This dissertation describes a new version of the Generalized Finite Element Method (GFEM), which is well suited for problems set in domains with a large number of internal features (e.g. voids, inclusions, etc.), which are practically impossible to solve using the standard FEM. The main idea is to employ the mesh-based handbook functions which are solutions of boundary value problems in domains extracted from vertex patches of the employed mesh and are pasted into the global approximation by the Partition of Unity Method (PUM). It is shown that the p-version of the Generalized FEM using mesh-based handbook functions is capable of achieving very high accuracy. It is also analyzed that the effect of the main factors affecting the accuracy of the method namely: (a) The data and the buffer included in the handbook domains, and (b) The accuracy of the numerical construction of the handbook functions. The robustness of the method is illustrated by several model problems defined in domains with a large number of closely spaced voids and/or inclusions with various shapes, including the heat conduction problem defined on domains with porous media and/or a real composite material.

O desgaste abrasivo de dois aços austeníticos ao manganês, materiais com grande utilização na mineração, foi estudado empregando metodologia multiescala (escalas: macro, meso e micro). Na macroescala foram estudados os mecanismos de dano e de desgaste de revestimento de britador utilizado em campo. Na mesoescala foram realizados ensaios de britador de mandíbula e de esclerometria linear. Na microescala o ensaio de esclerometria linear foi utilizado para avaliar os efeitos da camada encruada em campo e da orientação cristalográfica dos grãos austeníticos dos aços com 12 %Mn e 20 %Mn. As técnicas de caracterização utilizadas nesta pesquisa foram: macro e microdureza, nanodureza instrumentada, MO, MEV, DRX, EBSD, FIB e MET. A pesquisa foi dividida em três Capítulos, intitulados: \"Desgaste abrasivo dos aços austeníticos com 12 %Mn e 20 %Mn via ensaio de britador de mandíbula\"; \"Efeito do encruamento e da orientação cristalográfica no desgaste por riscamento dos aços austeníticos 12 %Mn e 20 %Mn\"; e \"Microestrutura da subsuperfície do aço austenítico com 12 %Mn deformado por desgaste abrasivo\". O primeiro Capítulo mostrou, a partir do ensaio de britador de mandíbulas (mesoescala), que o aço com 20 %Mn tem tendência de maior resistência ao desgaste que o aço com 12 %Mn. Este resultado foi obtido para a mandíbula fixa do britador, na qual a severidade de desgaste foi superior a mandíbula móvel, por apresentar microcorte e microsulcamento como micromecanismos predominantes, enquanto na mandíbula móvel o micromecanismo predominante foi a microendentação. No segundo Capítulo observou-se que o desgaste por riscamento (mesoescala e microescala) não depende do perfil de encruamento gerado em campo. Entretanto, foi identificado o efeito da orientação cristalográfica, planos (001), (111) e (101), no desgaste por riscamento dos aços com 12 %Mn e 20 %Mn. No último Capítulo a análise multiescala mostrou que a microestrutura deformada na subsuperfície sofre alterações semelhantes em diferentes intensidades. Nas três escalas de análise foram observadas uma camada com grãos ultrafinos (nanométricos), na subsuperfície, e uma de transição com maclas de deformação. A formação dos grãos ultrafinos foi associada à recristalização dinâmica por deformação plástica, na qual faz parte do mecanismo de auto reparação superficial. Além dos resultados apresentados, o desenvolvimento desta pesquisa de doutorado permitiu a elaboração de duas metodologias: i. análise do efeito da orientação cristalográfica no desgaste por microesclerometria; e ii. análise de microestrutura revelada por ataque iônico - FIB. / The abrasive wear of two manganese austenitic steels, materials broadly used in mining industry, was studied using multiscale methodology (scales: macro, meso and micro). In the macroscale the mechanisms of damage and wear of in-service crusher liner were studied. In the mesoscale, jaw