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Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure correction schemes used for the incompressible Navier Stokes flow computations. This version is validated on standard test cases with realistic boundary conditions using unstructured triangular meshes. We also pioneer investigations of the effects of CGP on the accuracy of the pressure field. It is found that although CGP reduces the pressure field accuracy, it preserves the accuracy of the pressure gradient and thus the velocity field, while achieving speedup factors ranging from approximately 2 to 30. Exploring the influence of boundary conditions on CGP, the minimum speedup occurs for velocity Dirichlet boundary conditions, while the maximum speedup occurs for open boundary conditions. We discuss the CGP method as a guide for partial mesh refinement of incompressible flow computations and show its application for simulations of flow over a backward facing step and flow past a cylinder. / Master of Science

The present thesis is on the error estimates of different energy based quasicontinuum (QC) methods, which are a class of computational methods for the coupling of atomistic and continuum models for micro- or nano-scale materials. The thesis consists of two parts. The first part considers the a priori error estimates of three energy based QC methods. The second part deals with the a posteriori error estimates of a specific energy based QC method which was recently developed. In the first part, we develop a unified framework for the a priori error estimates and present a new and simpler proof based on negative-norm estimates, which essentially extends previous results. In the second part, we establish the a posteriori error estimates for the newly developed energy based QC method for an energy norm and for the total energy. The analysis is based on a posteriori residual and stability estimates. Adaptive mesh refinement algorithms based on these error estimators are formulated. In both parts, numerical experiments are presented to illustrate the results of our analysis and indicate the optimal convergence rates. The thesis is accompanied by a thorough introduction to the development of the QC methods and its numerical analysis, as well as an outlook of the future work in the conclusion.

<p>This report examines the problem of real-time head pose estimation in low-resolution football footage. A method is presented for inferring the head pose using a combination of footage and knowledge of the locations of the football and players. An ensemble of randomized ferns is compared with a support vector machine for processing the footage, while a support vector machine performs pattern recognition on the location data. Combining the two sources of information outperforms either in isolation. The location of the football turns out to be an important piece of information.</p> / QC 20100707 / Capturing and Visualizing Large scale Human Action (ACTVIS)

Les protéines amyloïdes sont retrouvées sous forme de fibres dans de nombreuses maladies neurodégénératives. En tentant d’élucider le mécanisme de fibrillation, les chercheurs ont découvert que cette réaction se fait par un phénomène de nucléation passant par des oligomères. Il semblerait que ces espèces soient la principale cause de la toxicité observée dans les cellules des patients atteints d’amyloïdose. C’est pourquoi un intérêt particulier est donc porté aux premières étapes d’oligomérisation. Dans ce mémoire, nous nous intéressons à une séquence d’acide aminé fortement hydrophobe de l’α-synucléine appelée composante non β -amyloïde (Non-Amyloid β Component ou NAC). Cette dernière est retrouvée sous forme de fibres dans les corps et les neurites de Lewy des patients atteints de la maladie de Parkinson. De plus, elle constitue une composante minoritaire des fibres impliquées dans la maladie d’Alzheimer. Nous avons observé les changements structuraux qui ont lieu pour le monomère, le dimère et le trimère de la séquence NAC de l’α-synucléine. Nous nous sommes aussi intéressés aux conséquences structurelles observées dans des oligomères hétérogènes qui impliqueraient, Aβ1−40. Pour cela nous utilisons des dynamiques moléculaires, d’échange de répliques couplées au potentiel gros-grain, OPEP. Nous constatons une disparition des hélices α au profit des feuillets β , ainsi que le polymorphisme caractéristique des fibres amyloïdes. Certaines régions se sont démarquées par leurs capacités à former des feuillets β . La disparition de ces régions lorsque NAC est combinée à Aβ laisse entrevoir l’importance de l’emplacement des résidus hydrophobes dans des structures susceptibles de former des fibres amyloïdes. / Amyloid proteins are found in fiber form in many neurodegenerative diseases. In attempting to elucidate the mechanism of fibrillation, researchers have found that fibril formation occurs by a nucleation mechanisms involving oligomers. It seems, in particular, that the latter species are responsible for the toxicity observed in the cells of patients suffering from amyloidosis. That is why special interest is focused in the early stages of oligomerization. In this this work, we focus on a highly hydrophobic amino acid sequence of the α-synuclein called Non-Amyloid β Component (NAC). The NAC is recovered in the form of fibers in the body and Lewy neurites in patients with Parkin- son’s disease. Moreover, it is a minority component of the fibers involved in Alzheimer’s disease. In particular, we observe the structural changes taking place for the monomer, dimer and trimer of the NAC region of α-synuclein. We are also interested in the structural consequences observed in heterogeneous oligomers which involve Aβ1−40. We use Hamiltonian and temperature replica exchange molecular dynamics (HT-REMD) simulations combined with the coarse-grained OPEP potential. We observe a loss of α-helices in favor of β -strands and the characteristic polymorphism of amyloid fibers. We also find that some regions are distinguished by their ability to form β -strands. The disappearance of these regions when combined Aβ with NAC suggests the importance of the location of hydrophobic residues in amyloid fibers structures.

