
In this dissertation, I develop an approach, using matching methods, which jointly accounts for these complications. I apply the approach to evaluate the effects of Costa Rica s protected areas on land use and socioeconomic outcomes between 1960 and 2000.
I find that: (1) protection prevented the deforestation of only 10 percent or less of protected forests; (2) protection resulted in reforestation of only 20 percent of non-forest areas that were protected; (3) protection had little effect on land use outside protected areas, most likely because, as noted above, protected areas had only small effects on land use inside protected areas; and (4) there is little evidence that protected areas had harmful impacts on the livelihoods of local communities: on the contrary, I find that protection had small positive effects on socioeconomic outcomes. Furthermore, the methods traditionally used to conduct such evaluations are biased. In contrast to the findings above, those conventional methods overestimated the amount of avoided deforestation and erroneously implied that protection had negative impacts on the livelihoods of local communities.
This dissertation contributes to policymaking by providing empirical measures of protected area effectiveness. Although annual global expenditures on protected areas are about $6.5 billion, little is known to date about the returns on these investments. This study also indicates that policymakers should give careful consideration to current proposals to compensate communities living in or around protected areas: contrary to widely held assumptions, the findings suggest that protection may not have harmful effects on socioeconomic outcomes.
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[en] MODE-MATCHING TECHNIQUE ALONG OBLIQUE SURFACES AND APPLICATIONS TO THE MODELING OF CURVED WAVEGUIDES / [pt] MÉTODO DE CASAMENTO DE MODOS AO LONGO DE SUPERFÍCIES OBLÍQUAS E APLICAÇÕES PARA A MODELAGEM DE GUIAS DE ONDAS CURVADOSMARCELLO ALVES REIS 24 November 2023 (has links)
[pt] Guias de onda são amplamente utilizados na engenharia de
telecomunicações para a transmissão de sinais e construção de filtros e
outros dispositivos de micro-ondas. Neste trabalho, apresentamos uma
formulação baseada na técnica de casamento de modos (MMT) para a
análise de descontinuidades em guias de ondas cilíndricos causadas por
curvaturas no eixo longitudinal da linha de transmissão. Apresentamos e
validamos uma técnica para análise modal de guias de ondas curvos através
da aproximação da curvatura por uma sucessão de superfícies oblíquas por
meio de suas matrizes de espalhamento generalizadas (GSMs) extraídas do
MMT. A presente abordagem é uma alternativa computacionalmente eficiente
para modelar curvaturas em guias de ondas cilíndricos quando comparada
às técnicas usuais de força bruta numérica (tais como soluções baseadas
em elementos, volumes, ou diferenças finitas). Um algoritmo é apresentado
para calcular os elementos da matriz GSM para diferentes configurações
de junções de guias de onda. A novidade do presente método consiste em
considerar a projeção dos campos eletromagnéticos em superfícies oblíquas
para a aplicação do MMT. Apresentamos uma série de resultados numéricos
que mostram que a técnica apresentada neste estudo pode garantir resultados
com boa acurácia e precisão ao realizar a análise do comportamento modal
dos campos eletromagnéticos em descontinuidades provocados por curvaturas. / [en] Waveguides are widely used in telecommunications engineering for
transmitting signals and manufacturing filters and other devices in the
microwave applications. In this work, we present a formulation based on
the mode-matching technique (MMT) for the analysis of discontinuities in
cylindrical waveguides caused by curvatures in the longitudinal axis of the
transmission line. We present and validate a technique for modal analysis
of curved waveguides by approximating the curvature in a succession of
oblique surfaces by means of their generalized scattering matrices (GSMs)
extracted from the MMT. The present approach is a computationally efficient
alternative for modeling curvature in cylindrical waveguides when compared
to usual numerical brute force techniques (such as element-based, volumebased,
or finite difference solutions). An algorithm is presented to compute
the GSM matrix elements for different configurations of waveguide junctions.
The novelty of the present method consists in considering the projection of
electromagnetic fields onto oblique surfaces for the application of MMT. We
present a series of numerical results that show that the technique presented
in this study can guarantee results with good accuracy and precision when
performing the analysis of the modal behavior of electromagnetic fields at
discontinuities caused by curvatures.