crusher and linear scratch tests were performed. In the microscale the linear scratch test was used to evaluate the effects of the hardening layer and the crystallographic orientation of the austenitic grains of steels with 12 %Mn and 20 %Mn. The characterization techniques used in this research were: macro and microhardness, instrumented nanohardness, OM, MEV, DRX, EBSD, FIB and TEM. The research was divided into three chapters, entitled: \"Abrasive wear of steels with 12 %Mn and 20 %Mn via jaw crusher test\"; \"The effect of the in-service workhardening and crystallographic orientation on the micro-scratch wear of austenitic steels with 12 %Mn and 20 %Mn\"; and \"Subsurface microstructure of the deformed austenitic steel with 12 %Mn by abrasive wear\". The first chapter showed, from the jaw crusher tests (i.e. mesoscale), that the steel with 20 %Mn tends to be more wear resistant than the steel with 12 %Mn. This result was obtained to the fixed jaw crusher, in which the wear severity was superior to the movable jaw, since it presents microcutting and microploughing as predominant micromechanisms, whereas in the mobile jaw the predominant micromechanism was microendentation. In the second chapter, it was observed that scratch wear (i.e. meso and microscale) does not depend on the in-service work-hardening profile. However, it was identified the effect of crystallographic orientation, (001), (111) and (101) planes, on the scratch wear of the steels with 12% Mn and 20% Mn. In the last chapter, the multiscale analysis showed that the subsurface deformed microstructure changes with different intensities. At the three analysis scales, a layer with ultrafine grains was observed in the subsurface and mechanical twins. The formation of this layer, with nanometric grains, was associated with dynamic recrystallization by plastic deformation, in which it is part of the self healing effect. In addition to the results found, the development of this doctoral research allowed for the elaboration of two methodologies: i. Analysis of the effect of crystallographic orientation on the scratch wear; and ii. Microstructure analysis revealed by ion etching - FIB.

A noção de equilíbrio aplicada ao relevo foi alvo de várias discussões ao longo da edificação do pensamento geomorfológico. Vários autores trataram de ideias a ela relacionada e este se tornou um conceito de grande influência sobre o desenvolvimento da ciência geomorfológica. Apesar das várias nuances associadas ao conceito do ponto de vista geomorfológico, o equilíbrio do relevo admite que haja um comportamento balanceado entre os fluxos de matéria e energia que perpassam por entre os materiais, processos morfogenéticos e formas que constituem o relevo. Baseado na concepção de equilíbrio dinâmico como tentativa de explicar a paisagem da alta bacia do rio Piranga em termos das relações entre formas e processos geomorfológicos o objetivo deste estudo foi o de avaliar se o relevo dessa área planáltica, na região centro-sul de Minas Gerais, área de nascente de uma das grandes bacias hidrográficas da região sudeste do Brasil a do rio Doce apresenta condições morfodinâmicas que permitem caracterizá-lo como em estado de equilíbrio. Para isso foram consideradas análises morfométricas, pedológicas, geoquímicas das águas fluviais e da organização da rede de drenagem numa perspectiva multiescalar contemplando desde a compartimentação regional do relevo até os processos de vertente. Por meio dessas análises verificou-se que as condições dos materiais, processos e formas associados ao relevo, às coberturas pedológicas e à rede de drenagem verificadas no alto rio Piranga reúnem indícios condizentes com uma situação geomorfológica de desequilíbrio morfodinâmico recente e em vigência. Situação desencadeada sobretudo pelo processo de captura fluvial do alto rio Piranga, os resultados morfométricos obtidos são condizentes também com a influência de uma neotectônica regional. O desnivelamento do manto de intemperismo representado sobretudo pela proximidade diferenciada à superfície dos horizontes C de muitos