Pressure ulcers (PU) are localized damage to skin and underlying tissue that forms in response to ischemia and subsequent hypoxia from external applied mechanical loads such as pressure. We demonstrate how a multiscale and multiphysics finite element model can capture the process of pressure ulcer formation.

O Color Mixture é uma técnica para segmentação de imagens coloridas, que cria uma \"Retina Artificial\" baseada na mistura de cores, e faz a quantização da imagem projetando todas as cores em 256 planos no cubo RGB. Em seguida, atravessa todos esses planos com um classificador Gaussiano, visando à segmentação da imagem. Porém, a abordagem atual possui algumas limitações. O classificador atual resolve exclusivamente problemas binários. Inspirado nesta \"Retina Artificial\" do Color Mixture, esta tese define uma nova \"Retina Artificial\", propondo a substituição do classificador atual por uma rede neural artificial para cada um dos 256 planos, com o objetivo de melhorar o desempenho atual e estender sua aplicação para problemas multiclasse e multiescala. Para esta nova abordagem é dado o nome de Neural Color Mixture. Para a validação da proposta foram realizadas análises estatísticas em duas áreas de aplicação. Primeiramente para a segmentação de pele humana, tendo sido comparado seus resultados com oito métodos conhecidos, utilizando quatro conjuntos de dados de tamanhos diferentes. A acurácia de segmentação da abordagem proposta nesta tese superou a de todos os métodos comparados. A segunda avaliação prática do modelo proposto foi realizada com imagens de satélite devido à vasta aplicabilidade em áreas urbanas e rurais. Para isto, foi criado e disponibilizado um banco de imagens, extraídas do Google Earth, de dez regiões diferentes do planeta, com quatro escalas de zoom (500 m, 1000 m, 1500 m e 2000 m), e que continham pelo menos quatro classes de interesse: árvore, solo, rua e água. Foram executados quatro experimentos, sendo comparados com dois métodos, e novamente a proposta foi superior. Conclui-se que a nova proposta pode ser utilizada para problemas de segmentação de imagens coloridas multiclasse e multiescala. E que possivelmente permite estender o seu uso para qualquer aplicação, pois envolve uma fase de treinamento, em que se adapta ao problema. / The Color Mixture is a technique for color images segmentation, which creates an \"Artificial Retina\" based on the color mixture, and quantizes the image by projecting all the colors in 256 plans into the RGB cube. Then, it traverses all those plans with a Gaussian classifier, aiming to reach the image segmentation. However, the current approach has some limitations. The current classifier solves exclusively binary problems. Inspired by this \"Artificial Retina\" of the Color Mixture, we defined a new \"Artificial Retina\", as well as we proposed the replacement of the current classifier by an artificial neural network for each of the 256 plans, with the goal of improving current performance and extending your application to multiclass and multiscale issues. We called this new approach \"Neural Color Mixture\". To validate the proposal, we analyzed it statistically in two areas of application. Firstly for the human skin segmentation, its results were compared with eight known methods using four datasets of different sizes. The segmentation accuracy of the our proposal in this thesis surpassed all the methods compared. The second practical evaluation of the our proposal was carried out with satellite images due to the wide applicability in urban and rural areas. In order to do this, we created and made available a database of satellite images, extracted from Google Earth, from ten different regions of the planet, with four zoom scales (500 m, 1000 m, 1500 m and 2000 m), which contained at least four classes of interest: tree, soil, street and water. We compared our proposal with a neural network of the multilayer type (ANN-MLP) and an Support Vector Machine (SVM). Four experiments were performed, compared to two methods, and again the proposal was superior. We concluded that our proposal can be used for multiclass and multiscale color image segmentation problems, and that it possibly allows to extend its use to any application, as it involves a training phase, in which our methodology adapts itself to any kind of problem.