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[en] A MODE-MATCHINGBASED SOLUTION FOR THE ANALYSIS OF A CLASS OF ELECTROMAGNETIC WAVEGUIDE DEVICES / [pt] ANÁLISE ELETROMAGNÉTICA APLICADA A UMA CLASSE DE ESTRUTURAS GUIADAS BASEADA NO MÉTODO DE CASAMENTO DE MODOANDRE LUIZ DOS SANTOS LIMA 01 March 2021 (has links)
[pt] Esta tese apresenta uma solução semianalítica para a modelagem eletromagnética de estruturas guiadas com simetria cilíndrica no domínio da frequência. A técnica apresentada permite que uma classe abrangente de guias de ondas, acopladores, filtros, entre outros, sejam projetados de forma acurada e com custo computacional muito pequeno em termos de tempo de processamento e memória quando comparado com outras técnicas baseadas em diferenças finitas ou elementos finitos. Neste trabalho, a modelagem de estruturas guiadas relativamente complexas foi realizada usando uma decomposição em subdomínios computacionais nos quais conhecemos uma solução analítica para o problema de contorno associado.
Em uma segunda etapa, as condições de contorno de acoplamento entre os subdomínios foram então impostas por meio da conservação da reação e o formalismo do método do casamento de modos. Como consequência, obtemos uma solução analítica para o problema da conexão entre guias de ondas compostos por seções circulares e coaxiais acopladas. Ao nosso conhecimento, a formulação matemática desenvolvida para o acoplamento entre subdomínios circular e coaxial é inédita, e unifica vários modelos de acoplamento modais conhecidos até então sob um formalismo generalizado. Apresentamos uma série de resultados de validação que demonstram que a técnica introduzida neste trabalho permite modelar de forma acurada e
eficiente uma vasta classe de estruturas guiadas. Em adição, uma formulação matemática complementar foi introduzida para a descrição do acoplamento ortogonal entre as estruturas circulares e coaxiais acopladas com guias retangulares. Uma descrição criteriosa sobre as dificuldades matemáticas e suas consequências para a implementação numérica é também apresentada. / [en] This dissertation presents a semi-analytic solution for the electromagnetic wave modeling in guided structures with cylindrical symmetry in the frequency domain. The technique presented herein
allows that a comprehensive class of waveguides, couplers, filters, among others microwave devices, to be designed accurately, and with relatively low computational cost in terms of CPU processing time and RAM
memory when compared to other numerical methods based on the finite-difference or finite-element discretization of Maxwell’s equations. In this work, the electromagnetic modeling of a relatively complex
guided structure was performed by using successions of computational subdomain decompositions, in which we know an analytic solution for each associated subdomain boundary problem. In a second step, the coupling boundary conditions between the subdomains were then enforced by means of the conservation of the reaction and the formalism of the mode-matching technique. As a result, we were able to obtain an analytical solution for the coupling problem of the waveguide composed
by circular and coaxial sections. To the best of our knowledge, the mathematical formulation developed for the coupling between circular and coaxial subdomains is an original unprecedented scientific contribution,
and it unifies several modal-coupling models known hitherto under a generalized formalism. We present a series of validation results showing that the technique introduced in this work can model accurately and
efficiently a comprehensive class of electromagnetic waveguide devices. In addition, a supplementary mathematical formulation was introduced for describing the orthogonal coupling between the circular/coaxial structures with rectangular waveguides insert ports. A painstaking description
of the mathematical difficulties and their consequences for numerical implementation is presented as well.
