Neste trabalho apresentamos uma versão do Teorema de Poincaré-Bendixson para campos vetoriais contínuos na garrafa de Klein. Como conseqüência, mostramos que a garrafa de Klein não possui campo vetorial contínuo com trajetória injetiva recorrente / We present a version of the Poincaré-Bendixson Theorem on the Klein bottle for continuous vector fields. As a consequence, we obtain the fact that the Klein bottle does not admit continuous vector fields having a recurrent injective trajectory

Thss thesis presents the results of an experimental programme on the static mono-tonic response of cohesive-frictional granular materials. The purpose of this experimental programme was to gain insight into the mechanical behaviour of uncemented sands, and sands with small percentages of cementation. With this objective in sight, the research involved understanding and delineating the e ects of four variables: the intermediate principal stress, stress inclination, cohesion (or cementation), and particle morphology. The hollow cylinder torsion (HCT) apparatus, which allows control over both the magnitude and direction of principal stresses, was used in this study to carry out a series of elemental tests on the model materials. The test results were analysed in a plasticity theory based framework of critical state soil mechanics. Drained and undrained HCT tests were conducted on a model angular sand to understand the combined influence of intermediate principal stress ratio (b) and principal stress inclination ( ). Sand specimens were reconstituted to a given density and confining pressure, and were sheared to large strains towards a critical state. The stresses at the critical state with varying `b' were mapped on an octahedral plane to obtain a critical state locus. The shape of this locus closely resembles a curved triangle. Also these specimens showed increased non-coaxiality between the stress and strain increment directions at lower strains. This non-coaxiality decreased significantly, and the response at the critical state was by and large coaxial. The effect of `b' and ` ' on the flow potential, phase transformation, and critical state was also investigated. At phase transformation, ` ' plays a more dominant role in determining the flow potential than `b'. The shape and size of the critical state locus remained the same immaterial of the drainage conditions. Next, small amounts of cohesion (using ordinary Portland cement) was added to this sand ensemble to study the mechanical behaviour of weakly cemented sands. The peak in the stress strain curve was used to signal the breakdown of cohesion further leading to a complete destructuring of the sand at the critical state. The response of the cemented sand changes from brittle to ductile with increase in confining pressure, while reverses with increase in density and `b'. Stress-dilatancy response for the weakly cemented materials shows the non coincidence of peak stress ratio and maximum value of dilation unlike purely frictional materials. This mismatch in peak stress ratio and maximum dilation diminishes with increase in confining pressure. The peak stress (cemented structured sand) locus and the critical state (destructured) locus were constructed on the octahedral plane from these HCT tests. The critical state locus of the cemented sand when it is completely destructured almost coincides with the critical state locus of the clean sand. Using this experimental data set, some important stress-dilatancy relationships (like Zhang and Salgado) and failure criteria (Lade's isotropic single hardening failure criteria and SMP failure criteria) were benchmarked and their prediction capabilities of such models were discussed in detail. The effect of particle morphology was also investigated in this testing programme. Rounded glass ballotini and angular quartzitic sand which occupy two extreme shapes were selected, and a series of HCT tests at different `b' values were con-ducted. A larger sized CS locus was obtained for angular particles and it encompassed the critical state locus of the spherical glass ballotini. Spherical particles exhibit a predominantly dilative behaviour, however present a lower strength at the critical state. The mobilization of strength as a result of rearrangement of angular particles and the consequent interlocking is higher. Even with contractive behaviour which is reflected in the higher values of critical state friction angle and the larger size of the yield locus for sand. Finally, a series of unconfined compression tests were performed to understand if there exists a scale separation in cohesive frictional materials. Specimens were reconstituted to a range of sizes while maintaining a constant aspect ratio and density. As the specimen size increased, the peak strength also increases, counter to an idea of a generalized continuum for all model systems. The observed secondary length scale (in addition to the continuum length scale) is obverse to the one observed in quasi-brittle materials such as concrete, rock. In order to ascertain the reason behind this phenomenon, a series of tomography studies were carried out on these contact-bound ensembles. The presence of cohesion between the grains brings about an \entanglement" between the grains, which contributes to increase in strength, with increase in the size of the sample. This in e ect bringing forth a second length scale that controls the behaviour of these cohesive frictional granular materials. This experimental data set provides quantification of various aspects of the me-chanical response of both cemented and uncemented granular materials under myriad stress conditions. This data set is also extremely useful in developing and bench-marking constitutive models and simulations.

