L'attraction d'ondes dans des systèmes contra-propagatifs est un phénomène général, établi initialement en Physique dans le contexte de l'attraction de polarisation entre deux ondes contra-propagatives se propageant dans des fibres optiques. Ce phénomène a été observé expérimentalement, et ses propriétés étudiées via des simulations numériques. Les modèles qui s'y rattachent sont des systèmes hyperboliques d'équations aux dérivées partielles, avec des conditions aux bords dépendant du temps sur un intervalle fini. Le mécanisme sous-jacent peut être expliqué par l'existence de tores singuliers dans les équations stationnaires correspondantes. Le but de cette thèse est d'analyser en détail l'exemple le plus simple dans cette famille de modèles. Nous montrons que la plupart des phénomènes de processus d'attraction d'ondes sont en fait existants dans un modèle linéaire avec intéraction résonnante. Nous établissons l'existence et la régularité des solutions et analysons la relaxation vers la solution stationnaire qui caractérise les propriétés de l'attraction d'ondes. / Wave attraction in counter-propagating waves systems is a general phenomenon that was first established in Physics in the context of the attraction of the polarization between two counter-propagating waves in optical fibers. This phenomenon has been observed experimentally, and its properties were studied through numerical simulations. The models are Hamiltonian hyperbolic systems of partial differential equations, with time-dependent boundary conditions on a finite interval. The underlying mechanism can be traced back to the existence of singular tori in the corresponding stationary equations. In this work we analyze in detail the simplest example in this family of models. We show that most of the phenomena of the wave attraction process are already present in a linear model with resonant interaction. We establish the existence and regularity of the solutions and analyze the relaxation towards a stationary solution that features the wave attraction properties.

Paramagnetické niklem stabilizované tenké vrstvy plošně centrovaného kubického Fe, epitaxně narostené na monokrystalickém substrátu Cu(100) jsou známy svou schopností strukturní a magnetické fázové přeměny při ozáření iontovým svazkem, a to do prostorově centrované kubické struktury charakteristické feromagnetickými vlastnostmi. Monokrystalický Cu(100) substrát je možné také nahradit Si(100) s mezivrstvou Cu(100). Pomocí fokusovaného iontového svazku lze dále snadno lokálně modifikovat magnetické vlastnosti ozařované vrstvy. Tato metoda přímého zápisu magnetických struktur je alternativou k běžným litografickým technikám, nabízející nové jimi nedosažitelné možnosti. Připravené magnetické struktury následně využíváme k propagaci spinových vln. V práci je představen celý proces od růstu vrstev, přes přípravu mikrostruktur, až po studium jejich struktury a statických i dynamických magnetických vlastností. S využitím vektorového síťového analyzátoru studujeme ve vrstvách a v mikrostrukturách připravených fokusovaným iontovým svazkem feromagnetickou rezonanci a propagující se spinové vlny. Zdrojem spinových vln o definovaných vlnových vektorech jsou litograficky připravené koplanární vlnovody, sloužící také k induktivní detekci vln. Pomocí feromagnetické rezonance kvantitativně určujeme materiálové charakteristiky jako jsou saturační magnetizace a parametr útlumu a ze spekter propagujících módů následně určujeme charakteristiky spinových vln, které porovnáváme s dalšími feromagnetickými materiály.

