La rationalisation des processus chimiques élémentaires aux surfacesest d'intérêt primordial pour de nombreux phénomènes naturels ou d'intérêttechnologique. D'un point de vue fondamental, la façon dont l'énergie, concomitanteà toute réaction chimique, est distribuée parmi les degrés de liberté des moléculesformées et/ou transférée à la surface est loin d'être systématisée. Dans ce travail,des simulations, reposant sur la méthode des trajectoires quasi-classiques (QCT),sont réalisées pour examiner cette problématique lors de recombinaisons demolécules d'hydrogène (H2) et d'azote (N2) résultant de l'abstraction d'atomesadsorbés via collision par un atome provenant de la phase gazeuse sur des surfacesde Tungstène - W(100) et W(110) - à taux de couverture non nul. Ces processussont ici étudiés pour leur intérêt en physique des interactions plasma-paroi. Dessurfaces d'énergie potentielle, construites à partir de calculs de structure électroniquebasés sur la théorie de la fonctionnelle densité (DFT), sont utilisées pour simuler,dans le cadre de la mécanique classique - incluant les corrections semi-classiquespertinentes - les processus ultrarapides dit de "Eley-Rideal" et par "atomes-chauds"(sub-picoseconde). La mise en place de modèle effectifs, pour tenir compte de ladissipation de l'énergie aux phonons de la surface et aux excitations électroniques(paires électron-trou), permet de rationaliser la dynamique non-adiabatique del'abstraction atomique aux surfaces métalliques. / The rationalization of elementary processes at surfaces is of prime importance for numerous natural and technological areas. From a fundamental pointof view, the way the energy concomitant to any chemical reaction is distributed among the desorbing molecules degrees-of-freedom and the surface is far frombeing fully pictured. In this work, quasiclassical molecular dynamics (QCT)simulations have been carried out to investigate this issue for the recombination ofH2 and N2 resulting from atomic adsorbate abstraction by atom scattering off theW(100) and W(110) covered surfaces, these processes being of relevance inplasma-wall interactions. Potential energy surfaces, built from density functional(DFT) theory calculations, have been used to simulate, within the framework ofclassical dynamics (including semi-classical corrections), the subpicosecond Eley-Rideal and Hot-Atom processes. The implementation of effective models to accountfor energy dissipation to surface phonons and electron-hole pair excitations, have allowed to rationalize the non-adidabatic dynamics of atom abstraction at metalsurfaces.

Nuclear power plays a crucial role in energy supply in the world: around 15% of the electricity generated worldwide is provided from nuclear stations avoiding around 2.5 billion tonnes of CO2 emissions. As of January 2016, 442 reactors that generated 380+ GW were in operation and 66 new reactors were under construction. The seismic design of new nuclear power plants (NPPs) has gained much interest after the high-profile Fukushima Dai-ichi accident. In the UK, a tectonically stable continental region that possesses medium-to-low seismic activity, strong earthquakes capable of jeopardising the structural integrity of NPPs, although infrequent, can still occur. Despite that no NPP has been built in Great Britain after 1995, a New Build Programme intended to build 16 GW of new nuclear capacity by 2030 is currently under way. This PhD project provides a state-of-the-art framework for seismic probabilistic safety assessment and risk control of NPPs in Northwest Europe with particular application to the British Isles. It includes three progressive levels: (i) seismic input, (ii) seismic risk analysis, and (iii) seismic risk control. For seismic input, a suitable model to rationally define inputs in the context of risk assessments is proposed. Such a model is based on the stochastic simulation of accelerograms that are compatible with seismic scenarios defined by magnitude 4 < Mw < 6.5, epicentral distance 10 km < Repi < 100 km, and different types of soil (rock, stiff soil and soft soil). It was found to be a rational approach that streamlines the simulation of accelerograms to conduct nonlinear dynamic analyses for safety assessments. The model is a function of a few variables customarily known in structural engineering projects. In terms of PGA, PGV and spectral accelerations, the simulated accelerograms were validated by GMPEs calibrated for the UK, Europe and the Middle East, and other stable continental regions. For seismic risk analysis, a straightforward and logical approach to probabilistically assess the risk of NPPs based on the stochastic simulation of accelerograms is studied. It effectively simplifies traditional approaches: for seismic inputs, it avoids the use of selecting/scaling procedures and GMPEs; for structural outputs, it does not use Monte Carlo algorithms to simulate the damage state. However, it demands more expensive computational resources as a large number of nonlinear dynamic analyses are needed. For seismic risk control, strategies to control the risk using seismic protection systems are analysed. This is based on recent experience reported elsewhere of seismically protected nuclear reactor buildings in other areas of medium-to-low seismic activity. Finally, a scenario-based incremental dynamic analysis (IDA) is proposed aimed at the generation of surfaces for unacceptable performance of NPPs as function of earthquake magnitude and distance. It was found that viscous-based devices are more efficient than hysteretic-based devices in controlling the seismic risk of NPPs in the UK. Finally, using the proposed scenario-based IDA, it was found that when considering all controlling scenarios for a representative UK nuclear site, the risk is significantly reduced ranging from 3 to 5 orders of magnitude when using viscous-based devices.

