<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

Irradiation induces a high concentration of defects in the structural materials of nuclear reactors, which are typically of body-centered cubic Iron (BCC Fe) and its alloys. The primary effect of irradiation is hardening which is caused by the blocking of dislocations with defects and defect clusters like point defects, self-interstitial loops, and voids. The dislocation-defect interactions are atomistic in nature due to the very small length and time scales involved, i.e., of the order of nanometers and picoseconds. To predict the effect of dislocation-defect interactions on the macroscopic mechanical and plastic behavior of the material, it is critically important to develop robust coupling schemes by which accurate atomic level physics of the rate-limiting kinetic processes can be informed into a coarse-grained model such as crystal plasticity. In this thesis we will develop an atomistically informed constitutive model. Relevant atomistic processes are identified from molecular dynamics simulations. The respective unit process studies are conducted using atomistic reaction pathway sampling methods like Nudged Elastic Band method. Stress-dependent activation energies and activation volumes are computed for various rate-liming unit processes like thermally activated dislocation motion via kinkpair nucleation, dislocation pinning due to self interstitial atom, etc. Constitutive laws are developed based on transition state theory, that informs the atomistically determined activation parameters into a coarse-grained crystal plasticity model. The macroscopic deformation behavior predicted by the crystal plasticity model is validated with experimental results and the characteristic features explained in the light of atomistic knowledge of the constituting kinetics. We also investigate on unique irradiation induced defects such as stacking fault tetrahedra, that are formed under non-irradiated condition. This thesis also includes our work on materials with internal interfaces that can resist irradiation induced damage. Overall, the research presented in this thesis involves the implementation and development of novel computational paradigm that encompasses computational approaches of various length and time scales towards robust predictions of the mechanical behavior of irradiated materials.

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.

In this dissertation, we develop multiscale finite element methods and uncertainty quantification technique for Richards' equation, a mathematical model to describe fluid flow in unsaturated porous media. Both coarse-level and fine-level numerical computation techniques are presented. To develop an accurate coarse-scale numerical method, we need to construct an effective multiscale map that is able to capture the multiscale features of the large-scale solution without resolving the small scale details. With a careful choice of the coarse spaces for multiscale finite element methods, we can significantly reduce errors. We introduce several methods to construct coarse spaces for multiscale finite element methods. A coarse space based on local spectral problems is also presented. The construction of coarse spaces begins with an initial choice of multiscale basis functions supported in coarse regions. These basis functions are complemented using weighted local spectral eigenfunctions. These newly constructed basis functions can capture the small scale features of the solution within a coarse-grid block and give us an accurate coarse-scale solution. However, it is expensive to compute the local basis functions for each parameter value for a nonlinear equation. To overcome this difficulty, local reduced basis method is discussed, which provides smaller dimension spaces with which to compute the basis functions. Robust solution techniques for Richards' equation at a fine scale are discussed. We construct iterative solvers for Richards' equation, whose number of iterations is independent of the contrast. We employ two-level domain decomposition pre-conditioners to solve linear systems arising in approximation of problems with high contrast. We show that, by using the local spectral coarse space for the preconditioners, the number of iterations for these solvers is independent of the physical properties of the media. Several numerical experiments are given to support the theoretical results. Last, we present numerical methods for uncertainty quantification applications for Richards' equation. Numerical methods combined with stochastic solution techniques are proposed to sample conductivities of porous media given in integrated data. Our proposed algorithm is based on upscaling techniques and the Markov chain Monte Carlo method. Sampling results are presented to prove the efficiency and accuracy of our algorithm.

