Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"Riemannian Metric"”.
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Riemannian Metric Learning via Optimal Transport
… an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold. We neurally parametrize the metric as a spatially-varying matrix field and efficiently optimize our model's objective using backpropagation. …
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Recovering a Riemannian Metric from Knowledge of the Areas of Properly-Embedded, Area-Minimizing Surfaces
… that if (M,g) is a C3-smooth, 3-dimensional Riemannian manifold with mean convex boundary ∂M, which is additionally either a) C2-close to Euclidean or b) sufficiently thin, then knowledge of the least areas circumscribed by any simple closed curve γ ⊂ ∂M uniquely determines the metric. In …
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Intrinsic Geometric Flows on Manifolds of Revolution
An intrinsic geometric flow is an evolution of a Riemannian metric by a two-tensor. An extrinsic geometric flow is an evolution of an immersion of a manifold into Euclidean space. An extrinsic flow induces an evolution of a metric because any immersed manifold inherits a Riemannian metric from …
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On the Riemannian geometry of Seiberg-Witten moduli spaces
In this thesis, we give two constructions for Riemannian metrics on Seiberg-Witten moduli spaces. Both these constructions are naturally induced from the L2-metric on the configuration space. The construction of the so called quotient L2-metric is very similar to the one construction of an …
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Homology products on Z2-quotients of free loop spaces of spheres
… The energy functional on ΛM associated to a Riemannian metric on M is invariant under the group actions we consider. We therefore retain information about geometrically distinct closed geodesics.
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ΠΟΛΛΑΠΛΟΤΗΤΕΣ ΤΟΥ RIEMANN ΥΠΕΡΒΟΛΙΚΟΥ ΤΥΠΟΥ
… IS TO EXAMINE THE CLOSED GEODESICS ON COMPACT RIEMANNIAN MANIFOLDS OF HYPERBOLIC TYPE; THAT MEANS RIEMANNIAN MANIFOLDS WHICH CAN CARRY A RIEMANNIAN METRIC WITH STRICTLY NEGATIVE SECTIONAL CURVATURE. IT ISPROVED, THAT THE INDEX OF THE M- COVER OF ONE CLOSED GEODESIC ON A COMPACT RIEMANNIAN, …
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SPECIAL RIEMANNIAN STRUCTURES ON FOUR-MANIFOLDS: FROM TWISTOR SPACES TO UNOBSTRUCTED CONDITIONS
This thesis deals with special Riemannian metrics on smooth manifolds: in particular, we study the relations between the existence of metrics satisfying curvature properties and the topology of the manifold they are defined on. In the first part of the work, we introduce Riemannian twistor spaces, …
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A finite element segregated method for thermo-chemical equilibrium and nonequilibrium hypersonic flows using adapted grids
… value of its eigenvalues to finally produce a Riemannian metric. Using elementary differential geometry, the edge-based error estimate is thus defined as the length of the element edges in this Riemannian metric. This error is then equidistributed over the mesh edges by applying a mesh movement …
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An adaptive framework for high-order, mixed-element numerical simulations
… to the mesh generator through a field of Riemannian metric tensors, the adaptation algorithm used to compute this field is also discussed. The algorithm is first tested through the L² error control of isotropic and anisotropic problems and shows that optimal mesh gradings can be obtained. …
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Fully anisotropic split-tree adaptive refinement mesh generation using tetrahedral mesh stitching
Due to the myriad of geometric topologies that modern computational fluid dynamicists desire to mesh and run solutions on, the need for a robust Cartesian Mesh Generation algorithm is paramount. Not only do Cartesian meshes require less elements and often help resolve flow features but they also …
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Random conformally covariant metrics in the plane
… conformal symmetries and formally given by the Riemannian metric tensor "$e^{\gamma h} (dx^2+dy^2)$'' where $h$ is a Gaussian free field (GFF) on a planar domain and $\gamma \in (0,2)$. Duplantier and Sheffield constructed the $\gamma$-LQG area and boundary length measures, which fall under the …
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Towards Learning the Geometry of Data: From Diffusion Models to Riemannian Geometry
… modelling, self-supervised learning, and Riemannian geometry, paving the way for learning the intrinsic geometry of data manifolds. In chapter 3, we introduce CAFLOW, a conditional normalising flow that improves image-to-image translation by hierarchically modelling image distributions …
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Ambient Obstruction Solitons And Homogeneous Gradient Bach Solitons
… of objects. Endowing a smooth manifold with a Riemannian metric allows us to measure length and angle in a way such that length is positive. This enables us to examine measures of curvature on a manifold. The study of manifolds with such metrics is called Riemannian geometry. Using geometric …
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Ambient Obstruction Solitons and Homogeneous Gradient Bach Solitons
… of objects. Endowing a smooth manifold with a Riemannian metric allows us to measure length and angle in a way such that length is positive. This enables us to examine measures of curvature on a manifold. The study of manifolds with such metrics is called Riemannian geometry. Using geometric …
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An optimization framework for adaptive higher-order discretizations of partial differential equations on anisotropic simplex meshes
… a continuous optimization problem of the Riemannian metric field. The adaptation procedure consists of three key steps: sampling of the anisotropic error behavior using element-wise local solves; synthesis of the local errors to construct a surrogate error model based on an …
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An automated reliable method for two-dimensional Reynolds-Averaged Navier-Stokes simulations
… for improved non-linear solver robustness and Riemannian metric based anisotropic adaptation to efficiently resolve anisotropic features with arbitrary orientations in RANS flows. A fixed-fraction marking strategy is employed to redistribute element areas and steps toward meshes which …
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Geometry of Spaces of Planar Quadrilaterals
… studied by Kapovich and Millson [6], but the Riemannian geometry of these spaces has not been thoroughly examined. We study paths in the moduli space and the pre-moduli space. We compare intraplanar paths between points in the moduli space to extraplanar paths between those same points. We …
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Transformations of ODEs into gradient systems in stationary points
Tato bakalářská práce navazuje na článek Bárta, Chill a Fašangová [1]. V tomto článku bylo ukázáno, že každá obyčejná diferenciální rovnice s Lyapunovskou funkcí je i gradientovým systémem. Toto bylo ukázáno pro určitou Riemannovskou metriku na množině nestacionárních bodů. V této práci odvodíme …
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Conformal pseudo-metrics and some applications
… parts. In a first step we construct a conformal metric in a bounded regular domain $G\subset \mathbb{C}$ with prescribed non-positive Gaussian curvature $k(z)$ and prescribed singularities by solving the first boundary value problem for the Gaussian curvature equation $\Delta u =-k(z) e^{2u}$ in …
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Design and analysis of particle-based algorithms for nonlinear filtering and sampling
… The gradient flow with respect to the Riemannian metric induced by the Wasserstein distance, is known to lead to Markov Chain Monte-Carlo (MCMC) algorithms based on the Langevin equation. The main contribution is to present a methodology and numerical algorithms for constructing …