<p>У докторској дисертације предложен је механички модел средњег уха<br />заснован на динамици крутих тела која су са околином везана системом<br />фракционих вискоеластичних елемената. Ови елементи моделирани су<br />као стандардно фракционо линеарно вискоеластично тело познато као<br />фракциони Зенеров модел вискоеластичног тела. Диференцијалне<br />једначине кретања предложеног модела генерисане су Гибс-Апеловим<br />једначинама аналитичке механике. Као резултат добијен је математички<br />модел у форми система диференцијалних једначина произвољног<br />реалног реда. Овај систем решен је на два начина: применом<br />експанзионе формуле Атанацковића и Станковића и методом<br />Лапласове трансформације са нумеричком инверзијом.</p> / <p>U doktorskoj disertacije predložen je mehanički model srednjeg uha<br />zasnovan na dinamici krutih tela koja su sa okolinom vezana sistemom<br />frakcionih viskoelastičnih elemenata. Ovi elementi modelirani su<br />kao standardno frakciono linearno viskoelastično telo poznato kao<br />frakcioni Zenerov model viskoelastičnog tela. Diferencijalne<br />jednačine kretanja predloženog modela generisane su Gibs-Apelovim<br />jednačinama analitičke mehanike. Kao rezultat dobijen je matematički<br />model u formi sistema diferencijalnih jednačina proizvoljnog<br />realnog reda. Ovaj sistem rešen je na dva načina: primenom<br />ekspanzione formule Atanackovića i Stankovića i metodom<br />Laplasove transformacije sa numeričkom inverzijom.</p> / <p>In this theses, mechanical model of a middle ear based on the dynamics of<br />system of rigid bodies that are connected with the environment through a<br />system of fractional viscoelastic elements is proposed. These elements are<br />modeled as a standard fractional linear viscoelastic body known as the<br />fractional Zener model of viscoelastic body. Differential equations of motion<br />of the proposed model are generated by use of the Gibbs-Appeal equations<br />of analytical mechanics. As a result, mathematical model in form of a system<br />of differential equations of arbitrary real order is obtained. This system is<br />solved in two ways: by use of the Atanacković-Stankovic expansion formula<br />and method of the Laplace transform with numerical inversion.</p>

Este artículo consiste en analizar una nueva alternativa de control antisísmico de alta tecnología para la construcción de hospitales en el Perú, que en su normativa exige el uso de aislamiento de base para edificaciones esenciales. Para ello, se opta por la evaluación estructural de una edificación construida con aisladores sísmicos y la misma con implementación del sistema de disipación de energía SLB (Shear Link Bozzo). Los resultados analizados, para cada técnica estudiada de control antisísmico, son: derivas de entrepiso, aceleraciones de piso, balance energético y análisis de rotulas plásticas, en base a la filosofía de funcionalidad continua. / This article consists of analyzing a new high-tech anti-seismic control alternative for the construction of hospitals in Peru, which in its regulations requires the use of base insulation for essential buildings. For this, the structural evaluation of a building constructed with seismic isolators is chosen and the same with the implementation of the SLB (Shear Link Bozzo) energy dissipation system. The results analyzed for each anti-seismic control technique studied are: mezzanine drifts, floor accelerations, energy balance and analysis of plastic hinges, based on the philosophy of continuous functionality. / Trabajo de investigación

<p>  </p> <p>Architectured materials offer engineers more options for choosing materials with their desired properties. Segmenting materials to create topological interlocking materials (TIMs) creates materials, which can deform in greater amounts without failure and absorb more strain energy. Previous research on TIMs has shown that the stiffness and reaction force of these materials can be directly controlled by controlling the boundary forces offered by the frame which constrains these materials.