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Space-Time Discretization of Elasto-Acoustic Wave Equation in Polynomial Trefftz-DG Bases / Discrétisation Espace-Temps d'Équations d'Ondes Élasto-Acoustiques dans des Bases Trefftz-DG PolynomialesShishenina, Elvira 07 December 2018 (has links)
Les méthodes d'éléments finis de type Galerkine discontinu (DG FEM) ont démontré précision et efficacité pour résoudre des problèmes d'ondes dans des milieux complexes. Cependant, elles nécessitent un très grand nombre de degrés de liberté, ce qui augmente leur coût de calcul en comparaison du coût des méthodes d'éléments finis continus.Parmi les différentes approches variationnelles pour résoudre les problèmes aux limites, se distingue une famille particulière, basée sur l'utilisation de fonctions tests qui sont des solutions locales exactes des équations à résoudre. L'idée vient de E.Trefftz en 1926 et a depuis été largement développée et généralisée. Les méthodes variationnelles de type Trefftz-DG appliquées aux problèmes d'ondes se réduisent à des intégrales de surface, ce qui devrait contribuer à réduire les coûts de calcul.Les approches de type Trefftz ont été largement développées pour les problèmes harmoniques, mais leur utilisation pour des simulations en domaine transitoire est encore limitée. Quand elles sont appliquées dans le domaine temporel, les méthodes de Trefftz utilisent des maillages qui recouvrent le domaine espace-temps. C'est une des paraticularités de ces méthodes. En effet, les méthodes DG standards conduisent à la construction d'un système semi-discret d'équations différentielles ordinaires en temps qu'on intègre avec un schéma en temps explicite. Mais les méthodes de Trefftz-DG appliquées aux problèmes d'ondes conduisent à résoudre une matrice globale, contenant la discrétisation en espace et en temps, qui est de grande taille et creuse. Cette particularité gêne considérablement le déploiement de cette technologie pour résoudre des problèmes industriels.Dans ce travail, nous développons un environnement Tre#tz-DG pour résoudre des problèmes d'ondes mécaniques, y compris les équations couplées de l'élasto-acoustique. Nous prouvons que les formulations obtenues sont bien posées et nous considérons la difficulté d'inverser la matrice globale en construisant un inverse approché obtenu à partir de la décomposition de la matrice globale en une matrice diagonale par blocs. Cette idée permet de réduire les coûts de calcul mais sa précision est limitée à de petits domaines de calcul. Etant données les limitations de la méthode, nous nous sommes intéressés au potentiel du "Tent Pitcher", en suivant les travaux récents de Gopalakrishnan et al. Il s'agit de construire un maillage espace-temps composé de macro-éléments qui peuvent être traités indépendamment en faisant une hypothèse de causalité. Nous avons obtenu des résultats préliminaires très encourageants qui illustrent bien l'intérêt du Tent Pitcher, en particulier quand il est couplé à une méthode de Trefftz-DG formulée à partir d'intégrales de surface seulement. Dans ce cas, le maillage espace-temps est composé d'éléments qui sont au plus de dimension 3. Il est aussi important de noter que ce cadre se prête à l'utilisation de pas de temps locaux ce qui est un plus pour gagner en précision avec des coûts de calcul réduits. / Discontinuous Finite Element Methods (DG FEM) have proven flexibility and accuracy for solving wave problems in complex media. However, they require a large number of degrees of freedom, which increases the corresponding computational cost compared with that of continuous finite element methods. Among the different variational approaches to solve boundary value problems, there exists a particular family of methods, based on the use of trial functions in the form of exact local solutions of the governing equations. The idea was first proposed by Trefftz in 1926, and since then it has been further developed and generalized. A Trefftz-DG variational formulation applied to wave problems reduces to surface integrals that should contribute to decreasing the computational costs.Trefftz-type approaches have been widely used for time-harmonic problems, while their implementation for time-dependent simulations is still limited. The feature of Trefftz-DG methods applied to time-dependent problems is in the use of space-time meshes. Indeed, standard DG methods lead to the construction of a semi-discrete system of ordinary differential equations in time which are integrated by using an appropriate scheme. But Trefftz-DG methods applied to wave problems lead to a global matrix including time and space discretizations which is huge and sparse. This significantly hampers the deployment of this technology for solving industrial problems.In this work, we develop a Trefftz-DG framework for solving mechanical wave problems including elasto-acoustic equations. We prove that the corresponding formulations are well-posed and we address the issue of solving the global matrix by constructing an approximate inverse obtained from the decomposition of the global matrix into a block-diagonal one. The inversion is then justified under a CFL-type condition. This idea allows for reducing the computational costs but its accuracy is limited to small computational domains. According to the limitations of the method, we have investigated the potential of Tent Pitcher algorithms following the recent works of Gopalakrishnan et al. It consists in constructing a space-time mesh made of patches that can be solved independently under a causality constraint. We have obtained very promising numerical results illustrating the potential of Tent Pitcher in particular when coupled with a Trefftz-DG method involving only surface terms. In this way, the space-time mesh is composed of elements which are 3D objects at most. It is also worth noting that this framework naturally allows for local time-stepping which is a plus to increase the accuracy while decreasing the computational burden.