perfis pedológicos, tanto no alto quanto no baixo planalto, é apontado como indicativo de um processo de rejuvenescimento dos solos proporcionado pelas atuais condições morfogenéticas preponderantes às pedogenéticas. A falta de correlação dos gradientes fluviais de canais de 3ª ordem com os declives médios das vertentes demonstra um desajuste entre os processos de vertente e a incisão dos canais. O índice de Hack calculado para estes mesmos canais permite concluir sobre uma franca incisão desses canais nos seus trechos de médio curso. As taxas de desnudação geoquímica anual do relevo, baseadas na carga fluvial dissolvida e variando de 3,46 a 7,91 t/km2.ano, não demonstraram um padrão espacial que se possa associar a um determinado comportamento morfodinâmico relacionado à compartimentação morfológica do alto rio Piranga, por exemplo. A análise do manto de alteração associada a outros fatores em termos da evolução regional do relevo permite indicar com base nessas observações pelos menos duas fases morfogenéticas que estão bem marcadas na paisagem do alto rio Piranga. Uma mais antiga quando se desenvolveram as stone lines provavelmente associada a um soerguimento tectônico proeminente e outra mais recente e atual que se refere ao desequilíbrio geomorfológico em vigência. Por todos estes resultados conclui-se que o desequilíbrio também é uma condição natural nas terras altas da alta bacia do rio Piranga, decorrente de histórias geomorfológicas distintas unificadas a partir da captura do alto rio Piranga. / The concept of equilibrium applied in the study of relief has been central in various discussions over the history of Geomorphology. Several authors thought over ideas involving geomorphological equilibrium, which became an important concept to this science. Despite the slight variations in the core concept, equilibrium condition of relief always takes into account the balance among matter attributes, energy flow, processes and features. Based on the conception that dynamic equilibrium is an theoretical attempt to understand landscape in terms of the relationship between landforms and geomorphological processes, this thesis focused the assessment of the morphodynamical conditions that confirm the state of equilibrium of the relief in upper basin of Piranga River, southeastern Minas Gerais (Brazil). For this purpose were performed morphometric analysis, pedological analysis, geochemical analysis of channel water and drainage network features within a multiscale approach, considering regional relief and hillslope processes. All the analysis demonstrated that this highland has been under geomorphological disequilibrium over the recently time. Such situation has been triggered by a stream capture of upper course of the Piranga River. Results of morphometrical analysis are consonant with the regional neotectonics, which is confirmed by an evident difference in soil thickness, especially for the depth of horizon C in many soils profiles in both high plateau and low plateau. This setting was associated with a soil rejuvenation provided from recent morphogenetic conditions. In other hand, the lack of correlation between channel gradients and average slope shows an important misfit between earlier hillslope and channel processes. Hack\'s index measured for these channels indicate higher fluvial incision rates at middle river segments compared to the other ones. Annual geochemical denudation rates, based on dissolved load, ranging from 3.46 to 7.91 ton.y- 1.km-2, had not expressed any spatial pattern neither correlation to other data. The analysis of weathering mantle and other geomorphological factors permit the definition of two wellmarked morphogenetic phases for the upper Piranga River landscape: a previous phase, when stone lines are associated with an uplift condition; and the present one with an active disequilibrium. From the results, it was concluded that disequilibrium is a natural condition on both plateaus of Piranga River, due to their specific geomorphological evolution integrated by the stream capture of upper Piranga River.