</p> <p>The research presented in this paper investigated a TIM made into a 1-Dimension beam like structure called a lintel. This research investigated not only the mechanics of this structure, but also developed a method of directly controlling the reaction force at a given displacement using shape memory alloy (SMA) wires. These wires would actuate the boundary pieces used to constrain the system. These actuation wires coupled with force sensors imbedded into the lintel allowed a feedback control loop to be established, which would control the reaction force. The reaction force was then controlled to create a smart structure which could optimize the strain energy absorption under the constraint of a maximum allowable load, similar to cellular solids used in packaging and padding materials.</p> <p>To develop this smart structure, four separate investigations occurred. The first was finite element analysis (FEA) performed to model the loading response of the lintel. This experiment demonstrated that the Mises Truss Model was effective at modelling the lintel. The second was an experimental validation of the FEA model performed in the first investigation. This experiment validated the Mises Truss Model for the lintel. The third investigation simulated the active lintel using computational software and the model of the lintel established in the first two investigations. This experiment demonstrated computationally the ability of SMA wires to control the reaction force as desired in an idealized case. The fourth and final investigation experimentally validated the ability to create and active lintel and created a functioning prototype. This demonstrated experimentally the ability of the active lintel to control reaction force as desired.</p> <p>This project has demonstrated the viability to create smart structures using segmented materials, which in the future may be used in a variety of applications including robotics and adaptive structures in harsh environments. </p>

Um polieletrólito catiônico (poliamina), com baixo peso molecular e elevada densidade de carga, normalmente aplicado como agente coagulante do lixo aniônico, foi usado para estudos de retenção e drenagem na fabricação de papel. O uso do carboximentil celulose de sódio para simulação do teor de lixo aniônico e seu efeito na retenção de cargas minerais foi uma característica importante para este trabalho. Pode ser observado que o aumento da dosagem do polímero catiônico tanto melhora a retenção de cargas minerais, avaliada pela turbidez do filtrado, quanto melhora a drenagem do sistema, avaliada pela velocidade de escoamento. Entretanto, elevadas dosagens deste polímero comprometeram os resultados destes parâmetros devido à inversão de carga do sistema. Pode também ser confirmado que forças de cisalhamento excessivas prejudicam a retenção de cargas minerais. Ademais, um polianfótero, com peso molecular e densidade de carga elevados, contendo grupos positivo (N-[3-(N,N-dimetilamino)propil]acrilamida), negativo (ácido metileno butanodióico) e nulo (acrilamida) na mesma cadeia, foi testado como agente de resistência a seco do papel. Todos os estudos em nível molecular sobre o comportamento do polianfótero em solução e o seu comportamento de adsorção sobre superfícies modelos carregadas, em diferentes condições de pH e de força iônica, foram importantes para explicar tanto dos fenômenos de adsorção, envolvendo fibras celulósicas e polianfótero, quanto o seu efeito na resistência mecânica do papel. Foi observado que a solubilidade do polímero aumenta à medida que o pH se distancia do seu ponto isoelétrico, pHPIE 7,3, e reduz para valores de pH próximos ao pHPIE. O tamanho das estruturas do polianfótero depende do pH do meio de dispersão. As características de tamanho do polianfótero tanto sob a forma de cadeias individuais ou quanto sob a forma de agregados, foram medidas através da técnica de espalhamento dinâmico de luz. As propriedades viscoelásticas das camadas adsorvidas e a quantidade de polímero adsorvida foram medidas através da técnica da balança microgravimétrica com dissipação de energia. Estas duas determinações, associadas às imagens no microscópio de força atômica, foram importantes para o entendimento dos resultados práticos do uso do polianfótero como agente de resistência a seco do papel. Maiores resultados de resistência do papel, avaliada através da resistência à tração, foram alcançados para valores de pH próximos ao ponto isoelétrico onde foram encontrados o seguinte: (1) maiores tamanhos para as estruturas do polímero em solução, (2) maior quantidade de massa nas camadas adsorvidas e (3) a formação de camadas mais viscoelásticas. O fenômeno de separação de fases, associado