[pt] A grande maioria dos componentes estruturais possui entalhes que concentram localmente as tensões em torno de suas pontas. O fator de sensibilidade ao entalhe q, muito usado para quantificar o efeito deles em fadiga, pode ser associado à geração de trincas não propagantes quando SL(R)/Kt < σn < SL(R)/Kf, onde SL(R) é o limite de fadiga do material em uma dada razão R = σmin/σmax; Kt = σmax/σn é o fator de concentração de tensões (SCF, de stress concentration factor) do entalhe; σn é a amplitude de tensão nominal aplicada; σmax é a máxima tensão na ponta do entalhe; e Kf = 1 + q(Kt – 1) é o fator de concentração de tensões à fadiga, que quantifica o efeito dos entalhes na resistência à fadiga do componente entalhado. Partindo desse comportamento, recentemente foi desenvolvido um modelo para calcular q considerando a influência do gradiente de tensões à frente da raiz do entalhe no comportamento à fadiga de trincas mecanicamente curtas, usando apenas técnicas apropriadas de análise de tensões e as resistências à fadiga do material: o limite de fadiga e o limiar de propagação de trincas longas. Este modelo, cujas previsões foram validadas por vários experimentos apropriados, considera assim todas as características da geometria do entalhe e do carregamento em q, sem precisar de nenhum parâmetro ajustável. Nesse trabalho, esse critério é estendido para tratar problemas de Trincamento Assistido por Meios Corrosivos (EAC), considerando apropriadamente parâmetros de análise de tensão. O efeito da corrosão é quantificado pela resistência do material ao trincamento por EAC, SEAC, e pelo limiar de propagação em condições de EAC, KIEAC, ambos medidos no ambiente agressivo em questão. Esse modelo em particular prevê a existência de uma sensibilidade ao entalhe qc em problemas de EAC quando SEAC/Kt < σmax < SEAC/[1 + qc(Kt - 1)], que pode ser mecanicamente quantificada por técnicas análogas àquelas utilizadas com sucesso para quantificar q em fadiga. Para comprovar experimentalmente a validade do modelo nestas condições, foi escolhido o par {Alumínio (Al) 2024 recozido – Gálio (Ga)} na temperatura de 35ºC, devido à rapidez da sua reação de trincamento sob EAC, a qual permite que suas propriedades básicas, SEAC and KIEAC, sejam determinados rapidamente. Usando somente a mecânica proposta neste novo modelo e as resistências básicas do material à EAC, 8 corpos de prova entalhados foram projetados para alcançar e suportar a máxima tensão na ponta de seus entalhes duas vezes maiores do que SEAC. O modelo prevê que isso é possível devido à interação do gradiente de tensões à frente da ponta do entalhe com a pequena trinca nele iniciada, que permanece não propagante nessas condições. Como nenhum dos corpos de prova assim projetados falhou nesses testes, pode-se concluir que aqueles ensaios suportam a eficácia do modelo, o qual pode ser bastante útil como ferramenta de dimensionamento mecânico no tratamento do efeito de entalhes em problemas de EAC. / [en] The vast majority of structural components have notches that locally concentrate stresses around their tips. The notch sensitivity factor q, widely used to quantify the effect of such notches on fatigue, can be associated with the generation of non-propagating cracks at the notch tips in fatigue tests when SL(R)/Kt < σn < SL(R)/Kf, where SL(R) is the fatigue limit of the material at a given R = σmin/σmax ratio; Kt = σmax/σn is the stress concentration factor (SCF) of the notch; σn is the amplitude of the nominal stress that loads it; σmax is the maximum stress at the notch tip; and Kf = 1 + q(Kt – 1) is the (effective) fatigue SCF, which quantifies the actual notch effect on the fatigue strength of the notched component. Based on this behavior, a model was recently developed to calculate q considering the influence of the stress gradient ahead of the notch tip on the fatigue behavior of mechanically short cracks, using only proper stress analysis techniques and the basic fatigue properties of the material, its fatigue limit and long crack propagation threshold. This model, whose predictions were validated by various appropriated experiments, considers the entire notch geometry and loading characteristics on q, without the need of any data-fitting parameter. In this study, this criterion is extend to properly treat environmentally assisted cracking (EAC) problems considering stress analysis issues. The corrosion effects are quantified by the material resistance to EAC, SEAC, and by its crack propagation threshold under EAC conditions, KIEAC, both measured in the aggressive environment in question. This model in particular predicts the existence of a notch sensitivity qc in EAC problems as well, when SEAC/Kt < σmax < SEAC/[1 + qc(Kt - 1)], which can be mechanically quantified by techniques analogous to those successfully used to quantify q in fatigue. To experimentally prove the validity of this model under EAC conditions, the pair material/aggressive medium chosen is an annealed 2024 Al alloy and Ga at 35oC, due to its very fast EAC reaction, which allows its basic properties, SEAC and KIEAC, to be quickly determined. Using only the mechanics proposed in this new model and the basic material resistances to EAC, 8 notched test specimens were designed to reach and survive to maxima stresses at the tip of their notches twice as large as SEAC. The model predicts that this is possible due to the interaction of the stress gradient ahead of the notch tip with the small crack initiated there, which is non-propagating under such conditions. Since none of the specimens failed in the designed tests, it can be concluded that they support the effectiveness of the model, which may thus be quite useful as a mechanical tool to treat notch effects in EAC problems.

