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Université Paris-Sud – Paris XI

1. Dufour, Guillaume. Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds.

Degree: Docteur es, Mathématiques, 2012, Université Paris-Sud – Paris XI

Cette thèse est une contribution au domaine des cubulations de groupes hyperboliques au sens de Gromov. Nous nous intéressons au cas particulier des groupes fondamentaux de variétés hyperboliques réelles compactes. La philosophie inspirée dans ce domaine par les travaux de M. Sageev est que si un groupe hyperbolique possède suffisamment de sous-groupes de codimension 1 quasi-convexes, alors il agit géométriquement sur un complexe cubique CAT(0) de dimension finie. Nous démontrons un critère précis de cubulation pour les groupes fondamentaux de variétés hyperboliques compactes, à l'aide de constructions d'espaces à murs quasi-isométriques à l'espace hyperbolique réel. Nous nous restreignons par la suite au cas particulier de la dimension 3 et plus particulièrement aux 3-variétés hyperboliques compactes virtuellement fibrées sur le cercle. Nous exploitons alors une construction de surfaces immergées incompressibles dites coupées-croisées due à D. Cooper, D. Long et A. Reid dans une telle 3-variété M pour fabriquer des sous-groupes de surface de son groupe fondamental~G. En raffinant des arguments de J. Masters et en exploitant la structure de l'application de Cannon-Thurston, nous parvenons à construire des sous-groupes de surfaces quasi-convexes de G en quantité suffisante pour que leurs ensembles limites permettent de séparer toutes les paires de points distincts du bord du revêtement universel de M. En conséquence de cette construction, G agit géométriquement sur un complexe cubique CAT(0) de dimension finie. D. Wise soulève alors la question de savoir si ce groupe G peut agir géométriquement et également virtuellement co-spécialement (au sens de F. Haglund et D. Wise) sur un complexe cubique CAT(0). Une réponse positive résoudrait les conjectures selon lesquelles G est large et le premier nombre de Betti virtuel de M est infini. Nous faisons remarquer que pour obtenir une réponse positive à cette question, il suffit de trouver une surface coupée-croisée virtuellement plongée dans un revêtement fini fibré sur le cercle de M. Nous concluons en présentant des conditions algébriques, puis géométriques et cohomologiques suffisantes pour qu'une surface coupée-croisée donnée soit virtuellement plongée.

This thesis contributes to the study of geometric actions of word-hyperbolic groups on finite dimensional CAT(0) cube complexes. We are mainly interested in the case of fundamental groups of closed hyperbolic manifolds. The philosophy coming from pioneer work of M. Sageev is that a hyperbolic group with sufficiently many quasi-convex codimension one subgroups acts geometrically on a finite dimensional CAT(0) cube complex. We prove a precise criterion for cubulation in the case of closed hyperbolic manifolds, by constructing spaces with walls quasi-isometric to real hyperbolic space. We next focus on the case of three dimensional closed hyperbolic manifolds which are virtually fibered over the circle. In this setting, we use a construction of incompressibly immersed cut-and-cross-join surfaces due to D. Cooper, D. Long…

Advisors/Committee Members: Haglund, Frédéric (thesis director).

Subjects/Keywords: Espaces à murs; Complexes cubiques CAT(0); Groupes hyperboliques; 3-variétés hyperboliques compactes; Sous-groupes de surface; Surfaces coupéees-croisées; Spaces with walls; CAT(0) cube complexes; Hyperbolic groups; Closed hyperbolic 3-manifolds; Surface subgroups; Cut-and-cross-join surfaces

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Dufour, G. (2012). Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds. (Doctoral Dissertation). Université Paris-Sud – Paris XI. Retrieved from http://www.theses.fr/2012PA112053

Chicago Manual of Style (16th Edition):

Dufour, Guillaume. “Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds.” 2012. Doctoral Dissertation, Université Paris-Sud – Paris XI. Accessed June 05, 2020. http://www.theses.fr/2012PA112053.

