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Despite significant development over the last decades, a model able to describe the periphery region of magnetic confinement fusion devices, extending from the edge to the far scrape-off layer, is still missing. This is because this region is characterized by the presence of turbulent fluctuations at scales ranging from the Larmor radius to the size of the machine, the presence of strong flows, comparable amplitudes of background and fluctuating components, and a large range of collisionality regimes. The lack of a proper model has undermined our ability to properly simulate the plasma dynamics in this region, which is necessary to predict the heat flux to the vessel wall of future fusion devices, the L-H transition, and ELM dynamics. These are some of the most important issues on the way to a fusion reactor. In the present thesis, a drift-kinetic and a gyrokinetic model able to describe the plasma dynamics in the tokamak periphery are developed, which take into account electrostatic fluctuations at all relevant scales, allowing for comparable amplitudes of background and fluctuating components. In addition, the models implement a full Coulomb collision operator, and are therefore valid at arbitrary collisionality regimes. For an efficient numerical implementation of the models, the resulting kinetic equations are projected onto a Hermite-Laguerre velocity-space polynomial basis, obtaining a moment-hierarchy. The treatment of arbitrary collisionalities is performed by expressing the full Coulomb collision operator in guiding-center and gyrocentre coordinates, and by providing a closed formula for its gyroaverage in terms of the moments of the plasma distribution function, therefore filling a long standing gap in the literature. The use of systematic closures to truncate the moment-hierarchy equation, such as the semi-collisional closure, allows for the straightforward adjustment of the kinetic physics content of the model. In the electrostatic high collisionality regime, our models are therefore reduced to an improved set of drift-reduced Braginskii equations, which are widely used in scrape-off layer simulations. The first numerical studies based on our models are carried out, shedding light on the interplay between collisional, using the Coulomb collision operator, and collisionless mechanisms. In particular, the dynamics of electron-plasma waves and the drift-wave instability are studied at arbitrary collisionality. A comparison is made with the collisionless limit and simplified collision operators used in state-of-the-art simulation codes, where large deviations in the growth rates and eigenmode spectra are found, especially at the levels of collisionality relevant for present and future magnetic confinement fusion devices.
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To reduce the impact of the embodied energy and of the carbon dioxide emissions of concrete, the use of supplementary cementitious materials (SCMs) in the cement industry has become a common practice. However, the practical experience on such cements is limited due to the lower strength at early ages and the concern about long term performance, especially potentially higher carbonation rates due to a lower capacity to bind CO2. To increase the protection of the steel in the concrete where carbonation might be a risk, the full understanding of the microstructure changes due to carbonation is necessary. The main goal of this thesis is to characterise and to quantify the correlation between transport properties and modification of the microstructure in the carbonated concrete. We propose a new approach to obtain a representative specimen of âfully carbonatedâ material in relatively short time. The innovative idea of using a thin cement paste sample allowed the characterization of the gas diffusion properties in naturally carbonated cement paste. This, together with the measured changes in phase assemblage and pore structure, can be used to better understand the reactive transport model. The adaptation to natural exposure conditions ensures obtaining representative results. Investigating the governing parameters of carbonation and emphasizing the influence of the non-carbonated reference advanced the understanding of the carbonation mechanism, especially in the low carbon binders. This study sheds a new light at the problem of overestimating the effect of carbonation on the microstructure of the cementitious material. In particular, it shows the importance of subtracting the effect of the drying taking place during carbonation, to diminish the risk of attributing the changes in porosity only to carbonation. The monitoring of the changes in the phase assemblage and the assessment of the carbonation coefficient during exposure to carbonation showed a promising performance of the new ternary blend with 50 % clinker replacement by burnt oil shale, slag, and limestone. The obtained results on characterisation of the carbonating binders can be used to improve carbonation models, that are essential to predict the resistance of new types of cements. That could help to assess the balance between the benefits of using alternative materials, and the potential danger of low resistance against carbonation. The profit will be to make cement and concrete even more sustainable and a more environmentally friendly construction material.
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Adaptive isogeometric methods for the solution of partial diifferential equations rely on the construction of locally refinable spline spaces. A simple and efficient way to obtain these spaces is to apply the multi-level construction of hierarchical splines, that can be used on single-patch domains or in multi-patch domains with $C^0$ continuity across the patch interfaces. Due to the benefits of higher continuity in isogeometric methods, recent works investigated the construction of spline spaces with global $C^1$ continuity on two or more patches. In this paper, we show how these approaches can be combined with the hierarchical construction to obtain global $C^1$ continuous hierarchical splines on two-patch domains. A selection of numerical examples is presented to highlight the features and effectivity of the construction.