à mudança da solubilidade do polímero em solução devido ao balanço dos grupos positivos e negativos ionizados ao longo da faixa de pH estudada, foi considerado o principal aspecto para a variação em tamanho dos agregados. Embora este polímero tenha apresentado comportamento antipolieletrólito devido à expansão da sua cadeia e ao aumento da densidade de carga com o aumento da força iônica, considerando o efeito da força iônica para pH 4,3, o comportamento de adsorção do polianfótero foi avaliado como o comportamento de um polieletrólito monocarregado de alta densidade de carga. Maiores e menores quantidades de massas adsorvidas foram encontradas para valores intermediários e extremos de força iônica, respectivamente. As interações eletrostáticas foram consideradas as principais responsáveis pela adsorção do polímero sobre superfícies carregadas. Entretanto, a blindagem de cargas foi considerada a explicação para os baixos valores de massa adsorvida para valores mais elevados de força iônica. / A cationic polyelectrolyte (polyamine), with low molecular weight and high charge density, usually applied as anionic trash coagulant, was used for the retention and drainage studies in the papermaking. The use of sodium carboxymethyl cellulose to simulate the anionic trash content and its effect on the filler retention was an important feature of the work. It could be noted that the increasing of the cationic polymer dosage improves both the filler retention, evaluated by the turbidity of the filtrate, and the system drainage, evaluated by the flow speed. However, high dosages of this polymer compromised the results of these parameters due to the reversal of the system charge. It can also be confirmed that excessive shear forces affect the filler retention. Furthermore, a polyampholyte, with high molecular weight and charge density, containing positive (N-[3-(N,N- dimethylamino)propyl]acrylamide), negative (methylene butanedioic acid), and neutral (acrylamide) groups in the same chain, was tested as a dry strength agent. All of the studies at molecular level concerning to the polyampholyte behavior in the solution and its adsorption behavior on charged model surfaces at different conditions of pH and ionic strength, were important to explain both the adsorption phenomena, involving cellulosic fibers and polyampholyte, and its impact on the paper strength. It was observed that the polymer solubility increases as the pH moves away from its isoelectric point, pHIEP 7.3, and decreases when the pH approaches close to pHIEP. The sizes of the structures of the polyampholytes depend on the pH of the dispersion medium. Also the size characteristics of polyampholyte, both in individual and aggregated forms, were measured by dynamic light scattering technique. The viscoelastic properties of adsorbed layers, as well as the amount of the adsorbed polymer, were measured by quartz crystal microbalance technique with energy dissipation. These two measurements, associated with the atomic force microscopy images, were important to understand the practical results of polyampholyte usage as a dry strength agent. Best results of paper strength, evaluated by paper strength index, were achieved at pH close to the isoelectric point on which one were found the following features: (1) larger sizes of the polymer structures in solution, (2) higher amount of mass in the adsorbed layers, and (3) the formation of more viscoelastic layers. The phase separation phenomenon, associated with the change in the solubility of the polymer due to the balance of the positive and negative groups throughout the studied pH range, was considered the main aspect for the variation in size of the aggregates. Although this polymer shows antipolyelectrolyte behavior due to the expansion of the its chain and the increasing in charge density with the ionic strength, considering the effect of ionic strength at pH 4.3, the adsorption behavior of polyampholyte was evaluated as a monocharged polyelectrolyte behavior with high charge density. Major and minor amounts of adsorbed masses were found for intermediates and extremes values of ionic strength, respectively. The electrostatic interactions were considered the main cause of the adsorption on charged surfaces. However, the electrostatic screening was considered the explanation for the low values of adsorbed mass at higher values of ionic strength.