Advances in multiscale methods are presented from two perspectives which address the issue of computational complexity of optimizing and inverse analyzing nonlinear composite materials and structures at multiple scales. The optimization algorithm provides several solutions to meet the enormous computational challenge of optimizing nonlinear structures at multiple scales including: (i) enhanced sampling procedure that provides superior performance of the well-known ant colony optimization algorithm, (ii) a mapping-based meshing of a representative volume element that unlike unstructured meshing permits sensitivity analysis on coarse meshes, and (iii) a multilevel optimization procedure that takes advantage of possible weak coupling of certain scales. We demonstrate the proposed optimization procedure on elastic and inelastic laminated plates involving three scales. We also present an adaptive variant of the measure-theoretic approach (MTA) for stochastic characterization of micromechanical properties based on the observations of quantities of interest at the coarse (macro) scale. The salient features of the proposed nonintrusive stochastic inverse solver are: identification of a nearly optimal sampling domain using enhanced ant colony optimization algorithm for multiscale problems, incremental Latin-hypercube sampling method, adaptive discretization of the parameter and observation spaces, and adaptive selection of number of samples. A complete test data of the TORAY T700GC-12K-31E and epoxy #2510 material system from the NIAR report is employed to characterize and validate the proposed adaptive nonintrusive stochastic inverse algorithm for various unnotched and open-hole laminates. Advances in Multiscale methods also provides us a unique tool to study and analyze human bones, which can be seen as a composite material, too. We used two multiscale approaches for fracture analysis of full scale femur. The two approaches are the reduced order homogenization (ROH) and the novel accelerated reduced order homogenization (AROH). The AROH is based on utilizing ROH calibrated to limited data as a training tool to calibrate a simpler, single-scale anisotropic damage model. For bone tissue orientation, we take advantage of so-called Wolff’s law. The meso-phase properties are identified from the least square minimization of error between the overall cortical and trabecular bone properties and those predicted from the homogenization. The overall elastic and inelastic properties of the cortical and trabecular bone microstructure are derived from bone density that can be estimated from the Hounsfield units (HU). For model validation, we conduct ROH and AROH simulations of full scale finite element model of femur created from the QCT and compare the simulation results with available experimental data.

A multiscale approach, coined as the High Order Computational Continua (HC2), has been developed for efficient and accurate analysis and design of reinforced concrete structures. Unlike existing homogenization-like methods, the proposed multiscale approach is capable of handling large representative volume elements (RVE), i.e., the classical assumption of infinitesimally is no longer required, while possessing accuracy of direct numerical simulation (DNS) and the computational efficiency of classical homogenization methods. The multiscale beam and plate elements formulated using the proposed HC2 methodology can be easily incorporated into the existing reinforced concrete design practices. The salient features of the proposed formulation are: (i) the ability to consider large representative volume elements (RVE) characteristic to nonsolid beams,waffle and hollowcore slabs, (ii) versatility stemming from the ease of handling damage, prestressing, creep and shrinkage, and (iii) computational efficiency resulting from model reduction, combined with the damage law rescaling methods that yield simulation results nearly mesh-size independent. The multiscale formulation has been validated against experimental data for rectangular beams, I beams, pretensioned beams, continuous posttension beams, solid slabs, prestressed hollowcore slabs and waffle slabs.

The groundwater specialists and the reservoir engineers share the same interest in simulating multiphase flow in soil with heterogeneous intrinsic properties. They also both face the challenge of going from a well-modeled micrometer scale to the reservoir scale with a controlled loss of information. This upscaling process is indeed worthy to make simulation over an entire reservoir manageable and stochastically repeatable. Two upscaling steps can be defined: one from the micrometer scale to the Darcy scale, and another from the Darcy scale to the reservoir scale. In this thesis, a new second upscaling multiscale algorithm Finite Volume Mixed Hybrid Multiscale Methods (Fv-MHMM) is investigated. Extension to a two-phase flow system is done by weakly and sequentially coupling saturation and pressure via IMPES-like method.

