Tesis sobre el tema "Topologie en basses dimensions"
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Long, Yusen. "Diverse aspects of hyperbolic geometry and group dynamics". Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM016.
Texto completoThis thesis explores diverse topics related to hyperbolic geometry and group dynamics, aiming to investigate the interplay between geometry and group theory. It covers a wide range of mathematical disciplines, such as convex geometry, stochastic analysis, ergodic and geometric group theory, and low-dimensional topology, etc. As research outcomes, the hyperbolic geometry of infinite-dimensional convex bodies is thoroughly examined, and attempts are made to develop integral geometry in infinite dimensions from a perspective of stochastic analysis. The study of big mapping class groups, a current focus in low-dimensional topology and geometric group theory, is undertaken with a complete determination of their fixed-point on compacta property. The thesis also clarifies certain folklore theorems regarding the Gromov hyperbolic spaces and the dynamics of amenable groups on them. Last but not the least, the thesis studies the connectivity of the Gromov boundary of fine curve graphs, a combinatorial tool employed in the study of the homeomorphism groups of surfaces of finite type
Guillou, Lucien. "Topologie des variétés de basse dimension". Paris 11, 1991. http://www.theses.fr/1991PA112039.
Texto completoMesmay, Arnaud de. "Topics in low-dimensional computational topology". Paris, École normale supérieure, 2014. https://theses.hal.science/tel-04462650v1.
Texto completoTopology is the area of mathematics investigating the qualitative properties of shapes and spaces. Although it has been a classical field of study for more than a century, it only appeared recently that being able to compute the topological features of various spaces might be of great value for many applications. This idea forms the core of the blossoming field of computational topology, to which this work belongs. The three contributions of this thesis deal with the development and the study of topological algorithms to compute deformations and decompositions of low-dimensional objects, such as graphs, surfaces or 3-manifolds. The first question we tackle concerns deformations: how can one test whether two graphs embedded on the same surface are isotopic, i. E. , whether one can be deformed continuously into the other? This kind of problems is relevant to practical problems arising with morphings or geographic information systems, for example. Relying on hyperbolic geometry and ideas from the theory of mapping class groups, we first establish a combinatorial criterion to characterize isotopy, reproving and strengthening a result of Ladegaillerie (1984). Combined with earlier algorithms on the homotopy of curves, this allows us in turn to provide efficient algorithms to solve this graph isotopy problem. We then shift our focus to decompositions, by investigating how to cut surfaces along curves or graphs with prescribed topological properties, which is an important routine in graph algorithms or computer graphics, amongst others domains. By establishing a strong connection with the continuous setting, as well as studying a discrete model for random surfaces, we improve the best known bounds for several instances of this problem. In particular, this proves a conjecture of Przytycka and Przytycki from 1993, and one of our new bounds readily translates into an algorithm to compute short pants decompositions. Finally, we move up one dimension, where the best known algorithms for many topological problems, like for example unknot recognition, are exponential. Most of these algorithms rely on normal surfaces, a ubiquitous tool to study the surfaces embedded in a 3-manifold. We investigate a relaxation of this notion called immersed normal surfaces, whose more convenient algebraic structure makes them good candidates to solve topological problems in polynomial time. We show that when working with immersed normal surfaces, a natural problem on the detection of singularities arises, and we prove it to be NP-hard – this is noteworthy as hardness results are very scarce in 3-dimensional topology. Our reduction works by establishing a connection with a restricted class of constraint satisfaction problems which has been partially classified by Feder
Songvilay, Manila. "Structures et propriétés d'oxydes magnétiques à topologie frustrée et de basse dimension". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS403/document.
Texto completoThis thesis focuses on the study of a chromium oxide family in which the samples are synthsized into two forms with two different topologies : α-ACr₂O₄ (A=Sr, Ca, Ba) and β-CaCr₂O₄. In these compounds, the chromium ions carry a spin 3/2 and either form triangular spin chains or two dimensional triangular lattices. Our study was hence divided in two parts : the study of a quasi one-dimensional and of a two-dimensional antiferromagnet.The first part was dedicated to the β-CaCr₂O₄ compound. This system exhibits a classical behavior at low temperature associated to a three-dimensional long-range magnetic order and quantum properties typical of a spin chain above the Néel temperature.The aim o four study was therefore to understand the mecanism involved in this classical to quantum physics crossover.In this context, we explored the topological and structural effects on the magnetic properties of this system, through the study of the series of substituted compounds β-CaCr₂-xScxO₄, as well as a study of β-CaCr₂O₄ under pressure. This work was also supported by theoretical calculations on frustrated J₁-J₂ spin chains.The second part of this thesis focused on α-SrCr₂O₄. In particular, neutron scattering measurements on this compound highlighted the effects of the 2D character and the distortion of the triangular lattice on the ground state and dynamical properties in this system
Cao, Xiangyu. "Physique statistique des systèmes désordonnées en basses dimensions". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS067/document.
Texto completoThis thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transition in long-range random matrices.In the first part devoted to logREMs, we show how to characterise their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory.The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localisation transitions with mobility edges in the ``stretch--exponential'' parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class
Kadem, Abdelouahab. "Etude de la structure topologique de l'ensemble des systèmes affines contrôlables en basse dimension". Metz, 1988. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1988/Kadem.Abdelouahab.SMZ884.pdf.
