Les équations aux dérivées partielles (EDP) permettent d’aborder d’un point de vue mathématique des phénomènes observés dans tous les domaines des sciences. Certaines EDP non-linéaires modélisent des problèmes de mécanique statistique, mécanique des fluides, théories de la gravitation ou des mathématiques financières.L’objectif de ce travail de thèse est l’étude de certains problèmes d’ EDP non-linéaires et hamiltoniennes et la recherche des leurs solutions périodiques et quasi-périodiques. / The aim of this thesis is the research of periodic and quasi-periodic solutions for some non-linear hamiltonian PDEs.

Les produits issus des technologies Silicium tendent à exploiter au maximum les performancesdes transistors MOS tout en les soumettant à des profils de mission très agressifs du point de vuede la fiabilité. Les concepteurs sont ainsi à la recherche du meilleur compromis entre performanceet fiabilité.Historiquement, l’étude de la fiabilité du transistor MOS et le développement des modèlessous jacents ont été menés sur la base de contrainte de vieillissement statique. Avec le développementdes produits à hautes performances dans le domaine de la radiofréquence (RF), laquestion de la fiabilité pour ce type d’application se pose. Ainsi, une extension des modèles defiabilité doit être réalisée afin de quantifier le vieillissement des paramètres clés RF soumis àdes contraintes statiques mais également RF. C’est cette extension de la fiabilité des transistorsMOS dans le domaine RF qui constitue le sujet de ce travail de thèse.Dans ce manuscrit, le fonctionnement du transistor MOS est décrit et sa fiabilité est introduite.Les différents mécanismes de dégradation sont étudiés et leurs modèles associés décrits.Sont ensuite présentés un banc de mesure et une méthodologie nécessaire à l’étude du vieillissementdes transistors dans le domaine RF, ainsi qu’à l’extension des modèles de fiabilité audomaine RF. / Products using nowadays silicon technology are generally targeting aggressive specificationsand push the developers to determine the best compromise between performance and reliability.Main front-end degradation mechanisms are historically studied and modeled under static stressconditions and focus on the static MOS transistor parameters.With the development of product targeting high performances in the radio frequency (RF)domain, the reliability is becoming a first order concern. Thus an extension of the actual staticreliability models must be done to quantify the aging of key RF parameters under static andRF stress. In this context, this work focuses on the extension of the MOS transistor reliabilityregarding the study of RF parameters and also the application of RF stress.After describing the MOS transistor properties, the reliability aspect is introduced and theemphasis is put on the different degradation mechanisms and their associated models. Thisallows the development of an experimental setup and the required methodology to investigatethe device aging in the RF domain and to extend actual static models.

SILVA, A. K. V. Estimativas gradiente para autofunções do V-Laplaciano e métricas m-quasi-Einstein generalizadas compactas com bordo. 2017. 40 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-18T14:49:03Z No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322426 bytes, checksum: d6abc5541598409191f635ad25e1f501 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia Andrea, Por favor repasse esse e-mail para o aluno. Estou devolvendo o trabalho pois tem alguns itens que não estão normalizados. O ano que deve constar na capa, folha de rosto e ficha catalográfica é o da entrega. E na ficha catalográfica o nome do autor e o título do trabalho não é em caixa alta. Somente as iniciais e quando necessário. Atenciosamente, Rocilda Sales on 2017-04-19T11:01:58Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-19T13:11:59Z No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322367 bytes, checksum: c9bd22b4cb5917adacde8be99093e8d8 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Alterar o ano. on 2017-04-19T14:52:13Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-19T16:22:45Z No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322367 bytes, checksum: 1523e0c8bd0590358cda3a542819aa62 (MD5) / Rejected by Rocilda Sales (rocilda@ufc.br), reason: Correção