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京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22055号 / 工博第4636号 / 新制||工||1723(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 細田 尚, 教授 戸田 圭一, 准教授 音田 慎一郎 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This study presents a new Lagrangian model for predicting dynamics and transport in rivers and shallow water flows. A hydrostatic model is developed for the prediction of rivers and floodplain flow and lateral interactions between them. The model is extended to the Boussinesq weakly non-linear, non-hydrostatic model for the simulation of solitary waves and undular bores. A model for advection-diffusion transport of tracers in open channel flow is also presented. The simulation results are compared against an analytical solution and published laboratory data, field data and theoretical results. It is demonstrated that the Lagrangian moving grid eliminates numerical diffusion and oscillations; the model is dynamically adaptive, providing higher resolution under the wave by compressing the parcels (grid). It also allows flow over dry beds and moving boundaries to be handled efficiently. The hydrostatic model results have shown that the model accurately simulates wave propagation and non-linear steepening until wave breaking. The model is successfully applied to simulate flow and lateral interactions in a compound channel and flood wave movement in a natural river. The non-hydrostatic model has successfully reproduced the general features of solitary waves such as the balance between non-linearity and wave dispersion and non-linear interactions of two solitary waves by phase-shift. Also, the model successfully reproduced undular bores (high frequency short waves) from a long wave and the predicted maximum height of the leading wave agreed very well with the published results. It is shown that the simple second order accurate Lagrangian scheme efficiently simulates dispersive waves without any numerical diffusion. Lagrangian modeling of advection-diffusion transport of Gaussian tracer distributions, top hat tracer distributions and steep fronts (step function) in steady, uniform flow has provided exact results and has shown that the scheme allows the use of a large time step without any numerical diffusion and oscillations, including for the advection of steep fronts. The scheme can handle large Courant numbers (results are presented for Cr = 0 to 20) and the entire range of grid Peclet numbers from zero to infinity. The model is successfully applied to tracer transport due to flow induced by simple waves, solitary waves and undular bores

This work focuses on statistical methods to understand how frequently rare events occur and what the magnitude of extreme values such as large losses is. It lies in a field called extreme value analysis whose scope is to provide support for scientific decision making when extreme observations are of particular importance such as in environmental applications, insurance and finance. In the univariate case, I propose new techniques to model tails of discrete distributions and illustrate them in an application on word frequency and multiple birth data. Suitably rescaled, the limiting tails of some discrete distributions are shown to converge to a discrete generalized Pareto distribution and generalized Zipf distribution respectively. In the multivariate high-dimensional case, I suggest modeling tail dependence between random variables by a graph such that its nodes correspond to the variables and shocks propagate through the edges. Relying on the ideas of graphical models, I prove that if the variables satisfy a new notion called asymptotic conditional independence, then the density of the joint distribution can be simplified and expressed in terms of lower dimensional functions. This generalizes the Hammersley- Clifford theorem and enables us to infer tail distributions from observations in reduced dimension. As an illustration, extreme river flows are modeled by a tree graphical model whose structure appears to recover almost exactly the actual river network. A fundamental concept when studying limiting tail distributions is regular variation. I propose a new notion in the multivariate case called one-component regular variation, of which Karamata's and the representation theorem, two important results in the univariate case, are generalizations. Eventually, I turn my attention to website visit data and fit a censored copula Gaussian graphical model allowing the visualization of users' behavior by a graph.