Texto completoFrom a topological point of vien this work deals with the structure of a set of affine and controllable systems. From the work of (J. S. ), (A. S. V. ) it appeared that definite relations exist between topological structure of a set of affine controllable systems Ca and Ch. In particuler the properties of Fr Ca and the connexivy of Ca arise direcly from analogouds properties of Ch. We show that Ca gives rise to two types of boundary points. We can expect to have three types of boundary points. The interior of the closed set Ca contains affine controllable systems for which the trajectories are cycles. For the other cases they are on the exterior boundaries, we also show that the interior of Ca is uniquely composed of (J. S. ) and affine controllable systems to which correspond homogeneous non-controllable systems characterized by collinear fields (non-independent spirals). Our result is that the set of affine controllable systems Ca is connected
Plat, Xavier. "Étude de modèles magnétiques frustrés sous champ en basses dimensions". Toulouse 3, 2014. http://thesesups.ups-tlse.fr/2523/.
Texto completoThis thesis deals with the physics of magnetic systems in an external field and when frustration, arising either from the geometry or from competing interations, is present. We have studied several models in low dimensions, where the effects of the quantum fluctuations are more important and can lead to the apparition of new intersting quantum phases. This manuscript is divided in three parts, each one being dedicated to a given model. In the first two parts, we consider two one-dimensional spin tube models, respectively made of three and four coupled spin chains, that we study by using various analytical and numerical methods. We show that, beyond the appearance of magnetization plateaux, a rich physics can emerge, with the role of the non magnetic modes for the first model, or, in the second case, the consequences of a continuous degeneracy at the classical level on the quantum phase diagram. In the third part, we use numerical Quantum Monte-Carlo simulations to study an anisotropic spin model on the two-dimensional Kagomé lattice, designed for the search of topological phases. We obtain the phase diagram on one of the magnetization plateaux of this model, and use this example to discuss the relevance of the computation of the entanglement entropies in order to identify phases in numerical simulations
Rousseau, Valéry. "Etude de systèmes bosoniques et fermioniques dans les basses dimensions". Nice, 2004. http://www.theses.fr/2004NICE4083.
Texto completoA good number of physical systems may be modelled by quantum particles on a lattice. Strongly correlated systems in one and two dimensions are particularly interesting because of the enhanced quantum effects not well described by mean field. In addition there is growing number of real materials which are truly one or two dimensional such as helium adsorbed on graphite, high temperature superconductors and Bose-Einstein condensates on optical lattices to mention only a few. These systems are well described by the lattice Hubbard model which, by virtue of being on a lattice, is amenable to precision numerical simulations which don’t suffer from the many approximations needed in the analytical calculations. In this thesis we apply the Hubbard model to study some systems which are currently of high theoretical and experimental interest
Goryca, Mateusz. "Dynamique de spin dans les structures semi-conductrices de basses dimensions". Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00647043.
Texto completoDavid, Rénald. "Oxydes et ferromagnétisme de basse-dimensionnalité : nouvelles topologies à propriétés remarquables". Electronic Thesis or Diss., Lille 1, 2014. http://www.theses.fr/2014LIL10006.
Texto completoLow-dimensional oxides with disconnected magnetic units are of increasing interest due the peculiar properties and the versatile interplay between individual magnetic moments into an external magnetic field: metamagnetic transition, magnetization steps…. In addition to understanding these phenomena, the importance of this type of compounds is also emerging properties indirectly related to the specific magnetization of these systems that can be part of the field of "spintronic". Our work, upstream, is the synthesis and study of new compounds, mainly low dimensional oxides, which bring a new vision on such properties, due to their particular magnetic behaviors. The aim of this thesis was therefore to prepare and characterize novel compounds, but also to solve the structure-properties relationship. The results obtained through a work of reflected synthesis, have identified chemical systems favorable to the realization of low-dimensional magnetic materials. Several new phases with specific properties have been identified. It is clear that all the observed behaviors: 2D Ising-FM, SCM, magnetization step, reversible extrusion are relatively original and have led to important advances in the understanding of magnetism of weakly interacting subunits
David, Rénald. "Oxydes et ferromagnétisme de basse-dimensionnalité : nouvelles topologies à propriétés remarquables". Thesis, Lille 1, 2014. http://www.theses.fr/2014LIL10006/document.
Texto completoLow-dimensional oxides with disconnected magnetic units are of increasing interest due the peculiar properties and the versatile interplay between individual magnetic moments into an external magnetic field: metamagnetic transition, magnetization steps…. In addition to understanding these phenomena, the importance of this type of compounds is also emerging properties indirectly related to the specific magnetization of these systems that can be part of the field of "spintronic". Our work, upstream, is the synthesis and study of new compounds, mainly low dimensional oxides, which bring a new vision on such properties, due to their particular magnetic behaviors. The aim of this thesis was therefore to prepare and characterize novel compounds, but also to solve the structure-properties relationship. The results obtained through a work of reflected synthesis, have identified chemical systems favorable to the realization of low-dimensional magnetic materials. Several new phases with specific properties have been identified. It is clear that all the observed behaviors: 2D Ising-FM, SCM, magnetization step, reversible extrusion are relatively original and have led to important advances in the understanding of magnetism of weakly interacting subunits
Kadem, Abdelouahab. "Etude de la structure topologique de l'ensemble des systèmes affinés contrôlables en basse dimension". Grenoble 2 : ANRT, 1988. http://catalogue.bnf.fr/ark:/12148/cb37614620t.
