京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20917号 / 理博第4369号 / 新制||理||1627(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 嶺重 慎, 准教授 前田 啓一, 教授 太田 耕司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

The study of the instabilities in boiling water reactors is of significant importance to the safety withwhich they can be operated, as they can cause damage to the reactor posing risks to both equipmentand personnel. The instabilities that concern this paper are progressive growths in the oscillatingpower of boiling-water reactors. As thermal power is oscillatory is important to be able to identifywhether or not the power amplitude is stable. The main focus of this paper has been the development of a neural network estimator of these insta-bilities, fitting a non-linear model function to data by estimating it’s parameters. In doing this, theambition was to optimize the networks to the point that it can deliver near ”best-guess” estimationsof the parameters which define these instabilities, evaluating the usefulness of these networks whenapplied to problems like this. The goal was to design both MLP(Multi-Layer Perceptron) and SVR/KRR(Support Vector Regres-sion/Kernel Rigde Regression) networks and improve them to the point that they provide reliableand useful information about the waves in question. This goal was accomplished only in part asthe SVR/KRR networks proved to have some difficulty in ascertaining the phase shift of the waves.Overall, however, these networks prove very useful in this kind of task, succeeding with a reasonabledegree of confidence to calculating the different parameters of the waves studied.

In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzburg-Landau equations. These equations predict that the model exhibits bistability between travelling waves and Turing patterns. We present a study of interfaces separating wave and Turing patterns arising from the codimension-2 instability. We study theoretically and numerically the dynamics of such interfaces in the framework of the amplitude equations and compare these results with numerical simulations of the model near and far away from the codimension-2 instability. Near the instability, the dynamics of interfaces separating small amplitude Turing patterns and travelling waves is well described by the amplitude equations, while, far from the codimension-2 instability, we observe a locking of the interface velocities. This locking mechanism is imposed by the absence of defects near the interfaces and is responsible for the formation of drifting pattern domains, i.e. moving localised patches of travelling waves embedded in a Turing pattern background and vice versa.

In this thesis we investigate the formation of patterns in a simple activator-inhibitor model supplemented with an inhibitory nonlocal coupling term. This model exhibits a wave instability for slow inhibitor diffusion, while, for fast inhibitor diffusion, a Turing instability is found. For moderate values of the inhibitor diffusion these two instabilities occur simultaneously at a codimension-2 wave-Turing instability. We perform a weakly nonlinear analysis of the model in the neighbourhood of this codimension-2 instability. The resulting amplitude equations consist in a set of coupled Ginzburg-Landau equations. These equations predict that the model exhibits bistability between travelling waves and Turing patterns. We present a study of interfaces separating wave and Turing patterns arising from the codimension-2 instability. We study theoretically and numerically the dynamics of such interfaces in the framework of the amplitude equations and compare these results with numerical simulations of the model near and far away from the codimension-2 instability. Near the instability, the dynamics of interfaces separating small amplitude Turing patterns and travelling waves is well described by the amplitude equations, while, far from the codimension-2 instability, we observe a locking of the interface velocities. This locking mechanism is imposed by the absence of defects near the interfaces and is responsible for the formation of drifting pattern domains, i.e. moving localised patches of travelling waves embedded in a Turing pattern background and vice versa.