The purpose of this thesis is to show a method, that would transform given Turing machine into propagating scattered context grammar, which language contains all valid computational histories of that particular Turing machine. Afterwards this thesis deals with questions arising from existence of such algorithm, especially in regards to the current knowledge about power of propagating scattered context grammars. Practical examples and implementation of proposed algorithm is also part of this thesis.

Cette thèse porte sur les fronts de transition pour des équations de réaction-diffusion dans différents milieux. Les fronts de transition généralisent les notions habituelles de fronts progressifs ou pulsatoires. Les principaux résultats sont les suivants. Pour des réactions bistables, nous prouvons la monotonie en temps de tous les fronts de transition avec vitesse globale moyenne non nulle. Pour des réactions bistables périodiques en temps ou pour des réactions de type combustion, nous prouvons l’existence et l’unicité de la vitesse globale moyenne d’un front. De plus, nous montrons que les fronts presque plans sont en réalité plans et nous montrons l’existence de fronts de transitions non standard. Pour des réactions bistables périodiques en espace, nous montrons la continuité et la différentiabilité des vitesses et des profils de ces fronts pulsatoires par rapport à la direction e en supposant l’existence de fronts pulsatoires à vitesse non nulle dans toutes les directions $e$. Ensuite, nous prouvons que la vitesse de propagation d’un front de transition quelconque est comprise entre les vitesses minimales et maximales des fronts pulsatoires. Enfin, nous étudions les vitesses globales moyennes des fronts de transition bistables dans des domaines non bornés : domaines extérieurs ou domaines à branches multiples cylindriques. Dans ces deux types de domaines, nous prouvons l’existence et l’unicité de la vitesse globale moyenne de tous les fronts de transition sous certaines hypothèses. / This dissertation is concerned with transition fronts in various media, which generalize the standard notions of traveling fronts. The main results are as following. For bistable reaction, we prove the time monotonicity of all transition fronts with non-zero global mean speed, whatever shape their level sets may have. For time-periodic bistable reaction and combustion-type reaction, we prove the existence and the uniqueness of the global mean speed. Meantime, we show that almost-planar fronts are actually planar and we show the existence of non-standard transitions fronts in $\mathbb{R}^N$. For spatially periodic bistable reaction, we show some continuity and differentiability properties of the front speeds and profiles with respect to the direction $e$ by providing the existence of pulsating fronts with nonzero speed in all directions $e$. Then, we prove that the propagating speed of any transition front is bounded by the minimal speed and the maximal speed of pulsating fronts. Finally, we study the mean speed of bistable transition fronts in unbounded domains: exterior domains and domains with multiple cylindrical branches. In both domains, we prove the existence and uniqueness of the global mean speed of any transition front under some assumptions.

[pt] Neste trabalho, o fator de gradiente de tensões elastoplástico na frente da raiz de entalhe é utilizado para investigar o efeito real do entalhe na resistência à fadiga, quantificado pelo fator de concentração de tensões à fadiga. Este é geralmente menor que o fator de concentração de tensões do entalhe, o parâmetro linear elástico (Fator de concentração de tensão) , devido à tolerância do material a trincas curtas não propagantes. Considerando que a plasticidade localizada na vizinhança da raiz do entalhe afeta o comportamento de crescimento de trincas curtas dentro da zona plástica induzida pelo entalhe, uma abordagem baseada na Mecânica da Fratura é proposta para abranger os efeitos dos campos de tensões e deformações elastoplásticas no cálculo do (Fator de concentração de tensão de fadiga). Análises bidimensionais por elementos finitos são adotadas para calcular fatores de intensidade de tensão de espécimes planos e entalhados. O modelo de encruamento de Ramberg-Osgood e a regra de Neuber são usados para obter aproximações de fatores de intensidade baseados em deformação. Para validação da metodologia, as previsões numéricas geradas são comparadas com dados experimentais de S-N coletadas da literatura para espécimes com (Fator de concentração de tensão) . Estes possuem furo circular central ou entalhes tipo U ou V, são feitos de diferentes materiais e testados sob cargas axiais com razão igual a -1, 0 ou 0,1. A comparação mostra boa concordância e prova que a solução elastoplástica proporcione maior precisão do que a linear elástica. Os resultados mais discrepantes são obtidos em razões de carga de 0 e 0,1, no entanto, eles podem ser significativamente melhorados quando é considerada a correção de efeitos de tensão média não nula. / [en] Elasto-plastic stress gradient factors ahead of notch tips are used to evaluate actual notch effects in fatigue strength, quantified by fatigue stress concentration factor (Fatigue stress concentration factor). Usually, it is smaller than the linear elastic stress concentration factor of the notch, (Stress concentration factor) , due to material tolerance to non-propagating short cracks. Considering that local plasticity around notch tips plays a significant role in the growth behavior of short cracks within the notch plastic zone, a sound mechanical methodology is proposed to account for the effects of elasto-plastic stress and strain fields in the actual (Fatigue stress concentration factor) value. Two-dimensional finite element analyses are conducted to compute stress intensity factors of smooth and notched specimens. Ramberg-Osgood model and Neuber s rule are used to achieve approximations for strain-based intensity factors. For methodology validation, numerical predictions are compared to experimental stress-life data of center, U, and V-notched plate specimens made of different materials and tested under uniaxial load ratios of −1, 0, and 0.1 collected from the literature. The comparisons show good agreement proving that the elasto-plastic solution provides more accuracy than the linear elastic one. The most discrepant results are obtained at load ratios of 0 and 0.1, and they can be significantly improved if non-zero mean stress effects are considered.

