Multiphase flows are ubiquitous across engineering disciplines: water-sediment river flows in civil engineering, oil-water-sand transportation flows in petroleum engineering; and sorbent-flue gas reactor flows in chemical engineering. These multiphase flows can include a combination of momentum, heat, and mass transfer. Studying and understanding the behavior of multiphase, multiphysics flow configurations can be crucial for safe and efficient engineering design. In this work, a framework for the development and validation, verification and uncertainty quantification (VVUQ) of subgrid models for heat transfer in multiphase flows is presented. The framework is developed for a carbon capture reactor; however, the concepts and methods described in this dissertation can be generalized and applied broadly to multiphase/multiphysics problems. When combined with VVUQ methods, these tools can provide accurate results at many length scales, enabling large upscaling problems to be simulated accurately and with calculable errors. The system of interest is a post-combustion solid-sorbent carbon capture reactor featuring a solid-sorbent bed that is fluidized with post-combustion flue gas. As the flue gas passes through the bed, the carbon dioxide is exothermically adsorbed onto the sorbent particle’s surface, and the clean gas is passed onto further processes. To prevent overheating and degradation of the sorbent material, cooling cylinders are immersed in the flow to regulate temperatures. Simulating a full-scale, gas-particle reactor using traditional methods is computationally intractable due to the long time scale and variations in length scales: reactor, O(10 m); cylinders, O(1 cm); and sorbent particles, O(100 um). This research developed an efficient subgrid method for simulating such a system. A constitutive model was derived to predict the effective suspension-cylinder Nusselt number based on the local flow and material properties and the cylinder geometry, analogous to single-phase Nusselt number correlations. This model was implemented in an open source computational fluid dynamics code, MFIX, and has undergone VVUQ. Verification and validation showed great agreement with comparable highly-resolved simulations, achieving speedups of up to 10,000 times faster. Our model is currently being used to simulate a 1 MW, solid-sorbent carbon capture unit and is outperforming previous methods in both speed and physically accuracy. / 2017-06-21T00:00:00Z

Cette thèse explore les dernières évolutions du débruitage d'images, et elle essaie de développer une vision synthétique des techniques utilisées jusqu'à présent. Elle aboutit à un nouvel algorithme de débruitage d'image évitant les artefacts et avec un meilleur PSNR que tous les algorithmes que nous avons pu évaluer. La première méthode que nous présentons est DA3D, un algorithme de débruitage fréquentiel avec guide, inspiré de DDID. La surprise de cet algorithme, c'est que le débruitage fréquentiel peut battre l'état de l'art sans produire artefacts. Cet algorithme produit des bons résultats non seulement en PSNR, mais aussi (et surtout) en qualité visuelle. DA3D marche particulièrement bien pour améliorer les textures des images et pour enlever les effets de staircasing.DA3D, guidé par un autre algorithme de débruitage améliore presque toujours le résultat de son guide. L'amélioration est particulièrement nette quand le guide est un algorithme à patchs, et alors on combine deux principes différents: auto-similarité suivi de seuillage fréquentiel. Le deuxième résultat présenté est une méthode universelle de débruitage multi-échelle, applicable à tout algorithme. Une analyse qualitative montre en effet que les algorithmes de débruitage à patchs éliminent surtout les hautes fréquences du bruit, à cause de la taille limitée des voisinages traités. Plutôt que d'agrandir ces voisinages nous décomposons l'image en une pyramide basée sur la transformée en cosinus discrète, avec une méthode de recomposition évitant le ringing. Cette méthode traite le bruit à basse fréquence, et améliore la qualité de l'image. Le troisième problème sérieux que nous abordons est l'évaluation des algorithmes de débruitage. Il est bien connu que le PSNR n'est pas un indice suffisant de qualité. Un artefact sur une zone lisse de l'image est bien plus visible qu'une altération en zone texturée. Nous proposons une nouvelle métrique basée sur un Smooth PSNR et un Texture PSNR, pour mesurer les résultats d'un algorithme sur ces deux types des régions. Il apparaît qu'un algorithme de débruitage, pour être considéré acceptable, doit avoir des bons résultats pour les deux métriques. Ces métriques sont finalement utilisées pour comparer les algorithmes de l'état de l'art avec notre algorithme final, qui combine les bénéfices du multi-échelle et du filtrage fréquentiel guidé. Les résultats