Texto completoKadem, Abdelouahab Sallet Gauthier. "ETUDE DE LA STRUCTURE TOPOLOGIQUE DE L'ENSEMBLE DES SYSTEMES AFFINES CONTROLABLES EN BASSE DIMENSION /". [S.l.] : [s.n.], 1988. ftp://ftp.scd.univ-metz.fr/pub/Theses/1988/Kadem.Abdelouahab.SMZ884.pdf.
Texto completoNarimannejad, Majid. "Asymptotics of multicurves and handlebodies in TQFT via skein theory". Paris 7, 2007. http://www.theses.fr/2007PA077059.
Texto completoThis is a work around a fundamental problem of quantum topology: relating quantum invarinats of 3-manifolds to their geometrie properties. We study some asymptotics for a familly of topological quantum field theory (TQFT) in dimension 2-1-1. These TQFTs are constructed in a purely combinatorial way using skein theory and Kauffman bracket. We define and study the limits of the multicurves and handlebodies in these TQFTs and interpret these limits in a geometrie way. As a corollary we obtain a limit for the quantum représentations of mapping class groups in the Fell topology and give a new and simple proof for the asymptotic faithfulness of these representations. These results are presented in two chapters which constitutes the thesis. This work has been done in collaboration with Julien Marche. The first chapter will be published in Duke Mathematical Journal
Waintal, Xavier. "Effet de l'interaction coulombienne sur la localisation d'anderson dans des systemes de basses dimensions". Palaiseau, Ecole polytechnique, 1999. http://www.theses.fr/1999EPXX0020.
Texto completoDamiani, Céleste. "The topology of loop braid groups : applications and remarkable quotients". Caen, 2016. http://www.theses.fr/2016CAEN2021.
Texto completoIn this these we study loop braid groups, we explore some of their topological applications and some remarquable quotients. The thesis is composed by four parts:- Unifying the different approaches to loop braid groups. Several formulations are being used by researchers working with loop braid groups in different fields; we present these interpretations and prove their equivalence. - A topological version of Markov’s theorem for ribbon torus-links. Using the understanding of the interpretation of loop braids as knotted objects in the 4-dimensional space, we give a topological proof of a version of Markov theorem for loop braids with closure in a solid torus in the 4-dimensional space. - Alexander invariants for ribbon tangles. We define an Alexander invariant on ribbon tangles. From this invariant we extract a functorial generalization of the Alexander polynomial. This invariant has a deep topological meaning, but lacks a simple way of computation. To overcome this problem we establish a correspondence with Archibal’s multivariable Alexander polynomial for tangles. - Quotients of the virtual braid group. We study the groups of unrestricted virtual braids, a family of quotients of the loop braid groups, and describe their structure. As a consequence we show that any fused link admits as a representative the closure of a pure unrestricted virtual braid
Castellini, Roberto. "La topologie des déformations d’A’Campo des singularités : une approche par le lotus". Thesis, Lille 1, 2015. http://www.theses.fr/2015LIL10062/document.
Texto completoIn singularity theory, it is important to understand better the topology of the deformations of the parametrizations of plane curve singularities, particularly those whose fibres are divides: embeddings of intervals such that all intersections are transverse. This topology is still mysterious: one does not know descriptions either of the divides or of the singularities which appear in such deformations. Moreover, one knows only two algorithms whose results are divides, introduced by A'Campo and Gusein-Zade.In my thesis I described a canonical A'Campo divide associated to every topological type of plane curve singularities. In the case where the singularity is irreducible, I rediscovered the description given by Schulze-Robbecke in 1976. I've also described the multi-germ of singularities of curves obtained by partially applying A'Campo's algorithm. And this for every possible partial deformation. In the end, I studied in a detailed way the topology of the embedded resolution spaces of real plane curve singularities. All along my thesis I used in an essential way a recent encoding of the topological type of the initial singularity, its lotus, introduced by Popescu-Pampu. Therefore my work shows that the lotus is a particularly well adapted tool for the understanding of deformations
Calimici, Giulio. "State sum invariants of combed 3-manifolds". Thesis, Lille 1, 2019. http://www.theses.fr/2019LIL1I018/document.
Texto completoThis thesis concerns quantum topology, a branch of mathematics born in the 1980s after the work of Jones, Drinfeld and Witten. A fundamental example of a quantum invariant of 3-manifolds is due to Turaev-Viro in 1992. Their approach, in its general form due to Barrett and Westbury, uses a spherical fusion category as the main ingredient and consists in a state sum on a skeleton of the 3-manifold whose vertices are colored by the 6j-symbols of the category. The main result of the thesis is the construction of a topological invariant of combed 3-manifolds (that is, of 3-manifolds endowed with a nowhere-zero vector field) which generalizes that of Turaev-Viro. This new invariant is defined by means of a pivotal fusion category and consists in a state sum on a branched skeleton representing the combed 3-manifold. When the pivotal fusion category is not spherical, the invariant allows in general to distinguish non homotopic vector fields on the same 3-manifold. This is proved by considering a pivotal fusion category associated with a character of a finite group. For this category, the invariant corresponds to the evaluation by the character of the Euler class of a certain vector bundle of rank 2 associated to the vector field
Curmi, Octave. "Topologie des lissages de singularités non-isolées de surfaces complexes". Thesis, Lille 1, 2019. http://www.theses.fr/2019LIL1I030/document.