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Dislocation emission from a crack tip is a necessary mechanism for crack tip blunting and toughening. A material is intrinsically ductile under Mode I loading when the critical stress intensity $K_{Ie}$ for dislocation emission is lower than the critical stress intensity $K_{Ic}$ for cleavage. In intrinsically ductile fcc metals, a first partial dislocation is emitted, followed either by a trailing partial dislocation (''ductile'' behavior) or a twinning partial dislocation (''quasi-brittle''). $K_{Ie}^{first}$ for the first partial emission is usually evaluated using the approximate Rice theory, which predicts a dependence on the elastic constants and the unstable stacking fault energy $\gamma_{usf}$. Here, atomistic simulations across a wide range of fcc metals show that $K_{Ie}^{first}$ is systematically larger (10-30%) than predicted. However, the critical crack-tip shear displacement is up to 40% smaller than predicted. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. A new theory for Mode I emission is presented based on the ideas that (i) the stress resisting step formation at the crack tip creates ''lattice trapping'' against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. The new theory naturally includes the energy to form the step, and reduces to the Rice theory (no trapping) when the step energy is small. The new theory predicts a higher $K_{Ie}^{first}$ at a smaller critical shear displacement, rationalizing deviations of simulations from the Rice theory. The twinning tendency is estimated using the Tadmor and Hai extension of the Rice theory. Atomistic simulations reveal that the predictions of the critical stress intensity factor $K_{Ie}^{twin}$ for crack tip twinning are also systematically lower (20-35%) than observed. Energy change during nucleation reveal that twining partial emission is not accompanied by creation of a surface step while emission of the trailing partial creates a step. The absence of the step during twinning motivates a model for twinning nucleation that accounts for the fact that nucleation does not occur directly at the crack tip. New predictions are in excellent agreement with all simulations that show twinning. A second mode of twinning is found wherein the crack first advances by cleavage and then emits the twinning partial at the new crack tip. The stacking fault stress dependence is analyzed through (i) the generalized stacking fault potential energy (GSFE) and (ii) the generalized stacking fault enthalpy (GSFH). At an imposed shear displacement, there is also an associated inelastic normal displacement $\Delta_{n}$ around the fault. Atomistic simulations with interatomic potentials and/or first principle calculations reveal that GSFE and $\Delta_n$ both increase with tensile stress. An increasing GSFE contradicts long-standing wisdom and previous studies. Positive $\Delta_{n}$ coupled to the applied normal stress decreases the GSFH, but GSFH is not useful for general mechanics problems. ''Opening softening'' effects are not universal, and so the analysis of any particular nanomechanics problem requires precise implementation of the combination of GSFE and $\Delta_{n}$ rather than the GSFH.
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The higher-order singular values for a tensor of order d are defined as the singular values of the d different matricizations associated with the multilinear rank. When d≥3, the singular values are generally different for different matricizations but not completely independent. Characterizing the set of feasible singular values turns out to be difficult. In this work, we contribute to this question by investigating which first-order perturbations of the singular values for a given tensor are possible. We prove that, except for trivial restrictions, any perturbation of the singular values can be achieved for almost every tensor with identical mode sizes.This settles a conjecture from [Hackbusch and Uschmajew, 2016] for the case of identical mode sizes. Our theoretical results are used to develop and analyze a variant of the Newton method for constructing a tensor with specified higher-order singular values or, more generally, with specified Gramians for the matricizations. We establish local quadratic convergence and demonstrate the robust convergence behavior with numerical experiments.
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Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging and ultrafast contrast imaging. On the other hand, the mass adoption of mobile commodity devices pushes towards portable US imaging. These new paradigms require to rethink the imaging pipeline and come with a myriad of new challenges in terms of data rate, power considerations as well as software and hardware design. In this thesis, we explore several inverse problems related to these challenges, with an emphasis on data-rate reduction for imaging and localization. We follow the view of considering pulse-echo US imaging as a tomographic image reconstruction problem where sensor measurements can be seen as projections onto quadric surfaces. By appropriate parameterization of these surfaces, we devise efficient formulations of the measurement model associated with the image reconstruction problem and pave the way to large scale regularized US imaging. We introduce USSR, an UltraSound Sparse Regularization framework, which exploits the measurement model in the context of convex optimization algorithms. We describe three applications, namely sparsely regularized beamforming where high-quality images are obtained with few insonifications, compressed beamforming which aims to decrease the amount of data collected per insonification, and image restoration which exploits a model of non-stationary blur to enhance already reconstructed images. We suggest a compressive multiplexing approach for US signals. Such a technique achieves high-quality imaging with significantly fewer coaxial cables connecting the probe to the imaging system than existing methods. The compression is based on the compressive multiplexer, an analog compressed-sensing architecture, and the reconstruction relies on convex optimization algorithms. We propose two methods which exploit different low-dimensional models of US signals, namely the bandpass signal model and the pulse-stream model. We tackle the problem of localizing strong reflectors, with potential application in non-destructive evaluation and contrast-enhanced US imaging. We suggest a threefold approach composed of a time-of-flight (TOF)-sensing step, a TOF-labeling step and a localization step, which is capable of recovering the locations of strong reflectors with significantly fewer transducer elements and less sensor measurements than existing techniques. By exploring innovative methods for imaging and localization, this work contributes to a next generation of US imaging devices which will benefit from ultrafast US imaging to integrate advanced imaging modes into more and more compact systems.
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