étant très positifs, nous espérons que la thèse contribue à résoudre un vieux dilemme, pour lequel la méthode DDID avait apporté de précieuses indications : comment choisir entre le seuillage fréquentiel et les méthodes basées sur l'auto-similarité pour le débruitage d'images ? La réponse est qu'il ne faut pas choisir. Cette thèse termine avec quelques perspectives sur la faisabilité du débruitage "externe". Son principe est de débruiter un patch en utilisant une grande base de données externe de patches sans bruit. Un principe bayésien démontré par Levin et Nadler en 2011 implique que le meilleur résultat possible serait atteint avec cette méthode, à condition d'utiliser tous les patches observables. Nous donnons les arguments mathématiques prouvant que l'espace des patches peut être factorisé, ce qui permet de réduire la base de données de patches utilisés d'un facteur au moins 1000. / This thesis explores the last evolutions on image denoising, and attempts to set a new and more coherent background regarding the different techniques involved. In consequence, it also presents a new image denoising algorithm with minimal artifacts and the best PSNR performance known so far.A first result that is presented is DA3D, a frequency-based guided denoising algorithm inspired form DDID [Knaus-Zwicker 2013]. This demonstrates that, contrarily to what was thought, frequency-based denoising can beat state-of-the-art algorithms without presenting artifacts. This algorithm achieves good results not only in terms of PSNR, but also (and especially) with respect to visual quality. DA3D works particularly well on enhancing the textures of the images and removing staircasing effects.DA3D works on top of another denoising algorithm, that is used as a guide, and almost always improve its results. In this way, frequency-based denoising can be applied on top of patch-based denoising algorithms, resulting on a hybrid method that keeps the strengths of both. The second result presented is Multi-Scale Denoising, a framework that allows to apply any denoising algorithm on a multi-scale fashion. A qualitative analysis shows that current denoising algorithms behave better on high-frequency noise. This is due to the relatively small size of patches and search windows currently used. Instead of enlarging those patches, that can cause other sorts of problems, the work proposes to decompose the image on a pyramid, with the aid of the Discrete Cosine Transformation. A quantitative study is performed to recompose this pyramid in order to avoid the appearance of ringing artifacts. This method removes most of the low-frequency noise, and improves both PSNR and visual results for smooth and textured areas.A third main issue addressed in this thesis is the evaluation of denoising algorithms. Experiences indicate that PSNR is not always a good indicator of visual quality for denoising algorithms, since, for example, an artifact on a smooth area can be more noticeable than a subtle change in a texture. A new metric is proposed to improve on this matter. Instead of a single value, a ``Smooth PNSR'' and a ``Texture PSNR'' are presented, to measure the result of an algorithm for those two types of image regions. We claim that a denoising algorithm, in order to be considered acceptable, must at least perform well with respect to both metrics. Following this claim, an analysis of current algorithms is performed, and it is compared with the combined results of the Multi-Scale Framework and DA3D.We found that the optimal solution for image denoising is the application of a frequency shrinkage, applied to regular regions only, while a multiscale patch based method serves as guide. This seems to resolve a long standing question for which DDID gave the first clue: what is the respective role of frequency shrinkage and self-similarity based methods for image denoising? We describe an image denoising algorithm that seems to perform better in quality and PSNR than any other based on the right combination of both denoising principles. In addition, a study on the feasibility of external denoising is carried, where images are denoised by means of a big database of external noiseless patches. This follows a work of Levin and Nadler, in 2011, that claims that state-of-the-art results are achieved with this method if a large enough database is used. In the thesis it is shown that, with some observation, the space of all patches can be factorized, thereby reducing the number of patches needed in order to achieve this result. Finally, secondary results are presented. A brief study of how to apply denoising algorithms on real RAW images is performed. An improved, better performing version of the Non-Local Bayes algorithm is presented, together with a two-step version of DCT Denoising. The latter is interesting for its extreme simplicity and for its speed.