Texto completoThis thesis is dedicated to the study of the topology of smoothings of non-isolated singularities of complex surfaces. The question is to describe the topology of themanifold, called Milnor fiber, which appears during this process of smoothing. Consideringthe great difficulty of a description of the whole of this topology, many researches havefocused on the study of the boundary of the Milnor fiber. In the case of isolated singularities,it is known since the work of Mumford (1961) that this boundary is a graph manifold,isomorphic to the link of the singularity.Different results (Michel & Pichon 2003, 2014, Némethi & Szilárd 2012) have then provedthat, in the case of reduced non-isolated singularities, the boundary of the Milnor fiber isagain a graph manifold, while restraining to the case of a smooth total space of smoothing.Fernández de Bobadilla & Menegon-Neto (2014) have widened the context, consideringnon-reduced surfaces, and allowing the total space to have an isolated singularity. In thiswork, we pursue the extension of this result to a larger context, allowing the total spaceto present non-isolated singularities, while restraining ourselves to the study of reducedsurface singularities. Our proof is inspired by the one of Némethi and Szilard, and allows usfurthermore to provide a method for the computation of this manifold. This makes possiblethe actual computation of a large number of examples, representing a step forward in thequest for the comprehension of the manifolds that can actually appear as boundaries ofMilnor fibers.We apply in particular the method to Newton non-degenerate singularities defined on3-dimensional toric germs. This is a generalization of a theorem of Oka (1986), expressingthe boundary of the Milnor fiber in terms of the Newton polyhedron of the singularity
Kapikranian, Oleksandr. "Inuence du desordre sur le comportement a basse temperature de modeles de spins de symetrie continue a deux dimensions". Phd thesis, Université Henri Poincaré - Nancy I, 2009. http://tel.archives-ouvertes.fr/tel-00374650.
Texto completoMoriceau, Sebastien. "Surfaces de degré 4 avec un point double non dégénéré dans l'espace projectif réel de dimension 3". Rennes 1, 2004. http://www.theses.fr/2004REN10130.
Texto completoLarcanché, Audrey Bourdon Marc Belliart Michel. "Topologie locale des espaces de feuilletages des variétés fermées de dimension 3". Villeneuve d'Ascq : Université des sciences et technologies de Lille, 2007. https://iris.univ-lille1.fr/dspace/handle/1908/620.
Texto completoN° d'ordre (Lille 1) : 3509. Résumé en français et en anglais. Titre provenant de la page de titre du document numérisé. Bibliogr. p. 46-48.
Cazassus, Guillem. "Homologie instanton-symplectique : somme connexe, chirurgie de Dehn, et applications induites par cobordismes". Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30043/document.
Texto completoSymplectic instanton homology is an invariant for closed oriented three-manifolds, defined by Manolescu and Woodward, which conjecturally corresponds to a symplectic version of a variant of Floer's instanton homology. In this thesis we study the behaviour of this invariant under connected sum, Dehn surgery, and four-dimensional cobordisms. We prove a Künneth-type formula for the connected sum: let Y and Y' be two closed oriented three-manifolds, we show that the symplectic instanton homology of their connected sum is isomorphic to the direct sum of the tensor product of their symplectic instanton homology, and a shift of their torsion product. We define twisted versions of this homology, and then prove an analog of the Floer exact sequence, relating the invariants of a Dehn surgery triad. We use this exact sequence to compute the rank of the groups associated to branched double covers of quasi-alternating links, some plumbings of disc bundles over spheres, and some integral Dehn surgeries along certain knots. We then define invariants for four dimensional cobordisms as maps between the symplectic instanton homology of the two boundaries. We show that among the three morphisms in the surgery exact sequence, two are such maps, associated to the handle-attachment cobordisms. We also give a vanishing criteria for such maps associated to blow-ups
Morvan, Alexis. "Honeycomb lattices of superconducting microwave resonators : Observation of topological Semenoff edge states". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS037/document.
Texto completoThis thesis describes the realization and study of honeycomb lattices of superconducting resonators. This work is a first step towards the simulation of condensed matter systems with superconducting circuits. Our lattices are micro-fabricated and typically contains a few hundred sites. In order to observe the eigen-modes that appear between 4 and 8 GHz, we have developed a mode imaging technique based on the local dissipation introduced by a laser spot that we can move across the lattice. We have been able to measure the band structure and to characterize the edge states of our lattices. In particular, we observe localized states that appear at the interface between two Semenoff insulators with opposite masses. These states, called Semenoff states, have a topological origin. Our observations are in good agreement with ab initio electromagnetic simulations
Leleu, Xavier. "Géométries de courbure constante des 3-variétés et variétés de caractères de représentations dans SL2(C)". Aix-Marseille 1, 2000. http://www.theses.fr/2000AIX11052.