Dans ce travail, nous nous intéressons à une topologie pour les réseaux de capteurs sans fil. Un réseau de capteurs sans fil peut être modélisé comme un graphe non orienté G = (V,E). Chaque sommet de V représente un capteur et une arête e = {u, v} dans E indique une transmission directe possible entre deux capteurs u et v. Contrairement aux dispositifs filaires, les capteurs sans fil ne sont pas a priori agencé en réseau. Une topologie doit être créée en sélectionnant des noeuds "dominants" qui vont gérer les transmissions. Les architectures qui ont été examinées dans la littérature reposent essentiellement sur les ensembles dominants connexes et les ensembles dominants faiblement connexes. Cette étude est consacrée aux ensembles indépendants faiblement connexes. Un indépendant S ⊂ V est dit faiblement connexe si le graphe GS = (V, [S, V \S]) est connexe, où [S, V \S] est l’ensemble des arêtes e = {u, v} de E avec u ∈ S et v ∈ V \S. Une topologie basée sur les ensembles faiblement connexes permet de partitionner l’ensemble des capteurs en trois groupes, les esclaves, les maîtres et les intermédiaires. Les premiers effectuent les mesures, les seconds rassemblent les données collectées et les troisièmes assurent les communications inter-groupes. Nous donnons d’abord quelques propriétés de cette structure combinatoire lorsque le graphe non orienté G est connexe. Puis nous proposons des résultats de complexité pour le problème de la recherche de l’indépendant faiblement connexe de cardinalité minimale (MWCISP). Nous décrivons également un algorithme d’énumération exact de complexité O∗(1.4655|V |) pour le MWCISP. Des tests numériques de cette procédure exacte sont présentés. Nous formulons ensuite le MWCISP comme un programme linéaire en nombres entiers. Le polytope associé aux solutions de ce problème est complètement caractérisé lorsque G est un cycle impair. Nous étudions des opérations de composition de graphes et leurs conséquences polyédrales. Nous introduisons des inégalités valides notamment les contraintes dites de multibord. Par la suite, nous développons un algorithme de coupes et branchement sous CPLEX pour résoudre ce problème en utilisant des heuristiques pour la séparation de nos familles de contraintes. Des résultats expérimentaux de ce programme sont exposés. / In this work, we focus on a topology for Wireless Sensor Networks (WSN). A wireless sensor network can be modeled as an undirected graph G = (V,E). Each vertex of V represents a sensor and an edge e = {u, v} in E implies a direct transmission between the two sensors u and v. Unlike wired devices, wireless sensors are not a priori arranged in a network. Topology should be made by selecting some sensor as dominators nodes who manage transmissions. Architectures that have been studied in the literature are mainly based on connected dominating sets and weakly connected dominating sets.This study is devoted to weakly connected independent sets. An independent set S ⊂ V is said Weakly Connected if the graph GS = (V, [S, V \S]) is connected, where [S, V \S] is the set of edges with exactly one end in S. A sensor network topology based on weakly connected sets is partition into three groups, slaves, masters and bridges. The first performs the measurements, the second gathers the collected data and the later provides the inter-group communications. We first give some properties of this combinatorial structure when the undirected graph G is connected. Then we provide complexity results for the problem of finding the minimum weakly connected independent set problem (MWCISP). We also describe an exact enumeration algorithm of complexity O∗(1.4655|V |) (for the (MWCISP)). Numerical tests of this exact procedure are also presented. We then present an integer programming formulation for the minimum weakly connected independent set problem and discuss its associated polytope. Some classical graph operations are also used for defining new polyhedra from pieces. We give valid inequalities and describe heuristical separation algorithms for them. Finally, we develop a branch-and-cut algorithm and test it on two classes of graphs.