na folha de aprovação. on 2017-04-19T16:39:17Z (GMT) / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-04-19T17:04:43Z No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322112 bytes, checksum: e3087741f0e7bb8b966418fb10253c7b (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-04-24T11:14:14Z (GMT) No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322112 bytes, checksum: e3087741f0e7bb8b966418fb10253c7b (MD5) / Made available in DSpace on 2017-04-24T11:14:14Z (GMT). No. of bitstreams: 1 2015_tese_akvsilva.pdf: 322112 bytes, checksum: e3087741f0e7bb8b966418fb10253c7b (MD5) Previous issue date: 2015-08-17 / The main of this work was to study properties of Riemannian when subjected to conditions on Bakry-Émery-Ricci tensor. Essentially we study two cases. In the first case, motivated by the work of Barros and Ribeiro Jr. (2014), He, Petersen and Wylie (2012) and Miao and Tam (2011), was introduced generalized m-quasi-Einstein metrics compact with boundary, where we get a result that classify these metrics; more specifically, assuming that gradient field of the exponential of potential function is a conformal vector field, we obtain that this must be a geodesic ball in a simply connected space form. That we get some results that implies when these are trivial metrics. In the second case, we work the Bakry-Émery-Ricci tensor bounded bellow, initially in a compact Riemannian, with or without boundary, and later on balls in complete Riemannian. With this study, we obtain gradient estimates for eigenfunctions of V-Laplacian operator, that generalize results of (Li, 2005) and (Li, 2015). Finally, as consequence theses results, we show an Harnack’s inequality. / Este trabalho tem como principal objetivo estudar propriedades de variedades Riemannianas quando submetidas a condições sobre tensores de Ricci-Bakry-Émery. Essencialmente estudamos dois casos. No primeiro caso, motivados pelos trabalhos de Barros e Ribeiro Jr (2014), He, Petersen e Wylie (2012) e por Miao e Tam (2011), introduzimos métricas m-quasi-Einstein generalizadas compactas com bordo, donde obtemos um resultado que garante uma classificação para estas métricas; mais precisamente, assumindo que o gradiente da exponencial da função potencial é um campo conforme, obtemos que aquela deve ser uma bola geodésica de uma forma espacial simplesmente conexa. Disso, obtemos alguns resultados em que garantimos quando estas métricas são triviais. No segundo caso, trabalhos o tensor de Ricci-Bakry-Émery limitado por baixo, inicialmente, em variedades Riemannianas compactas, com bordo ou sem bordo, e posteriormente, sobre bolas em variedades Riemannianas completas. Com esse estudo, obtivemos estimativas do gradiente para autofunções do operador V-Laplaciano, generalizando resultados de (Li, 2005) e (Li, 2015). Finalmente, como consequências desses resultados, exibimos uma desigualdade de Harnack.

Submitted by ROQUE PIRES VERCESI null (rpvercesi@hotmail.com) on 2016-05-16T01:58:21Z No. of bitstreams: 1 Roque_Dissetação omega-final1.doc: 677376 bytes, checksum: fea7d0634be1eb734c838cbff432cc85 (MD5) / Rejected by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: A versão final da dissertação/tese deve ser submetida no formato PDF (Portable Document Format). O arquivo PDF não deve estar protegido e a dissertação/tese deve estar em um único arquivo, inclusive os apêndices e anexos, se houver. Por favor, corrija o formato do arquivo e realize uma nova submissão. 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Agradecemos a compreensão. on 2016-05-19T17:12:43Z (GMT) / Submitted by ROQUE PIRES VERCESI null (rpvercesi@hotmail.com) on 2016-05-20T12:52:26Z No. of bitstreams: 1 Roque_Dissetação -final.pdf: 1290554 bytes, checksum: f4ed86c7ef444aa9fde6621e3e82bc57 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-05-20T20:21:24Z (GMT) No. of bitstreams: 1 vercesi_rp_me_mar.pdf: 1290554 bytes, checksum: f4ed86c7ef444aa9fde6621e3e82bc57 (MD5) / Made available in DSpace on 2016-05-20T20:21:24Z (GMT). No. of bitstreams: 1 vercesi_rp_me_mar.pdf: 1290554 bytes, checksum: f4ed86c7ef444aa9fde6621e3e82bc57 (MD5) Previous issue date: 2016-03-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho está inserido no contexto da Filosofia da Lógica e no tópi-co teorias da verdade. As reflexões das teorias da verdade colocam em evi-dência a seguinte questão de interesse no ambiente filosófico, científico e ló-gico: “O que é a verdade?”