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[en] PSEUDO-ANALYTICAL MODELING FOR ELECTROMAGNETIC WELL-LOGGING TOOLS IN COMPLEX GEOPHYSICAL FORMATIONS / [pt] MODELAGEM PSEUDOANALÍTICA PARA FERRAMENTAS DE PERFILAGEM ELETROMAGNÉTICA EM FORMAÇÕES GEOFÍSICAS COMPLEXASGUILHERME SIMON DA ROSA 17 July 2017 (has links)
[pt] Esta tese apresenta um estudo sobre técnicas de modelagem numérica utilizadas na análise da propagação eletromagnética em formações geofísicas comumente encontradas na perfuração de poços de petróleo. O emprego de sensores eletromagnéticos adjacentes à broca de perfuração permite a inferência dos parâmetros constitutivos do solo ao redor do poço. Nos últimos anos, os avanços da tecnologia de perfilagem eletromagnética permitiram a modelagem em tempo real do problema, possibilitando direcionar a perfuração do poço a fim de maximizar a exploração de petróleo, gás, e outros hidrocarbonetos fósseis. Formações geofísicas complexas são predominantes neste tipo de problema, e geralmente são modeladas usando técnicas numéricas de força bruta como os métodos de diferenças finitas, dos elementos finitos ou dos volumes finitos. No entanto, estas técnicas têm um custo computacional relativamente alto em termos de memória e tempo de processamento. O avanço da tecnologia de perfilagem em tempo real requer
abordagens mais eficientes. Neste trabalho nós empregamos o método do casamento de modos combinado com uma série de características positivas dos métodos pseudoanalíticos conhecidos na literatura para obter uma técnica inédita que permite analisar poços direcionais com estratificações radiais e longitudinais em formações geofísicas anisotrópicas. A técnica proposta permite modelar problemas ainda não explorados, mas com motivação tecnológica iminente, como a propagação eletromagnética ao longo de poços curvados e a perfuração em camadas inclinadas em relação ao eixo axial do poço. Nós apresentamos uma série de resultados de validação que demonstram que a técnica introduzida neste trabalho pode modelar de forma acurada e eficiente sensores de perfilagem eletromagnética usados na exploração de petróleo e gás. / [en] This research presents a study on numerical techniques to model the electromagnetic propagation in geophysical formations commonly encountered in oil well drilling. The employment of electromagnetic sensors surrounding the drill bit allows inferring the constitutive parameters of the soil around the well. In recent years, advances in electromagnetic logging technology have enabled the real-time modeling of this problem. In this way, the drilling direction can be guided in order to maximize the exploitation of oil, gas, and other fossil hydrocarbons. The complex geophysical formations that are prevalent in this type of problem can be effectively handled using brute-force numerical techniques such as finite-differences, finite-elements and finite-volumes. However, these techniques suffer from relatively high cost in terms of both computer memory and CPU time. The advancement of real-time logging technology demands approaches that are more efficient than purely numerical methods. In this work, we employ the mode-matching
technique combining attractive features of the well-known pseudo-analytical approaches to obtain a new technique for analyzing directional well-logging tools in anisotropic formations with both radial and axial stratifications. The proposed technique allows to model problems not yet explored, but with a strong technological motivation, such as electromagnetic propagation along curved wells and drilling along inclined layers. We present a series of validation results showing that the novel technique introduced in this study
can model accurately and efficiently electromagnetic logging sensors used in oil and gas exploration.
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Essays on the Evaluation of Land Use Policy: The Effects of Regulatory Protection on Land Use and Social WelfareAndam, Kwaw Senyi 24 October 2007 (has links)
Societies frequently implement land use policies to regulate resource extraction or to regulate development. However, two important policy questions remain unresolved. First, how effective are land use regulations? Second, how do land use regulations affect socioeconomic conditions? Three issues complicate the evaluation of land use policies: (1) overt bias may lead to incorrect estimates of policy effects if implementation is nonrandom; (2) the policy may affect outcomes in neighboring unregulated lands; and (3) unobservable differences between regulated and unregulated lands may lead to biased assessments. Previous evaluations of land use policies fail to address these sources of bias simultaneously. In this dissertation, I develop an approach, using matching methods, which jointly accounts for these complications. I apply the approach to evaluate the effects of Costa Rica s protected areas on land use and socioeconomic outcomes between 1960 and 2000. I find that: (1) protection prevented the deforestation of only 10 percent or less of protected forests; (2) protection resulted in reforestation of only 20 percent of non-forest areas that were protected; (3) protection had little effect on land use outside protected areas, most likely because, as noted above, protected areas had only small effects on land use inside protected areas; and (4) there is little evidence that protected areas had harmful impacts on the livelihoods of local communities: on the contrary, I find that protection had small positive effects on socioeconomic outcomes. Furthermore, the methods traditionally used to conduct such evaluations are biased. In contrast to the findings above, those conventional methods overestimated the amount of avoided deforestation and erroneously implied that protection had negative impacts on the livelihoods of local communities. This dissertation contributes to policymaking by providing empirical measures of protected area effectiveness. Although annual global expenditures on protected areas are about $6.5 billion, little is known to date about the returns on these investments. This study also indicates that policymakers should give careful consideration to current proposals to compensate communities living in or around protected areas: contrary to widely held assumptions, the findings suggest that protection may not have harmful effects on socioeconomic outcomes.
