Cette Thèse de Doctorat est dédiée à la simulation numérique des détonations, et plus particulièrement aux détonations confinées par un gaz inerte. Cette configuration correspond en partie à l’écoulement rencontré au sein des moteurs à détonations rotatives, dans lesquels le combustible est confiné par les gaz brûlés issus du cycle précédent. Le code de calcul employé s’appuie sur des schémas numériques d’ordre élevé adaptés à la capture des discontinuités (interpolation MP d’ordre 9, solveur HLLC et intégration temporelle d’ordre3). Une attention particulière a été portée à la caractérisation de l’écoulement au travers de son évolution moyenne dans le repère de la détonation. Les simulations ont été réalisées pour différentes valeurs de l’énergie d’activation, qui traduit la sensibilité du milieu réactif,pour des couches réactives de dimensions variées et enfin pour des confinements inertes à différentes températures. La base de données résultante démontre l’existence de deux comportements distincts suivant l’énergie d’activation du milieu réactif. Le déficit de la célérité de la détonation peut être globalement appréhendé comme fonction du ratio de l’épaisseur hydrodynamique par le rayon de courbure sur l’axe. Enfin, la présence d’une couche inerte à haute température modifie de façon importante la topologie de la détonation et en étend les limites de propagation. / This dissertation is devoted to the numerical study of detonation waves, and more specifically to the dynamics of detonations bounded by an inert gaseous layer. This configuration is similar to the flow field within the rotating detonation engines, in which the fuel is confined by the burned gases produced during the previous combustion cycle. The computational solver is based on high-order schemes designed for capturing discontinuities (9thorder MP interpolation, HLLC solver and 3rd order temporal integration). The detonation was investigated by calculating the averaged profile in the shock frame of reference. The simulations were performed for various values of the activation energy, which control the mixture sensitivity, for different heights of the reactive layer and for different temperature of the inert medium. The resulting database shows that according to the activation energy, two different behaviors can be observed. The presence of a high-temperature inert layer strongly affects the detonation structure and extends the propagation limits. The detonation deficit can be globally expressed as a function of the ratio of the hydrodynamic thickness to the radius of curvature on the axis.

In recent decades, there have been new management principles, which seek innovation and flexibility, from the findings that the models of organizational rigidity , based on bureaucratic ideals, are being replaced by an systemic view of activities. In the context of universities, institutions focusing on knowledge, the need for modernization is even higher due ace own innovations and knowledge produced in this environment. To assist in this process, strategic planning and foundations of GesPública seem essential to develop specific skills and innovative capacity. The university in the context of public administration finds limits and difficulties that often hinder the implementation of innovations that the university develops and encourages society to desenvover and run. Such impediments stem from several factors, the legislation that governs its processes, and own internal management of the institution setting. Thus, the focus of this study was investigate the limits and knows the strategies adopted and the perception of CESNORS management, a decentralized unit of UFSM, with a unique proposition in Brazil. A center with two university units in geographically distant municipalities and 70 km away from the seat 270 km. To achieve these goals we used the methodology of the case study, with quantitative and qualitative approach and descriptive and exploratory. The survey was conducted with the following instruments: a literature review, participant observation, questionnaire and conducting interviews. The collected data were verified through content analysis and Likert scale and subsequent processing of the collected data ( Excel and SPSS Software). It is expected with this study provide support for further discussion and contribute to the continuous improvement of university management. The results obtained from the survey showed main limits legislation , the distance between the units , fragmentation between segments and between units. As management strategies lean structure , innovation in university administration with an organizational culture teams as well as the active participation of Cesnors at Headquarters UFSM / Nas últimas décadas, surgiram novos princípios de gestão, os quais buscam inovação e flexibilidade, a partir das constatações de que os modelos de rigidez organizacional, com base nos ideais burocráticos, estão sendo substituídos por uma proposta embasada em informação e visão sistêmica das atividades. No contexto das universidades, instituições com foco no conhecimento, a necessidade de modernização se faz ainda maior, devido ás próprias inovações e conhecimentos produzidos neste ambiente. Para auxiliar nesse processo o planejamento estratégico e os princípios e fundamentos do GesPública, parecem fundamentais para desenvolverem competências específicas e capacidade