In Analysis and Numerik differential-algebraischer Gleichungen P. Kunkel and V. Mehrmann give a survey of relevant conditions for consistent systems, for existence and uniqueness of solutions, and touch numerical procedures for obtaining the solutions.

Most ab initio simulation packages based on Density Functional Theory (DFT) use the Superposition of Atomic Densities (SAD) as a starting point of the self-consistent fi eld (SCF) iteration. However, this trial charge density without modeling atomic iterations nonlinearly may lead to a relatively slow or even failed convergence. This thesis proposes a machine learning-based scheme to improve the initial guess. We train a 3-Dimensional Convolutional Neural Network (3D CNN) to map the SAD initial guess to the corresponding converged charge density with simple structures. We show that the 3D CNN-processed charge density reduces the number of required SCF iterations at different unit cell complexity levels.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19522号 / 理博第4182号 / 新制||理||1600(附属図書館) / 32558 / 京都大学大学院理学研究科化学専攻 / (主査)教授 吉村 一良, 教授 有賀 哲也, 教授 北川 宏 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

We aim to investigate the stability of various stock-flow consistent economic models, and the potential causes for economic collapse therein. Through parameter sensitivity analysis, we study models that feature a public sector, an active central bank, and a household sector with independent consumption. Our final, most comprehensive economic system combines all of the intricacies of each model, prominently featuring a demand-driven economy that is stabilized by an expansionary monetary policy. In addition, we incorporate a climate module for each economic system, and analyze public sector intervention through carbon taxes and abatement subsidies. We find that the most common feature of economic instability is a lack of demand, driven by decreases in capital investment from firms, as well as a decline in household consumption. In order to maintain a stable growth path and prevent a permanent economic contraction, we propose the implementations of an expansionary monetary policy, increased public sector subsidies of abatement costs, and stricter carbon taxes. / Thesis / Master of Science (MSc)

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Titanium is a widely applied material in industries and characterized by highly anisotropic mechanical behaviour. To study the special property of titanium, many kinds of mechanical loading tests have been conducted. Moreover, researchers attempted to reproduce these experiments with numerical methods. This paper will present an overview about the deformation mechanisms and related representative studies of titanium. Among the numerical methods, Taylor type and self-consistent crystal plasticity models are two of the most common ones seen in literature. Simulation of some mechanical loading tests using visco-plastic self-consistent model was carried out and compared with the results given by Taylor type model. It has been found that self-consistent model prevails in the reproduction of stress-strain response and texture evolution. During the calculation of self-consistent model, there are totally 4 kinds of self-consistent schemes available for linearization process. The author investigated 4 groups of simulation works using different self-consistent schemes. But no evident distinction has been observed. The application of visco-plastic self-consistent model in commercial purity titanium is studied at the end. The simulation results successfully captured the general features of 9 mechanical loading tests. / Thesis / Master of Applied Science (MASc)

The development of the semi-empirical atomistic potential called the embedded atom method (EAM) has allowed for the efficient modeling of solid-state environments, at a lower computational cost than afforded by density functional theory (DFT). This offers the capability of EAM to model the energetics of solid-state phases of varying coordination, including defects, such as vacancies and self-interstitials. This dissertation highlights the development and application of two EAMs: a Ti potential constructed with the multi-state modified embedded atom method (MS-MEAM), and a Ni potential constructed with the fragment Hamiltonian (FH) method. Both potentials exhibit flexibility in the description of different solid-states phases and applications. This dissertation also outlines two applications of DFT. First, a study of structure and stability for solid-state forms of NixCy (in which x and y are integers) is investigated using plane-wave DFT. A ground state phase for Ni2C is elucidated and compared to known and hypothesized forms of NixCy. Also, a set of correlation consistent basis sets, previously constructed using the B3LYP and BLYP density functionals, are studied. They are compared to the well-known to the correlation consistent basis sets that were constructed with higher-level ab initio methodologies through computations of enthalpies of formation and combustion enthalpies. The computational accuracy with regard to experiment is reported.

<p>For many applications within the defense, aerospace, and electricity-producing industries, available material choices for high-performance devices that fulfill necessary requirements are limited. Choosing a metallic material or a ceramic material may be optimal for only some of the required properties. For instance, choosing a metal may optimize ductility but compromise oxidation resistance, yield strength, or creep resistance. Of potential interest, ceramic-metal (cermet) composites can address several fundamental concerns such as high temperature mechanical toughness and stiffness and oxidation/corrosion resistance. However, cost-effective, scalable manufacturing of complex-shaped, high-temperature cermets can be challenging.</p> <p>A cermet of interest is niobium and yttrium oxide, Y2O3. Both materials exhibit high melting points with similar coefficients of thermal expansion. Basic thermodynamic calculations suggest that these materials are chemically compatible, and that Y2O3/Nb cermets may be generated by reactive melt infiltration using the patented Displacive Compensation of Porosity (DCP) process. With the DCP process, a liquid fills a porous perform, and a displacement reaction occurs to produce products of larger solid volume. This reaction yields the cermet of interest, formed in a reduced-stress condition, while maintaining a generally near net shape and high relative density.</p> <p>In order to get to the point of designing cermet components for various applications, a focus of this work has been to create a Y2O3/Nb composite by hot pressing powders at high temperatures at the predicted stoichiometric ratios, and then characterizing the thermal and mechanical properties. The reduction reaction between liquid yttrium and solid niobium (IV) oxide (NbO2) was then characterized to evaluate kinetic mechanisms affecting the reaction rate which is necessary for future DCP-based cermet component manufacturing.</p> <p>Lastly, the mechanical behavior of this cermet was modeled and compared to another cermet processed using liquid metal infiltration using a temperature-dependent elasto-visco-plastic self-consistent model. The effects of cooling from processing temperatures, as well as thermally cycling of these cermets, were quantified. As high temperature experiments can be time intensive with high costs, it is advantageous to have a computationally efficient, desktop design tool to quantify the impacts of changing processing and use conditions on material performance.</p>

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