Complex industrial processes are represented by data that are well known to be multiscaled due to the variety of events that occur in a process at different time and frequency localizations. Wavelet based multiscale analysis approaches provide an excellent means to examine these events. However, the scope of the existing wavelet based methods in the fields of statistical applications, such as process monitoring and defect identification are still limited. Recent literature contains several wavelet decomposition based multiscale process monitoring approaches including many real life process monitoring applications, such as tool-life monitoring, bearing defect monitoring, and monitoring of ultra-precision processes such as chemical mechanical planarization (CMP) in wafer fabrication. However, all of the above mentioned wavelet based methodologies are offline and depend on the visual observations of the wavelet coefficients and details. The offline analysis paradigm was imposed by the high computation needs of the multiscale analysis, whereas the visual observation based approach was necessitated by the lack of statistical means to identify undesirable events. One of the most recent multiscale application, that deals with detecting delamination in CMP, addressed the need for online analysis by developing a moving window based approach to reduce computation time. This research presents 1) development of a fully online multiscale analysis approach where the speed of wavelet based analysis of the data matches the rate of data generation, 2) development of a statistical tool based on Sequential Probability Ratio Test (SPRT) to detect events of interest, and 3) development of an approach to display the analysis results through real time graphs for ease of process supervisory decision making. The developed methodologies are programmed using MATLAB 6.5 and implemented on several data sets obtained from metal and oxide CMP of wafer fabrication. The results and analysis are presented.

<p>This work deals with the problem of estimating the intrinsic dimension of noisy, high-dimensional point clouds. A general class of sets which are locally well-approximated by <italic>k</italic> dimensional planes but which are embedded in a <italic>D</italic>>><italic>k</italic> dimensional Euclidean space are considered. Assuming one has samples from such a set, possibly corrupted by high-dimensional noise, if the data is linear the dimension can be recovered using PCA. However, when the data is non-linear, PCA fails, overestimating the intrinsic dimension. A multiscale version of PCA is thus introduced which is robust to small sample size, noise, and non-linearities in the data.</p> / Dissertation

The analysis of wave propagation in solids with complex microstructures, and local heterogeneities finds extensive applications in areas such as material characterization, structural health monitoring (SHM), and metamaterial design. Within continuum mechanics, sources of heterogeneities are typically associated to localized defects in structural components, or to periodic microstructures in phononic crystals and acoustic metamaterials. Numerical analysis often requires computational meshes which are refined enough to resolve the wavelengths of deformation and to properly capture the fine geometrical features of the heterogeneities. It is common for the size of the microstructure to be small compared to the dimensions of the structural component under investigation, which suggests multiscale analysis as an effective approach to minimize computational costs while retaining predictive accuracy. This research proposes a multiscale framework for the efficient analysis of the dynamic behavior of heterogeneous solids. The developed methodology, called Geometric Multiscale Finite Element Method (GMsFEM), is based on the formulation of multi-node elements with numerically computed shape functions. Such shape functions are capable to explicitly model the geometry of heterogeneities at sub-elemental length scales, and are computed to automatically satisfy compatibility of the solution across the boundaries of adjacent elements. Numerical examples illustrate the approach and validate it through comparison with available analytical and numerical solutions. The developed methodology is then applied to the analysis of periodic media, structural lattices, and phononic crystal structures. Finally, GMsFEM is exploited to study the interaction of guided elastic waves and defects in plate structures.