inovadora. A universidade por estar inserida no contexto da administração pública, encontra limites e dificuldades que muitas vezes impedem a implementação das inovações que ela própria desenvolve e incentiva a sociedade a buscá-las e efetivá-las. Tais impedimentos decorrem entre vários fatores, da legislação vigente, que rege seus processos, e da configuração da própria gestão interna da instituição. Diante disso, o foco desse estudo foi a gestão de universidade, e o propósito de compreender a configuração, investigar os limites bem como conhecer as estratégias adotadas e a percepção da gestão do CESNORS, uma unidade descentralizada da UFSM, com uma proposta de gestão diferenciada. Um centro (uma gestão) com duas unidades universitárias em municípios distante geograficamente 70 km e distantes 270 km de Santa Maria. Para atingir tais objetivos foi utilizada a metodologia do estudo de caso, com abordagem quantitativa e qualitativa e caráter descritivo-exploratório. A pesquisa foi realizada com os seguintes instrumentos: revisão da literatura, observação participante, aplicação de questionário e realização de entrevista. Os dados coletados foram verificados por meio da análise de conteúdo e escala de Likert e posterior tratamento estatístico dos dados coletados (Excel e Software SPSS). Os resultados obtidos pela pesquisa evidenciaram como principais limites a legislação, a distância entre as unidades, a fragmentação entre os segmentos e entre as unidades. Como estratégias de gestão a estrutura enxuta, inovação na administração universitária com uma cultura organizacional de equipes bem como a participação ativa do Cesnors junto a Sede da UFSM.

The present study if it projects her/it an attempt of demonstrating the consolidation of the limits of the Brazilian National State, in the Fronteira Oeste of Rio Grande do Sul with Uruguay in the first half of the century XIX (1801 - 1850), leaving of the appropriation and ownership of the lands devolutas allowed by the Portuguese Crown through the regime of sesmarias donations, motivating like this the fixation of stays for the accomplishment of your interest in fastening those limits. Like this, it is demonstrated to the proprietors' of the stays relationship with Fronteira West's configuration in the first half of the already mentioned century. For the accomplishment of this study it is used besides the pré-existent bibliography, I tell of travelers and of the archaeology that you/they bring with itself the reality of the time, as well as, the retractation of the daily and of the material and social relationships inside of the universe estancieiro; and still, it is included the resource of the documentation that corroborates with the mentioned methodology here. It is verified that the people's fixation to the earth in this rural and distant universe becomes necessary due to the successive attempts of Spanish domain for the border. The Fronteira Oeste will be defined by your limitations territorial estancieiras and configured culturally inside of these patterns. It is noticed although starting from the installation of the Law of Lands of 1850, in this area, in other words, with the passage of the ownership for the private property, the Crown practically forced a frontier definition. In this context, the institution landowner is perpetuated: the old sesmarias are with the great gentlemen, the lands taken possession devolutas and not registered the Crown and the result they were returned of that it is that have immense spaces today sub taken advantage of as if they go bordering internal in that our notion doesn't penetrate / O presente estudo se projeta a uma tentativa de demonstrar a consolidação dos limites do Estado Nacional Brasileiro, na Fronteira Oeste do Rio Grande do Sul com o Uruguay na primeira metade do século XIX (1801 1850), partindo da apropriação e posse das terras devolutas permitidas pela Coroa Portuguesa através do regime de doações de sesmarias, incentivando assim a fixação de estâncias para a realização de seu interesse em fixar esses limites. Assim, demonstra-se à relação dos proprietários das estâncias com a configuração da Fronteira Oeste na primeira metade do já citado século. Para a realização deste estudo utiliza-se além da bibliografia pré-existente, relatos de viajantes e da arqueologia que trazem consigo a realidade da época, bem como, a retratação do cotidiano e das relações materiais e sociais dentro do universo estancieiro; e ainda, engloba-se aqui o recurso da documentação que corrobora com a metodologia citada. Constata-se que a fixação de pessoas à terra neste universo rural e longínquo torna-se necessária devido às sucessivas tentativas de domínio espanhol pela fronteira. A Fronteira Oeste vai ser definida pelas suas limitações territoriais estancieiras e configurada culturalmente dentro destes padrões. Percebe-se ainda que a partir da instalação da Lei de Terras de 1850, nesta região, ou seja, com a passagem da posse para a propriedade particular, a Coroa praticamente forçou uma definição fronteiriça. Neste contexto, perpetua-se a instituição latifundiária: as antigas sesmarias ficam com os grandes senhores, as terras devolutas apossadas e não registradas foram devolvidas a Coroa e o resultado disso é que temos hoje imensos espaços sub aproveitados como se fossem fronteiras internas em que nossa noção não penetra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This