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Band gaps and waveguiding of surface acoustic waves in pillars-based phononics crystals / Bandes interdites et propagation d'ondes guidées de surface dans un cristal phononique à résonance localeAl lethawe, Mohammed abdulridha 18 December 2015 (has links)
[…] Dans ce travail de thèse, nous nous sommes intéressés à ces bandes interdites et à ces modes de propagations dans le cas d’un cristal photonique constitué d’une matrice de piliers déposés en surface d’un milieu semi-fini. L’étude des interactions entre les piliers résonants localement avec la surface du milieu semi fini nous a permis d’identifier de nouveaux modes de propagation […]Nous avons également montré comment obtenir une réfraction négative omnidirectionnelle[…] La dernière partie de ce travail a été consacré à l’étude des mécanismes permettant la propagation et le confinement d’ondes guidées[…] .Nous avons également explicité les mécanismes qui permettent de crée ce type d’ondes guidées sub-longeur d’onde et le confinement des photons de surface. / [...] We present the features of the interaction between surface acoustic wave and locally resonant pillar on the top of demi infinite medium. We shown that the photonic crystal we proposed possess an acoustic metamaterial feature for surface acoustic waves in the manner that pillars on the top of the surface introduce new guide modes in the non radiative region of the substrate outside sound cone. We also demonstrate the these guided modes are resonant modes that have frequencies greatly lower than those expected from the Bragg mechanism. […]
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Transporte eletrônico em sistemas de baixa dimensionalidade com interação elétron-fônon e campos elétricos / Electronic transport on low dimensionality systems mediated by electron-phonon interaction and electric fieldRanciaro Neto, Adhemar 30 June 2016 (has links)
In this work we studied electron dynamics in two 1-D distinct systems: (1) anharmonic lattice with electron-phonon interaction under the effect of a static parallel electric field and (2) harmonic alloy with uncorrelated diagonal disorder, electron-phonon interaction and under the effect of surface acoustic wave (SAW). In both cases we used quantum mechanics formalism for the electron and a classical Hamiltonian for chain vibrations. Moreover, electron-phonon coupling was described by a transfer energy function which depends on relative distance of nearest neighbor ions. We developed numerical calculation employing Taylor truncated expansion method for Schrödinger's equation time evolution operator and other two for lattice deformation (Euler and finite difference). Results (1) point out to the existence of a competition among electron-lattice coupling and electric field. The former promotes a electron-soliton pair formation, which moves along the chain and the latter traps electron around initial position generating Bloch-like oscillations. On system (2), association between SAW and eletron-phonon interaction promotes the breakdown of Anderson localization and charge transport even in a high disorder level. We had acceptable numerical tolerance and our calculations are in agreement to the theory. / Neste trabalho foi estudado o problema dinâmica de um elétron em dois sistemas unidimensionais distintos: (1) rede não harmônica com interação elétron-fônon e sob a ação de um campo elétrico estático aplicado paralelamente a ela e (2) rede harmônica com desordem diagonal não correlacionada, com interação elétron-fônon e sob a influência de ondas acústicas de superfície (SAW). Nos dois casos, foram utilizados formalismo quântico para o estudo do elétron e uma hamiltoniana clássica para as vibrações da cadeia. Além disso, o acoplamento do ente quântico com a rede foi descrito a partir da energia de transferência entre íons vizinhos, com aquela sendo dependente da distncia efetiva destes. Foi aplicado o método numérico de expansão truncada de Taylor para a evolução temporal da equação de Schrödinger dependente do tempo em ambos os casos, enquanto para a dinâmica das deformações foram empregados métodos distintos (Euler e diferenças finitas). Os resultados de (1) apontaram para a ocorrência de uma competição entre o acoplamento elétron-fônon e o campo elétrico. O primeiro promove um par elétron-soliton que se move ao longo da cadeia e o segundo aprisiona o elétron em torno de sua posição inicial criando oscilações semelhantes às de Bloch. No sistema (2), a associação entre SAW e a interação elétron-rede destroem o fenômeno da localização de Anderson permitindo o transporte de carga, mesmo em níveis altos de desordem. Os níiveis de precisão numérica são aceitáveis e os cálculos estão em consonância com os preceitos teóricos.