. Esta tradição é bem longa, com reflexões que remontam à Antiguidade e ainda hoje são bastante pertinentes no mundo acadêmico, como podemos observar pela recente literatura sobre o assunto. Aristóteles foi um precursor desta busca ao propor que a verdade pode-ria ser caracterizada segundo sua máxima: “Dizer do que é, que ele não é, ou do que não é, que ele é, é falso; enquanto dizer do que é, que ele é, ou do que não é, que ele não é, é verdadeiro”. Posteriormente, essa questão referente à verdade foi minuciosamente tratada por muitos autores, que elaboraram teorias e/ou buscaram princípios para determinar o que é verdade ou o que torna algo verdadeiro (critério de verdade). Entre as teorias da verdade usualmente discu-tidas encontramos as teorias correspondencial, coerencial, pragmática, da re-dundância e a concepção semântica de Tarski. Dedicaremos um capítulo inicial a estas teorias da verdade, quando elencamos as suas características essenciais. Recentemente, a teoria da qua-se verdade tem conquistado importância nas reflexões sobre a verdade, que tem como um precursor o professor Newton da Costa, expoente brasileiro no âmbito da Lógica. Em 1986, Mikenberg, da Costa e Chuaqui introduziram a teoria da quase verdade no artigo Pragmatic truth and approximation to truth, publicado no “The Journal of Symbolic Logic”. Uma segunda meta desta Dissertação é o entendimento desta concep-ção de verdade, a quase verdade, e seu respectivo formalismo. Como este de-senvolvimento teórico da quase-verdade foi motivada pela concepção semân-tica de Tarski, a qual é entendida como uma das muitas teorias da quase ver-dade, então antes do nosso desenvolvimento sobre a quase-verdade, faremos um capítulo sobre a verdade segundo Alfred Tarski. A seguir, apresentamos o nosso entendimento da quase-verdade. Revi-sitamos os textos iniciais e outros que trouxeram novas contribuições para a quase-verdade, como a quase-satisfação de Bueno e de Souza de 1996. Tam-bém tratamos da recente versão de Silvestrini, de 2011, que traz inovações so-bre a formalização da quase-verdade. No Capítulo seguinte, apresentamos outra concepção filosófica relevan-te para esta Dissertação, o pragmatismo. Como está no título do artigo inicial da quase-verdade de 1986: “Verdade pragmática e aproximação à verdade”, a quase-verdade foi vinculada com aspectos do pragmatismo. O pragmatismo é um tema filosófico muito amplo e, certamente, não da-ríamos conta de retratá-lo no texto. Mesmo a versão da concepção pragmática da verdade é bastante extensa. Assim, consideraremos uma apresentação de três pioneiros do pragmatismo: Charles Pierce, Willian James e John Dewey. Procuramos destacar aspectos que destacam suas visões sobre a teoria da verdade. No capítulo final, faremos uma análise de quanto há de pragmatismo na teria da quase-verdade que buscamos entender no desenvolvimento desta Dissertação. / This work is inserted in the context of the Philosophy of Logic and in the topic theories of truth. Reflections of theories of truth put in evidence questions of interest in the philosophical, scientific and logical environment: "What is the truth?". This tradition is very long, with reflections that go back to antiquity and are still very relevant in the academic world, as can be seen by the recent litera-ture about this issue. Aristotle was a precursor of this search by proposing that the truth could be characterized according to their maximum: "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true”. Posteriorly, this question of the truth was carefully treated by many authors who have developed theories and/or principles to de-termine what is true or what makes something true (criteria of truth). Among the theories of truth usually discussed, we find the theories: correspondence, co-herence, pragmatic, redundancy and semantic conception of Tarski. We dedicate an initial chapter to these theories of truth, when we list their essential characteristics. Recently, the theory of quasi-truth has gained importance in the reflections about the truth, which has as a precursor Profes-sor Newton da Costa, Brazilian exponent in the context of Logic. In 1986, Mikenberg, Costa and Chuaqui introduced the theory of