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Modeling the effect of injecting low salinity water on oil recovery from carbonate reservoirsAl Shalabi, Emad Waleed 10 February 2015 (has links)
The low salinity water injection technique (LSWI) has become one of the important research topics in the oil industry because of its possible advantages for improving oil recovery. Several mechanisms describing the LSWI process have been suggested in the literature; however, there is no consensus on a single main mechanism for the low salinity effect on oil recovery. As a result of the latter, there are few models for LSWI and especially for carbonates due to their heterogeneity and complexity. In this research, we proposed a systematic approach for modeling the LSWI effect on oil recovery from carbonates by proposing six different methods for history matching and three different LSWI models for the UTCHEM simulator, empirical, fundamental, and mechanistic LSWI models. The empirical LSWI model uses contact angle measurements and injected water salinity. The fundamental LSWI model captures the effect of LSWI through the trapping number. In the mechanistic LSWI model, we include the effect of different geochemical reactions through Gibbs free energy. Moreover, field-scale predictions of LSWI were performed and followed by a sensitivity analysis for the most influential design parameters using design of experiment (DoE). The LSWI technique was also optimized using the response surface methodology (RSM) where a response surface was built. Also, we moved a step further by investigating the combined effect of injecting low salinity water and carbon dioxide on oil recovery from carbonates through modeling of the process and numerical simulations using the UTCOMP simulator. The analysis showed that CO₂ is the main controller of the residual oil saturation whereas the low salinity water boosts the oil production rate by increasing the oil relative permeability through wettability alteration towards a more water-wet state. In addition, geochemical modeling of LSWI only and the combined effect of LSWI and CO₂ were performed using both UTCHEM and PHREEQC upon which the geochemical model in UTCHEM was modified and validated against PHREEQC. Based on the geochemical interpretation of the LSWI technique, we believe that wettability alteration is the main contributor to the LSWI effect on oil recovery from carbonates by anhydrite dissolution and surface charge change through pH exceeding the point of zero charge. / text
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[en] APLICATION OF NUMERICAL MODE-MATCHING METHOD IN THE STUDY OF WELL LOGGING OIL WITH MULTIPLE KNOTS / [pt] APLICAÇÃO DO MÉTODO DE CASAMENTOS DE MODOS COM B-SPLINES DE MÚLTIPLOS NÓS AO ESTUDO DE PERFILAGEM DE POÇOS PETROLÍFEROSMAIQUEL DOS SANTOS CANABARRO 06 April 2017 (has links)
[pt] No processo de perfilagem de poços de petróleo e gás, as propriedades entre duas camadas axiais podem apresentar diferenças. Estas descontinuidades das propriedades algumas vezes trazem dificuldades na representação do comportamento dos campos electromagnéticos. Nas análises eletromagnéticas de perfilagem de poço de petróleo, o Método de Casamento de Modos (NMM) vem sendo utilizado a partir da combinação de técnicas numéricas com analíticas e da resolução das equações de Maxwell em meios heterogêneos, cujos campos eletromagnéticos, na direção axial, são representados via decomposição espectral, e, na direção radial, por meio de solução das equações diferenciais ordinárias. Assim, com o objetivo de explorar a representação dos campos eletromagnéticos sobre as interfaces axiais via NMM, este trabalho propõe a utilização de funções B-Splines cúbicas na expansão dos campos, na direção axial, bem como a incorporação da multiplicidade de nós, que permitem uma melhor representação do comportamento dos campos nas interfaces axiais. O algoritmo implementado foi validado nas suas diversas etapas ao comparar os autovalores da representação modal com os obtidos analiticamente em problemas canônicos, e os resultados finais comparados com exemplos apresentados na literatura e calculados com o Método de Diferenças Finitas no Tempo (FDTD). O método NMM, combinado às funções B-Splines cúbicas, foi aplicado a vários perfis de poços de petroléo que serviram de exemplo neste estudo. Um estudo comparativo mostrou que o uso das funções B-Splines cúbicas com multiplicidade dos nós sobre as descontinuidades permitiu uma redução no número total de nós nas expansões dos campos eletromagnéticos. / [en] In the logging process of gas and oil wells, differences in the properties between two axial layers can usually be found. These property discontinuities can bring difficulties for the representation of electromagnetic fields behavior. For electromagnetic analysis of well logging, the Numerical Mode-Matching - NMM method has been used. It combines numerical and analytical techniques, by solving equations Maxwell s in a heterogeneous media. There, the electromagnetic fields in the axial direction are represented by spectral decomposition and in the radial direction are represented by the solution of Ordinary Differential Equations (ODE). With the objective of explorer the representation of the electromagnetic fields on axial interfaces in the Numerical Mode Matched Method, this work explores the use of B-Splines cubic functions to expand the fields in the axial direction, as well as the incorporation of the multiple knots fetching to become the representation of fields behavior most optimized and realistic on axial interfaces. The NMM algorithm was implemented and it was validated by comparing the final results with those obtained by using Finite Difference Time-Domain – FDTD to analyse examples shown in the literature. To validate the results obtained for the eigenvalues, they were compared with the analytical solutions obtained for canonical configurations. The use of NMM Method combined with B-Spline cubic has been applied to several well profiles shown in the literature. The comparative study showed that the use B-Spline cubic with multiple knots near the discontinuities allows a reduction in the overall number of knots employed in the field expansion.