<p>One of the key mechanisms that mediate renal autoregulation is the tubuloglomerular feedback (TGF) system, which is a negative feedback loop in the kidney that balances glomerular filtration with tubular reabsorptive capacity. In this dissertation, we develop several mathematical models of the TGF system to study TGF-mediated model dynamics. </p><p>First, we develop a mathematical model of compliant thick ascending limb (TAL) of a short loop of Henle in the rat kidney, called TAL model, to investigate the effects of spatial inhomogeneous properties in TAL on TGF-mediated dynamics. We derive a characteristic equation that corresponds to a linearized TAL model, and conduct a bifurcation analysis by finding roots of that equation. Results of the bifurcation analysis are also validated via numerical simulations of the full model equations. </p><p>We then extend the TAL model to explicitly represent an entire short-looped nephron including the descending segments and having compliant tubular walls, developing a short-looped nephron model. A bifurcation analysis for the TGF loop-model equations is similarly performed by computing parameter boundaries, as functions of TGF gain and delay, that separate differing model behaviors. We also use the loop model to better understand the effects of transient as well as sustained flow perturbations on the TGF system and on distal NaCl delivery.</p><p>To understand the impacts of internephron coupling on TGF dynamics, we further develop a mathematical model of a coupled-TGF system that includes any finite number of nephrons coupled through their TGF systems, coupled-nephron model. Each model nephron represents a short loop of Henle having compliant tubular walls, based on the short-looped nephron model, and is assumed to interact with nearby nephrons through electrotonic signaling along the pre-glomerular vasculature. The characteristic equation is obtained via linearization of the loop-model equations as in TAL model. To better understand the impacts of parameter variability on TGF-mediated dynamics, we consider special cases where the relation between TGF delays and gains among two coupled nephrons is specifically chosen. By solving the characteristic equation, we determine parameter regions that correspond to qualitatively differing model behaviors. </p><p>TGF delays play an essential role in determining qualitatively and quantitatively different TGF-mediated dynamic behaviors. In particular, when noise arising from external sources of system is introduced, the dynamics may become significantly rich and complex, revealing a variety of model behaviors owing to the interaction with delays. In our next study, we consider the effect of the interactions between time delays and noise, by developing a stochastic model. We begin with a simple time-delayed transport equation to represent the dynamics of chloride concentration in the rigid-TAL fluid. Guided by a proof for the existence and uniqueness of the steady-state solution to the deterministic Dirichlet problem, obtained via bifurcation analysis and the contraction mapping theorem, an analogous proof for stochastic system with random boundary conditions is presented. Finally we conduct multiscale analysis to study the effect of the noise, specifically when the system is in subcritical region, but close enough to the critical delay. To analyze the solution behaviors in long time scales, reduced equations for the amplitude of solutions are derived using multiscale method.</p> / Dissertation

While traditional management of the boreal forests results in even-aged forests with low landscape scale variability, recent work has suggested that much of the eastern boreal forest of North America is subject to long natural fire return-intervals. This has led to the development of new management strategies to maintain a mosaic of even and multi-aged stands. In this context I investigated the relationships between diameter-distributions, stand age, forest structure and bird communities. Results showed weak associations of the bird community with cohort classes, but that diameter-distributions can work to succinctly describe some of the variation in stand structure and bird communities. I also explored the utility of LiDAR to measure important structural features for bird communities. Results showed that LiDAR can outperform traditional measures of stand structure at explaining bird communities at differing scales.

While traditional management of the boreal forests results in even-aged forests with low landscape scale variability, recent work has suggested that much of the eastern boreal forest of North America is subject to long natural fire return-intervals. This has led to the development of new management strategies to maintain a mosaic of even and multi-aged stands. In this context I investigated the relationships between diameter-distributions, stand age, forest structure and bird communities. Results showed weak associations of the bird community with cohort classes, but that diameter-distributions can work to succinctly describe some of the variation in stand structure and bird communities. I also explored the utility of LiDAR to measure important structural features for bird communities. Results showed that LiDAR can outperform traditional measures of stand structure at explaining bird communities at differing scales.

