Estudamos o amortecimento radiativo e o ruído de spins de um material magnético acoplado a um circuito ressonante. O amortecimento radiativo em ressonância magnética é um fenômeno de dissipação, na qual a magnetização preparada após um pulso de Rabi sofre um decaimento até seu estado de equilíbrio. O material magnético perde energia através do seu acoplamento com o circuito ressonante, que deve estar sintonizado na freqüência de Larmor dos spins do material. Apesar deste fenômeno ter sido estudado há vários anos, nenhuma descrição quântica completa lhe foi dada. Apresentamos um modelo hamiltoniano quântico que descreve o amortecimento radiativo. Para isto usamos o método de equações de Langevin quânticas. Mostramos que além do amortecimento radiativo do material magnético, se o circuito está em um estado inicial coerente, a magnetização adquire um movimento complicado não-trivial. Usando as mesmas equações de Langevin, estudamos a influência da amostra no ruído do circuito ressonante. Calculamos a densidade espectral da corrente no caso em que todo o sistema está em equilíbrio térmico. Pudemos verifcar a efcácia do método comparando-o com estudos anteriores. Além disso, estudamos as alterações do ruído do circuito quando uma tensão oscilante externa é aplicada. Nesta situação surgem dois outros picos laterais ao pico central do espectro de absorção da amostra magnética. Isso leva a três depressões no espectro da corrente do circuito. Este efeito deve-se à separação dupla dos estados de energia dos spins. Comentamos sobre a analogia deste fenômeno com a fluorescência ressonante observada na Óptica Quântica. / We study the radiation damping and the spin noise of a magnetic material coupled with a resonant circuit. Radiation damping in magnetic resonance is a dissipation phenomenon, where magnetization prepared after a Rabi pulse decays toward its equilibrium state. The magnetic sample loses its energy by the coupling with resonant circuit, that must be tuned in Larmor frequency of the sample spins. Even though this phenomenon had been studied many years ago, no full quantum description was done. We present a quantum Hamiltonian model, that explains the radiation damping. We use quantum Langevin equation method for this task. Beyond radiation damping, we show the magnetization acquires an unusual intrincate motion, if the circuit initial state is coherent. Using the same Langevin equation, we study the sample influence on the resonant circuit noise. We calculate the current spectral density in the case of thermal equilibrium of whole system. We can verify the method efectiveness, comparing former papers. Moreover we study modifcations in the circuit noise, if an external oscillating tension is applied. In this situation, other two peaks emerge in the central peak sidebands of the sample absorption spectrum. It leads to appear three dips in circuit current spectrum. This efect is due to the splitting of the spin energy states. We comment about the analogy between this phenomenon and the resonance fluorescence in Quantum Optics.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A análise de fundações sob solicitações dinâmicas é algo sempre presente em projetos na área industrial. É um campo pouco explorado na área de engenharia geotécnica, onde existem relativamente poucas informações no Brasil, de maneira geral. O método mais comum de realizar essas análises é a simplificação de modelos estruturais a partir do uso de molas. Sabe-se que esses coeficientes de reação têm uma variação relativamente grande e que esse enfoque de projeto pode, em alguns casos, mostrar-se contra a segurança ou levar a superdimensionamentos desnecessários. Verifica-se, então, a necessidade de uma avaliação mais criteriosa, utilizando a interação solo x estrutura, onde as molas comumente utilizadas nas análises vibratórias convencionais são substituídas pela rigidez real do solo quando concebido como um meio contínuo, através de sua discretização pelo método dos elementos finitos. A presente dissertação analisa o problema através do módulo de dinâmica do programa Plaxis 2D. Neste tipo de análise, além da modelagem do solo como um meio contínuo, torna-se possível introduzir condições de contorno específicas ao problema em estudo, múltiplas camadas de solo, sejam horizontais ou inclinadas, além da introdução de amortecedores capazes de evitar a reflexão espúria das ondas incidentes nos limites da malha de elementos finitos e assim modelar mais adequadamente a perda de energia por radiação. A presente dissertação compara medições experimentais e soluções eficientes de métodos vibratórios clássicos com a resposta obtida pelo MEF, mostrando resultados bastante satisfatórios tanto pelos métodos clássicos quanto pelo MEF. / The foundation analysis by dynamic