In this thesis, we study two stochastic reaction diffusion models - the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching the boundary of a properly embedded open set, termed the reaction region (or more generally some fixed lower dimensional sub-manifold). The Doi model uses reaction potentials, supported in the reaction region, whereby two molecules react with a fixed probability per unit time, λ, upon entering the reaction region. The problem considered is that of obtaining estimates for convergence rates, in λ, of the Doi model to the Smoluchowski model. This problem fits into the theory of singular perturbation or optimization, depending on which reactive boundary conditions one considers, and we solve it - at least for the bimolecular reaction with one stationary target.

Recommender System (RS) has become one of the most important component for many companies, such as YouTube and Amazon. A recommender system consists of a series of algorithms which predict and recommend products to users. This report covers the selection of many open source recommender system projects, and movie predictions are made using the selected recommender system. Based on the predictions, a comparison was made between precision and an improved precision algorithm. The selected RS uses singular value decomposition in the field of collaborative filtering. Based on the recommendation results produced by the RS, the comparison between precision and the improved precision algorithms showed that the result of improved precision is slightly higher than precision in different cutoff values and different dimensions of eigenvalues. / Rekommendationssystem har blivit en av de viktigaste beståndsdelar för många företag, såsom YouTube och Amazon. Ett rekommendationssystem består av en serie av algoritmer som förutsäger och rekommenderar produkter till användare. Denna rapport omfattar valet av många öppen källkod rekommendationssystem projekt, och filmprognoser görs med det valda rekommendationssystemet. Baserat på filmprognoser, gjordes en jämförelse mellan precision och en förbättrad precision algoritmer. Det valda rekommendationssystemet använder singulärvärdesuppdelning som kollaborativ filtrering. Baserat på rekommendationsresultat som produceras av rekommendationssystemet, jämförelsen mellan precision och den förbättrade precisions algoritmer visade att resultatet av förbättrad precision är något högre än precision i olika brytvärden och olika dimensioner av egenvärden.

To contribute to the design of next-generation high performance and low emission combustion devices, this study provides a series of high fidelity numerical simulations of turbulent premixed combustion and autoignition with different clean fuels. The first part of the thesis consists of the direct numerical simulations (DNS) of the lean hydrogen-air turbulent premixed flames at a wide range of Karlovitz number (Ka) conditions up to Ka = 1,126. Turbulence-chemistry interaction is discussed in terms of statistical analysis of the turbulent flame speed and flame structure. Global and local flame speed are separately studied through the fuel consumption speed and displacement speed of the flame front, respectively, and the results are compared with the reference laminar flames as well as similar studies in the literature. The global flame structure is assessed via cross-sectional and conditional averages, and modeling implication is further discussed. Detailed analysis of the local flame structure along the positive and negative curvature is also conducted, providing an understanding of the different behavior of local heat release response. Finally, as the modeling perspectives for Reynolds-averaged Navier-Stokes (RANS) and large eddy simulations (LES), the mean quantities of major species, intermediate species, density, the reaction rate of the progress variable, and heat release rate are assessed in the context of the probability density function (PDF). The second part of the thesis consists of applications of the advanced mathematical tool called the computational singular perturbation (CSP). A skeletal chemical mechanism is developed using the CSP algorithm for the autoignition of methanol and dimethyl ether blends, and the ignition delay time and laminar flame speed are validated for a wide range of mixture conditions. A series of autoignition simulations are carried out in the canonical counter flow mixing layer using the developed skeletal mechanism, and detailed analyses of the autoignition for the methanol and dimethyl ether blends at a wide range of strain rate conditions are provided using the CSP diagnostics tools for a wide range of chemical and fluid combinations.