Texto completoVirelizier, Alexis. "Algèbres de Hopf graduées et fibrés plats sur les 3-variétés". Université Louis Pasteur (Strasbourg) (1971-2008), 2001. http://www.theses.fr/2001STR13181.
Texto completoSoni, Medha. "Investigation of exotic correlated states of matter in low dimension". Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30381/document.
Texto completoQuantum statistics is an important aspect of quantum mechanics and it lays down the rules for identifying dfferent classes of particles. In this thesis, we study two projects, one that surveys models of Fibonacci anyons and another that delves into fermions in optical lattices. We analyse the physics of mobile non-Abelian anyons beyond one-dimension by constructing the simplest possible model of 2D itinerant interacting anyons in close analogy to fermionic systems and inspired by the previous anyonic studies. In particular, we ask the question if spin-charge separation survives in the ladder model for non-Abelian anyons. Furthermore, in the study of this model, we have found a novel physical effective model that possibly hosts a topological gapped state. For fermions in one dimensional optical lattices, we survey the effects of non-adiabatic lattice loading on four different target states, and propose protocols to minimise heating of quantum gases. The evaporative cooling of a trapped atomic cloud, i.e. without the optical lattice potential, has been proven to be a very effective process. Current protocols are able to achieve temperatures as low as T/TF ≈ 0.08, which are lost in the presence of the optical lattice. We aim to understand if defects caused by poor distribution of particles during lattice loading are important for the fermionic case, forbidding the atoms to cool down to the desired level. We device improved ramp up schemes where we dynamically change one or more parameters of the system in order to reduce density defects
Larcanché, Audrey. "Topologie locale des espaces de feuilletages des variétés fermées de dimension 3". Phd thesis, Université des Sciences et Technologie de Lille - Lille I, 2004. http://tel.archives-ouvertes.fr/tel-00008258.
Texto completoBrugallé, Erwan. "Courbes algébriques réelles et courbes pseudoholomorphes réelles dans les surfaces réglées". Phd thesis, Université Rennes 1, 2004. http://tel.archives-ouvertes.fr/tel-00008652.
Texto completoDupas, Alexandre. "Opérations et Algorithmes pour la Segmentation Topologique d'Images 3D". Phd thesis, Université de Poitiers, 2009. http://tel.archives-ouvertes.fr/tel-00466706.
Texto completoJacques, Isabelle. "Aspects combinatoires en modélisation 2D et 3D et application à l'énumération des cartes et des solides". Mulhouse, 1991. http://www.theses.fr/1991MULH0185.
Texto completoDuval, Benoît. "Optimisation de maillages non structurés dans des géométries déformables". Rouen, 1996. http://www.theses.fr/1996ROUES022.
Texto completoAzzouz, Mohamed. "Etudes du modèle t-J sur le réseau triangulaire et des systèmes de spin quantiques quasi-unidimensionnels". Grenoble 1, 1992. http://www.theses.fr/1992GRE10109.
Texto completoBoisbouvier, Jérôme. "Utilisation de la corrélation croisée CSA-Dipolaire pour l'étude RMN des acides ribonucléiques : détermination simultanée de la structure des protéines et de la topologie des ponts disulfures par modélisation moléculaire sous contraintes RMN". Université Joseph Fourier (Grenoble), 2000. http://www.theses.fr/2000GRE10062.
Texto completoCaby, Théophile. "Extreme value theory for dynamical systems, with applications in climate and neuroscience". Thesis, Toulon, 2019. http://www.theses.fr/2019TOUL0017.
Texto completoThroughout the thesis, we will discuss, improve and provide a conceptual framework in which methods based on recurrence properties of chaotic dynamics can be understood. We will also provide new EVT-based methods to compute quantities of interest and introduce new useful indicators associated to the dynamics. Our results will have full mathematical rigor, although emphasis will be placed on physical applications and numerical computations, as the use of such methods is developing rapidly. We will start by an introductory chapter to the dynamical theory of extreme events, in which we will describe the principal results of the theory that will be used throughout the thesis. After a small chapter where we introduce some abjects that are characteristic of the invariant measure of the system, namely local dimensions and generalized dimensions, w1 devote the following chapters to the use of EVT to compute such dimensional quantities. One of these method defines naturally a navel global indicator on the hyperbolic properties of the system. ln these chapters, we will present several numerical applications of the methods, bath in real world and idealized systems, and study the influence of different kinds of noise on these indicators. We will then investigate a matter of physical importanc related to EVT: the statistics of visits in some particular small target subsets of the phase-space, in particular for partly random, noisy systems. The results presented in this section are mostly numerical and conjectural, but reveal some universal behavior of the statistics of visits. The eighth chapter makes the connection betweer several local quantities associated to the dynamics and computed using a finite amount of data (local dimensions, hitting times, return times) and the generalized dimensions of the system, that are computable by EVT methods. These relations, stated in the language of large deviation theory (that we will briefly present), have profound physical implications, and constitute a conceptual framework in which the distribution of such computed local quantities can be understood. We then take advantage of these connections to design further methods to compute the generalized dimensions of a system. Finally, in the last part of the thesis, which is more experimental, we extend the dynamical theory of extreme events to more complex observables, which will allow us to study phenomena evolving over long temporal scales. We will consider the example of firing cascades in a model of neural network. Through this example, we will introduce a navel approach to study such complex systems
Darolles, Cédric. "Invariants d'isotopies pour surfaces différentiables dans des variétés de dimension 4". Toulouse 3, 2002. http://www.theses.fr/2002TOU30093.