master thesis presents a reconstruction of the problem of the unity of reason in Kant s critical-transcendental philosophy. Bearing in mind that there is much disagreement in the literature, not only as to the critical answer to this problem, but also as to its specificity and systematic function within the various moments in which it is considered by Kant, this approach centers essentially on Kant s own argumentation. The aim of this research is to show that Kant s treatment of the problem follows the development of the critical-transcendental philosophy and that it can only be understood insofar as this development is presented. Therefore, a search for the systematic localization of the moments in which Kant approaches the problem of the unity of reason has been carried out, with the intention of justifying that this approach is fundamentally connected with the critical intention of establishing the boundaries that guarantee legitimacy to reason and assure its authenticity to operate in the theoretical as well as in the practical domain. The investigation is guided by the necessity to understand that both the negative results at which Kant arrives in the search of the demonstration of the unity of reason and the only critical answer admitted to this problem have their genesis in the systematic possibilities considered by the critical philosophy as a whole. Initially, in view of the argumentation that corresponds to the first period of this philosophy, an examination of Kant s search for a solution to the problem of the unity of reason from the theoretical use is carried out. Secondly, the systematic identification of the impossibility of solving the problem through this route leads to the consideration of an effort to establish the unity from the practical use and, likewise, to the discovery that the theoretical and practical uses of reason must be legitimized in two distinct domains of reason and, thus, the unity of reason cannot be guaranteed from either of its uses. Finally, faced with this situation, an exploration of the answer guaranteed to the problem of the unity of reason by the Kantian argumentation that considers the relation of the theoretical and practical domains in a regulative manner is carried out. As a result of the systematic impossibility to establish the unity of reason from one of its uses, the necessary self-sufficient validation of these uses, and, also, the fact that the relation of their domains can only be admitted as regulative, the conclusion reached is that the unity of reason is a fundamental presupposition of the critical philosophy in the articulation of its entirety, but that the critical answer to this problem consists in the justification of the impossibility of its demonstration. / Este trabalho apresenta uma reconstrução do problema da unidade da razão na filosofia crítica-transcendental kantiana. Dado que a literatura discorda não apenas acerca da resposta crítica a esse problema, mas até mesmo sobre a sua especificidade e a sua função sistemática nos diversos momentos nos quais ele é considerado, a abordagem centra-se essencialmente na própria argumentação kantiana. Procura-se, outrossim, mostrar que o tratamento do mesmo problema segue o desenvolvimento da filosofia crítica-transcendental e que ele só pode ser compreendido desde que apresentado tal desenvolvimento. Assim sendo, busca-se uma localização sistemática dos momentos onde Kant aborda o problema da unidade da razão no intuito de justificar que a mesma abordagem é fundamentalmente vinculada à intenção crítica de determinar os limites que garantem legitimidade à própria razão e asseguram que esta tem autenticidade para operar tanto no domínio teórico como no domínio prático. A investigação é conduzida pela necessidade de se compreender que tanto os resultados negativos que Kant chega na busca da demonstração da unidade da razão como a única resposta crítica admitida para tal problema têm sua gênesis nas possibilidades sistemáticas consideradas pela filosofia crítica no seu todo. Tomando em consideração a argumentação que corresponde ao período do início da mesma filosofia investiga-se, primeiramente, a procura de Kant de uma solução para o problema da unidade da razão a partir do uso teórico. A identificação sistemática da impossibilidade de qualquer tentativa de resposta mediante esse percurso conduz, num segundo momento, ao apreço de uma tentativa de estabelecer a unidade a partir do uso prático e, ainda, à descoberta sistemática de que os usos teórico e prático devem ser legitimados em dois domínios distintos e, assim, a unidade da razão não pode ser garantida partindo-se de um dos seus usos. Frente a essa situação, num último momento, pondera-se a resposta ao problema da unidade da razão garantida pela argumentação kantiana que considera de modo regulativo a relação dos domínios teórico e prático. Como resultado da impossibilidade sistemática de estabelecer a unidade da razão a partir de um dos seus usos, da necessária legitimação auto-suficiente dos mesmos e, ainda, do fato de que a relação dos seus domínios só pode ser admitida como regulativa, apresenta-se a conclusão de que a unidade da razão é um pressuposto fundamental para a articulação da filosofia crítica-transcendental em todos os seus momentos, mas que a resposta crítica a esse problema consiste na justificativa da impossibilidade da sua demonstração.