Climate variability is important to understand as its effects on groundwater are complex than surface water. Climate association between Groundwater Storage (GWS) and sea level changes have been missing from the Intergovernmental Panel on Climate Change, demanding a requisite study of their linkage and responses. The current dissertation is primarily focused on the ongoing issues that have not been focused on the previous literatures. Firstly, the study evaluated the effects of short-term persistence and abrupt shifts in sea level records along the US coast by utilizing popular robust statistical techniques. Secondly, the study evaluated the variability in groundwater due to variability in hydroclimatic variables like sea surface temperature (SST), precipitation, sea level, and terrestrial water storage. Moreover, a lagged correlation was also analyzed to obtain their teleconnection patterns. Lastly, the relationship between the groundwater rise and one of the most common short-term climate variability, ENSO was obtained. To accomplish the research goals the current dissertation was subdivided into three research tasks.The first task attempted to answer a major question, Is sea level change affected by the presence of autocorrelation and abrupt shift? This question reflects the importance of trend and shift detection analysis in sea level. The primary factor driving the global sea level rise is often related to climate change. The current study investigates the changes in sea level along the US coast. The sea level records of 59 tide gauge data were used to evaluate the trend, shift, and persistence using non-parametric statistical tests. Mann-Kendall and Pettitt’s tests were utilized to estimate gradual trends and abrupt shifts, respectively. The study also assessed the presence of autocorrelation in sea level records and its effect on both trend and shift was examined along the US coast. The presence of short-term persistence was found in 57 stations and the trend significance of most stations was not changed at a 95% confidence level. Total of 25 stations showed increasing shift between 1990–2000 that was evaluated from annual sea level records. Results from the current study may contribute to understanding sea level variability across the contiguous US. The second task dealt with variability in the Hydrologic Unit Code—03 region. It is one of the major U.S. watersheds in the southeast in which most of the variability is caused by Sea Surface Temperature (SST) variability in the Pacific and Atlantic Ocean, was identified. Furthermore, the SST regions were identified to assess its relationship with GWS, sea level, precipitation, and terrestrial water storage. Temporal and spatial variability were obtained utilizing the singular value decomposition statistical method. A gridded GWS anomaly from the Gravity Recovery and Climate Experiment (GRACE) was used to understand the relationship with sea level and SST. The negative pockets of SST were negatively linked with GWS. The identification of teleconnections with groundwater may substantiate temporal patterns of groundwater variability. The results confirmed that the SST regions exhibited El Niño Southern Oscillation patterns, resulting in GWS changes. Moreover, a positive correlation between GWS and sea level was observed on the east coast in contrast to the southwestern United States. The findings highlight the importance of climate-driven changes in groundwater attributing changes in sea level. Therefore, SST could be a good predictor, possibly utilized for prior assessment of variabilities plus groundwater forecasting. The primary goal of the third task is to better understand the effects of ENSO climate patterns on GWS in the South Atlantic-Gulf region. Groundwater issues are complex and different studies focused on groundwater depletion while few emphasized, “groundwater rise”. The current research is designed to develop an outline for assessing how climate patterns can affect groundwater fluctuation, which might lead to groundwater rise. The study assessed the effect of ENSO phases on spatiotemporal variability of groundwater using Spearman Rank Correlation. A significant positive correlation between ENSO and GWS was observed. An increasing trend was detected in GWS where most grids were observed in Florida by utilizing the non-parametric Mann-Kendall. A positive magnitude of the trend was also detected by utilizing Theil-Sen’s Slope method with high magnitude in the mid-Florida region. The highest GWS anomalies were observed in the peak of El Niño events and the lowermost GWS was observed during La Niña events. Furthermore, most of the stations were above normal groundwater conditions. This study provides a better understanding of the research gap between groundwater rise and ENSO.

Bekanntlich sind atmosphärische Rossbywellezüge (RWTs) Lösungen der Singular Vector Analyse eines gedämpften, barotropen Modells mit Nordwinter Grundströmen. In den SV Basen der verwendeten 40 DJF Grundströme konnten nur wenige wachsende den Rossbywellenzügen ähnliche (RWT Moden) Singulären Vektoren (SVen) gefunden werden. Die RWT Moden kommen nur in wenigen Gebieten der Erde vor. Die instabilste Mode entwickelt sich in der Region des Nordpazifiks (NPACs) innerhalb von 4 Tagen in jedem der verwendeten beobachteten DJF Grundströme. Alle anderen RWT Moden kommen nur bei Verwendung einiger der Grundströme vor. Ihre Entwicklungspfade sind eindeutig für Entwicklungszeiten bis zu 96 h und streuen für längere Zeiten. Die NPAC Mode erklärt zum Optimierungszeitpunkt 96 h bis zu 60 % der atmosphärischen kinetischen Energie (KE) auf der 300 hPa Fläche in der NPAC Region. Es konnte auch gezeigt werden, daß die Zeitreihe des beobachteten Wachstums der NPAC Mode mit dem berechneten Wachstum (den Eigenwerten) konsistent ist. Interessanterweise zeigt die NPAC-KE zum Optimierungszeitpunkt 96 h auch eine schwach signifikante Korrelation mit dem PNA-Index, die für die Optimierungszeit 144 h nicht mehr existiert. Die Ergebnisse legen die Vermutung nahe, daß die verwendeten Grundströme die Entwicklung der RWT Moden bis zu einer Entwicklungszeit von 4 Tagen dominieren und daß die finite Instabilität maßgeblich zur Entwicklung der beobachteten NPAC Rossbywellenzüge in der Atmosphäre beiträgt. Die Ergebnisse geben Hinweise darauf, daß die NPAC mode auch einen Beitrag zur Entwicklung der PNA leistet.

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京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第17968号 / 情博第512号 / 新制||情||91(附属図書館) / 30798 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 西村 直志, 准教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

原著論文リスト[A1]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-012-9607-5.”. [A2]: “The final publication is available at Springer via http://dx.doi.org/10.1007/s10092-013-0085-5.”, [A3]: DOI“10.1016/j.camwa.2015.11.022” / 京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19859号 / 情博第610号 / 新制||情||106(附属図書館) / 32895 / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 中村 佳正, 教授 矢ｹ崎 一幸, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

In this dissertation we study positive solutions to a singular p-Laplacian elliptic boundary value problem on a bounded domain with smooth boundary when a positive parameter varies. Our main focus is the analysis of a challenging class of singular p-Laplacian problems. We establish the existence of a positive solution for all positive values of the parameter and the existence of at least two positive solutions for a certain explicit range of the parameter. In the Laplacian case, we also prove the uniqueness of the positive solution for large values of the parameter. We extend our existence and multiplicity results to classes of singular systems and to the case when a domain is an exterior domain. We prove our existence and multiplicity results by the method of sub and supersolutions and our uniqueness result by establishing apriori and boundary estimates. Such results are well known in the literature for the nonsingular case. In this study, we extend these results to the more difficult singular case.

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