solicitations is always present in industrial projects. It is an area which is poorly explored in geotechnical engineering and there are few information about this subject in Brazil, in general. The most common method to realize this analysis consists in simplifies structural models by using springs. It is known that these reaction coefficients have a large range of variation and this projects focus can, in some cases, be against the safety side or lead to unnecessary over designs. This proves the necessity to do a more criterious evaluation by using the interaction soil x structure where the springs usually used in common vibration analysis are replaced by the real stiffness of soil when designed as a continuous medium through its discretization by finite element method. This present dissertation analyzes the problem through the dynamic modulus of the software PLAXIS 2D. In this sort of analysis, besides the modeling of soil as a continuous medium, it becomes possible to introduce specific boundary conditions associated to the studied problem, multiple soil layer, that can be horizontals or inclined, in addition to the introduction of dampers able to avoid the spurious reflection of incident waves on the boundary of finite element mesh and then to model more efficiently the energy loss by radiation. This present dissertation compares experimental measurements and efficient solutions of classical vibration methods with the response obtained by FEM, showing results quite satisfactory both by classical methods and by FEM.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A análise de fundações sob solicitações dinâmicas é algo sempre presente em projetos na área industrial. É um campo pouco explorado na área de engenharia geotécnica, onde existem relativamente poucas informações no Brasil, de maneira geral. O método mais comum de realizar essas análises é a simplificação de modelos estruturais a partir do uso de molas. Sabe-se que esses coeficientes de reação têm uma variação relativamente grande e que esse enfoque de projeto pode, em alguns casos, mostrar-se contra a segurança ou levar a superdimensionamentos desnecessários. Verifica-se, então, a necessidade de uma avaliação mais criteriosa, utilizando a interação solo x estrutura, onde as molas comumente utilizadas nas análises vibratórias convencionais são substituídas pela rigidez real do solo quando concebido como um meio contínuo, através de sua discretização pelo método dos elementos finitos. A presente dissertação analisa o problema através do módulo de dinâmica do programa Plaxis 2D. Neste tipo de análise, além da modelagem do solo como um meio contínuo, torna-se possível introduzir condições de contorno específicas ao problema em estudo, múltiplas camadas de solo, sejam horizontais ou inclinadas, além da introdução de amortecedores capazes de evitar a reflexão espúria das ondas incidentes nos limites da malha de elementos finitos e assim modelar mais adequadamente a perda de energia por radiação. A presente dissertação compara medições experimentais e soluções eficientes de métodos vibratórios clássicos com a resposta obtida pelo MEF, mostrando resultados bastante satisfatórios tanto pelos métodos clássicos quanto pelo MEF. / The foundation analysis by dynamic solicitations is always present in industrial projects. It is an area which is poorly explored in geotechnical engineering and there are few information about this subject in Brazil, in general. The most common method to realize this analysis consists in simplifies structural models by using springs. It is known that these reaction coefficients have a large range of variation and this projects focus can, in some cases, be against the safety side or lead to unnecessary over designs. This proves the necessity to do a more criterious evaluation by using the interaction soil x structure where the springs usually used in common vibration analysis are replaced by the real stiffness of soil when designed as a continuous medium through its discretization by finite element method. This present dissertation analyzes the problem through the dynamic modulus of the software PLAXIS 2D. In this sort of analysis, besides the modeling of soil as a continuous medium, it becomes possible to introduce specific boundary conditions associated to the studied problem, multiple soil layer, that can be horizontals or inclined, in addition to the introduction of dampers able to avoid the spurious reflection of incident waves on the boundary of finite element mesh and then to model more efficiently the energy loss by radiation. This present dissertation compares experimental measurements and efficient solutions of classical vibration methods with the response obtained by FEM, showing results quite satisfactory both by classical methods and by FEM.