Cette thèse vise à développer des méthodologies originales et appropriées pour modéliser la propagation des ondes EM dans des tunnels de forme quelconque et à proposer des méthodologies pour optimiser les spécifications, la conception et le positionnement des antennes en tunnel. Nous avons proposé une méthode originale d’analyse modale full-wave pour traiter le cas de la propagation des ondes EM dans des structures de grandes dimensions électriques ou en milieux confinés de forme quelconque tels que les tunnels. Cette méthode consiste en une approche modale qui s’appuie sur l’algorithme 2,5D TLM et l’algorithme Matrix Pencil pour la discrimination des modes dans des structures à pertes dans lesquelles la densité modale est élevée et les modes se superposent. Nous avons considéré de nouvelles conditions aux limites appelées SIBC (Surface Impedance Boundary Condition) pour les guides d’ondes diélectriques à pertes. Afin de pouvoir analyser les cas généraux et plusieurs configurations de tunnel réalistes, nous avons proposé une nouvelle nomenclature des modes. En effet, la nomenclature des modes existante n’est plus applicable en raison des effets de dépolarisation des modes dans certains cas réalistes. Une nouvelle méthodologie pour la détermination des spécifications et des positions des antennes en milieux confinés ou guidés a ensuite été développée. Cette méthodologie repose sur la combinaison d’une analyse modale et de techniques d’optimisation afin d’ajuster le poids des différents modes dans le tunnel. Cette approche est utilisée dans le cas des antennes adaptatives mais elle n’a jamais été appliquée au cas de la propagation multi modes en tunnel. / This thesis aims to develop original and appropriate methodologies to model the propagation of EM waves in tunnels of any shape and to propose methodologies to optimize the specification, design and positioning of the antenna in the tunnel. We proposed a novel method for full-wave modal analysis to treat the case of EM wave propagation in structures of large electric dimensions or confined environments of any shape such as tunnels. This method is a modal approach which is based on the 2.5D TLM algorithm and Matrix Pencil algorithm for the discrimination of modes in lossy structures in which the modal density is high and the modes overlap. We considered new boundary conditions called SIBC (Surface Impedance Boundary Condition) for dielectric waveguides with losses. To analyze the general case and several realistic tunnel configurations, we proposed a new classification of modes. Indeed, the classification of existing methods is no longer applicable due to depolarization effects in some realistic cases. A new methodology for determining the specifications and positions of antennas in confined or guided structures was then developed. This methodology is based on a combination of modal analysis and optimization techniques to adjust the weights of the different modes in the tunnel. This approach is used in the case of adaptive antennas, but it has never been applied to the case of multipath propagation modes in the tunnel.

Cette thèse porte sur la modélisation numérique des écoulements ouverts de convection naturelle au sein d'un canal vertical asymétriquement chauffé à flux constant. Elle s'inscrit dans un contexte national de comparaison associant approches numériques (benchmark de la Société Française de Thermique SFT) et expérimentales. La particularité de ce type d'écoulement réside dans le fait que le moteur du mouvement est situé au sein même de l'écoulement, rendant alors difficile la modélisation des interfaces et par conséquent la définition des conditions aux limites à appliquer aux frontières ouvertes du domaine de calcul. Nous proposons ici deux approches numériques de modélisation de ce type d'écoulement. La première approche consiste à inclure à la fois le canal vertical et son environnement extérieur dans le domaine de calcul. Cette approche intègre les interactions canal - environnement extérieur de manière implicite et nous permet d'obtenir une description complète de l'écoulement et ainsi de caractériser les interfaces du canal. Sur la base de ces simulations, des solutions numériques de référence modélisant un écoulement de convection naturelle dans un canal vertical immergé dans un environnement infini sont établies. La deuxième approche consiste à restreindre le domaine de calcul aux limites géométriques du canal. Plusieurs méthodes de résolution et modélisation des interfaces sont alors proposées et comparées avec les solutions de référence précédentes. Une approche originale basée sur des conditions limites de type Robin pour la pression motrice montre ainsi de très bon accords avec les solutions de référence. / This thesis focuses on the numerical modeling of natural convection flows in a vertical channel asymmetrically heated at constant heat flux. It takes place in a national context of comparison of numerical approaches (benchmark of the French Thermic Society SFT) and experimental approaches. The main issues result in the fact that the driving forces lie within the computational domain so inlet and outlet flow cannot be a priori prescribed. Therefore it is difficult to model the interfaces and to prescribe boundary conditions at the open frontiers of the computational domain. We propose two numerical approaches for modeling this type of flow. In the first approach the numerical domain includes the vertical channel and its external surroundings in the computational domain. This approach implicitly integrates interactions between the channel and its external environment. This allows us to obtain a complete description of the flow and thus to characterize the channel interfaces. Based on these simulations, numerical reference solutions which are modeling a natural convection flow in a vertical channel immersed in a infinite environment are established. In the second approach the computational domain is restricted to the geometric limits of the channel. Several methods for the numerical resolution and for modeling of the interfaces are proposed and then compared with the previous reference solutions. An original modeling based on Robin boundary conditions for the driving pressure is described and shows very good agreement with the reference solutions.