quasi-truth in the arti-cle Pragmatic truth and approximation to truth, published in "The Journal of Symbolic Logic". A second goal of this Dissertation is the understanding of this concep-tion of true, the quasi-truth, and their respective formalism. As the theoretical development of quasi-truth was motivated by the semantic conception of Tar-ski, which is understood as one of many theories about quasi-truth, then be-fore our development on the quasi-truth, we will present a chapter about truth, according to Alfred Tarski. Next, we presented our understanding about the quasi-truth. We visited the original texts and others who brought new contributions to the quasi-truth, as the quasi-satisfaction of Bueno and Souza (1996). We also discussed about the recent version developed by Silvestrini (2011) that brings innovations on the formalization of quasi-truth. In the next chapter, we present another philosophical relevant concep-tion to this thesis, the pragmatism. As described in the title of the first article of quasi-truth of 1986: "Pragmatic truth and approach to the truth," the quasi-truth was linked with aspects of pragmatism. Pragmatism is a very broad philosophical theme and for this reason, we will discuss just a part of this theory in the text. Even the version of the prag-matic conception of truth is quite extensive. Thereby, we consider a presenta-tion of three pioneers of pragmatism: Charles Pierce, William James and John Dewey. We emphasize the aspects that highlight their views about the theory of truth. In the final chapter, we will analyze how much exist of the pragmatism in the quasi-truth theory, which we sought to understand during the thesis devel-opment.

Algebraic geometric codes were first introduced by V.D.Goppa . They were well recognized and developed by Tsfasman, Vladut and Zink because they have parameters better than Gilbert-Varshmov bound and thus giving rise to Tsfasman Vladut-Zink bound. While the codes given by Ihara, Tsfasman, Vladut and Zink have complicated construction, Garcia and Stichtenoth on the other hand gave an explicit construction of codes attaining Tsfasman-Vlasut-Zink bound using the terminology of function fields. In coding theory one of the challenging problem is to find a sequence of cyclic codes that are asymptotically good. While this has not been achieved, Stichtenoth generalized cyclic codes to transitive codes and constructed a sequence of asymptotically good transitive codes on algebraic function fields over quadratic finite fields that attain Tsfasman-Vladut-Zink bound. In the case of cubic finite fields, Bezerra, Garcia and Stichtenoth constructed a tower of function fields over cubic finite fields whose limit attains a lower bound and the codes constructed over this tower turns out to be asymptotically good attaining a positive lower bound. Bassa used this tower and constructed quasi transitive codes which are a generalization of transitive codes and proved that they are also asymptotically good and attain the same positive lower bound. Later Bassa, Garcia and Stichtenoth constructed a new tower of function fields over cubic finite fields whose structure is less complicated compared to that of Bezerra, Garcia and Stichtenoths' and proved that codes constructed over it also attain the same positive lower bound. In this work along the lines of Bassa and Stichtenoth we construct quasi transitive codes over the tower given by Bassa, Garcia and Stichtenoth and prove that these quasi transitive codes are also asymptotically good and also attain the same lower bound.

Made available in DSpace on 2015-05-15T11:46:25Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 450936 bytes, checksum: 7e53189000f5416171ee58a4623b8aa6 (MD5) Previous issue date: 2010-02-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Bertholf and Walls provided a characterization for the class of groups quasi-injective finite. Furthermore, Juriaans, Bastos Azevedo and give a rating for the injective type groups, which are a distinct class of the former despite being quite close. / Bertholf e Walls forneceram uma caracterização para a classe de grupos quasi-injetivos finitos. Além disso, Juriaans, Bastos e Azevedo dão uma classificação para os grupos do tipo injetivo, os quais são uma classe distinta da anterior apesar de serem bastante próximas.

Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-11-09T17:13:45Z No. of bitstreams: 2 Dissertação - Ilton Ferreira de Menezes - 2016.pdf: 1261743 bytes, checksum: d8e7ce96b09f78e6c7a8c4d534a9d401 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-11-09T17:13:57Z (GMT) No. of bitstreams: 2 Dissertação - Ilton Ferreira de Menezes - 2016.pdf: 1261743 bytes, checksum: d8e7ce96b09f78e6c7a8c4d534a9d401 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-11-09T17:13:57Z (GMT). No. of bitstreams: 2 Dissertação - Ilton Ferreira de Menezes - 2016.pdf: 1261743 bytes, checksum: d8e7ce96b09f78e6c7a8c4d534a9d401 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-10-14 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is based on [10] and aims to classify quasi-Einstein manifolds that are locally conformally flat. We prove that every complete, locally conformally flat, quasi-Einstein manifold, with dimension n ≥ 3, is either globally conformally equivalent to spaceform or locally the warped product, R×Ffn−1, in which the fiber has constant curvature. / Este trabalho está baseado em [10] e tem por objetivo classificar variedades quasi- Einstein que são localmente conformemente planas. Provamos que toda variedade quasi- Einstein localmente conformente plana, completa e de dimensão n ≥ 3 é globalmente conformemente equivalente a um dos espaços modelos ou é localmente o produto torcido R×Ffn−1 onde a fibra tem curvatura constante.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / O objetivo deste trabalho à estudar a geometria das mÃtricas tipo-Einstein (solitons de Ricci, quase solitons de Ricci e mÃtricas quasi-Einstein). Mais especificamente, vamos obter equaÃÃes de estrutura, exemplos, fÃrmulas integrais e estimativas que permitirÃo caracterizar estas classes de mÃtricas. / The purpose of this work is study the geometric of the like-Einstein metrics (Ricci soliton, almost Ricci solitons and quasi-Einstein metrics). More specifically, we obtain structure equations, examples, integral formulae and estimates that will enable characterize these classes of metrics.

Le quasi-contrat est consacré comme une source autonome d’obligation dans le code civil. Pourtant, l’unité de la notion est problématique. En effet, la loi définit le quasi-contrat comme un fait volontaire dont il résulte un engagement alors que la doctrine le présente comme une notion à mi-chemin entre le contrat et la responsabilité civile extra-contractuelle en raison de l’application du régime contractuel en dehors d’un accord de volontés des parties. Or, en pratique, hormis la gestion d’affaires qui obéit au régime du mandat sans pouvoir exprès, l’enrichissement sans cause, (désormais enrichissement injustifié) et la répétition de l’indu n’obéissent pas à un régime contractuel. Si la doctrine a tenté de proposer le critère du transfert de valeurs dépourvu de cause pour justifier l’unité de la notion, ce critère se trouve mis à mal par la jurisprudence sur les loteries publicitaires. La thèse tente ainsi de rechercher une nouvelle unité, recherche qui s’avère difficile, voire impossible, dans la mesure où chaque quasi-contrat répond à des règles tantôt propres au contrat, tantôt propres à la responsabilité civile extra-contractuelle, ce qui vient alors fausser l’autonomie du quasi-contrat / Quasi-contracts are set as an autonomous part of the civil code, yet the notion answers to no unity. Law defines the notion as a voluntary fact leading to bind its author but scholars are considering quasi-contracts to be halfway between contract law and tort law due to the lack of will leading nevertheless to binding obligations. Practice shows that, except for the business management based on a mandate without any express will, the other quasi-contracts, unjust enrichment and repetition of undue do not follow any contractual regime. Scholars have attempted to propose the transfer of value for explaining the unity of the notion but this criterion is no longer relevant since cases creating a new quasi-contracts: lotteries. This work aims to discover a new criterion to find back unity of quasi-contracts. Impossible task as each quasi-contract shares common aspects of contract law and of tort law