Texto completoBénard, Léo. "Reidemeister torsion on character varieties". Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS020/document.
Texto completoIn this PhD dissertation, we study a topological invariant of 3-manifolds, namely the Reidemeister torsion, as globally defined on character varieties of the fundamental group in SL(2,C). The « adjoint » torsion will be the torsion of the cohomological complex associated to the adjoint representation. We explain that it can be seen as a meromorphic differential form on the character variety, and we aim to understand its poles and zeros. They will be related with -singular points of the character variety -the topology of incompressible surfaces embedded in the 3-manifold, provided by the Culler-Shalen theory. As an application, we prove a relation between the genus of those incompressible surface and the genus of the character variety. The « acyclic » torsion of the standard complex is a rational function on the character variety. We study its poles at infinity in the character variety, and we give sufficient conditions for this torsion to be non constant
Pont, Mathieu. "Analysis of Ensembles of Topological Descriptors". Electronic Thesis or Diss., Sorbonne université, 2023. http://www.theses.fr/2023SORUS436.
Texto completoTopological Data Analysis (TDA) forms a collection of tools to generically, robustly and efficiently reveal implicit structural patterns hidden in complex datasets. These tools allow to compute a topological representation for each member of an ensemble of datasets by encoding its main features of interest in a concise and informative manner. A major challenge consists then in designing analysis tools for such ensembles of topological descriptors. Several tools have been well studied for persistence diagrams, one of the most used descriptor. However, they suffer from a lack of specificity, which can yield identical data representations for significantly distinct datasets. In this thesis, we aimed at developing more advanced analysis tools for ensembles of topological descriptors, capable of tackling the lack of discriminability of persistence diagrams and going beyond what was already available for these objects. First, we adapt to merge trees, descriptors having a better specificity, the tools already available for persistence diagrams such as distances, geodesics and barycenters. Then, we want to go beyond this notion of average being the barycenter in order to study the variability within an ensemble of topological descriptors. We then adapt the Principal Component Analysis framework to persistence diagrams and merge trees, resulting in a dimensionality reduction method that indicates which structures in the ensemble are most responsible for the variability. However, this framework allows only to detect linear patterns of variability in the ensemble. To tackle this we propose to generalize this framework to Auto-Encoder in order to detect non-linear, i.e. more complex, patterns in an ensemble of merge trees or persistence diagrams. Specifically, we propose a new neural network layer capable of processing natively these objects. We present applications of all this work in feature tracking in a time-varying ensemble, data reduction to compress an ensemble of topological descriptors, clustering to form homogeneous groups in an ensemble, and dimensionality reduction to create a visual map indicating how the data are organized regarding each other in the ensemble
Mora, Christophe. "Gaz de bosons et de fermions condensés : phases de Fulde-Ferrell-Larkin-Ovchinnikov et quasicondensats". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2004. http://tel.archives-ouvertes.fr/tel-00005472.
Texto completoFFLO. Celles-ci peuvent apparaître dans les supraconducteurs
ou les gaz d'atomes froids fermioniques en présence d'une différence
homogène de potentiels chimiques entre les deux états de spin.
Nous regardons la compétition
entre les différentes phases FFLO près de la transition.
A 2D, nous utilisons une approche de type Ginzburg-Landau
pour prédire une cascade de transitions entre des phases inhomogènes
de plus en plus complexes.
A 3D ou la transition FFLO est du premier ordre,
nous présentons une méthode numérique
de résolution des équations quasiclassiques d'Eilenberger
basée sur un développement de Fourier.
Nous déterminons ainsi les phases inhomogènes de plus basse énergie.
Dans la seconde partie, nous étendons la théorie perturbative
de Bogoliubov aux quasicondensats dans une représentation densité-phase.
Nous obtenons des prédictions pour différentes observables.
Marchand, Pierre. "The spatio-temporal topological operator dimension, a hyperstructure for multidimentsional spatio-temporal exploration and analysis /". 2004. http://proquest.umi.com/pqdweb?did=790267621&sid=3&Fmt=2&clientId=9268&RQT=309&VName=PQD.
Texto completoTutschku, Christian Klaus. "Anomaly Induced Transport And Hall Viscous Effects In 2+1 Space-Time Dimensions". Doctoral thesis, 2021. https://doi.org/10.25972/OPUS-23913.