Um polieletrólito catiônico (poliamina), com baixo peso molecular e elevada densidade de carga, normalmente aplicado como agente coagulante do lixo aniônico, foi usado para estudos de retenção e drenagem na fabricação de papel. O uso do carboximentil celulose de sódio para simulação do teor de lixo aniônico e seu efeito na retenção de cargas minerais foi uma característica importante para este trabalho. Pode ser observado que o aumento da dosagem do polímero catiônico tanto melhora a retenção de cargas minerais, avaliada pela turbidez do filtrado, quanto melhora a drenagem do sistema, avaliada pela velocidade de escoamento. Entretanto, elevadas dosagens deste polímero comprometeram os resultados destes parâmetros devido à inversão de carga do sistema. Pode também ser confirmado que forças de cisalhamento excessivas prejudicam a retenção de cargas minerais. Ademais, um polianfótero, com peso molecular e densidade de carga elevados, contendo grupos positivo (N-[3-(N,N-dimetilamino)propil]acrilamida), negativo (ácido metileno butanodióico) e nulo (acrilamida) na mesma cadeia, foi testado como agente de resistência a seco do papel. Todos os estudos em nível molecular sobre o comportamento do polianfótero em solução e o seu comportamento de adsorção sobre superfícies modelos carregadas, em diferentes condições de pH e de força iônica, foram importantes para explicar tanto dos fenômenos de adsorção, envolvendo fibras celulósicas e polianfótero, quanto o seu efeito na resistência mecânica do papel. Foi observado que a solubilidade do polímero aumenta à medida que o pH se distancia do seu ponto isoelétrico, pHPIE 7,3, e reduz para valores de pH próximos ao pHPIE. O tamanho das estruturas do polianfótero depende do pH do meio de dispersão. As características de tamanho do polianfótero tanto sob a forma de cadeias individuais ou quanto sob a forma de agregados, foram medidas através da técnica de espalhamento dinâmico de luz. As propriedades viscoelásticas das camadas adsorvidas e a quantidade de polímero adsorvida foram medidas através da técnica da balança microgravimétrica com dissipação de energia. Estas duas determinações, associadas às imagens no microscópio de força atômica, foram importantes para o entendimento dos resultados práticos do uso do polianfótero como agente de resistência a seco do papel. Maiores resultados de resistência do papel, avaliada através da resistência à tração, foram alcançados para valores de pH próximos ao ponto isoelétrico onde foram encontrados o seguinte: (1) maiores tamanhos para as estruturas do polímero em solução, (2) maior quantidade de massa nas camadas adsorvidas e (3) a formação de camadas mais viscoelásticas. O fenômeno de separação de fases, associado à mudança da solubilidade do polímero em solução devido ao balanço dos grupos positivos e negativos ionizados ao longo da faixa de pH estudada, foi considerado o principal aspecto para a variação em tamanho dos agregados. Embora este polímero tenha apresentado comportamento antipolieletrólito devido à expansão da sua cadeia e ao aumento da densidade de carga com o aumento da força iônica, considerando o efeito da força iônica para pH 4,3, o comportamento de adsorção do polianfótero foi avaliado como o comportamento de um polieletrólito monocarregado de alta densidade de carga. Maiores e menores quantidades de massas adsorvidas foram encontradas para valores intermediários e extremos de força iônica, respectivamente. As interações eletrostáticas foram consideradas as principais responsáveis pela adsorção do polímero sobre superfícies carregadas. Entretanto, a blindagem de cargas foi considerada a explicação para os baixos valores de massa adsorvida para valores mais elevados de força iônica. / A cationic polyelectrolyte (polyamine), with low molecular weight and high charge density, usually applied as anionic trash coagulant, was used for the retention and drainage studies in the papermaking. The use of sodium carboxymethyl cellulose to simulate the anionic trash content and its effect on the filler retention was an important feature of the work. It could be noted that the increasing of the cationic polymer dosage improves both the filler retention, evaluated by the turbidity of the filtrate, and the system drainage, evaluated by the flow speed. However, high dosages of this polymer compromised the results of these parameters due to the reversal of the system charge. It can also be confirmed that excessive shear forces affect the filler retention. Furthermore, a polyampholyte, with high molecular weight and charge density, containing positive (N-[3-(N,N- dimethylamino)propyl]acrylamide), negative (methylene butanedioic acid), and neutral (acrylamide) groups in the same chain, was tested as a dry strength agent. All of the studies at molecular level concerning to the polyampholyte behavior in the solution and its adsorption behavior on charged model surfaces at different conditions of pH and ionic strength, were