Indiana University-Purdue University Indianapolis (IUPUI) / Glaucoma is a multifactorial ocular disease progressively leading to irreversible blindness. There is clear evidence of correlations between alterations in ocular hemodynamics and glaucoma; however, the mechanisms giving rise to these correlations are still elusive. The objective of this thesis is to develop mathematical models and methods to help elucidate these mechanisms. First, we develop a mathematical model that describes the deformation of ocular structures and ocular blood flow using a reduced-order fluid-structure interaction model. This model is used to investigate the relevance of mechanical and vascular factors in glaucoma. As a first step in expanding this model to higher dimensions, we propose a novel energy-based technique for coupling partial and ordinary differential equations in blood flow, using operator splitting. Next, we combine clinical data and model predictions to propose possible explanations for the increase in venous oxygen saturation in advanced glaucoma patients. We develop a computer-aided manipulation process of color Doppler images to extract novel waveform parameters to distinguish between healthy and glaucomatous individuals. The results obtained in this work suggest that: 1) the increase in resistance of the retinal microcirculation contributes to the influence of intraocular pressure on retinal hemodynamics; 2) the influence of cerebrospinal fluid pressure on retinal hemodynamics is mediated by associated changes in blood pressure; 3) the increase in venous oxygen saturation levels observed among advanced glaucoma patients depends on the value of the patients’ intraocular pressure; 4) the normalized distance between the ascending and descending limb of the ophthalmic artery velocity profile is significantly higher in glaucoma patients than in healthy individuals.

Indiana University-Purdue University Indianapolis (IUPUI) / Glaucoma is a multi-factorial ocular disease associated with death of retinal ganglion cells and irreversible vision loss. Many risk factors contribute to glaucomatous damage, including elevated intraocular pressure (IOP), age, genetics, and other diseases such as diabetes and systemic hypertension. Interestingly, alterations in retinal hemodynamics have also been associated with glaucoma. A better understanding of the factors that contribute to these hemodynamic alterations could lead to improved and more appropriate clinical approaches to manage and hopefully treat glaucoma patients. In this thesis, we develop several mathematical models aimed at describing ocular hemodynamics and oxygenation in health and disease. Precisely we describe: (i) a time-dependent mathematical model for the retinal circulation that includes macrocirculation, microcirculation, phenomenological vascular regulation, and the mechanical effect of IOP on the retinal vasculature; (ii) a steady-state mathematical model for the retinal circulation that includes macrocirculation, microcirculation, mechanistic vascular regulation, the effect of IOP on the central retinal artery and central retinal vein, and the transport of oxygen in the retinal tissue using a Krogh cylinder type model; (iii) a steady-state mathematical model for the transport of oxygen in the retinal microcirculation and tissue based on a realistic retinal anatomy; and (iv) a steady-state mathematical model for the production and drainage of aqueous humor (AH). The main objective of this work is to study the relationship between IOP, systemic blood pressure, and the functionality of vascular autoregulation; the transport and exchange of oxygen in the retinal vasculature and tissue; and the production and drainage of AH, that contributes to the level of IOP. The models developed in this thesis predict that (i) the autoregulation plateau occurs for different values of IOP in hypertensive and normotensive patients. Thus, the level of blood pressure and functionality of autoregulation affect the changes in retinal hemodynamics caused by IOP and might explain the inconsistent outcomes of clinical studies; (ii) the metabolic and carbon dioxide mechanisms play a major role in the vascular regulation of the retina. Thus, the impairment of either of these mechanisms could cause ischemic damage to the retinal tissue; (iii) the multi-layer description of transport of oxygen in the retinal tissue accounts for the effect of the inner and outer retina, thereby improving the predictive ability of the model; (iv) a greater reduction in IOP is obtained if topical medications target AH production rather that AH drainage and if IOP-lowering medications are administrated to patients that exhibit a high initial level of IOP. Thus, the effectiveness of IOP-lowering medications depend on a patient’s value of IOP. In conclusion, the results of this thesis demonstrate that the insight provided by mathematical modeling alongside clinical studies can improve the understanding of diseases and potentially contribute to the clinical development of new treatments.