Estudamos o amortecimento radiativo e o ruído de spins de um material magnético acoplado a um circuito ressonante. O amortecimento radiativo em ressonância magnética é um fenômeno de dissipação, na qual a magnetização preparada após um pulso de Rabi sofre um decaimento até seu estado de equilíbrio. O material magnético perde energia através do seu acoplamento com o circuito ressonante, que deve estar sintonizado na freqüência de Larmor dos spins do material. Apesar deste fenômeno ter sido estudado há vários anos, nenhuma descrição quântica completa lhe foi dada. Apresentamos um modelo hamiltoniano quântico que descreve o amortecimento radiativo. Para isto usamos o método de equações de Langevin quânticas. Mostramos que além do amortecimento radiativo do material magnético, se o circuito está em um estado inicial coerente, a magnetização adquire um movimento complicado não-trivial. Usando as mesmas equações de Langevin, estudamos a influência da amostra no ruído do circuito ressonante. Calculamos a densidade espectral da corrente no caso em que todo o sistema está em equilíbrio térmico. Pudemos verifcar a efcácia do método comparando-o com estudos anteriores. Além disso, estudamos as alterações do ruído do circuito quando uma tensão oscilante externa é aplicada. Nesta situação surgem dois outros picos laterais ao pico central do espectro de absorção da amostra magnética. Isso leva a três depressões no espectro da corrente do circuito. Este efeito deve-se à separação dupla dos estados de energia dos spins. Comentamos sobre a analogia deste fenômeno com a fluorescência ressonante observada na Óptica Quântica. / We study the radiation damping and the spin noise of a magnetic material coupled with a resonant circuit. Radiation damping in magnetic resonance is a dissipation phenomenon, where magnetization prepared after a Rabi pulse decays toward its equilibrium state. The magnetic sample loses its energy by the coupling with resonant circuit, that must be tuned in Larmor frequency of the sample spins. Even though this phenomenon had been studied many years ago, no full quantum description was done. We present a quantum Hamiltonian model, that explains the radiation damping. We use quantum Langevin equation method for this task. Beyond radiation damping, we show the magnetization acquires an unusual intrincate motion, if the circuit initial state is coherent. Using the same Langevin equation, we study the sample influence on the resonant circuit noise. We calculate the current spectral density in the case of thermal equilibrium of whole system. We can verify the method efectiveness, comparing former papers. Moreover we study modifcations in the circuit noise, if an external oscillating tension is applied. In this situation, other two peaks emerge in the central peak sidebands of the sample absorption spectrum. It leads to appear three dips in circuit current spectrum. This efect is due to the splitting of the spin energy states. We comment about the analogy between this phenomenon and the resonance fluorescence in Quantum Optics.