Reservoir management typically focuses on maximizing oil and gas recovery from a reservoir based on facts and information while minimizing capital and operating investments. Modern reservoir management uses history-matched simulation model to predict the range of recovery or to provide the economic assessment of different field development strategies. Geological models are becoming increasingly complex and more detailed with several hundred thousand to million cells, which include large sets of subsurface uncertainties. Current issues associated with history matching, therefore, involve extensive computation (flow simulations) time, preserving geologic realism, and non-uniqueness problem. Many of recent rate optimization methods utilize constrained optimization techniques, often making them inaccessible for field reservoir management. Field-scale rate optimization problems involve highly complex reservoir models, production and facilities constraints and a large number of unknowns. We present a hierarchical multiscale calibration approach using global and local updates in coarse and fine grid. We incorporate a multiscale framework into hierarchical updates: global and local updates. In global update we calibrate large-scale parameters to match global field-level energy (pressure), which is followed by local update where we match well-by-well performances by calibration of local cell properties. The inclusion of multiscale calibration, integrating production data in coarse grid and successively finer grids sequentially, is critical for history matching high-resolution geologic models through significant reduction in simulation time. For rate optimization, we develop a hierarchical analytical method using streamline-assisted flood efficiency maps. The proposed approach avoids use of complex optimization tools; rather we emphasize the visual and the intuitive appeal of streamline method and utilize analytic solutions derived from relationship between streamline time of flight and flow rates. The proposed approach is analytic, easy to implement and well-suited for large-scale field applications. Finally, we present a hierarchical Pareto-based approach to history matching under conflicting information. In this work we focus on multiobjective optimization problem, particularly conflicting multiple objectives during history matching of reservoir performances. We incorporate Pareto-based multiobjective evolutionary algorithm and Grid Connectivity-based Transformation (GCT) to account for history matching with conflicting information. The power and effectiveness of our approaches have been demonstrated using both synthetic and real field cases.

abstract: Advanced composites are being widely used in aerospace applications due to their high stiffness, strength and energy absorption capabilities. However, the assurance of structural reliability is a critical issue because a damage event will compromise the integrity of composite structures and lead to ultimate failure. In this dissertation a novel homogenization based multiscale modeling framework using semi-analytical micromechanics is presented to simulate the response of textile composites. The novelty of this approach lies in the three scale homogenization/localization framework bridging between the constituent (micro), the fiber tow scale (meso), weave scale (macro), and the global response. The multiscale framework, named Multiscale Generalized Method of Cells (MSGMC), continuously bridges between the micro to the global scale as opposed to approaches that are top-down and bottom-up. This framework is fully generalized and capable of modeling several different weave and braids without reformulation. Particular emphasis in this dissertation is placed on modeling the nonlinearity and failure of both polymer matrix and ceramic matrix composites. / Dissertation/Thesis / Ph.D. Aerospace Engineering 2011

Dans cette thèse, nous proposons deux algorithmes multi-échelles pour la simulation de modèles géologiques de réservoir. Le premier algorithme relève des méthodes géostatistiques à deux points. Il s'agit d'une simulation séquentielle Gaussienne avec variable secondaire. Dans notre approche multi-échelle, la variable secondaire est supposée connue à une deuxième échelle, de résolution plus grossière. Elle représente alors la tendance ou moyenne de la variable principale. A partir d'une paramétrisation adéquate, on montre que le calage des propriétés du modèle géologique à l'échelle grossière est plus efficace que le calage de ces mêmes propriétés à l'échelle fine. Notre méthode est applicable aux variables continues et aux variables discrètes.Le deuxième algorithme est une adaptation d'un algorithme de synthèse de texture aux problèmes de réservoir. C'est un algorithme de simulation multipoints qui nécessite l'utilisation d'une image d'entrainement. Il permet de reproduire des objets géologiques de formes complexes comme des chenaux ou des réseaux de fractures. Comme tous les algorithmes multipoints, il requiert des temps de calcul important. Nous montrons alors comment l'introduction d'une échelle intermédiaire permet de diminuer ce temps de calcul et d'améliorer la reproduction des grandes structures. Nous testons deux techniques pour diminuer davantage encore le temps de calcul : le scan partiel de l'image d'entrainement ou l'organisation des informations extraites de cette même image. / In this manuscript, we propose two multiscale algorithms for the simulation of geological reservoir models.The first algorithm is based on two-points statistics methods. It is based upon the sequential Gaussian simulation with a secondary variable. In our multiscale approach, the scale of the secondary variable is considered as a second scale of coarser resolution. It represents the trend or the average of the primary variable. In the context of history-matching, it can be shown that adjusting the properties of the geological model at the coarse scale is more effective than doing the same at the fine scale provided a suitable parameterization technique is used. Our method holds for both continuous and discrete variables. The second algorithm is rooted in texture synthesis techniques developed in computer graphics and modified to cope with reservoir simulation. This is a multipoint simulation algorithm. As such, it requires the use of a training image. It permits to simulates complex geological objects like channels or networks of fractures. However, as all multipoint algorithms, it requires significant computation times. We show how the introduction of an intermediate scale reduces the computation time and improves the reproduction of large structures. We also test two techniques to further reduce the computation time: the partial scan of the training image and the preliminary organization of the information extracted from this image.