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Aperfeiçoamento do algoritmo algébrico sequencial para a identificação de variações abruptas de impedância acústica via otimização / Identification of rough impedance profile using an improved acoustic wave propagation algorithmFilipe Otsuka Taminato 21 February 2014 (has links)
Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Neste trabalho são utilizados a técnica baseada na propagação de ondas acústicas e o
método de otimização estocástica Luus-Jaakola (LJ) para solucionar o problema inverso
relacionado à identificação de danos em barras. São apresentados o algoritmo algébrico
sequencial (AAS) e o algoritmo algébrico sequencial aperfeiçoado (AASA) que modelam o
problema direto de propagação de ondas acústicas em uma barra. O AASA consiste nas
modificações introduzidas no AAS. O uso do AASA resolve com vantagens o problema de
identificação de danos com variações abruptas de impedância. Neste trabalho são obtidos,
usando-se o AAS-LJ e o AASA-LJ, os resultados de identificação de cinco cenários de danos.
Três deles com perfil suave de impedância acústica generalizada e os outros dois abruptos.
Além disso, com o objetivo de simular sinais reais de um experimento, foram introduzidos
variados níveis de ruído. Os resultados alcançados mostram que o uso do AASA-LJ na
resolução de problemas de identificação de danos em barras é bastante promissor, superando
o AAS-LJ para perfis abruptos de impedância. / In this work the techniques based on the wave propagation approach and the Luus-
Jaakola optimization method to solve the inverse problem of damage identification in bars are
applied. The sequential algebraic algorithm (SAA) and the improved sequential algebraic
algorithm (ISAA) that model the direct problem of acoustic wave propagation in bars are
presented. The ISAA consists on modifications of the SAA. The use of the ISAA solves with
advantages the problem of damage identification when the generalized acoustical impedance
variations are abrupt. In this work the results of identification of five damage scenarios are
obtained using the SAA and the ISAA. Three of them are smooth impedance profiles and the
other two are rough ones. Moreover, to simulate signals obtained experimentally, different
noise levels were introduced. It is shown that using the ISAA-LJ in solving problems of
damage identification in bars is quite promising, furnishing better results than the SAA-LJ,
specially when the impedance profiles are abrupt.