Le premier projet de ce travail de doctorat a consisté à étudier l’activité catalytique de complexes à base de gallium(I), pour continuer à rechercher des alternatives aux catalyseurs à base de métaux nobles, plus communs, mais réputés coûteux et/ou toxiques. Le savoir-faire de l’équipe en catalyse par des complexes de gallium(III) a pu être réinvesti dans l’étude de ce bas degré d’oxydation du gallium, rarement étudié dans la littérature scientifique, dans l’espoir de détecter des réactivités et/ou sélectivités différentes d’avec des complexes de gallium(III). Ainsi, le complexe cationique bien défini de gallium(I) [Ga(PhF)2][Al(OC(CF3)3)4] a été employé dans une large gamme de réactions dans lesquelles les catalyseurs à base de gallium(III) avaient déjà fait leurs preuves, telles que l’hydroarylation d’arénynes, la réaction de Friedel-Crafts ou encore l’hydrogénation d’alcènes par transfert, pour laquelle une réactivité supérieure à celle des complexes usuellement utilisés au sein de l’équipe a été observée. Un analogue à base d’indium(I), [In(PhF)2][Al(OC(CF3)3)4], a également été étudié dans ces réactions, sans succès. En revanche, il s’est avéré efficace dans le cadre de réactions d’hydroamination d’aminoalcènes.En parallèle a été conduit un projet basé sur l’étude en tant qu’abstracteurs d’halogénures de complexes de divers métaux (argent, lithium, potassium, thallium(I)) comportant l’anion perfluoré, très volumineux et très faiblement coordinant [Al(OC(CF3)3)4]-. Dans le cadre de l’activation de pré-catalyseurs à base d’or(I), de gallium(III) ou d’indium(III) par abstraction d’halogénures, les sels d’argent sont les plus communément employés dans la littérature. Cependant, ces sels d’argents ne sont pas innocents en termes de réactivité. Par ailleurs, si les cations métalliques des sels employés en abstraction d’halogénures font l’objet d’un nombre raisonnable d’études dans la littérature, ce n’est pas autant le cas des anions qui leur sont associés : notre étude s’oriente selon ces deux problématiques. Il s’est avéré que les propriétés très faiblement coordinantes de l’anion [Al(OC(CF3)3)4]- ont mené à des réactivités et sélectivités différentes de celles obtenues avec l’emploi de sels plus usuels, AgSbF6 plus particulièrement, dans le cadre de réaction classiquement catalysées par l’or(I) ou le gallium(III) et déjà étudiées dans le premier projet de ce travail de thèse. Les complexes à base de gallium(I) et d’indium(I) impliqués dans le premier projet ont également été, succinctement, étudiés dans ce projet parallèle. / In the main project of this thesis work, the catalytic activity of gallium(I)-based complexes was explored. The aim was to keep on looking for alternatives to noble metals-based, more common catalysts, which have a reputation for being expensive and/or toxic. The know-how developed in the team on gallium(III)-based catalysis was reinvested into the study of this low oxidation degree of gallium, only scarcely studied in the literature. It was hoped to then detect different reactivity and/or selectivity than with gallium(III) complexes. Thus, the well-defined, cationic, gallium(I)-based complex [Ga(PhF)2][Al(OC(CF3)3)4] was used in a large array of reactions that were already successfully studied with gallium(III)-based catalysts, such as the hydroarylation of arenynes, the Friedel-Crafts reaction or the transfer hydrogenation of alkenes. In this later reaction in particular, the observed reactivity was superior to that achieved with the catalysts more commonly used in the team. An indium(I)-based analogue, [In(PhF)2][Al(OC(CF3)3)4], was also tested in these reactions, without any success. However, it was actually efficient in the context of aminoalkenes hydroamination reactions.The side-project of this work consisted in the study as halide abstractors of complexes, based on diverse metals (silver, lithium, potassium, thallium(I)) and containing the perfluorinated, very bulky and very weakly coordinating anion (WCA) [Al(OC(CF3)3)4]-. In the frame of the activation of gold(I), gallium(III) or even indium(III)-based pre-catalysts by halide abstraction, silver salts are the most frequently used. However, these silver salts are not non-innocent in terms of reactivity. Besides, if the cationic metal of the salts used in halide abstraction are the subject of a reasonable amount of studies in the literature, it is not the case of their anionic counterparts: we planned to address these two problematics with this project. It appeared that the very weakly coordinating properties of the anion [Al(OC(CF3)3)4]- in the context of the previously referred to reactions classically catalyzed by gold(I) or gallium(III)-based complexes led to different reactivity and selectivity than those achieved with the usual salts and in particular AgSbF6. The gallium(I) and indium(I)-based complexes involved into the main project were also briefly studied in this side-project.

The paper is dedicated to the modeling and the simulation of random processes and fields. Using the concept and the theory of weakly correlated functions a consistent representation of sufficiently smooth random processes will be derived. Special applications will be given with respect to the simulation of road surfaces in vehicle dynamics and to the confirmation of theoretical results with respect to the zeros of random polynomials.

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.

The thesis is focused on the investigation of Rayleigh-Bénard problem in an extended setting approximating the conditions in the Earth's mantle. The aim is to evaluate the influence of depth- and temperature- dependent material parameters, dissipation, adiabatic heating/cooling and heat sources on the qualitative characteristics of thermal convection. We identify the critical values of dimensionless parameters that determine the onset of convection and characterize the dominating convection patterns in marginally supercritical states. These issues are addressed by the application of linear stability analysis and weakly non-linear analysis. It has been found that the character of convection differ substantially from the standard case of Rayleigh-Bénard convection. Powered by TCPDF (www.tcpdf.org)