Dynamic soil-structure interaction problems are characterized by an unbounded soil-domain and thus by radiation damping. This radiation damping arises due to wave propagation from the excited structure into the subsoil and may lead to a reduction of the structural response. A consistent description of this radiation damping has been carried out by means of different concepts. A widely used approach truncates the unbounded medium by a special kind of absorbing boundaries which are free of artificial reflection. The resulting finite domain can be treated as usually by finite elements. In this report, an alternative method to represent an unbounded medium in a dynamic analysis is presented. In principle, it is a conjunction of the boundary element method (BEM) in the frequency domain to reproduce the far-field and the finite element method (FEM) in the time domain to analyze the near-field. This alternative procedure avoids the introduction of any artificial boundaries. The procedure is based on a rational approximation of the dynamic stiffness of the unbounded domain in the frequency-domain. In this report, the dynamic stiffness of the unbounded domain is obtained from the BEM. The matrix-valued coefficients of the rational approximation function are determined by means of a least-square procedure. The time-domain representation is achieved by splitting the rational force-displacement relation into a series of linear functions in the frequency-domain corresponding with first order differential equations in the time-domain. This splitting process has been demonstrated as numerically effective and in addition, no Fourier transformation is necessary. In this thesis, dynamic soil-structure interaction problems with a relatively large number of degrees of freedom have been examined. These degrees of freedom arise from the discretization of the coupling interface, internal variables from the splitting procedure and from modeling the structure. The new method is especially suitable for systems with transient excitations as arising from rotating machines at startup and shutdown. The theoretical part of the thesis contains elements of system theory and discusses particularly stability problems arising from the rational approximation. The practical part presents a large amount of convergence studies and numerical results for layered soil and finally represents the propagation damping as a kind of damping ratio which is typically used in elementary structural dynamics. / In der Dynamik der Boden-Bauwerk-Interaktion wird der Boden in vielen Fällen durch ein unbegrenztes elastisches Medium beschrieben, wodurch das Phänomen der Abstrahldämpfung begründet wird. Diese Dämpfung entsteht durch Energietransfer von der erregten Struktur in den Boden durch Wellenausbreitung und reduziert somit die Strukturschwingungen. Um das infinite Bodengebiet dennoch durch finite Elemente beschreiben zu können, werden üblicherweise als Hilfsmaßnahme künstliche sogenannte absorbierende Ränder eingeführt. In dieser Arbeit wird eine alternative Methode zur Darstellung des unbegrenzten Mediums in der Dynamik vorgelegt. Im Prinzip handelt es sich um eine Kopplung der Rand-Element-Methode (REM) für den unendlichen Boden (das sogenannte Fernfeld) im Frequenzbereich und der Finite-Element-Methode (FEM) für das Nahfeld im Zeitbereich. Dieses alternative Verfahren vermeidet die Einführung künstlicher Ränder. Das Verfahren basiert auf einer rationalen Beschreibung der dynamischen Steifigkeit des Fernfeldes im Frequenzbereich. Diese Steifigkeit wird in der vorliegenden Arbeit durch die Rand-Element-Methode erzeugt. Die Matrix-wertigen Koeffizienten der rationalen Frequenzfunktion werden durch Minimierung des Fehlerquadrates berechnet. Die Transformation dieser Frequenzdarstellung in den Zeitbereich gelingt durch algebraische Überführung der rationalen Funktion in ein in der Frequenz lineares Hypersystem mit einer zugeordneten Zustandsgleichung erste Ordnung im Zeitbereich. Dieser Prozess hat sich als numerisch effektiv erwiesen und erfordert darüberhinaus keine Fourier-Transformation. Das entwickelte Vorgehen wird in dieser Arbeit an Problemen der dynamischen Boden-Bauwerk-Interaktion mit einer großen Anzahl von Freiheitsgraden erprobt. Diese Freiheitsgrade folgen aus der Diskretisierung in der Koppelfuge zwischen Boden und Struktur, der Diskretisierung der Struktur selbst und aus der Überführung in das Hypersystem mittels interner Variablen. Das neue Verfahren eignet sich insbesondere für Systeme mit transienter Erregung, wie sie beim An- und Auslaufen von Rotationsmaschinen ensteht. Der theoretische Teil der Arbeit wird geprägt durch Elemente der Systemtheorie und setzt sich zudem mit typischen Stabilitätsproblemen auseinander, die aus der rationalen Beschreibung entstehen. Der praktische Teil präsentiert Konvergenzstudien und numerische Ergebnisse für Boden-Bauwerk- Interaktionsprobleme mit geschichtetem Boden bei transienter Erregung mit Resonanzdurchlauf. Zudem gelingt eine Darstellung der Abstrahldämpfung in Form des Dämpfungsgrades D, wie er in der klassischen Strukturdynamik verwendet wird.

