Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations
Visualitza/Obre
10.5821/dissertation-2117-94814
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/94814
Càtedra / Departament / Institut
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
Tipus de documentTesi
Data de defensa2012-11-12
EditorUniversitat Politècnica de Catalunya
Condicions d'accésAccés obert
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continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
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Reconeixement-NoComercial 3.0 Espanya
Abstract
In many applications, one would like to perform calculations on smooth manifolds of dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. In this thesis, we approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients: (1) partitioning of the point set into subregions of trivial topology, (2) the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques, (3) the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and (4) patching together the local representations by means of a partition of unity.
In this thesis we show the generality, flexibility, and accuracy of the method in four different problems. First, we exercise it in the context of Kirchhoff-Love thin shells, (d=2, D=3). We test our methodology against classical linear and non linear benchmarks in thin-shell analysis, and highlight its ability to handle point-set surfaces of complex topology and geometry. We then tackle problems of much higher dimensionality. We perform reduced order modeling in the context of finite deformation elastodynamics, considering a nonlinear reduced configuration space, in contrast with classical linear approaches based on Principal Component Analysis (d=2, D=10000's). We further quantitatively unveil the geometric structure of the motility strategy of a family of micro-organisms called Euglenids from experimental videos (d=1, D~30000's). Finally, in the context of enhanced sampling in molecular dynamics, we automatically construct collective variables for the molecular conformational dynamics (d=1...6, D~30,1000's).
Descripció
Premi extraordinari doctorat 2012-2013
CitacióMillán, D. Point-set manifold processing for computational mechanics: thin shells, reduced order modeling, cell motility and molecular conformations. Tesi doctoral, UPC, Departament de Matemàtica Aplicada III, 2012. DOI 10.5821/dissertation-2117-94814. Disponible a: <http://hdl.handle.net/2117/94814>
GuardóDocument premiat
Dipòsit legalB. 14913-2013
Col·leccions
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