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Towards quantum optics experiments with single flying electrons in a solid state system / L'expériences d'optique quantique avec un unique électron volant dans la matière condenséeBautze, Tobias 19 December 2014 (has links)
Ce travail de thèse porte sur l’étude fondamentale de systèmes nano-électroniques,mesurés à très basse température. Nous avons réalisé des interféromètres électroniques àdeux chemins à partir d’électrons balistiques obtenus dans un gaz 2D d’électrons d’unehétéro-structure GaAs/AlGaAs. Nous montrons que la phase des électrons, et ainsileur état quantique,peut être contrôlée par des grilles électrostatiques. Ces dispositifsse révèlent être des candidats prometteurs pour la réalisation d’un qubit volant. Nousavons développé une simulation numérique évoluée d’un modèle de liaisons fortes à partirde transport quantique ballistique qui décrit toutes les découvertes expérimentales etnous apporte une connaissance approfondie sur les signatures expérimentales de cesdispositifs particuliers. Nous proposons des mesures complémentaires de ce système dequbit volants. Pour atteindre le but ultime, à savoir un qubit volant à un électron unique,nous avons assemblé la source à électron unique précédemment développée dans notreéquipe à un beam splitter électronique. Les électrons sont alors injectés depuis une boîtequantique à un train de boîte quantiques en mouvement. Ce potentiel électrostatique enmouvement est généré par des ondes acoustiques de surface créées par des transducteursinter-digités sur le substrat GaAs piézo-électrique. Nous avons étudié et optimisé chacunde ces composants fondamentaux nécessaires à la réalisation d’un beam splitter à électronunique et développé un procédé local et fiable de fabrication. Ce dispositif nous permet d’étudier les interactions électroniques pour des électrons isolés et pourra servir de basede mesure pour des expériences d’optique quantiques sur un système électronique del’état condensé. Enfin, nous avons développé un outil puissant de simulation du potentielélectrostatique à partir de la géométrie des grilles. Ceci permet d’optimiser la conceptiondes échantillons avant même leur réalisation. Nous proposons ainsi un prototype optimiséde beam splitter à électron unique. / This thesis contains the fundamental study of nano-electronic systems at cryogenictemperatures. We made use of ballistic electrons in a two-dimensional electron gasin a GaAs/AlGaAs heterostructure to form a real two-path electronic interferometerand showed how the phase of the electrons and hence their quantum state can becontrolled by means of electrostatic gates. The device represents a promising candidateof a flying qubit. We developed a sophisticated numerical tight-binding model based onballistic quantum transport, which reproduces all experimental findings and allows togain profound knowledge about the subtle experimental features of this particular device.We proposed further measurements with this flying qubit system. With the ultimate goalof building a single electron flying qubit, we combined the single electron source that hasbeen developed in our lab prior to this manuscript with an electronic beam splitter. Theelectrons are injected from static quantum dots into a train of moving quantum dots.This moving potential landscape is induced in the piezoelectric substrate of GaAs bysurface acoustic waves from interdigial transducers. We studied and optimized all keycomponents, which are necessary to build a single electron beam splitter and built up areliable local fabrication process. The device is capable of studying electron interactionson the single electron level and can serve as a measurement platform for quantum opticsexperiments in electronic solid state systems. Finally, we developed a powerful toolcapable of calculating the potential landscapes of any surface gate geometry, which canbe used as a fast feedback optimization tool for device design and proposed an optimizedprototype for the single electron beam splitter.
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Aperfeiçoamento do algoritmo algébrico sequencial para a identificação de variações abruptas de impedância acústica via otimização / Identification of rough impedance profile using an improved acoustic wave propagation algorithmFilipe Otsuka Taminato 21 February 2014 (has links)
Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Neste trabalho são utilizados a técnica baseada na propagação de ondas acústicas e o
método de otimização estocástica Luus-Jaakola (LJ) para solucionar o problema inverso
relacionado à identificação de danos em barras. São apresentados o algoritmo algébrico
sequencial (AAS) e o algoritmo algébrico sequencial aperfeiçoado (AASA) que modelam o
problema direto de propagação de ondas acústicas em uma barra. O AASA consiste nas
modificações introduzidas no AAS. O uso do AASA resolve com vantagens o problema de
identificação de danos com variações abruptas de impedância. Neste trabalho são obtidos,
usando-se o AAS-LJ e o AASA-LJ, os resultados de identificação de cinco cenários de danos.
Três deles com perfil suave de impedância acústica generalizada e os outros dois abruptos.