This thesis study two promising methods used to define the multiscale CAPM - the wavelet-based decomposition and the fractal regression. Their estimates, obtained on monthly excess return on ten portfolios formed on beta in the US market, are compared in the period from November 2000 to October 2020 and, subsequently, in the period from November 1965 to October 2020. In the first period, the multiscale beta is not significantly different from the original single-scale beta for most of the portfolios. Contrary, both methods uncover significant multiscale behavior of the beta in the second period. Specifically, the high-beta portfolios have higher multiscale beta at longer investment horizons, mainly at wavelet scale 3 and scales 12-24 of the fractal regression. Overall, both methods deliver consistent results, and seem suitable for extending the CAPM with an investment horizon. JEL Classification Keywords G12, C20 CAPM, asset pricing, multiscale analysis, wavelets, fractal regression Title Investment horizon in the CAPM: A comparison of a wavelet-based decomposition and the fractal regression

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20374号 / 工博第4311号 / 新制||工||1668(附属図書館) / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 山川 宏, 教授 松尾 哲司 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21757号 / 工博第4574号 / 新制||工||1713(附属図書館) / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 西脇 眞二, 教授 髙田 滋, 教授 鈴木 基史 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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This study focuses on molecular dynamics (MD) simulations, coupled with a discrete mathematical framework, and crystal plasticity (CP) simulations to investigate micro void nucleation and the plastic spin. The origin and historical use of the plastic spin are discussed with particular attention to quantifying the plastic spin at the atomistic scale. Two types of MD simulations are employed: (a) aluminum single crystals undergoing simple shear and (b) aluminum triple junctions (TJ) with varying grain orientations and textures undergoing uniaxial tension. The high-angle grain boundary simulations nucleate micro voids at or around the TJ and the determinant of the deformation gradient shows the ability to predict such events. Crystal plasticity simulations are used to explore the stress-state of the aluminum TJ from uniaxial tension at a higher length scale with results indicating a direct correlation between CP stress-states and the location of micro void nucleation in the MD simulations.

When an anode electrode potential is larger than the lowest unoccupied molecular orbital (LUMO) of the electrolyte, Li-ions and electrolyte molecules will participate in reduction reactions on the anode surface and form a solid electrolyte interface (SEI) layer. Active Li-ion consumption in the formation reactions is the main source of capacity loss (>50) and ageing in Li-ion batteries (LIBs). Due to the fast-occurring and complex nature of the electrochemical processes, conventional experimental techniques are not a feasible approach for capturing and characterizing the SEI formation phenomenon. The lack of experimental data and consequently the absence of potential parameters for crystal structures in this layer makes molecular dynamics~(MD) simulations inapplicable to it. Also, due to the multi-component multi-layer structure of the SEI, the smallest system representing an SEI layer is too large for employing the principles of quantum mechanics~(QM), that traditionally work with much smaller system sizes. Addressing this, this thesis presents a novel computational framework for coupling QM and MD calculations to simulate a system with the size limits of MD simulations independent of the experimental data. The QM evaluates sub-atomic properties such as energy barriers against diffusion and employs seven new algorithms to estimate potential parameters as the input of the MD simulations. Then MD simulations forecast SEI's properties including density, Young's Modules, Poisson's Ratio, thermal conductivity, and diffusion coefficient mechanisms. The output of the QM and MD calculations are employed to develop two macro-scale mathematical models for predicting battery ageing and battery performance, incorporating the impact of the SEI layer in addition to the cathode, anode, and separator parts. Finally, the results obtained have been validated with respect to the experimental data in different operational conditions. / Thesis / Doctor of Philosophy (PhD) / The limited lifespan of expensive batteries is the main obstacle to electrification of the transport sector, despite its necessity for addressing the current environmental issues. Li+/electrolyte reduction on the electrode surface is responsible for more than 50% of capacity loss and the consequent ageing is a complex and fast-occurring phenomenon (few ns) that cannot be easily resolved using conventional experimental and computational techniques. This thesis presents the development of some computational frameworks and demonstrates their employment to investigate this phenomenon from a multi-scale perspective, i.e., from a few electrons to an entire battery length scale, with the operating cycles ranging from a few ps to several months, employing Quantum Mechanics, Molecular Dynamics, and Macro-Scale Modeling. The frameworks have been successfully validated with respect to experimental data from the literature and have been applied successfully to highlight the parameters that impact ageing in batteries. The findings presented in this thesis can be used as the base for further research on next-gen durable batteries with liquid and solid-state electrolytes.