Dynamic soil-structure interaction problems are characterized by an unbounded soil-domain and thus by radiation damping. This radiation damping arises due to wave propagation from the excited structure into the subsoil and may lead to a reduction of the structural response. A consistent description of this radiation damping has been carried out by means of different concepts. A widely used approach truncates the unbounded medium by a special kind of absorbing boundaries which are free of artificial reflection. The resulting finite domain can be treated as usually by finite elements. In this report, an alternative method to represent an unbounded medium in a dynamic analysis is presented. In principle, it is a conjunction of the boundary element method (BEM) in the frequency domain to reproduce the far-field and the finite element method (FEM) in the time domain to analyze the near-field. This alternative procedure avoids the introduction of any artificial boundaries. The procedure is based on a rational approximation of the dynamic stiffness of the unbounded domain in the frequency-domain. In this report, the dynamic stiffness of the unbounded domain is obtained from the BEM. The matrix-valued coefficients of the rational approximation function are determined by means of a least-square procedure. The time-domain representation is achieved by splitting the rational force-displacement relation into a series of linear functions in the frequency-domain corresponding with first order differential equations in the time-domain. This splitting process has been demonstrated as numerically effective and in addition, no Fourier transformation is necessary. In this thesis, dynamic soil-structure interaction problems with a relatively large number of degrees of freedom have been examined. These degrees of freedom arise from the discretization of the coupling interface, internal variables from the splitting procedure and from modeling the structure. The new method is especially suitable for systems with transient excitations as arising from rotating machines at startup and shutdown. The theoretical part of the thesis contains elements of system theory and discusses particularly stability problems arising from the rational approximation. The practical part presents a large amount of convergence studies and numerical results for layered soil and finally represents the propagation damping as a kind of damping ratio which is typically used in elementary structural dynamics. / In der Dynamik der Boden-Bauwerk-Interaktion wird der Boden in vielen Fällen durch ein unbegrenztes elastisches Medium beschrieben, wodurch das Phänomen der Abstrahldämpfung begründet wird. Diese Dämpfung entsteht durch Energietransfer von der erregten Struktur in den Boden durch Wellenausbreitung und reduziert somit die Strukturschwingungen. Um das infinite Bodengebiet dennoch durch finite Elemente beschreiben zu können, werden üblicherweise als Hilfsmaßnahme künstliche sogenannte absorbierende Ränder eingeführt. In dieser Arbeit wird eine alternative Methode zur Darstellung des unbegrenzten Mediums in der Dynamik vorgelegt. Im Prinzip handelt es sich um eine Kopplung der Rand-Element-Methode (REM) für den unendlichen Boden (das sogenannte Fernfeld) im Frequenzbereich und der Finite-Element-Methode (FEM) für das Nahfeld im Zeitbereich. Dieses alternative Verfahren vermeidet die Einführung künstlicher Ränder. Das Verfahren basiert auf einer rationalen Beschreibung der dynamischen Steifigkeit des Fernfeldes im Frequenzbereich. Diese Steifigkeit wird in der vorliegenden Arbeit durch die Rand-Element-Methode erzeugt. Die Matrix-wertigen Koeffizienten der rationalen Frequenzfunktion werden durch Minimierung des Fehlerquadrates berechnet. Die Transformation dieser Frequenzdarstellung in den Zeitbereich gelingt durch algebraische Überführung der rationalen Funktion in ein in der Frequenz lineares Hypersystem mit einer zugeordneten Zustandsgleichung erste Ordnung im Zeitbereich. Dieser Prozess hat sich als numerisch effektiv erwiesen und erfordert darüberhinaus keine Fourier-Transformation. Das entwickelte Vorgehen wird in dieser Arbeit an Problemen der dynamischen Boden-Bauwerk-Interaktion mit einer großen Anzahl von Freiheitsgraden erprobt. Diese Freiheitsgrade folgen aus der Diskretisierung in der Koppelfuge zwischen Boden und Struktur, der Diskretisierung der Struktur selbst und aus der Überführung in das Hypersystem mittels interner Variablen. Das neue Verfahren eignet sich insbesondere für Systeme mit transienter Erregung, wie sie beim An- und Auslaufen von Rotationsmaschinen ensteht. Der theoretische Teil der Arbeit wird geprägt durch Elemente der Systemtheorie und setzt sich zudem mit typischen Stabilitätsproblemen auseinander, die aus der rationalen Beschreibung entstehen. Der praktische Teil präsentiert Konvergenzstudien und numerische Ergebnisse für Boden-Bauwerk- Interaktionsprobleme mit geschichtetem Boden bei transienter Erregung mit Resonanzdurchlauf. Zudem gelingt eine Darstellung der Abstrahldämpfung in Form des Dämpfungsgrades D, wie er in der klassischen Strukturdynamik verwendet wird.