<p>A specific class of small-scale plasmas (column diameters in a sub-mm to mm range) at rarefied pressures (under 10 Torr) enclosed in glass tubes hold significant interest currently in the scope  of  tunable  plasma  devices.  Specifically,  applications  of  these  plasmas  include  plasma antennas and plasma photonic crystals. Reliable diagnostics are necessary for the development and implementation of these technologies as conventional tools are inadequate in such small-scale plasmas.</p> <p>Coherent microwave scattering in the Thomson regime (TMS) was recently demonstrated for diagnostics of electron number density in miniature free-standing laser-induced plasmas in air under  10  Torr  with  plasma  column  diameters  <  0.5  mm.  However,  measurements  by  TMS diagnostics have never been applied for small-scale plasma objects enclosed within glass tubes. Additionally, TMS measurements were never independently confirmed with a previously verified experimental technique. This work aims to validate results of TMS measurements for small-scale plasma  objects  enclosed  within  glass  tubes  using  the  previously  established  and  well-known hairpin resonator probe. A DC discharge plasma column of fairly large diameter (about 1.5 cm) is used in the experiments to ensure reliable non-intrusive measurements by the hairpin resonator probe.</p> <p>The experiments were conducted in a DC discharge tube with a diameter of 1.5 cm and a length of 7 cm. TMS diagnostics yielded electron number densities of about 5.9×10¹⁰cm^-3, 2.8 ×10¹⁰cm^-3and  1.8 ×10¹⁰cm^-3at  pressures  of  0.2,  0.5  and  2.5  Torr,  respectively.  The corresponding  densities  measured  with  the  hairpin  resonator  probe  were  4.8×10¹⁰cm^-3,  3.8 ×10¹⁰cm^-3 and 2.6 ×10¹⁰cm^-3. Discrepancies between the two techniques were within 30% and can be attributed mainly to inaccuracies in the sheath thickness estimation required the hairpin resonator probe results.</p>

In this thesis we study the global existence of small data solutions to the Cauchy problem for semilinear damped wave equations with an effective dissipation term, where the data are supposed to belong to different classes of regularity. We apply these results to the Cauchy problem for weakly coupled systems of semilinear effectively damped waves with respect to the defined classes of regularity for different power nonlinearities. We also presented blow-up results for semi-linear systems with weakly coupled damped waves.

Dans cette dissertation, nous discutons comment utiliser les données du regard humain pour améliorer la performance du modèle d'apprentissage supervisé faible dans la classification des images. Le contexte de ce sujet est à l'ère de la technologie de l'information en pleine croissance. En conséquence, les données à analyser augmentent de façon spectaculaire. Étant donné que la quantité de données pouvant être annotées par l'humain ne peut pas tenir compte de la quantité de données elle-même, les approches d'apprentissage supervisées bien développées actuelles peuvent faire face aux goulets d'étranglement l'avenir. Dans ce contexte, l'utilisation de annotations faibles pour les méthodes d'apprentissage à haute performance est digne d'étude. Plus précisément, nous essayons de résoudre le problème à partir de deux aspects: l'un consiste à proposer une annotation plus longue, un regard de suivi des yeux humains, comme une annotation alternative par rapport à l'annotation traditionnelle longue, par exemple boîte de délimitation. L'autre consiste à intégrer l'annotation du regard dans un système d'apprentissage faiblement supervisé pour la classification de l'image. Ce schéma bénéficie de l'annotation du regard pour inférer les régions contenant l'objet cible. Une propriété utile de notre modèle est qu'elle exploite seulement regardez pour la formation, alors que la phase de test est libre de regard. Cette propriété réduit encore la demande d'annotations. Les deux aspects isolés sont liés ensemble dans nos modèles, ce qui permet d'obtenir des résultats expérimentaux compétitifs. / In this dissertation, we discuss how to use the human gaze data to improve the performance of the weak supervised learning model in image classification. The background of this topic is in the era of rapidly growing information technology. As a consequence, the data to analyze is also growing dramatically. Since the amount of data that can be annotated by the human cannot keep up with the amount of data itself, current well-developed supervised learning approaches may confront bottlenecks in the future. In this context, the use of weak annotations for high-performance learning methods is worthy of study. Specifically, we try to solve the problem from two aspects: One is to propose a more time-saving annotation, human eye-tracking gaze, as an alternative annotation with respect to the traditional time-consuming annotation, e.g. bounding box. The other is to integrate gaze annotation into a weakly supervised learning scheme for image classification. This scheme benefits from the gaze annotation for inferring the regions containing the target object. A useful property of our model is that it only exploits gaze for training, while the test phase is gaze free. This property further reduces the demand of annotations. The two isolated aspects are connected together in our models, which further achieve competitive experimental results.