A norma que prescreve o cálculo de alvenaria estrutural de blocos vazados de concreto, NBR 10837:1989, encontra-se em fase de revisão, sendo que a principal alteração é a introdução do método dos estados limites no dimensionamento e na verificação dos elementos de alvenaria. Neste trabalho, estudam-se duas normas para alvenaria, a NBR 10837:1989 e EC 6:1996, e o texto proposto para revisão da NBR 10837. A escolha do EC 6:1996 se deu pela sua importância em relação à comunidade européia e porque muitas das prescrições contidas nessa norma foram adaptadas para o texto de revisão da NBR 10837. Quando necessárias, são realizadas comparações entre as duas normas e o texto de revisão, com o intuito de auxiliar no entendimento das implicações que a mudança de abordagem causará. Vários exemplos que simulam situações típicas de projeto, como compressão simples, flexão e cisalhamento, são apresentados. Com a variação dos diversos parâmetros envolvidos no dimensionamento dos elementos de alvenaria, é possível a elaboração de gráficos e ábacos. Desta forma consegue-se englobar uma grande variedade de situações, e a comparação entre as respostas obtidas com cada uma das normas e com o texto de revisão torna-se bem mais simples e precisa. Pretende-se, com este trabalho, contribuir para a introdução do método dos estados limites na norma de cálculo de alvenaria estrutural, bem como avaliar as mais importantes adaptações propostas. / The code that regulates the design of concrete blockwork structural masonry, NBR 10837:1989, is under revision phase. The main change is the introduction of limit state method for the design and verification of masonry elements. In this work, two masonry codes (NBR 10837:1989 and EC 6:1996) and a proposed revised text for the NBR 10837 are studied. The choice for EC 6:1996 is justified by its importance to european community and because many clauses of the revised text are adapted from that code. When necessary, comparisons between the two codes and revised text are carried out, to help the understanding of the changes implications. Some examples, that simulate typical design situation, such as axial compression, bending and shear are presented. A parametric study on the masonry elements design is carried out, allowing for the elaboration of graphs and abacus. Thus, various situations are explored, showing different results corresponding to each one of the codes and the revision text, in order to clarify the comparisons. The general aim of this work is help the introduction of the limit state method in the masonry code, and to evaluate the most important changes in the proposed revised text of the brazilian code.