Texto completoDas zentrale Leitmotiv dieser Dissertation besteht darin, zwei unterschiedliche theoretische Konzepte aus verschiedenen Teilbereichen der Physik zu verbinden, um dadurch neue Perspektiven zu erschließen. Im Wesentlichen zielt die Arbeit darauf ab, die quantenfeldtheoretischen Konstrukte der Paritäts- als auch der chiralen Anomalie aus der Hochenergiephysik auf die Festkörperphysik von sogenannten zwei-dimensionalen Quanten Anomalen Hall (QAH) Isolatoren zu übertragen. Die Dirac-artige Bandstruktur dieser neuartigen Materialien ermöglicht es, Effekte freier quantenelektrodynamischer Teilchen in 2+1 Raumzeit Dimensionen im Festkörperlabor direkt messbar zu machen. Um die zentralen Erkenntnisse dieser Arbeit nachvollziehen zu können ist das Verständnis zweier Konstrukte unumgänglich: (1) Unter einer Quantenanomalie versteht man den Symmetriebruch einer klassischen Theorie während des Quantisierungsprozesses. Um eine konsistente Quantentheorie formulieren zu können, ist es in einem quanten-anomalen System nicht möglich, alle klassischen Symmetrien auf der Quantenebene aufrechtzuerhalten. (2) Unter zwei-dimensionalen QAH Isolatoren versteht man planare Halbleiter mit einer endlichen, transversalen (Hall-) Leitfähigkeit in der Abwesenheit eines externen Magnetfeldes. Derartige Halbleiter werden zum Beispiel in (Hg,Mn)Te/CdTe Schichtsystemen oder in dünnen magnetisierten (Bi,Sb)Te Filmen vorhergesagt und zum Teil bereits experimentell nachgewiesen. Die nieder-energie Theorie um die Bandlücke der oben genannten QAH Systeme wird gemeinsam durch die Physik zweier sogenannter Chern Isolatoren beschrieben. Jeder Chern Isolator besitzt eine lineare Dispersion im Impulsraum und gleicht somit der Theorie quantenelektrodynamischer Teilchen in 2+1 Raumzeit Dimensionen QED\(_{2+1}\). Darauf basierend ist jeder Chern Isolator für sich direkt mit der Paritätsanomalie verbunden. Um die effektive Bandkrümmung im Festkörper zu charakterisieren unterscheidet sich das Modell eines Chern Isolators von der entsprechenden QED\(_{2+1}\) Theorie um einen quadratischen Masse-Term im Impuls, die sogenannte Newtonsche Masse \( B \vert \mathbf{k}\vert^2 \). Zusammen mit dem impulsunabhängigen Dirac Masseterm \(m\) definiert jene paritätsbrechende Masse die Energielücke eines Chern Isolators. Wie bereits in (1) erwähnt tritt die Paritätsanomalie während der Quantisierung klassisch paritätssymmetrischer Systeme auf. Quantisiert man beispielsweise eine masselose QED\(_{2+1}\) Theorie, so induziert man während der Berechnung der Fermion Determinante paritätsbrechende Terme in der zugehörigen effektiven Wirkung. Obgleich eine nichtverschwindende Dirac-Masse die Paritätssymmetrie auf klassischer Ebene bricht, ist die zugehörige Fermion Determinante UV divergent als auch Eichsymmetrie brechend und Bedarf daher eines geeigneten Regularisierung/Renormierungsschemas. Diese Eigenschaft erlaubt es Konsequenzen der Paritätsanomalie ebenfalls in massiven Systemen zu identifizieren. Die Auswirkungen einer Dirac-Masse für die Berechnung der effektiven Wirkung eines QED\(_{2+1}\) Systems wurden inertial in der wegweißenden Publikation Phys. Rev. Lett. 51, 2077 (1983) analysiert. Im Rahmen dieser Dissertation eruieren wir die Implikationen der Newtonschen Masse eines Chern Isolators auf die entsprechende Berechnung der Fermion Determinante und beleuchten damit die effektive Bandkrümmung eines Festkörpers im Kontext einer diskreten Raumzeit Anomalie. Wir zeigen insbesondere, dass die Newtonsche Masse vor dem unumgänglichen Renormierungprozess den paritätsbrechenden Elementen verschiedener hochenergetischer Regularisierungsschemata ähnelt, wie zum Beispiel Wilson Fermionen. Mittels dieser Berechnung leiten wir ebenfalls die Wechselstromleitfähigkeit der genannten QAH Isolatoren her. Wir zeigen, dass die führende Frequenzkorrektur in diesen Systemen einen Term proportional zur Chern Zahl enthält. Jener Beitrag basiert auf der zugrundeliegenden Galilei Invarianz und ist insbesondere durch magneto-optische Experimente nachzuweisen. Weiter eruieren wir, dass der genannte Term fundamental die Resonanzstruktur der Hall Leitfähigkeit beeinflusst, sodass diese maßgeblich von der entsprechenden Größe eines puren Dirac Systems wie Graphen abweicht. Zudem analysieren wir in dieser Arbeit die Physik von 2+1 dimensionalen Chern Isolatoren in externen Magnetfeldern die orthogonal auf der zugrundeliegenden Raum-Mannigfaltigkeit stehen -sogenannte orbitale Magnetfelder. Wir zeigen dass als direkte Konsequenz der Paritätsanomalie die QAH Phase in orbitalen Magnetfelder überlebt, darin