[pt] No presente trabalho faz-se uma análise sobre quantidades estatísticas de cadeias lineares e não lineares na situação em que o fluxo de calor que atravessa estes sistemas encontra-se no regime estacionário. A discussão inicial é feita sobre um modelo geral de cadeia linear, com acoplamentos arbitrários entre suas partículas e alimentada por reservatórios gaussianos. Uma análise detalhada sobre quantidades como fluxo de calor e distribuição de temperaturas do sistema é feita, onde todas as expressões analíticas correspondentes a estas quantidades são demonstradas e comparadas com resultados numéricos. Estudam-se então as mudanças quantitativas e qualitativas apresentadas pelas grandezas supracitadas quando modificam-se os acoplamentos de ancoragem entre o sistema e os reservatórios. Verifica-se que as mudanças nos perfis de temperaturas estão relacionadas aos extremos dos cumulantes do fluxo de calor, o que motiva uma investigação sobre a possível ocorrência de uma transição de fase no sistema. Buscando encontrar possíveis comportamentos críticos, definem-se as funções de correlação entre as velocidades quadráticas e de velocidades entre pares de partículas. A partir destas definições é possível verificar o comprimento de correlação associado à estas grandezas. Este estudo leva a um dos pontos mais interessantes do trabalho, onde conectam-se as mudanças apresentadas por grandezas do sistema como quantidades estatísticas do fluxo de calor, distribuição de temperaturas do sistema e os seus modos vibracionais frente às mudanças nos acoplamentos de ancoragem com os reservatórios. Ao estudar o fenômeno de condução de calor de uma forma mais realística e rigorosa, é imprescindível acrescentar interações não-lineares na cadeia. Considerando que a solução exata para este tipo de sistema não pode ser obtida, utiliza-se teoria de perturbação e outras ferramentas matemáticas para discutir as principais caracterísiticas do fluxo de calor em uma cadeia anarmônica. A técnica desenvolvida nesta tese permite calcular o fluxo de calor em cadeias de tamanho arbitrário, e é válida para sistemas sob ação de reservatórios de qualquer natureza. Aplica-se o método para cadeias alimentadas por reservatórios gaussianos e poissonianos, de onde verifica-se o impacto das não linearidades sobre estes sistemas e comparam-se os resultados obtidos com o caso linear. Para a análise em que o reservatório poissoniano injeta energia no sistema, ilustra-se o efeito de cumulantes de ordem superior do ruído descontínuo sobre o fluxo de calor e como estes novos elementos podem levar a resultados que a primeira vista parecem fisicamente incoerentes. / [en] In the present work I make an analysis about statistical quantities for linear and nonlinear chains in the stationary state. We start the discussion from a general linear model, with arbitrary couplings and connected to Gaussian reservoirs. A detailed analysis for quantities like heat ow and site temperatures is obtained, where all analytical expressions respective to those quantities are derived and a compared with numerical results. Then I study the quantitative and qualitative changes presented by the aforementioned quantities when the pinnings related to the reservoirs are modified. The changes in temperature profiles are related with the extrema of heat flux cumulants, motivating the investigation of whether phase transitions in the chain might occur. In order to investigate possible critical behaviors, I define velocity correlation functions between pair particles and squared velocities correlation functions. From where, one is able to estabilish a correlation length respective to these quantities. This study leads to one of the most remarkable achievements of this work, which is the connection made between the changes presented by some important statistical quantities of heat flux, the system s temperature, vibrational modes and the reservoirs pinnings. By treating the phenomenon of heat conduction in a more realistic and rigorous way, I develop a study to describe the transport properties in an anharmonic chain. Pondering that an exact solution for this sort of system is unfeasible, I use perturbation theory and other mathematical tools to discuss the main features of heat flux in a nonlinear chain. The technique developed throughout this thesis allows one to compute the heat current for a chain of arbitrary size, and is valid for systems under in fluence of reservoirs of any nature. We apply the method for chains governed by Gaussian and Poissonian reservoirs, verifying the impact of the nonlinearities over those systems, and comparing the obtained results to the linear case. In the case where there is a Poissonian bath injecting energy into the system, I shed some light on the effects of higher order cumulants related to the discontinous noise in the heat flux and I show how these new elements can lead to some results that at first glance seem physically incoherents.