Ce travail de thèse porte sur la conception, la réalisation et l’évaluation expérimentale d’ un microsystème d’analyse dont l’originalité repose sur l’intégration d’une micro antenne planaire de spectroscopie par résonance magnétique nucléaire (SRMN) sur un système micro fluidique à base d’un polymère, le Cyclique Oléfine Copolymère (COC). La détermination des caractéristiques géométriques optimales du microsystème afin d’optimiser le couplage électromagnétique entre la micro antenne de détection et l’échantillon est effectuée à l’aide d’un modèle de calcul numérique, ce qui permet l’optimisation du rapport signal sur bruit (RSB). La réalisation du microsystème avec des procédés de micro fabrication développés au laboratoire ont permis de valides son fonctionnement dans un spectromètre dont le champ magnétique statique atteint 11.74 Tesla (fréquence de Larmor du proton égale à 500MHz). Travailler dans un champ aussi intense permet d’améliorer la sensibilité de détection mais nécessite de porter une attention particulière à l’homogénéité du champ magnétique qui, dans notre cas, peut être dégradée en raison de l’introduction du microsystème dans le spectromètre. En effet, les distorsions du champ magnétique, dues aux différentes susceptibilités magnétiques des matériaux constituant la microsonde, ont un impact direct sur la résolution spectrale. C’est pourquoi, une modélisation 3D par éléments finis est proposée afin de prévoir l’influence du microsystème sur la forme des raies spectrales et donc d’en déduire la résolution spectrale pouvant être espérée. La comparaison des résultats expérimentaux et ceux issus des simulations permet de valider le modèle de calcul numérique. Il apparait cependant nécessaire d’inclure le phénomène d’amortissement radiatif afin de pouvoir rendre compte des résultats expérimentaux relatifs à la résolution spectrale effectivement observée. / The work presented in this thesis involves the design, the development and the experimental evaluation of an analysis micro system. The originality of the work lies in the integration of a planar micro coil of spectroscopy by nuclear magnetic resonance (SNMR) on a micro fluidic system based on a polymer, cyclo olefin copolymer (COC). The determination of the optimum geometric characteristics of the micro system to improve electromagnetic coupling between the detection micro coil and the sample is performed with the aid of a numerical model that ensures the optimization of the signal to noise ratio (SNR). Using micro fabrication techniques developed in the laboratory, the micro system was developed and its behaviour was validated in spectrometer producing a static magnetic field off 11.74 Tesla (Larmor frequency of the proton equal to 500MHz). Working in such an intense field results in improved sensitivity of detection but requires paying close attention to the homogeneity of magnetic field. In this case the homogeneity can be degraded due to the introduction of the micro system in the spectrometer. Indeed, the distortions of the magnetic field, due to the different magnetic susceptibilities of the materials constituting the microprobe, have a direct impact on the spectral resolution. As such, 3D modelling by finite elements is proposed to predict the influence of the micro system on the shape of the spectral lines and to determine the best expected spectral resolution. The comparison of the experimental results to those obtained from simulation allows the validation of the numerical model. However, it appears necessary to include the effect of the radiation damping in the model to be able to justify the experimental results relative to the spectral resolution that was observed.