MLA Handbook (7th Edition):

Dufour, Guillaume. “Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds.” 2012. Web. 05 Jun 2020.

Vancouver:

Dufour G. Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds. [Internet] [Doctoral dissertation]. Université Paris-Sud – Paris XI; 2012. [cited 2020 Jun 05]. Available from: http://www.theses.fr/2012PA112053.

Council of Science Editors:

Dufour G. Cubulations de variétés hyperboliques compactes : Cubulations of closed hyperbolic manifolds. [Doctoral Dissertation]. Université Paris-Sud – Paris XI; 2012. Available from: http://www.theses.fr/2012PA112053


University of Utah

2. Nelson, Blake William. Accurate and interactive visualization of high-order finite element fields.

Degree: PhD, Computing (School of), 2012, University of Utah

High-order finite element methods, using either the continuous or discontinuous Galerkin formulation, are becoming more popular in fields such as fluid mechanics,solid mechanics and computational electromagnetics. While the use of these methods is becoming increasingly common, there has not been a corresponding increase in the availability and use of visualization methods and software that are capable of displaying visualizations of these volumes both accurately and interactively. A fundamental problem with the majority of existing visualization techniques is that they do not understandnor respect the structure of a high-order field, leading to visualization error.Visualizations of high-order fields are generally created by first approximating the field with low-order primitives and then generating the visualization using traditionalmethods based on linear interpolation. The approximation step introduces error into the visualization pipeline, which requires the user to balance the competing goals of image quality, interactivity and resource consumption. In practice, visualizationsperformed this way are often either undersampled, leading to visualization error, or oversampled, leading to unnecessary computational effort and resource consumption.Without an understanding of the sources of error, the simulation scientist is unable to determine if artifacts in the image are due to visualization error, insufficient mesh resolution, or a failure in the underlying simulation. This uncertainty makes it difficultfor the scientists to make judgments based on the visualization, as judgments made on the assumption that artifacts are a result of visualization error when they are actually a more fundamental problem can lead to poor decision-making.This dissertation presents new visualization algorithms that use the high-order data in its native state, using the knowledge of the structure and mathematicalproperties of these fields to create accurate images interactively, while avoiding the error introduced by representing the fields with low-order approximations. First, a new algorithm for cut-surfaces is presented, specifically the accurate depiction of colormapsand contour lines on arbitrarily complex cut-surfaces. Second, a mathematical analysis of the evaluation of the volume rendering integral through a high-orderfield is presented, as well as an algorithm that uses this analysis to create accurate volume renderings. Finally, a new software system, the Element Visualizer (ElVis),is presented, which combines the ideas and algorithms created in this dissertation in a single software package that can be used by simulation scientists to create accurate visualizations. This system was developed and tested with the assistance of the ProjectX simulation team. The utility of our algorithms and visualization system are then demonstrated with examples from several high-order fluid flow simulations.

Subjects/Keywords: Cut surfaces; GPU programming; High-order finite elements; Visualization; Volume rendering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Nelson, B. W. (2012). Accurate and interactive visualization of high-order finite element fields. (Doctoral Dissertation). University of Utah. Retrieved from http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/1120/rec/128

Chicago Manual of Style (16th Edition):

Nelson, Blake William. “Accurate and interactive visualization of high-order finite element fields.” 2012. Doctoral Dissertation, University of Utah. Accessed June 05, 2020. http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/1120/rec/128.

MLA Handbook (7th Edition):

Nelson, Blake William. “Accurate and interactive visualization of high-order finite element fields.” 2012. Web. 05 Jun 2020.

Vancouver:

Nelson BW. Accurate and interactive visualization of high-order finite element fields. [Internet] [Doctoral dissertation]. University of Utah; 2012. [cited 2020 Jun 05]. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/1120/rec/128.

Council of Science Editors:

Nelson BW. Accurate and interactive visualization of high-order finite element fields. [Doctoral Dissertation]. University of Utah; 2012. Available from: http://content.lib.utah.edu/cdm/singleitem/collection/etd3/id/1120/rec/128

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