Des modèles géométriques ont été proposés pour reconstruire la géométrie de plis associés aux rampes (par exemple pli sur flexure de faille), en identifiant en particulier la profondeur de niveau de décollement et le déplacement total sur la rampe. Ces méthodes de reconstruction géométrique sont appliquées pour des plis partiellement érodés. Au cours de l'érosion, le cut-off de la rampe peut être érodé et, par conséquent, le déplacement sur la rampe est difficile à quantifier. Dans cette thèse, nous développons onze modèles thermo-géométriques. Les modèles combinent les données géométriques et les données d’enfouissement pour proposer une évolution cinématique d’un pli avec cut-off érodé. Nous supposons que la mise en place d'une unité tectonique produit une anomalie thermique dans le mur de la faille, et que cette anomalie thermique pourrait indiquer une épaisseur de bloc chevauchant. Les modèles fournissent une estimation de la profondeur de décollement et le déplacement total sur une rampe érodée, qui ne dépend pas de taux d’érosion. Dans le cas de chevauchements actifs, les modèles proposent un taux de déplacement et un âge de l'initiation de la faille en fonction de taux d'érosion. Ces données sont utilisées pour proposer un développement cinématique de coupes érodées. Nous appliquons les modèles sur les plis érodés et actif à Taiwan dans les zones de Choshui et Miaoli. On propose des coupes régionales équilibrées en utilisant la technique de modélisation directe. Dans la section Choshui, nous proposons un niveau de détachement de ~5 km à ~14 km, marquée par deux sauts successifs de rampes de ~5 km and ~4 km. En supposant un taux d'érosion à 4 mm/an, l'âge de l’initiation de chevauchement active est entre 3,3 Ma dans la partie intérieure de prisme (Chevauchement de Tili) à 0,9 Ma dans la partie extérieur (Chevauchement de Chelungpu). Le raccourcissement totale sur la coupe de Choshui est ~100 km et le taux de déplacement calculé est ~1 cm/an. Pour tester nos modèles thermo-géométriques dans une chaîne plissée inactive, on applique nos modèles sur les plis érodés associés aux failles de Pine Mountain et Jones Valley dans la chaîne plissée des Appalaches. L'application des modèles thermo-géométriques nous permet d’estimer une quantité de déplacement sur les deux failles et expliquer de manière satisfaisante l'anomalie thermique dans le mur des failles de Pine Mountain et Jones Valley. Afin d'améliorer la description de l’anomalie thermique qui se développe dans le soubassement des failles, on a étudié l'évolution des minéraux magnétiques des roches argileuses le long de quatre sections dans la chaîne plissée à Taiwan. On a remarqué que la greigite (Fe3S4) domine l'assemblage magnétique dans les roches enfouies à moins à moins de de 70°C. La magnétite (Fe3O4) se développe pour des températures d’enfouissement de ~50°C et domine l’assemblage magnétique jusqu'à ~350° C. A partir ~300°C, la pyrrhotite monoclinique (Fe7S8) se développe aux dépens de la magnétite, et à ~350°C, la magnétite n'est plus détecté. Ces résultats peuvent être utilisés en complément d'autres géothermomètres pour identifier les anomalies thermiques dans une gamme de de 50-70°C et de 300-350°C où les caractéristiques des minéraux magnétiques sont identifiées / Geometric models have been proposed to account satisfactorily for ramp-related folds (e.g. fault-bend fold), identifying in particular detachment depth and total shortening. These methods of geometric reconstruction are applied on partially eroded folds. During erosion, the fault cut-off may be removed and as a result, the displacement is difficult to quantify. In this thesis, we develop 11 thermo-geometric models combining geometric description of folds and burial data to propose kinematic evolution of folds with eroded cut-offs. We assume that the emplacement of a tectonic unit will result in a thermal anomaly in the footwall, and that this thermal anomaly might indicate a thickness of the overriding unit. The models provide an estimation of the detachment depth and the total shortening on an eroded ramp, independent of the erosion rate. In the case of active thrusts, the models provide an estimation of the slip rate and the age of the initiation of the thrust as a function of the erosion rate. These data are used to unravel the kinematic development of eroded cross-sections. We apply the models on eroded folds from Taiwan underlined by active thrusts in the Choshui and Miaoli sections. We propose regional balanced cross-sections using forward modeling technique. In the Choshui section, we propose a detachment profile with a depth between ~ 5 km and ~ 14 km, marked by two steps of ~ 5 km. Assuming erosion rate at 4 mm/a, the age of initiation of the active thrusts is ranging from 3.3 Ma inward (Tili thrust) to 0.9 Ma outward (Chelungpu thrust). The total shortening from the whole section is ~100 km and the calculated slip rate is about 1 cm/a. To test our models in a non-active fold-and-thrust belt, we study eroded folds associated to the Pine Mountain thrust and Jones Valley thrust from the Appalachian belt. The application of the thermo-geometric models provides a value of the total shortening and explains satisfactorily the thermal anomaly in the footwall of the Jones Valley thrust. In order to improve the description of the thermal anomaly, we have studied the evolution of magnetic minerals of argillaceous rocks in four sections from the Taiwan thrust belt. We found that the iron sulfide greigite (Fe3S4) is dominating the magnetic assemblage in the less buried rocks (<70°C). The magnetite (Fe3O4) develops at burial temperature of ~50°C and is dominating the magnetic assemblage up to ~350°C. By ~300°C, the monoclinic pyrrhotite (Fe7S8) develops at the expense of magnetite, and at ~350°C, the magnetite is no longer detected. These results can be used complementary to other geothermometers to identify thermal anomalies in the range 50-70°C and 300-350°C where characteristic magnetic minerals are identified