Facultat de Matemàtiques i Estadística: Recent submissions
Now showing items 1-20 of 120
Floer homology for 𝑏-symplectic manifolds
(English) In this thesis we investigate various aspects of the dynamics of Hamiltonian vector fields in singular symplectic manifolds. We concentrate on two questions: first, we investigate a generalization of the Arnold ...
Canonical realizations of Bondi-Metzner-Sachs–like symmetries in field theory
(English) The BMS group appears as an infinite-dimensional group of isometries of asymptotically flat spacetimes first introduced by Bondi, Metzner, van der Burg, and Sachs in 1962. This group has gained interest recently ...
Numerical optimisation of worm locomotion on frictional substrates
(English) Optimal control theory provides a framework to determine optimal inputs for mechanical systems modeled as initial value problems. The resulting minimisation problem may be solved with known direct and indirect ...
Poisson structures on moduli spaces and group actions
(English) In this thesis, we study Poisson Structures on Moduli Spaces and Group actions. In particular, we focus on b^m-symplectic structures that can be seen both as symplectic structures with singularities and a particular ...
Simulation of two-fluid immiscible Stokes flows using hybrid nonconforming methods and geometrically unfitted meshes
(English) We consider two-fluid problems involving immiscible Stokes fluids in contact and with surface tension at their interface. We develop, analyze, and compare two approaches for space discretization, the Hybrid ...
Rational-design of new candidates targeting bak and bombesin receptors in cancer
(English) Cancer is the second leading cause of death globally, only behind cardiovascular diseases, being a major public health issue. Cancer comprises a wide group of diseases characterized by abnormal cell growth, which ...
Coercion-resistant cast-as-intended verifiability in electronic voting systems
(English) One of the most common fears regarding electronic voting is that a voting device will disregard the voter's intent and cast a different vote instead. An undetectable attack like that on a large scale will allow ...
Mathematical and computational modeling of flexoelectricity at fixed and moving interfaces, fracture surfaces and contact
(English) Flexoelectricity is a two-way coupling between strain gradient and polarisation or strain and polarization-gradient. Harnessing flexoelectricity as a functional property requires gradient engineering. This is a ...
Elliptic problems: regularity of stable solutions and a nonlocal Weierstrass extremal field theory
(English) This PhD dissertation deals with qualitative questions from the theory of elliptic Partial Differential Equations (PDE) and integro-differential equations. We are primarily interested in a distinguished class of ...
High-performance computing fluid-structure interaction model of bioprosthetic aortic valve replacements
(English) Computational modeling and simulation (CM&S) provides a powerful cost- and time-efficient tool to access detailed mechanistic information of biomedical problems, which is not accessible in either clinical imaging ...
Unstable motions in the three body problem
(English) The 3 Body Problem (3BP) models the motion of three bodies interacting via Newtonian gravitation. It is called restricted when one body has zero mass and the other two, the primaries, have strictly positive masses. ...
Theory and computation of multiscale epithelial mechanics : from active gels to vertex models
(English) Epithelial monolayers perform a variety of mechanical functions, which include maintaining a cohesive barrier or developing 3D shapes, while undergoing stretches over a wide range of magnitudes and loading rates. ...
Discrete operators and distances on subdivision networks
(English) The research we have carried out lies within the domain of diffusion problems for elliptic operators that are defined on discrete structures called networks, that are graphs that are capable of discriminating ...
Flexoelectricity at surface instabilities and stress singularities
(English) The flexoelectric effect, the two-way linear coupling between strain gradient and electric polarization (direct flexoelectricity) or electric field gradient and strain (converse flexoelectricity) universally ...
Mathematical and computational modeling of active cellular flows
(English) During development, cellular tissues undergo dramatic reconfigurations as a result of organized flows driven by active forces. Depending on the system, cellular flows and active forces can be understood from a ...
Mechanics of epithelial tissue subjected to controlled pressure
(English) Epithelial sheets form specialized 3D structures suited to their physiological roles, such as branched alveoli in the lungs, tubes in the kidney, and villi in the intestine. To generate and maintain these structures, ...
Theta correspondences and arithmetic intersections
(English) The thesis is mainly divided into two parts. In essence, the first one is an extension of the paper [Ter22]. Using the regularized Siege-Weil formula of [GQT14] we obtain an explicit expression for the truncated ...
First order logic of random sparse structures
(English) This work is dedicated to the study several models of random structures from the perspective of first-order logic. We prove that the asymptotic probabilities of first-order statements converge in a general model ...
A theoretical and computational study of the active self-organization of nematic patterns in thin cytoskeletal layers and their effect on curvature
(English)The structure and dynamics of important biological systems, ranging from cytoskeletal gels to tissues, are controlled by an interplay between activity, dissipation, nematic order, density, and geometry. In particular, ...
Lattice-based zero-knowledge proofs of knowledge
(English) The main goal of this dissertation is to develop new lattice-based cryptographic schemes. Most of the cryptographic protocols that each and every one of us use on a daily basis are only secure under the assumption ...