Além disso, com o objetivo de simular sinais reais de um experimento, foram introduzidos
variados níveis de ruído. Os resultados alcançados mostram que o uso do AASA-LJ na
resolução de problemas de identificação de danos em barras é bastante promissor, superando
o AAS-LJ para perfis abruptos de impedância. / In this work the techniques based on the wave propagation approach and the Luus-
Jaakola optimization method to solve the inverse problem of damage identification in bars are
applied. The sequential algebraic algorithm (SAA) and the improved sequential algebraic
algorithm (ISAA) that model the direct problem of acoustic wave propagation in bars are
presented. The ISAA consists on modifications of the SAA. The use of the ISAA solves with
advantages the problem of damage identification when the generalized acoustical impedance
variations are abrupt. In this work the results of identification of five damage scenarios are
obtained using the SAA and the ISAA. Three of them are smooth impedance profiles and the
other two are rough ones. Moreover, to simulate signals obtained experimentally, different
noise levels were introduced. It is shown that using the ISAA-LJ in solving problems of
damage identification in bars is quite promising, furnishing better results than the SAA-LJ,
specially when the impedance profiles are abrupt.
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Système microfluidique à onde élastique de surface : vers la duplication d'ADN par PCR / Microfluidic system using surface acoustic wave : Toward the DNA amplification by PCRRoux-Marchand, Thibaut 02 December 2013 (has links)
Un système microfluidique à onde élastique de surface a été développé dans le but de réaliser une réaction d'amplification de brins d'ADN par PCR. Nous avons principalement étudié la température et l'uniformité de l'échauffement des gouttes irradiées par des ondes de type Rayleigh. Ces dernières sont générées à la surface d'un substrat piézoélectrique de Niobate de Lithium (LiNbO3). Nous avons pensé un système consommant le moins d'énergie électrique possible pour atteindre les températures désirées et permettant une meilleure uniformité de la température des gouttes. Pour cela, un dispositif à transducteur enterré a été réalisé sous une couche isolante de silice. Les gouttes sont ainsi directement posées sur le transducteur ce qui limite les pertes et améliore la répartition de la chaleur au sein des gouttes. Nous avons ensuite vérifié que les réactifs de la PCR ne sont pas affectés par les ondes de Rayleigh ce qui laisse présager que la PCR peut être réalisée à l'aide d'un système d'échauffement par ondes de Rayleigh. Par ailleurs, le déplacement de goutte sur ce type de substrat de LiNbO3 est important pour des applications de type laboratoire sur puce. Ce substrat ayant des propriétés hydrophiles, des revêtements ont été développés afin de minimiser la force nécessaire à l'actionnement des gouttes. Dans ces travaux, nous proposons un nouveau type de couche à base de copolymère P(VDF-TrFe) dont la fabrication est simplement réalisée par dissolution et étalement par spin-coating. Nous avons montré que ce type de couche n'affecte que très peu la propagation des ondes de Rayleigh et les propriétés hydrophobes sont équivalentes à d'autres revêtements / In this work, a microfluidic system based on surface acoustic wave has been developed in order to achieve the amplification of DNA strands by temperature cycling (PCR). We studied mainly the temperature and the heat uniformity of microdroplets irradiated by Rayleigh waves. These waves are generated at the surface of a lithium niobate substrate. We propose a system allowing better temperature uniformity within microdroplets with an optimal energy consumption. For this, a device with buried transducer has been developed under an insulating layer (Silice). The droplets are then placed directly on the transducer which limits losses and improves the distribution of heat within the microdroplets. We then verified that the PCR reagents are not affected by the Rayleigh waves which suggests that PCR can be performed using a heating system by Rayleigh waves. Moreover, the move of microdroplets on this kind of LiNbO3 substrate is important for lab on chip applications. This substrate having hydrophilic properties, some coatings have been developed to minimize the required force to actuate the microdroplets. In this work, we developed a new hydrophobic layer based on copolymer P(VDF-TrFe) whose production is simply made by dissolving and spreading by spin-coating. We have shown that this kind of layer is compatible with Rayleigh waves and that the hydrophobic properties are equivalent to other coatings
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Device Applications of Epitaxial III-Nitride SemiconductorsShetty, Arjun January 2015 (has links) (PDF)
Through the history of mankind, novel materials have played a key role in techno- logical progress. As we approach the limits of scaling it becomes difficult to squeeze out any more extensions to Moore’s law by just reducing device feature sizes. It is important to look for an alternate semiconductor to silicon in order to continue making the progress predicted by Moore’s law. Among the various semiconductor options being explored world-wide, the III-nitride semiconductor material system has certain unique characteristics that make it one of the leading contenders. We explore the III-nitride semiconductor material system for the unique advantages that it offers over the other alternatives available to us.