No description available.

Die vorliegende Arbeit beschreibt einen neuartigen Fügeprozess, das sogenannte reaktive Fügen bzw. Bonden. Hierbei werden sich selbsterhaltene exotherme Reaktionen in nanoskaligen Schichtsystemen als lokale Wärmequelle für das Fügen unterschiedlichster Substrate der Mikrosystemtechnik verwendet. Das Bonden mit den reaktiven Systemen unterscheidet sich von herkömmlichen Verfahren der Aufbau- und Verbindungstechnik primär dadurch, dass durch die rasche Reaktionsausbreitung bei gleichzeitig kleinem Reaktionsvolumen die Fügetemperaturen unmittelbar auf die Fügefläche beschränkt bleiben. Entgegen den herkömmlichen Fügeverfahren mit Wärmeeintrag im Volumen, schont das neue Verfahren empfindliche Bauteile und Materialien mit unterschiedlichsten thermischen Ausdehnungskoeffizienten lassen sich besser verbinden. In der vorliegenden Arbeit werden die Grundlagen zur Dimensionierung, Prozessierung und Integration der gesputterten reaktiven Materialsysteme beschrieben. Diese Systeme werden verwendet, um heterogene Materialien mit unterschiedlichen Durchmessern innerhalb kürzester Zeit auf Wafer-Ebene und bei Raumtemperatur zu bonden. Die so erzeugten Verbindungen werden hinsichtlich der Mikrostruktur, der Zuverlässigkeit sowie der Dichtheit untersucht und bewertet. Zusätzlich wird die Temperaturverteilung in der Fügezone während des Fügeprozesses mit numerischen Methoden vorhergesagt.

Die vorliegende Arbeit beschreibt einen neuartigen Fügeprozess, das sogenannte reaktive Fügen bzw. Bonden. Hierbei werden sich selbsterhaltene exotherme Reaktionen in nanoskaligen Schichtsystemen als lokale Wärmequelle für das Fügen unterschiedlichster Substrate der Mikrosystemtechnik verwendet. Das Bonden mit den reaktiven Systemen unterscheidet sich von herkömmlichen Verfahren der Aufbau- und Verbindungstechnik primär dadurch, dass durch die rasche Reaktionsausbreitung bei gleichzeitig kleinem Reaktionsvolumen die Fügetemperaturen unmittelbar auf die Fügefläche beschränkt bleiben. Entgegen den herkömmlichen Fügeverfahren mit Wärmeeintrag im Volumen, schont das neue Verfahren empfindliche Bauteile und Materialien mit unterschiedlichsten thermischen Ausdehnungskoeffizienten lassen sich besser verbinden. In der vorliegenden Arbeit werden die Grundlagen zur Dimensionierung, Prozessierung und Integration der gesputterten reaktiven Materialsysteme beschrieben. Diese Systeme werden verwendet, um heterogene Materialien mit unterschiedlichen Durchmessern innerhalb kürzester Zeit auf Wafer-Ebene und bei Raumtemperatur zu bonden. Die so erzeugten Verbindungen werden hinsichtlich der Mikrostruktur, der Zuverlässigkeit sowie der Dichtheit untersucht und bewertet. Zusätzlich wird die Temperaturverteilung in der Fügezone während des Fügeprozesses mit numerischen Methoden vorhergesagt.