ED Mathématiques et Informatique
Stochastic and combinatorial geometry
by Ludovic MORIN (LaBRI - Laboratoire Bordelais de Recherche en Informatique)
The defense will take place at 14h00 - AMPHI (050) LaBRI, Domaine universitaire, 351, cours de la Libération, 33405 Talence
in front of the jury composed of
- Jean-François MARCKERT - Directeur de recherche - Université de Bordeaux - Directeur de these
- Pierre CALKA - Professeur des universités - Laboratoire de Mathématiques Raphaël Salem - Rapporteur
- Matthias REITZNER - Professeur des universités - Université d'Osnabrück - Institut für Mathematik - Rapporteur
- Anna GUSAKOVA - Professeur - Université de Münster - Institut für Mathematische Stochastik - Examinateur
- Adrien RICHOU - Maître de conférences - Université de Bordeaux - Institut de Mathématiques de Bordeaux - Examinateur
- Laurent DECREUSEFOND - Professeur des universités - Télécom Paris - Examinateur
This thesis is part of the field of stochastic geometry, whose aim is to understand the statistical properties of random geometric models. In general, the alea concerns the position in R^d of the usual objects of Euclidean geometry, such as a point, a line, a polygon... The questions, however, concern higher-level objects, such as Voronoi cell laws, intersection properties, percolation... This thesis is devoted to the study of the convex hull of random points in a fixed domain. In most of our work, for a previously fixed dimension, we uniformly and independently draw n points in a convex domain K, and look at the convex hull of these points, either taken together in K, or taken together with a portion of the boundary of K. In the first chapter of this thesis, we draw n+m uniform i.i.d. points in a triangle and take the convex hull of these points with two vertices of the triangle chosen in advance. We then show that when we condition by a number n of points on the boundary, if m is linear or sublinear in n the limit shape of the convex hull boundary is none other than a piece of hyperbola. For the same values of n and m, we also give the asymptotics of the probability of such events. In Chapters 2 and 3, we draw n points uniformly in a convex polygon K, then study the probability that these n points form the vertices of a convex polygon in K, intrinsically linked to a particular case of the model istudied in Chapter 1. We demonstrate an equivalent of this probability, which affines results by Bárány and Valtr dating from the late 90's. We also explicit the law of a set of points conditioned to be in a convex position, and the fluctuations of the convex chain around its limit. These results were obtained in two stages, first in the case where K is a regular polygon, then a general convex polygon. We also treated a broader model, in all dimensions, which consists of drawing points above a flat base, below a concave shape and looking at the probability of the points being in a convex position with the base. In this way, we carried out an extensive study of this model, between shape optimization and the upper and lower bounds of this probability in certain specific cases (e.g. in a tetrahedron or a cone). In Chapter 5, a little different from the others, we study models of random convex polytopes in high dimension. Based on the Gauss-Minkowski theorem, which establishes the correspondence between probability measures on the sphere and convex bodies, we present two algorithms for reconstructing, given vectors summing to 0, the polytope whose normal for each face is one of these vectors and whose face area is the norm of the vector.
ED Sciences Physiques et de l'Ingénieur
Development of a pyromechanics model applied to biomass pyrolysis
by Flora LAHOUZE (I2M - Institut de Mécanique et d'Ingénierie de Bordeaux)
The defense will take place at 9h00 - A9 Amphi 2 351 cours de la libération, 33400 Talence
in front of the jury composed of
- Gérald DEBENEST - Professeur des universités - Toulouse INP - Rapporteur
- Hervé JEANMART - Professeur - Université Catholique de Louvain - Rapporteur
- Antonio COSCULLUELA - Ingénieur de recherche - CEA CESTA - Examinateur
- Jean-Christophe MINDEGUIA - Maître de conférences - Université de Bordeaux - Examinateur
- Michaël MEYER - Maître de conférences - Université de la Nouvelle-Calédonie - Examinateur
- Nicolas DELLINGER - Ingénieur de recherche - ONERA - Examinateur
- Jean LACHAUD - Professeur - Université de Bordeaux - Directeur de these
- Wahbi JOMAA - Professeur - Université de Bordeaux - CoDirecteur de these
The thermo-chemical conversion of biomass plays a key role in the development of sustainable energy pathways and the valorization of renewable lignocellulosic resources. Among the various steps of this process, pyrolysis represents a key phase during which the material undergoes strongly coupled physical, chemical, and mechanical transformations. Understanding and modeling these multi-physical phenomena are essential for predicting material behavior, optimizing processes, and designing efficient systems. This thesis aims to develop a homogenized anisotropic pyromechanics model, specifically applied to wood as a representative material of lignocellulosic biomass. The term pyromechanics refers to the integrated modeling of mechanical, thermal, and pyrolysis-induced deformations within a framework that couples chemical kinetics, mass, and heat transfer. A macroscopic model is formulated using the volume averaging approach, leading to a system of homogenized equations solved numerically by the finite volume method. The complete model is implemented in the open-source software PATO (Porous material Analysis Toolbox based on OpenFOAM). Model development and validation are supported by X-ray microtomography experiments conducted at the SOLEIL synchrotron, as well as by comparisons with reference data from the literature on biomass pyrolysis.