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[pt] CARACTERIZAÇÃO ELETROMAGNÉTICA DE GUIAS DE ONDA CILÍNDRICOS NÃO HOMOGÊNEOS USANDO O MÉTODO DO CASAMENTO DE MODOS / [en] ELECTROMAGNETIC CHARACTERIZATION OF INHOMOGENEOUS CYLINDRICAL WAVEGUIDES USING MODE-MATCHING-BASED METHODS29 September 2020 (has links)
[pt] Muitos dispositivos e estruturas empregados para guiar ondas
eletromagnéticas apresentam conformidade cilíndrica. Aplicações sensíveis
de engenharia de micro-ondas e de dispositivos ópticos integrados empregam,
muitas vezes, materiais não homogêneos, anisotrópicos e dissipativos, de modo
que a pesquisa por modelos computacionais robustos e acurados é um tópico
de notável interesse para a Engenharia Elétrica. Este trabalho apresenta uma
técnica semianalítica para resolver problemas de valor de contorno associados a
guias de onda cilíndricos, anisotrópicos e não homogêneos. Nossa metodologia
permite modelar estruturas com camadas radiais, com anisotropia uniaxial, e
com perdas. A solução proposta parte das equações de Maxwell para campos
harmônicos no tempo, e emprega uma expansão modal em termos da série de
Bessel-Fourier. Os autovalores associados ao problema são obtidos por meio
do método do winding number, em que diversas abordagens para o cálculo das
integrais de caminho no plano complexo são exploradas. Para analisar junções
entre guias de ondas estratificados, empregamos a técnica de casamento de
modos baseada na conservação da Reação dos campos. Nossa formulação é
capaz de avaliar os efeitos da excitação e do acoplamento entre modos puros
(TM, TE, e TEM) em guias de ondas homogêneos, bem como dos modos
híbridos em estruturas complexas. Uma série de resultados numéricos são
apresentados e mostram a capacidade da metodologia desenvolvida nesta
pesquisa para caracterizar corretamente estruturas cilíndricas compostas por
meios complexos (não homogêneos, anisotrópicos e dissipativos) de forma
robusta e computacionalmente eficiente se comparado com outras técnicas
convencionais de eletromagnetismo computacional. / [en] Many devices and structures used to guide electromagnetic waves are
conformal with the cylindrical coordinates. Sensitive applications of microwave
engineering and integrated optical devices often use non-homogeneous,
anisotropic and dissipative materials, so that the research for robust
and accurate computational models is a topic of remarkable interest for
Electrical Engineering. This work presents a semi-analytical technique for
solving boundary-value problems associated with cylindrical, anisotropic,
and non-homogeneous waveguides. Our methodology allows us to model
structures with radial layers, with uniaxial anisotropy, and with losses.
The proposed solution starts from Maxwell s equations for time-harmonic
electromagnetic fields and employs a modal expansion in terms of the
Bessel-Fourier series. The eigenvalues associated with the problem are
obtained using the winding number method, in which several approaches for
calculating complex-plane contour integrals are explored in detail. In order
to properly analyze the junctions between sections of stratified waveguides,
we employ a mode-matching technique based on the conservation of the
Reaction of the fields. Our formulation can handle the effects of excitation
and coupling between pure modes (TM, TE, and TEM) in homogeneous
waveguides, as well as hybrid modes in complex structures. A series of
numerical results are presented and show the capacity of the methodology
developed here to correctly characterize cylindrical structures composed of
complex media (inhomogeneous, anisotropic, and dissipative) in a robust
and computationally-efficient fashion if compared to other conventional
computational electromagnetic techniques.
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