The construction of mesoscopic (micrometer scale) constitutive laws in materialsscience is studied for a long time. However, the constant progress in high performance computing changes the perspectives. Indeed, constitutive laws now aim at explicitly take into account the microstructure and its underlying physics at the atomic scale, for which simulation techniques prove to be very accurate but definitely expensive. The multiscale approach is therefore perfectly adapted to such a challenge and the dialogue between scales necessary. In this thesis, the mechanical behavior of the energetic material TATB in temperature and pressure is investigated using molecular dynamics simulations in order to understand the microscopic deformation mechanisms responsible for plastic activity. The local computation of mechanical variables was developed in atomistic simulations, allowing the dialogue with continuum mechanical methods. Additionally, prescribed deformation paths were coupled with molecular dynamics, allowing to reveal the plasticity mechanism of TATB single crystal. Nucleation of complex dislocation structures with intrinsic dilatancy, twinning transition pathway and a twinning-buckling pseudo phase transition are three distinct behaviors triggered for different loading directions. Then, mesoscopic simulations inferred by atomic scale observations aim at reproducing the twinning-buckling pseudo-phase transition under tri-axial compression using a Lagrangian code. The comparison between both simulation techniques is made possible thanks to the mechanical tools that have been implemented in themolecular dynamics code. Finally, polycrystalline TATB is simulated with non linear elasticity and we demonstrate the necessity to consider an equation of state compatible with this pseudo phase transition, which has a strong influence on the polycristal behavior. / La conception de lois de comportement en science des matériaux n’est pas nouvelle. Cependant, le progrès constant en calcul haute performance change la donne. En effet, ces lois visent désormais à tenir compte de la microstructure et de la physique sous-jacente, à l’échelle atomique, pour laquelle les techniques de simulation sont précises mais très coûteuses. L’approche multiéchelles semble parfaitement adaptée à ces problématiques et le dialogue entre échelles nécessaire. Dans cette thèse, le comportement mécanique du matériau énergétique TATB en température et en pression est étudié via des simulations de dynamique moléculaire afin de caractériser les mécanismes microscopiques responsable de son comportement irréversible. Le calcul local de variables mécaniques a été développé dans des simulations atomistiques, permettant le dialogue avec les méthodes continues. De plus, une méthode d’application de chemins de déformation a été couplée avec la dynamique moléculaire, menant à la caractérisation de la réponse mécanique très anisotrope du monocristal de TATB. Nucléation de dislocations au cœur complexe, chemin de transition pour le maclage et pseudo-transition de phase de type maclage-flambage sont trois comportements distincts associés à trois types de sollicitation dans différentes directions. Des simulations à l’échelle mésoscopique, alimentées par les données calculées à l’échelle microscopique, sont ensuite effectuées et visent à reproduire la pseudo-transition de phase sous compression triaxiale dans un code Lagrangien. La comparaison des résultats aux deux échelles est rendue possible par les outils de mécanique des milieux continus implémentés dans le code de dynamique moléculaire. Finalement, un polycristal de TATB est simulé en élasticité non linéaire et nous montrons l’importance de considérer une équation d’état compatible avec cette pseudo-transition de phase, qui semble avoir une forte influence sur le comportement du polycristal.

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