Cette thèse traite de problèmes liés à la théorie des limitesd'objets combinatoires, une récente théorie qui a permis de tisserdes liens entre différents domaines tels que la combinatoire,l'analyse, la géométrie ou la théorie de la probabilité.Cette thèse applique des méthode venant de cette théorie à des problèmesde combinatoire extrémale.Dans un premier chapitre, je développe une théorie des limites d'objetsappelés emph{types d'ordre}, un objets qui encode des configurationsd'ensembles de points du plan. Le type d'ordre d'un ensemble de pointssuffit à caractériser de nombreuses propriétés essentielles de cet ensemblede point comme, par exemple, son enveloppe convexe.Je montre qu'une limite de type d'ordre peut être représentée par un objetanalogue à un graphon à valeurs O ou 1.Je fais ensuite le lien entre limites de type d'ordre et la distributionnaturelle de limite de type d'ordre obtenue par l’échantillonnage de pointsdu plan suivant une certaine probabilité.De cette manière, toute probabilité sur le plan engendre une limite de typed'ordre. Je montre d'une part que cette correspondance n'est pas surjective-c'est à dire qu'il existe des limites de type d'ordre ne venant pas de probabilitédu plan- et j'étudie d'autre part son injectivité.Je montre que si le support d'une mesure de probabilité est assez gros, par exemple siil contient une boule ouvert, alors la limite que cette mesure engendre suffit à caractériser cette mesure à une transformation projective près.Un second chapitre traite de test de propriété.Un testeur de propriété est un algorithme aléatoire permettant de séparerles objets ayant une certaine propriété des objet à distance au moins εde l'avoir, au sens de la distance d'édition.Ce domaine donne des algorithmes extrêmement rapides, et en particulierdes algorithmes dont la complexité ne dépends pas de la taille de l'entréemais seulement du paramètre de précision ε.Un résultat fondamental de cet domaine pour les graphes montré par Alonet Shapira est le suivant : toute classe de graphe héréditaire possède un teltesteur.Cette thèse contribue à la question suivante :Quelles classes de graphes possède un testeur dont la complexité est unpolynôme en 1/ε ?Je montre qu'en particulier la classe des graphes d'intervales possède un teltesteur.La théorie des algèbres de drapeaux est un outil étroitement lié aux limites degraphes denses qui donne une méthode pour démontrer des bornes sur certainsparamètres combinatoires à l'aide d'un ordinateur.Dans un troisième chapitre, je présente un programme écrit durant ma thèsequi implémente cette méthode.Ce programme fonctionne comme une bibliothèque pour calculer dans les algèbresde drapeaux, manipuler des inégalités sur les drapeaux ou encoder des problèmesd'optimisations par une instance de programme semi-défini positif qui peutensuite être résolu par un solveur externe.Ce programme est en particulier utilisé pour obtenir un nouvelle borne pour le cas triangulaire de la conjecture de Caccetta-Häggkvist. / This thesis is focused on problems related to the theory of combinatorial limits.This theory opened links between different fields such asanalysis, combinatorics, geometry and probability theory.In this thesis, we apply ideas coming from this framework toproblems in extremal combinatorics.In a first chapter we develop a theory of limits for emph{order types},a geometrical object that encodes configuration of a set of points in theplane by the mean of the orientations of their triangles.The order type of a point set suffices to determine many of its properties,such as for instance the boundary of its convex hull.We show that the limit of a converging sequence of order typescan be represented by random-free object analogous to a graphon.Further, we link this notion to the natural distributions of order typesarising from the sampling of random points from some probability measureof the plane.We observe that in this mean, every probability measure gives rise to a limitof order types.We show that this map from probability measure on the plane to limit oforder type is not surjective.Concerning its injectivity,we prove that if a measure has large enough support, for instance if its supportcontains an open ball, the limit of order types the measure generatessuffices to essentially determine this measure.A second chapter is focused on property testing.A tester is a randomized algorithm for distinguishing between objects satisfyinga property from those that are at some distance at least εfrom having itby means of the edition distance.This gives very efficient algorithms, and in particular algorithms whosecomplexity does not depend on the size of the input but only on the parameter ε.For graphs, it has been shown by Alon and Shapira that every hereditary propertyhas such a tester.We contribute to the following question :which classes of graphs have a one-sided property tester with a number of queries that is a polynomial in 1/ε ?We give a proof that the class of interval graphs has such a tester.The theory of flag algebras is a framework introduced by Razborovclosely related to dense limit of graphs, that gives a way to systematicallyderive bounds for parameters in extremal combinatorics.In a third chapter we present a program developed during my Phd.that implements this method.This program works as a library that can compute flag algebras,manipulate inequalities on densities and encode the optimization of some parameterin a semi-definite positive instance that can be given to a dedicated solverto obtain a bound on this parameter.This program is in particular used to obtain a new bound forthe triangle case of the Caccetta-Häggkvist conjecture.