Master of Science / Department of Horticulture and Natural Resources / Adam A. Ahlers / The muskrat (Ondatra zibethicus) is an economically and ecologically important furbearer species that occupy wetlands throughout North America. However, populations across the United States (US) are declining and there is little evidence as to the cause of this decline. Wetlands in the upper Midwest, US, are shifting into more homogeneous vegetation states due to an invasive hybrid cattail species, Typha x glauca (hereafter ‘T. x glauca’), outcompeting native vegetation. This hybrid cattail species is now an abundant potential resource for muskrats and has outcompeted native wetland vegetation. I investigated how landscape composition and configuration affected multiscale habitat use by muskrats during the summers of 2016 – 2017. Additionally, I assessed how fetch (impact of wind and wave action), a process dictated by large-scale landscape configuration, influenced muskrat habitat use at a local-scale representing a resource patch. I randomly selected 71 wetland sites within Voyageurs National Park, Minnesota, and used presence/absence surveys to assess site occupancy by muskrats. Each year, multiple surveys were conducted at each site and I used multiseason occupancy modeling to investigate how both local and landscape factors affect site occupancy and turnover. I predicted a positive relationship between local-scale (2 ha) sites, characterized by shallower and less open water, and muskrat occupancy and colonization rates. I also predicted increased occupancy probabilities and colonization rates in wetlands that contain higher amounts of T. x glauca. However, I expected the amount of fetch at each site to negatively influence site occupancy probabilities and colonization rates. At the landscape-scale (2 km), I expected habitat use by muskrats to be positively related to the percentage of T. x glauca and area of wetlands surrounding sites. At the local-scale, muskrats occupied wetlands that contained shallower water depths and less open water. As predicted, site occupancy probabilities were greater in areas with greater amounts of T. x glauca coverage. My results revealed a cross-scale interaction between the severity of fetch impacts and percent of T. x glauca coverage at sites. Muskrats were more likely to colonize areas with greater fetch impacts if there was also greater coverage of T. x glauca at these sites. At the landscape-scale, site-occupancy probabilities were positively influenced by the percent of open water and landscape heterogeneity surrounding each site. My study was the first to document how invasive T. x glauca populations can mitigate negative effects that high wave intensity may have on muskrat spatial distributions. I was also the first to identify multiscale factors affecting the spatial distribution of muskrats in lacustrine ecosystems.

O Color Mixture é uma técnica para segmentação de imagens coloridas, que cria uma \"Retina Artificial\" baseada na mistura de cores, e faz a quantização da imagem projetando todas as cores em 256 planos no cubo RGB. Em seguida, atravessa todos esses planos com um classificador Gaussiano, visando à segmentação da imagem. Porém, a abordagem atual possui algumas limitações. O classificador atual resolve exclusivamente problemas binários. Inspirado nesta \"Retina Artificial\" do Color Mixture, esta tese define uma nova \"Retina Artificial\", propondo a substituição do classificador atual por uma rede neural artificial para cada um dos 256 planos, com o objetivo de melhorar o desempenho atual e estender sua aplicação para problemas multiclasse e multiescala. Para esta nova abordagem é dado o nome de Neural Color Mixture. Para a validação da proposta foram realizadas análises estatísticas em duas áreas de aplicação. Primeiramente para a segmentação de pele humana, tendo sido comparado seus resultados com oito métodos conhecidos, utilizando quatro conjuntos de dados de tamanhos diferentes. A acurácia de segmentação da abordagem proposta nesta tese superou a de todos os métodos comparados. A segunda avaliação prática do modelo proposto foi realizada com imagens de satélite devido à vasta aplicabilidade em áreas urbanas e rurais. Para isto, foi criado e disponibilizado um banco de imagens, extraídas do Google Earth, de dez regiões diferentes do planeta, com quatro escalas de zoom (500 m, 1000 m, 1500 m e 2000 m), e que continham pelo menos quatro classes de interesse: árvore, solo, rua e água. Foram executados quatro experimentos, sendo comparados com dois métodos, e novamente a proposta foi superior. Conclui-se que a nova proposta pode ser utilizada para problemas de segmentação de imagens coloridas multiclasse e multiescala. E que possivelmente permite estender o seu uso para qualquer aplicação, pois envolve uma fase de treinamento, em que se adapta ao problema. / The Color Mixture is a technique for color images segmentation, which creates an \"Artificial Retina\" based on the color mixture, and quantizes the image by projecting all the colors in 256 plans into the RGB cube. Then, it traverses all those plans with a Gaussian classifier, aiming to reach the image segmentation. However, the current approach has some limitations. The current classifier solves exclusively binary problems. Inspired by this \"Artificial Retina\" of the Color Mixture, we defined a new \"Artificial Retina\", as well as we proposed the replacement of the current classifier by an artificial neural network for each of the 256 plans, with the goal of improving current performance and extending your application to multiclass and multiscale issues. We called this new approach \"Neural Color Mixture\". To validate the proposal, we analyzed it statistically in two areas of application. Firstly for the human skin segmentation, its results were compared with eight known methods using four datasets of different sizes. The segmentation accuracy of the our proposal in this thesis surpassed all the methods compared. The second practical evaluation of the our proposal was carried out with satellite images due to the wide applicability in urban and rural areas. In order to do this, we created and made available a database of satellite images, extracted from Google Earth, from ten different regions of the planet, with four zoom scales (500 m, 1000 m, 1500 m and 2000 m), which contained at least four classes of interest: tree, soil, street and water. We compared our proposal with a neural network of the multilayer type (ANN-MLP) and an Support Vector Machine (SVM). Four experiments were performed, compared to two methods, and again the proposal was superior. We concluded that our proposal can be used for multiclass and multiscale color image segmentation problems, and that it possibly allows to extend its use to any application, as it involves a training phase, in which our methodology adapts itself to any kind of problem.