important to explain both the adsorption phenomena, involving cellulosic fibers and polyampholyte, and its impact on the paper strength. It was observed that the polymer solubility increases as the pH moves away from its isoelectric point, pHIEP 7.3, and decreases when the pH approaches close to pHIEP. The sizes of the structures of the polyampholytes depend on the pH of the dispersion medium. Also the size characteristics of polyampholyte, both in individual and aggregated forms, were measured by dynamic light scattering technique. The viscoelastic properties of adsorbed layers, as well as the amount of the adsorbed polymer, were measured by quartz crystal microbalance technique with energy dissipation. These two measurements, associated with the atomic force microscopy images, were important to understand the practical results of polyampholyte usage as a dry strength agent. Best results of paper strength, evaluated by paper strength index, were achieved at pH close to the isoelectric point on which one were found the following features: (1) larger sizes of the polymer structures in solution, (2) higher amount of mass in the adsorbed layers, and (3) the formation of more viscoelastic layers. The phase separation phenomenon, associated with the change in the solubility of the polymer due to the balance of the positive and negative groups throughout the studied pH range, was considered the main aspect for the variation in size of the aggregates. Although this polymer shows antipolyelectrolyte behavior due to the expansion of the its chain and the increasing in charge density with the ionic strength, considering the effect of ionic strength at pH 4.3, the adsorption behavior of polyampholyte was evaluated as a monocharged polyelectrolyte behavior with high charge density. Major and minor amounts of adsorbed masses were found for intermediates and extremes values of ionic strength, respectively. The electrostatic interactions were considered the main cause of the adsorption on charged surfaces. However, the electrostatic screening was considered the explanation for the low values of adsorbed mass at higher values of ionic strength.

With the advent of micro and nano electromechanical systems (MEMS/NEMS), there has been rapid development in the design and fabrication of sensitive resonant sensors. Sensitivity of such devices depends on the resonant frequency and the quality factor (Q). The Q of these devices are dependent on process induced prestress in the structural geometry, interaction with the external environment, and the encapsulation method. For high frequency sensors operating in air and under encapsulation condition, the Q is dominated by structural and fluid-structure interaction losses. In this thesis, we set out to study the dominant energy dissipative mechanisms that are constituent of the experimentally observed loss (Q-factor) in two specific test geometries—uncapped and capped circular MEMS drumhead resonators. Considering the importance of various factors, we consider four important problems pertaining to the uncapped as well as capped resonators. In the first problem, the most important factors perhaps are the acoustic radiation losses emanating from the annular plate, and the effect of added mass effect on the natural frequencies of the annular plate. The second problem is to investigate the dominant contribution of squeeze film losses and acoustic radiation losses with respect to various natural frequencies of the annular plate. The third problem is to consider the effect of prestress on the natural frequencies of the annular plate and its associated fluid-structure interaction losses (quality factors due to squeeze film damping and acoustic radiation losses). The fourth problem is to study the dominant fluid-structure interaction losses and structural losses that are constituent of experimentally measured Q-factors of the encapsulated annular plate (conceptual representation of MEMS device under packaged conditions). In the first problem, we study the mode dependent acoustic radiation losses in an uncapped drumhead microresonator which is represented by a annular circular plate fixed at its outer edge, suspended over a fixed substrate. There are two main effects which are associated with such systems due to the fluid-structure interaction. First is the “added mass effect,” which reduces the effective resonance frequency of the structure. The second is the acoustic radiation loss from the top side of the resonator, that affects the quality factor of the vibrating structure. In deriving the analytical solution, we first obtain the exact mode shapes of the structure ignoring any effect of the surrounding fluid (air) on the mode shape. Subsequently, we use these mode shapes to study the effect of the surrounding fluid on the associated natural frequencies and the Q-factor. The effect of “added mass” on the frequencies of the structure is found to be negligible. However, the acoustic