Les propriétés mécaniques des polymères et des copolymères à blocs ont été étudiées par simulation de type dynamique moléculaire (modèle billes-ressorts). Les échantillons polymères ont été générés par la méthode de « radical like polymerisation ». Ces échantillons ont été soumis à des essais de traction uniaxiaux et triaxiaux dans le but d’étudier leurs réponses mécaniques. Dans la première partie de ce travail on a comparé deux méthodes de traction : « méthode de traction homogène» et la traction « pilotée par les bords » de l’échantillon. Les résultats montrent que les deux méthodes sont équivalentes à faible vitesse de traction. Le changement de distance entre enchevêtrement dans un polymère modèle sous traction est analysé, les résultats montrent que le désenchevêtrèrent des chaines est plus prononcé lorsque la déformation de l’échantillon est uniaxiale du fait de la relaxation latérale de l’échantillon. La nucléation des cavités dans les polymères amorphes soumis à une déformation triaxial a été également étudiée. On a trouvé que les cavités se forment dans des zones qui sont caractérisées par un faible module d’incompressibilité élastique. Ces zones sont identifiables dès le début de la déformation à une température très basse (T~0K). La seconde partie de ce travail se concentre sur la simulation de la réponse mécanique des copolymères à blocs. L’influence de l’architecture moléculaire sur le comportement mécanique de l’échantillon a été analysée. Les résultats montrent que le comportement mécanique des échantillons est piloté par le taux des chaines liantes qui assurent la transmission des contraintes entre les phases. Le flambement des lamelles dans les copolymères à blocs a été également étudié, l’influence de la taille de l’échantillon et de la vitesse de déformation sur la réponse mécanique de l’échantillon a été explorée. Les résultats montrent un changement de mode du flambement selon la vitesse de déformation imposée. Un nouveau modèle qui prend en compte le facteur cinétique du flambement est proposé pour décrire la compétition entre les modes. / We use molecular dynamics simulation of a coarse grained model to investigate the mechanical properties of homogenous polymers and lamellar block copolymers. Polymer samples have been generated using “radical like polymerisation” method. These samples were submitted to uniaxial and triaxial tensile tests in order to study their mechanical responses. First we compare two tensile test methods: the “homogenous deformation method” and the “boundary driven deformation method”. We find that the two methods lead to similar results at low strain rate. The change of the entanglement network in polymer sample undergoing a tensile deformation was investigated. We have found that the sample exhibits an increase of its entanglement length in uniaxial deformation test compared to triaxial deformation one. Our finding was interpreted by the pronounced chain disentanglement observed in the uniaxial deformation test due to the lateral relaxation of the sample. The cavity nucleation in amorphous polymers has been also studied. We have found that the cavities nucleate preferentially in zones that exhibit a low elastic bulk modulus. These zones can be identified from the initial undeformed state of the sample at low temperature (T~0K). The second part of the work focused in the simulation of the mechanical response of block copolymers. The influence of chain architecture on the mechanical properties was investigated: our finding reveals an important role of the bridging molecules (cilia chains and knotted loop chains) on the stress transmission between phases at high strain. The initiation of plasticity in copolymer samples was also studied. The role of the buckling has been found to be determinant in the mechanical response of the sample The dependence of the buckling instability with the sample size and the deformation rate was investigated. We have found that the fundamental (first) mode of buckling develops at relatively low strain rate whereas at high strain rate the buckling of the sample occurs with the second or higher mode of buckling. A new model that takes into account the buckling kinetic was developed to describe this competition between the buckling modes.