This thesis studies the device applications of epitaxial III-nitride films and nanos- tructures grown using plasma assisted molecular beam epitaxy (PAMBE)
The material characterisation of the PAMBE grown epitaxial III-nitrides was car- ried out using techniques like high resolution X-ray diffraction (HR-XRD), field emis- sion scanning electron microscopy (FESEM), room temperature photoluminescence (PL) and transmission electron microscopy (TEM). The epitaxial III-nitrides were then further processed to fabricate devices like Schottky diodes, photodetectors and surface acoustic wave (SAW) devices. The electrical charcterisation of the fabricated devices was carried out using techniques like Hall measurement, IV and CV measure- ments on a DC probe station and S-parameter measurements on a vector network analyser connected to an RF probe station.
We begin our work on Schottky diodes by explaining the motivation for adding an interfacial layer in a metal-semiconductor Schottky contact and how high-k di- electrics like HfO2 have been relatively unexplored in this application. We report the work carried out on the Pt/n-GaN metal-semiconductor (MS) Schottky and the Pt/HfO2/n-GaN metal-insulator-semiconductor (MIS) Schottky diode. We report an improvement in the diode parameters like barrier height (0.52 eV to 0.63 eV), ideality factor (2.1 to 1.3) and rectification ratio (35.9 to 98.9 @2V bias) after the introduction of 5 nm of HfO2 as the interfacial layer. Temperature dependent I-V measurements were done to gain a further understanding of the interface. We observe that the barrier height and ideality factor exhibit a temperature dependence. This was attributed to inhomogeneities at the interface and by assuming a Gaussian distribution of barrier heights.
UV and IR photodetectors using III-nitrides are then studied. Our work on UV photodetectors describes the growth of epitaxial GaN films. Au nanoparticles were fabricated on these films using thermal evaporation and annealing. Al nanostruc- tures were fabricated using nanosphere lithography. Plasmonic enhancement using these metallic nanostructures was explored by fabricating metal-semiconductor-metal (MSM) photodetectors. We observed plasmonic enhancement of photocurrent in both cases. To obtain greater improvement, we etched down on the GaN film using reac tive ion etching (RIE). This resulted in further increase in photocurrent along with a reduction in dark current which was attributed to creation of new trap states. IR photodetectors studied in this thesis are InN quantum dots whose density can be controlled by varying the indium flux during growth. We observe that increase in InN quantum dot density results in increase in photocurrent and decrease in dark current in the fabricated IR photodetectors.
We then explore the advantages that InGaN offers as a material that supports surface acoustic waves and fabricate InGaN based surface acoustic wave devices. We describe the growth of epitaxial In0.23 Ga0.77 N films on GaN template using molecular beam epitaxy. Material characterisation was carried out using HR-XRD, FESEM, PL and TEM. The composition was determined from HR-XRD and PL measurements and both results matched each other. This was followed by the fabrication of interdigited electrodes with finger spacing of 10 µm. S-parameter results showed a transmission
peak at 104 MHz with an insertion loss of 19 dB. To the best of our knowledge, this is the first demonstration of an InGaN based SAW device.
In summary, this thesis demonstrates the practical advantages of epitaxially grown film and nanostructured III-nitride materials such as GaN, InN and InGaN using plasma assisted molecular beam epitaxy for Schottky diodes, UV and IR photodetec- tors and surface acoustic wave devices.