radiation losses found to be significant. Additionally, we found that the variation in Qac over the first few modes (< 40 MHz) is marked with a local maximum and a minimum. Beyond this range, Qac increases monotonically over the higher frequency modes. It is also found that such kind of variation can be described using different acoustics parameters. Finally, comparing the acoustics radiation loss based quality factor with the experimental results for the uncapped drumhead resonator, the acoustic damping dominates only at higher modes. Therefore, our second problem forms the basis of finding other fluid-related damping. In the second problem, we explore the fluid losses due to squeeze film damping in the uncapped drumhead micro resonator. In this case, the squeeze film loss is due to the flow of the fluid film between the bottom surface of the annular plate and the fixed substrate. Based on the literature survey, it is found that the squeeze film damping reduces with increase in the air-gap thickness and the operating frequencies respectively. However, the squeeze film effect can not be ignored at lower frequencies. In order to investigate the contribution of squeeze film damping in uncapped resonator, we determine squeeze-film damping based quality factor Qsq corresponding to different modes of the resonators using FEM based software, ANSYS. On comparing Qsq with the experiments, we found that Qsq matches well with the experiments corresponding to the lower modes. Therefore, it is found that Qsq dominates at low frequencies (< 20 MHz) and Qac plays significant role at high frequencies (> 40 MHz). Both types of damping should be considered while modeling the fluid damping in uncapped resonator. In the next study, we discuss the effects of prestress on the resonant frequencies and quality factor. In the third study, we discuss the applicability of thin-plate theory with prestress and membrane theory in computing the frequencies and quality factor due to acoustic and squeeze film losses in the uncapped drumhead resonator. In the first two studies, although the quality factor due to acoustic losses and the squeeze film captures the correct trend of the experimental results, there is a mismatch between the experimental and theoretical frequencies computed with added mass effect. In order to improve the computation of frequencies corresponding to measured modes, we first used membrane theory to predict the frequencies, and finally we quantify that there exists discrepancy between computed and the corresponding experimental frequencies with error of about 8–55%. Since, both the membrane as well as thin plate theory without prestress do not correctly model the frequencies, we used the thin plate theory with prestress. For a prestress level of 96 MPa, we found the match between the computed frequencies and the corresponding quality factors with the measured values. However, we also found that there exists strong dependence of prestress on the acoustic radiation loss, with decrease in the acoustic loss based quality factors with increase in the prestress level. In the subsequent problem, we focus on the computation of losses in capped drumhead resonator which leads to a design possibility of improving the quality factor by containing the acoustic radiation losses. In the fourth problem, we study the structural and fluid-structure interaction losses which are dominant constituent of net Q-factor observed in experiments due to encapsulation of uncapped drumhead resonator. Essentially, the geometry of the capped resonator constitutes upper and lower cavities subjected to fluid-structure interaction losses on both sides of the annular plate. The dominant fluid-structure interaction loss is found to be due to squeezing action acting simultaneously in the upper and lower cavities. However, as we go to the higher modes, squeeze film damping become very small and the damping due to structure related losses such as clamping and thermoelastic losses becomes significant. We found the thermoelastic damping to be the dominant source of structural damping at higher resonant modes, whereas, the clamping losses are found to be relatively smaller. Finally, on comparing the net quality factor with the experimental results, we observed that the squeeze film losses are dominant at lower frequencies, and thermoelastic losses dominate at the higher frequencies. However, there remains some discrepancy between theoretical and experimental Q-factors particularly over higher frequency range. Such discrepancy may be due to some unaccounted factors which may be explored to improve the modeling of damping in capped resonators. The emphasis of this work has been towards developing a comprehensive understanding of different dominant dissipative mechanisms, classified into the fluid-structure interaction and the structural losses, that are constituent of the Q-factor at various resonant modes of uncapped and capped drumhead resonators.