O desgaste abrasivo de dois aços austeníticos ao manganês, materiais com grande utilização na mineração, foi estudado empregando metodologia multiescala (escalas: macro, meso e micro). Na macroescala foram estudados os mecanismos de dano e de desgaste de revestimento de britador utilizado em campo. Na mesoescala foram realizados ensaios de britador de mandíbula e de esclerometria linear. Na microescala o ensaio de esclerometria linear foi utilizado para avaliar os efeitos da camada encruada em campo e da orientação cristalográfica dos grãos austeníticos dos aços com 12 %Mn e 20 %Mn. As técnicas de caracterização utilizadas nesta pesquisa foram: macro e microdureza, nanodureza instrumentada, MO, MEV, DRX, EBSD, FIB e MET. A pesquisa foi dividida em três Capítulos, intitulados: \"Desgaste abrasivo dos aços austeníticos com 12 %Mn e 20 %Mn via ensaio de britador de mandíbula\"; \"Efeito do encruamento e da orientação cristalográfica no desgaste por riscamento dos aços austeníticos 12 %Mn e 20 %Mn\"; e \"Microestrutura da subsuperfície do aço austenítico com 12 %Mn deformado por desgaste abrasivo\". O primeiro Capítulo mostrou, a partir do ensaio de britador de mandíbulas (mesoescala), que o aço com 20 %Mn tem tendência de maior resistência ao desgaste que o aço com 12 %Mn. Este resultado foi obtido para a mandíbula fixa do britador, na qual a severidade de desgaste foi superior a mandíbula móvel, por apresentar microcorte e microsulcamento como micromecanismos predominantes, enquanto na mandíbula móvel o micromecanismo predominante foi a microendentação. No segundo Capítulo observou-se que o desgaste por riscamento (mesoescala e microescala) não depende do perfil de encruamento gerado em campo. Entretanto, foi identificado o efeito da orientação cristalográfica, planos (001), (111) e (101), no desgaste por riscamento dos aços com 12 %Mn e 20 %Mn. No último Capítulo a análise multiescala mostrou que a microestrutura deformada na subsuperfície sofre alterações semelhantes em diferentes intensidades. Nas três escalas de análise foram observadas uma camada com grãos ultrafinos (nanométricos), na subsuperfície, e uma de transição com maclas de deformação. A formação dos grãos ultrafinos foi associada à recristalização dinâmica por deformação plástica, na qual faz parte do mecanismo de auto reparação superficial. Além dos resultados apresentados, o desenvolvimento desta pesquisa de doutorado permitiu a elaboração de duas metodologias: i. análise do efeito da orientação cristalográfica no desgaste por microesclerometria; e ii. análise de microestrutura revelada por ataque iônico - FIB. / The abrasive wear of two manganese austenitic steels, materials broadly used in mining industry, was studied using multiscale methodology (scales: macro, meso and micro). In the macroscale the mechanisms of damage and wear of in-service crusher liner were studied. In the mesoscale, jaw crusher and linear scratch tests were performed. In the microscale the linear scratch test was used to evaluate the effects of the hardening layer and the crystallographic orientation of the austenitic grains of steels with 12 %Mn and 20 %Mn. The characterization techniques used in this research were: macro and microhardness, instrumented nanohardness, OM, MEV, DRX, EBSD, FIB and TEM. The research was divided into three chapters, entitled: \"Abrasive wear of steels with 12 %Mn and 20 %Mn via jaw crusher test\"; \"The effect of the in-service workhardening and crystallographic orientation on the micro-scratch wear of austenitic steels with 12 %Mn and 20 %Mn\"; and \"Subsurface microstructure of the deformed austenitic steel with 12 %Mn by abrasive wear\". The first chapter showed, from the jaw crusher tests (i.e. mesoscale), that the steel with 20 %Mn tends to be more wear resistant than the steel with 12 %Mn. This result was obtained to the fixed jaw crusher, in which the wear severity was superior to the movable jaw, since it presents microcutting and microploughing as predominant micromechanisms, whereas in the mobile jaw the predominant micromechanism was microendentation. In the second chapter, it was observed that scratch wear (i.e. meso and microscale) does not depend on the in-service work-hardening profile. However, it was identified the effect of crystallographic orientation, (001), (111) and (101) planes, on the scratch wear of the steels with 12% Mn and 20% Mn. In the last chapter, the multiscale analysis showed that the subsurface deformed microstructure changes with different intensities. At the three analysis scales, a layer with ultrafine grains was observed in the subsurface and mechanical twins. The formation of this layer, with nanometric grains, was associated with dynamic recrystallization by plastic deformation, in which it is part of the self healing effect. In addition to the results found, the development of this doctoral research allowed for the elaboration of two methodologies: i. Analysis of the effect of crystallographic orientation on the scratch wear; and ii. Microstructure analysis revealed by ion etching - FIB.