This thesis concentrates on laboratory measurements of the Electron Drift Instrument (EDI), focussing primarily on the EDI optics of the system. The EDI is a device used on spacecraft to measure electric fields by emitting an electron beam and measuring the E X B drift of the returning electrons after one gyration. This drift velocity is determined using two electron beams directed perpendicular to the magnetic field returning to be detected by the spacecraft. The EDI will be used on the Magnetospheric Multi-Scale Mission. The EDI optic's testing process takes measurements of the optics response to a uni-directional electron beam. These measurements are used to verify the response of the EDI's optics and to allow for the optimization of the desired optics state via simulation. The optics state tables were created in simulations and we are using these measurements to confirm their accuracy. The setup consisted of an apparatus made up of the EDI's optics and sensor electronics was secured to the two axis gear arm inside a vacuum chamber. An electron beam was projected at the apparatus which then used the EDI optics to focus the beam into the micro-controller plates and onto the circular 32 pad annular ring that makes up the sensor. The concentration of counts per pad over an interval of 1ms were averaged over 25 samples and plotted in MATLAB. The results of the measurements plotted agreed well with the simulations, providing confidence in the EDI instrument.

A multi-scale Monte Carlo simulation was performed on nine streams of increasing Horton order to investigate the role that variability in hydraulic geometry and resistance play in modifying a flood hydrograph. This study attempts to determine the potential to replace actual cross-sections along a stream reach with a prismatic channel that has mean cross-sectional properties. The primary finding of this work is that the flood routing model is less sensitive to variability in the channel geometry as the Horton order of the stream increases. It was also established that even though smaller streams are more sensitive to variability in hydraulic geometry and resistance, replacing cross-sections along the channel with a characteristic reach wise average cross-section, is still a suitable approximation. Finally a case study of applying this methodology to a natural river is performed with promising results.

While rheological and microstructural complexities have posed tremendous challenges to researchers in developing first principles models and simulation techniques that can accurately and robustly predict the dynamical behaviour of polymeric flows, the past two decades have offered several significant advances towards accomplishing this goal. These accomplishments include: (1). Stable and accurate formulation of continuum-level viscoelastic constitutive models and their efficient implementation using operator splitting methods to explore steady and transient flows in complex geometries, (2). Prediction of rheology of polymer solutions and melts based on micromechanical models as well as highly parallel self-consistent multiscale simulations of non-homogeneous flows. The main objective of this study is to leverage and build upon the aforementioned advances to develop a quantitative understanding of the flow-micro-structure coupling mechanisms in viscoelastic polymeric fluids and in turn predict, consistent with experiments, their essential macroscopic flow properties e.g. frictional drag, interface shape, etc. To this end, we have performed extensive continuum and multiscale flow simulations in several industrially relevant bulk and free surface flows. The primary motivation for the selection of the specific flow problems is based on their ability to represent different deformation types, and the ability to experimentally verify the simulation results as well as their scientific and industrial significance.