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Propagation d'ondes acoustiques dans une suspension de grains mobiles immergés : couplage de modèles discret et continu par la méthode des domaines fictifs / Acoustic wave propagation through a suspension of submerged movable grains : coupling discrete and continuous models using the fictitious domain methodImbert, David 29 November 2013 (has links)
Lorsqu'une onde acoustique se propage dans un milieu granulaire, elle est susceptible de provoquer la mobilité des grains, aussi infime soit-elle. Inversement, la mobilité d'un grain dans une matrice fluide peut induire un champ acoustique et dans les deux cas, l'énergie acoustique peut être transférée à la fois au travers des pores et des contacts entre grains. Nous avons mis au point un modèle original permettant de considérer ces deux modes de transfert d'énergie pour simuler la propagation d'ondes acoustiques dans les milieux granulaires immergés. Dans le cas des milieux granulaires secs, l'inertie du fluide est telle que l'énergie transférée dans l'air peut être négligée et le milieu modélisé avec des algorithmes de type "dynamique moléculaire". Au contraire, dans le cas de milieux immergés, l'énergie portée par le fluide ne peut pas être négligée et nous montrons que la méthode des domaines fictifs basée sur les multiplicateurs de Lagrange distribués permet de coupler les équations de la dynamique et l'équation d'onde. Nous utilisons la méthode des éléments finis pour propager l'onde dans le fluide, les grains étant modélisés en 2D par des sphères rigides et incompressibles afin de satisfaire les hypothèses de l'algorithme de dynamique moléculaire. Les résultats du modèle sur des expériences numériques simples mais pour lesquelles existent des solutions analytiques de l'acoustique mettent en évidence la validité du nouveau modèle. Nous en donnons une illustration pour l'étude des interactions subies par un empilement réaliste de multiples grains mobiles soumis à un signal acoustique. / When an acoustic wave propagates through a granular medium, it causes the grains to move, usually very slightly. In the same way, the movement of a grain embedded in a fluid matrix generates an acoustic wave. In both cases, acoustic energy is transmitted by the fluid and by the inter-granular contacts. We have developed a new numerical model for simulating wave propagation in submerged granular media that takes into account these two modes of energy transport. For the case of dry granular media, the grains are embedded in air whose inertia is so low that the energy it carries can be neglected. These media can be modeled with "Molecular Dynamics" or related methods. On the contrary, when granular media are submerged in water, the energy carried by the fluid cannot be neglected, rendering their modelization much more difficult. We use the fictitious domain method with distributed Lagrange multipliers to couple the equation of motion of the grains to the wave equation of the fluid. We use finite elements to propagate the wave in the fluid, and the grains are modeled in 2D by rigid, incompressible spheres compatible with the hypotheses of Molecular Dynamics. To validate the model, we perform series of numerical experiments whose results are compared to analytic solutions from acoustics. We also perform a simulation with hundreds of grains under an incident wave to demonstrate the possibilities of the model.
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La fissuration thermique dans les roches / Thermal microcracking in rockGriffiths, Luke 23 February 2018 (has links)
Lorsqu'elle est chauffée, la roche peut subir une microfissuration thermique, qui influence ses propriétés physiques, mécaniques, thermiques, et de transport. La surveillance de la microfissuration thermique en laboratoire a été principalement réalisée pendant le chauffage, et rarement lors du refroidissement ou du chauffage cyclique que la roche subit dans les volcans et les réservoirs géothermiques. Un nouvel appareil a été élaboré pour surveiller les émissions acoustiques et mesurer les vitesses des ondes élastiques à haute température. L'état de fissuration a été évalué grâce à un nouvel algorithme d'analyse microstructurale, et l'influence des microfissures sur les propriétés des roches a été mesurée et modélisée. Selon la microstructure, la microfissuration peut avoir lieu pendant le chauffage ou le refroidissement, et les microfissures existantes peuvent s’ouvrir et se fermer de façon réversible avec des changements de température, et influencer les propriétés de la roche. / Rock may undergo thermal microcracking when heated, affecting its physical, mechanical, thermal, and transport properties. Thermal microcrack monitoring in the laboratory has mainly been performed during heating, and rarely during the cyclic heating and cooling relevant for volcanoes and geothermal reservoirs. For this, a new dedicated apparatus for the acoustic emission monitoring and wave velocity measurement at high temperatures was elaborated, building on previous designs. Microcrack damage was assessed with a new algorithm for quantitative microstructural analysis, and the influence of thermal microcracks on rock properties was measured and modelled. Depending on the rock type and initial microcrack content, microcracking occurred during either heating, cooling, or neither, and existing microcracks reversibly opened or closed with increasing temperature. In Earth's crust, the evolution of rock properties with temperature may be significant and is determined by the microstructure.
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