La découverte du graphène en 2004 constitue une double avancée en physique de la matière condensée. D'une part, ses propriétés électroniques sont celles d’un gaz de fermions de Dirac sans masse. D'autre part, sa structure fournit le tout premier exemple d’un matériau ordonné à deux dimensions.Cette seconde caractéristique est étudiée dans cette thèse par microscopie à effet tunnel (STM), dans le cas du graphène synthétisé en ultra-haut vide sur la face (0001) du rhénium. A deux dimensions, l’ordre cristallin est en effet impossible, et il est prédit qu’un quasi-ordre à longue distance s’y substitue, où la phase du paramètre d’ordre fluctue. Le substrat de rhénium intervient alors comme une influence extérieure qui peut restaurer l’ordre cristallin, en forçant la structure du graphène à épouser une relation d’épitaxie avec le rhénium.L’étude proposée de la structure du graphène démontre qu’elle est en fait tributaire de contraintes cinétiques héritées de sa croissance. Plusieurs nanostructures caractéristiques ont ainsi été identifiées à l’échelle atomique, permettant de remonter au mécanisme de croissance. Deux chemins réactionnels y entrent ainsi en compétition. Le premier aboutit à une famille d’agrégats de carbone métastables, de structures bien définies, en épitaxie sur le rhénium. Le second mène à la croissance d’îlots de graphène qui s’étendent sur quelques nanomètres. La coalescence de ces îlots et l’incorporation des agrégats en leur sein conduit à des défauts structurels dont la structure atomique est détaillée pour la première fois. Cette étude exhaustive révèle la diversité des chemins réactionnels lors de la croissance de graphène sur rhénium, qui sont autant de compromis entre cinétique et thermodynamique.Au terme de cette croissance, le graphène obtenu n’est pas uniforme, mais constitué de domaines s'étendant sur des distances de l'ordre de 10 nm. Chaque domaine présente une relation d'épitaxie entre le graphène et le rhénium qui lui est propre, où le graphène s'avère à la fois tourné et cisaillé par rapport à son substrat, comme le montre une méthode d’analyse d’images STM développée à cet effet. L’élaboration d’une classification universelle de ces relations d'épitaxie montre leur grande diversité. Deux interprétations se confrontent alors. Les parois entre domaines de graphène peuvent en effet être interprétées comme des défauts topologiques dans l’ordre cristallin imposé au graphène par le substrat de rhénium. Alternativement, ce sont des modes de fluctuations dont la dynamique est gelée par l’interaction avec le substrat. Ces résultats remettent donc en question la notion d’ordre cristallin imposé par son substrat à un matériau bidimensionnel. Ils montrent qu’au lieu de forcer une relation d'épitaxie particulière, l’interaction du graphène avec son substrat donne lieu à une phase dite chaotique. / The discovery of graphene in 2004 is a two-fold breakthrough in condensed matter physics. On the one hand, its electronic properties are that of a massless Dirac fermion gas. On the other hand, its structure is the very first example of an ordered material in two dimensions.This second characteristics is studied in this thesis by scanning tunneling microscopy (STM), in the case of graphene grown in ultra-high vacuum on the (0001) surface of rhenium. In two dimensions, crystalline order is indeed impossible, and it is predicted to be replaced by a quasi-long-range order, for which the phase of the order parameter fluctuates. The rhenium substrate then acts as an outside influence that can restore crystalline order, as it forces graphene's structure to adopt an epitaxial relation with rhenium.The study of graphene's structure proposed here proves it actually originates from kinetic constraints inherited from its growth. Many typical nanostructures have indeed been identified at the atomic scale, giving access to the growth mechanism. Two reaction pathways compete. The first one gives rise to a family of metastable carbon clusters with well-defined structures in epitaxy on rhenium. The second one leads to growing graphene islands of a few nanometers in size. The coalescence of these islands and the incorporation of the carbon clusters ends up forming structural defects whose atomic structure is detailed for the first time. This exhaustive study reveals reaction pathways in the growth of graphene on rhenium are diverse, and constitute compromises between kinetics and thermodynamics.At the end of that growth, the obtained graphene is not uniform, but made of roughly 10 nm-large domains. Each domain displays a specific epitaxial relation with rhenium, in which graphene is both twisted and sheared with respect to rhenium, as revealed a STM image analysis method developed for this purpose. Elaborating a universal classification of such epitaxial relations shows they are very diverse. Two interpretations of this morphology are possible. The graphene domain walls can indeed be interpreted as topological defects in the crystalline order set in graphene by the rhenium substrate. Otherwise, they are fluctuation modes whose dynamics is frozen by the interaction with the substrate. These results put into question the notion of crystalline order set by a substrate to a two-dimensional material. They show that instead of forcing a specific epitaxial relationship, the graphene-substrate interaction gives rise to a so-called chaotic phase.