Diese Arbeit beschäftigt sich mit Coarse-Graining (dt. ``Vergröberung", ``Zusammenfassung von Zuständen") für Gradientensysteme und Markov-Prozesse. Coarse-Graining ist ein etabliertes Verfahren in der Mathematik und in den Naturwissenschaften und hat das Ziel, die Komplexität eines physikalischen Systems zu reduzieren und effektive Modelle herzuleiten. Die mathematischen Probleme in dieser Arbeit stammen aus der Theorie der Systeme interagierender Teilchen. Hierbei werden zwei Ziele verfolgt: Erstens, Coarse-Graining mathematisch rigoros zu beweisen, zweitens, mathematisch äquivalente Beschreibungen für die effektiven Modelle zu formulieren. Die ersten drei Teile der Arbeit befassen sich mit dem Grenzwert schneller Reaktionen für Reaktionssysteme und Reaktions-Diffusions-Systeme. Um effektive Modelle herzuleiten, werden nicht nur die zugehörigen Reaktionsratengleichungen betrachtet, sondern auch die zugrunde liegende Gradientenstruktur. Für Gradientensysteme wurde in den letzten Jahren eine strukturelle Konvergenz, die sogenannte ``EDP-Konvergenz", entwickelt. Dieses Coarse-Graining-Verfahren wird in der vorliegenden Arbeit auf folgende Systeme mit langsamen und schnellen Reaktionen angewandt: lineare Reaktionssysteme (bzw. Markov-Prozesse auf endlichem Zustandsraum), nichtlineare Reaktionssysteme, die das Massenwirkungsgesetz erfüllen, und lineare Reaktions-Diffusions-Systeme. Für den Grenzwert schneller Reaktionen wird eine mathematisch rigorose und strukturerhaltende Vergröberung auf dem Level des Gradientensystems inform von EDP-Konvergenz bewiesen. Im vierten Teil wird der Zusammenhang zwischen Gleichungen mit Gedächtnis und Markov-Prozessen untersucht. Für Gleichungen mit Gedächtnisintegralen wird explizit ein größer Markov-Prozess konstruiert, der die Gleichung mit Gedächtnis als Teilsystem enthält. Der letzte Teil beschäftigt sich mit verschieden Diskretisierungen für den Fokker-Planck-Operator. Dazu werden numerische und analytische Eigenschaften untersucht. / This thesis deals with coarse-graining for gradient systems and Markov processes. Coarse-graining is a well-established tool in mathematical and natural sciences for reducing the complexity of a physical system and for deriving effective models. The mathematical problems in this work originate from interacting particle systems. The aim is twofold: first, providing mathematically rigorous results for physical coarse-graining, and secondly, formulating mathematically equivalent descriptions for the effective models. The first three parts of the thesis deal with fast-reaction limits for reaction systems and reaction-diffusion systems. Instead of deriving effective models by solely investigating the associated reaction-rate equation, we derive effective models using the underlying gradient structure of the evolution equation. For gradient systems a structural convergence, the so-called ``EDP-convergence", has been derived in recent years. In this thesis, this coarse-graining procedure has been applied to the following systems with slow and fast reactions: linear reaction systems (or Markov process on finite state space), nonlinear reaction systems of mass-action type, and linear reaction-diffusion systems. For the fast-reaction limit, we perform rigorous and structural coarse-graining on the level of the gradient system by proving EDP-convergence. In the fourth part, the connection between memory equations and Markov processes is investigated. Considering linear memory equations, which can be motivated from spatial homogenization, we explicitly construct a larger Markov process that includes the memory equation as a subsystem. The last part deals with different discretization schemes for the Fokker–Planck operator and investigates their analytical and numerical properties.

<p>The main goal of this thesis research is to expand the range of unique properties of phase transforming cellular materials (PXCMs), a new class of architected materials, and to extend their applicability both in the engineering disciplines and in the medical field. A novel aspect of PXCMs is their unique energy dissipation during loading via a snapping mechanism associated with a geometric transition between one stable configuration to another stable configuration at the unit cell level. Phase transformation is analogous to displacive transformations, such as martensitic transformations in shape memory alloys, with no change in configurational entropy. To accomplish this goal, three problem areas are addressed with the first exploring the effects of length scale as added structural hierarchy on material properties and energy dissipation, the second providing an analysis of the durability of architected materials via a novel additive manufacturing method, and the third, an extension into the medical field. Two examples are provided that demonstrate the effects of length scale as added structural hierarchy on material properties, and a machine learning approach for the feasible design of materials with additional levels of structural hierarchy is presented. A simple design approach coupled with a novel additive manufacturing method is discussed for the design of architected materials with high durability. Lastly, a concept for de-clogging bile stents via a temperature driven, shape-memory mechanism inspired by peristaltic locomotion in the human esophagus is presented.</p>