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131	Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory. Boalch, Philip 12 December 2012 (has links) (PDF) Short summary of main work since 1999 Geometry moduli spaces meromorphic connections on curves Stokes data wild nonabelian Hodge theory hyperkahler manifolds isomonodromic deformations Painleve equations Lie theory
132	Déformations des applications harmoniques tordues Spinaci, Marco 25 November 2013 (has links) (PDF) On étudie les déformations des applications harmoniques $f$ tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de $f$ en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie $E$ coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour les construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de $E$ aux points critiques. Applications harmoniques tordues Espaces de modules Fibrés de Higgs Variations de Structures de Hodge Groupes de Kähler Fonctionnelle d'énergie
133	Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces Axelsson, Andreas, kax74@yahoo.se January 2002 (has links) The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwells equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwells equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator. Dirac operator Maxwell's equations transmission problem Hodge decomposition Cauchy integral double layer potential Lipschitz surface singular integral Carleson measure boundary integral method oblique boundary value problem Fredholm theory exterior algebra Clifford analysis Rellich inequality Banach algebra projection operator Toeplitz operator Calderón projection
134	A Fractional Step Zonal Model and Unstructured Mesh Generation Frame-work for Simulating Cabin Flows Tarroc Gil, Sergi January 2021 (has links) The simulation of physical systems in the early stages of conceptual designs has shown to be a key factor for adequate decision making and avoiding big and expensive issues downstream in engineering projects. In the case of aircraft cabin design, taking into account the thermal comfort of the passengers as well as the proper air circulation and renovation can make this difference. However, current numerical fluid simulations (CFD) are too computationally expensive for integrating them in early design stages where extensive comparative studies have to be performed. Instead, Zonal Models (ZM) appear to be a fast-computation approach that can provide coarse simulations for aircraft cabin flows. In this thesis, a Zonal Model solver is developed as well as a geometry-definition and meshing framework, both in Matlab®, for performing coarse, flexible and computationally cheap flow simulations of user-defined cabin designs. On one hand, this solver consists of a Fractional Step approach for coarse unstructured bi-dimensional meshes. On the other, the cabin geometry can be introduced by hand for simple shapes, but also with Computational Aided Design tools (CAD) for more complex designs. Additionally, it can be chosen to generate the meshes from scratch or morph them from previously generated ones. / <p>The presentation was online</p> Zonal Model Thermal Comfort Fluid Simulation Aircraft Cabin Design NURBS Morphing Radial Basis Functions Meshing Co-located Mesh Unstructured Mesh Mesh Quality Mesh Smoothing Enlarged Orientation Theorem Fractional Step Method Boussinesq Adam Bashforth Helmholtz-Hodge Theorem Rhie and Chow Difference Schemes Gradient Evaluation Differential Heated Cavity Driven Cavity Draught Rate Aerospace Engineering Rymd- och flygteknik Fluid Mechanics and Acoustics Strömningsmekanik och akustik

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