Nous étendons la théorie des espaces de tentes, définis classiquement sur R^n, à différents espaces métriques. Pour les espaces doublant nous montrons que la théorie usuelle «globale» reste valide, et pour les espaces «non-uniformément localement doublant» (y compris R^n avec la mesure gaussienne) nous établissons une théorie locale satisfaisante. Dans le contexte doublant nous prouvons des résultats de plongement du type Hardy–Littlewood–Sobolev pour des espaces de tentes a poids, et dans le cas particulier des espaces métriques non-bornes AD-réguliers nous identifions les espaces d’interpolation réelle (les «espaces-Z») des espaces de tentes a poids. Les espaces de tentes a poids et les espaces-Z sur R^n sont ensuite utilises pour construire les espaces de Hardy–Sobolev et de Besov adaptes a des opérateurs de Dirac perturbes. Ces espaces jouent un rôle clé dans la classification des solutions de systèmes du premier ordre de type Cauchy–Riemann (ou de manière équivalente, la classification des gradients conormaux des solutions de systèmes elliptiques de second ordre) dans les espaces de tentes à poids et les espaces-Z. Nous établissons cette classification, et en corollaire nous obtenons une classification utile des cas ou les problèmes de Neumann et de Régularité; sont bien poses, pour des systèmes elliptiques de second ordre avec coefficients complexes et données dans les espaces de Hardy–Sobolev et de Besov d’ordre s en (-1,0). / We extend the theory of tent spaces from Euclidean spaces to various types of metric measure spaces. For doubling spaces we show that the usual `global' theory remains valid, and for `non-uniformly locally doubling' spaces (including R^n with the Gaussian measure) we establish a satisfactory local theory. In the doubling context we show that Hardy–Littlewood–Sobolev-type embeddings hold in the scale of weighted tent spaces, and in the special case of unbounded AD-regular metric measure spaces we identify the real interpolants (the `Z-spaces') of weighted tent spaces.Weighted tent spaces and Z-spaces on R^n are used to construct Hardy–Sobolev and Besov spaces adapted to perturbed Dirac operators. These spaces play a key role in the classification of solutions to first-order Cauchy–Riemann systems (or equivalently, the classification of conormal gradients of solutions to second-order elliptic systems) within weighted tent spaces and Z-spaces. We establish this classification, and as a corollary we obtain a useful characterisation of well-posedness of Regularity and Neumann problems for second-order complex-coefficient elliptic systems with boundary data in Hardy--Sobolev and Besov spaces of order s in (-1,0).

Comment fonctionne le cerveau ? Peut-on créer un cerveau artificiel ? Une étape essentielle en vue d'obtenir une réponse à ces questions est la modélisation mathématique des phénomènes à l'œuvre dans le cerveau. Ce manuscrit se focalise sur l'étude de modèles de réseaux de neurones inspirés de la réalité.Cette thèse se place à la rencontre entre trois grands domaines des mathématiques - l'étude des équations aux dérivées partielles (EDP), les probabilités et la statistique - et s'intéresse à leur application en neurobiologie. Dans un premier temps, nous établissons les liens qui existent entre deux échelles de modélisation neurobiologique. À un niveau microscopique, l'activité électrique de chaque neurone est représentée par un processus ponctuel. À une plus grande échelle, un système d'EDP structuré en âge décrit la dynamique moyenne de ces activités. Il est alors montré que le modèle macroscopique peut se retrouver de deux manières distinctes : en étudiant la dynamique moyenne d'un neurone typique ou bien en étudiant la dynamique d'un réseau de $n$ neurones en champ-moyen quand $n$ tend vers l’infini. Dans le second cas, la convergence vers une dynamique limite est démontrée et les fluctuations de la dynamique microscopique autour de cette limite sont examinées. Dans un second temps, nous construisons une procédure de test d'indépendance entre processus ponctuels, ces derniers étant destinés à modéliser l'activité de certains neurones. Ses performances sont contrôlées théoriquement et vérifiées d'un point de vue pratique par une étude par simulations. Pour finir, notre procédure est appliquée sur de vraies données / How does the brain compute complex tasks? Is it possible to create en artificial brain? In order to answer these questions, a key step is to build mathematical models for information processing in the brain. Hence this manuscript focuses on biological neural networks and their modelling. This thesis lies in between three domains of mathematics - the study of partial differential equations (PDE), probabilities and statistics - and deals with their application to neuroscience. On the one hand, the bridges between two neural network models, involving two different scales, are highlighted. At a microscopic scale, the electrical activity of each neuron is described by a temporal point process. At a larger scale, an age structured system of PDE gives the global activity. There are two ways to derive the macroscopic model (PDE system) starting from the microscopic one: by studying the mean dynamics of one typical neuron or by investigating the dynamics of a mean-field network of $n$ neurons when $n$ goes to infinity. In the second case, we furthermore prove the convergence towards an explicit limit dynamics and inspect the fluctuations of the microscopic dynamics around its limit. On the other hand, a method to detect synchronisations between two or more neurons is proposed. To do so, tests of independence between temporal point processes are constructed. The level of the tests are theoretically controlled and the practical validity of the method is illustrated by a simulation study. Finally, the method is applied on real data