die Onsager Relationen bricht und somit von konventionellen QH Systemen unterschieden werden kann, obgleich beide topologischen Phasen durch die selbe Chern Klasse beschrieben sind. Als experimentelle Signatur der QAH Phase in adiabatisch zunehmenden orbitalen Magnetfeldern sagen wir den Übergang eines quantisierten Hall Plateaus mit \(\sigma_\mathrm{xy}= -\mathrm{e}^2/\mathrm{h}\) zu einem nicht-quantisierten, rauschenden Hall Plateau vorher. Der Mittelwert des letzteren Plateaus hängt stark von Streuprozessen zwischen entgegengesetzt propagierenden QH und QAH Randzuständen ab. Insbesondere in (Hg,Mn)Te/CdTe Schichtsystemen ist der vorhergesagte Übergang von großem Interesse da in jenen Systemen die Austauschwechelwirkung mit dem polarisierenden Magnetfeld konkurriert. All die oben genannten Ergebnisse vernachlässigen thermische Effekte. Um den Einfluss einer endlichen Umgebungstemperatur auf die Physik von QAH Isolatoren zu untersuchen, analysieren wir im Rahmen dieser Dissertation ebenfalls die Hall Leitfähigkeit 2+1 dimensionaler Chern Isolatoren bei endlicher Temperatur und unter dem Einfluss beliebiger chemischer Potentiale sowie orbitaler Magnetfelder. Wie oben bereits erwähnt hängt dieser nicht dissipative Transportkoeffizient direkt mit der Paritätsanomalie eines masselosen QED\(_{2+1}\) Systems zusammen. Wir zeigen mittels unserer Analyse, dass die Paritätsanomalie an sich nicht durch endliche Temperatureffekte beeinflusst wird. Allerdings induziert jene Anomalie in der effektiven Wirkung eines Chern Isolators zwei Beitrage unterschiedlichen physikalischen Ursprungs. Einer der Terme ist unabhängig vom chemischen Potential und der Temperatur da er ausschließlich die intrinsische topologische Phase des Systems codiert. Der andere Term definiert die thermisch angeregten Zustände im Leitungs- bzw. im Valenzband und ist somit nicht-topologischen Ursprungs. Insbesondere zeigen wir, dass in der topologisch nicht trivialen Phase eines Chern Isolators die Dirac Masse den endlichen Temperatureffekten entgegenwirkt, während die nicht-relativistische Newtonsche Masse jene Korrekturen verstärkt. Neben diesen Effekten bei verschwindendem orbitalem Magnetfeld verallgemeinern wir unsere thermischen Betrachtungen hinsichtlich der Effekte quantisierender orbitaler Magnetfelder. Insbesondere verknüpfen wir die Leitfähigkeit von QAH Isolatoren bei endlicher Temperatur zur sogenannten Spektralen Asymmetrie. Diese Größe kann als Signatur der Paritätsanomalie in orbitalen Magnetfeldern interpretiert werden. Im zweiten großen Kapitel dieser Dissertation analysieren wir den hydrodynamischen Ladungs-transport in zwei-dimensionalen Elektronensystemen, in denen sowohl die Zeitumkehr- als auch die Paritätssymmetrie gebrochen sind. Unseren Forschungsschwerpunkt legen wir hierbei vor Allem auf nicht-dissipative Transporteigenschaften, die sich mittels der Hall Viskosität aus den Navier-Stokes Gleichungen ergeben. In orbitalen Magnetfeldern konkurrieren aufgrund dieses paritätsbrechenden Transportkoeffizient zwei transversale Kräfte miteinander: Die sogenannte Hall viskose Kraft und die wohlbekannte Lorentzkraft. Zusammen definieren beide Kräfte die gesamte Hall Spannung des Systems. In den Ausführungen dieser Arbeit zeigen wir wie die genannten unterschiedlichen Beiträge in zweidimensionalen Transportkanälen anhand ihrer verschiedenen funktionellen Abhängigkeiten von den Systemparametern unterschieden werden können. Wir eruieren, dass das Verhältnis zwischen dem Hall viskosen Beitrag und dem Lorentz basierten Beitrag negativ ist und dessen Absolutbetrag mit zunehmender Kanalbreite, Rutsch-Länge [engl. slip length] und Ladungsträgerdichte abnimmt. Im Gegensatz dazu wächst jener Betrag mit der mittleren Elektron-Elektron Streulänge. Im Rahmen dieser Dissertation zeigen wir, dass in typischen GaAs Fermi Flüssigkeiten der Hall viskose Beitrag das Lorentz Signal bis hin zu einer orbitalen Magnetfeldstärke im zehnstelligen Milli-Tesla Bereich dominieren kann. Im Anschluss nimmt das Verhältnis dieser Größen ab, verschwindet bei einem kritischen Magnetfeld und wird schlussendlich durch das Lorentz Signal dominiert. Zuletzt zeigen wir, dass das transversale elektrische Feld in den genannten Experimenten eine parabolische Form besitzt, welche auf dem Lorentz Beitrag basiert. Im Gegensatz dazu ist der konstante Offset dieser Parabel hauptsächlich durch die Hall Viskosität definiert. Zusammen weisen die hier genannten Eigenschaften einen möglichen Weg zur experimentellen Bestimmung der Hall Viskosität mittels lokaler- oder globaler Spannungsmessungen auf