京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22418号 / 工博第4679号 / 新制||工||1730(附属図書館) / 京都大学大学院工学研究科社会基盤工学専攻 / (主査)教授 KIM Chul-Woo, 教授 清野 純史, 教授 杉浦 邦征 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The goal of this master thesis is to develop an algorithm for solving cables on pulleys, which would be more efficient and accurate than existing algorithm used in software RFEM. This algorithm was integrated to the program for static and dynamic analysis of structures, in the form of particular program module. This work also contains examples of using this algorithm. The comparison of expected results with outcomes from the program is presented. The suitability for common practise is examined based on this comparison. The examples showed that the new algorithm for solving of cables on pulleys is more powerful and more accurate than existing solutions and most likely does not has equivalent competition.

Les microcavités à semiconducteurs apparaissent aujourd’hui comme une plateforme particulièrement propice à l’étude des fluides quantiques en interactions. Dans ces cavités, la lumière et les excitations électroniques sont confinées dans de petits volumes et leur couplage est rendu si fort que les propriétés optiques sont gouvernées par des quasi-particules hybrides lumière-matière appelées polaritons de cavité. Ces quasi-particules se propagent comme des photons, mais interagissent avec leur environnement via leur partie matière. Elles peuvent occuper massivement un même état quantique et se comporter comme une onde macroscopique cohérente et non-linéaire. On parle alors de fluide quantique de lumière. Dans cette thèse, nous étudions la dynamique de fluides quantiques de polaritons dans différentes microstructures unidimensionnelles. La technologie de gravure de microcavités planaires, développée au C2N, permet de réaliser une ingénierie complète du potentiel dans lequel nous générons ces fluides de polaritons et d’implémenter des géométries complexes. Dans une première partie, nous avons étudié les propriétés de localisation des états propres de réseaux synthétiques quasi-périodes. L’exploration théorique du diagramme de phase de localisation des modes propres a dévoilé une nouvelle transition de type délocalisation-localisation lors d’une déformation originale d’un quasi-cristal, transition que nous avons pu observer expérimentalement. Une deuxième partie de la thèse est consacrée à l’étude de la dynamique non-linéaire de deux fluides contra-propageant dans un canal unidimensionnel. La compétition entre énergie cinétique et énergie d’interactions conduit alors à l’apparition de solitons sombres, dont le nombre discret et la position peuvent être contrôlés optiquement. Nous avons mis en évidence une bistabilité contrôlée par la différence de phase imprimée sur les deux fluides. La dernière partie du travail concerne l’étude des non-linéarités pour un fluide de polaritons occupant une bande plate. L’énergie cinétique du fluide y est nulle, si bien que sa propagation est gelée. Nous observons alors la formation de domaines non-linéaires de taille quantifiée. Ce travail ouvre des perspectives prometteuses, tout particulièrement pour l’exploration de phases topologiques de bosons en interactions. De plus, augmenter les interactions permettrait d’utiliser notre plate-forme comme un simulateur quantique. / Semiconductor microcavities have emerged as a powerful platform for the study of interacting quantum fluids. In these cavities, light and electronic excitations are confined in small volumes, and their coupling is so strongly enhanced that optical properties are governed by hybrid light-matter quasiparticles, known as cavity polaritons. These quasiparticles propagate like photons and interact with their environment via their matter part. They can macroscopically occupy a single quantum state and then behave as an extended coherent nonlinear wave, i.e. as a quantum fluid of light. In this thesis, we study the nonlinear dynamics of polariton quantum fluids in various one-dimensional microstructures. The possibility to etch microstructures out of planar cavities, a technology developed at C2N, allows full engineering of the potential landscape for the polariton fluid, and implementing complex geometries. In a first part, we have studied the localization properties of the eigenstates in synthetic quasiperiodic lattices. Theoretical exploration of the localization phase diagram revealed a novel delocalization-localization transition in an original deformation of a quasicrystal and we have experimentally evidenced this transition. A second part of the thesis is dedicated to the study of the nonlinear dynamics of two counterpropagating polariton fluids in a one-dimensional channel. The interplay between kinetic and interaction energy is responsible for the formation of dark solitons, whose number and position can be controlled by optical means. We have evidenced a bistable behaviour controlled by the phase twist imprinted on the two fluids. The last part of this work addresses the study of nonlinearities for a fluid injected in a flat band. Therein, the kinetic energy of the fluid is quenched, so that propagation is frozen. We then observe the formation of nonlinear domains with quantized size. This work opens us exciting perspectives, specifically towards the exploration of topological phases of interacting bosons. Enhancing interactions would also allow using our platform for quantum simulation.

Diplomová práce se věnuje analýze chaotického chování v řadách (pseudo)pozorovaných a simulovaných klimatických veličin. Nejprve objasňuji ně- které základní teoretické pojmy související s dynamickými systémy. Potom se zabývám zp·soby rekonstrukce fázového prostoru a uvedu metody odhadu kore- lační dimenze a největšího Ljapunovova exponentu. V praktické části se zabývám pr·měrnou denní teplotou z reanalýz ERA-40 a reanalýzami NCEP/NCAR v tlakových hladinách 850 a 500 hPa z let 1960-2000. Nejprve zkoumám podrobně jednu vybranou řadu. Používám např. metodu falešných soused· a určuji míru vzájemné informace. Zjiš'uji, že korelační dimenze nenabývá konkrétní hodnotu. Pro analýzu celých tlakových hladin vyvíjím program, který počítá divergenci blízkých trajektorií, což je postup používaný při výpočtu největšího Ljapunovo- va exponentu. Tento program postupně aplikuji na oblasti velikosti 20◦ × 30◦ kterými je pokryta celá zeměkoule. Postupně ukazuji a srovnávám výsledky pro reanalýzy v obou tlakových hladinách s ročním chodem a odečteným ročním cho- dem. Tuto metodu aplikuji na výstupy globálních klimatických model· HadCM3 a MPI-ESM-MR v hladině 500 hPa. Podobnou analýzu ještě uskutečňuji u jed- nodimenzionálních řad teploty u reanalýz a u model·. Výsledky opět vizuálně srovnávám. 1

Heterogeneity in lattice potentials (like random or quasiperiodic) can localize linear, non-interacting waves and halt their propagation. Nonlinearity induces wave interactions, enabling energy exchange and leading to chaotic dynamics. Understanding the interplay between the two is one of the topical problems of modern wave physics. In particular, one questions whether nonlinearity destroys localization and revives wave propagation, whether thresholds in wave energy/norm exist, and what the resulting wave transport mechanisms and characteristics are. Despite remarkable progress in the field, the answers to these questions remain controversial and no general agreement is currently achieved. This thesis aims at resolving some of the controversies in the framework of nonlinear dynamics and computational physics. Following common practice, basic lattice models (discrete Klein-Gordon and nonlinear Schroedinger equations) were chosen to study the problem analytically and numerically. In the disordered linear case all eigenstates of such lattices are spatially localized manifesting Anderson localization, while nonlinearity couples them, enabling energy exchange and chaotic dynamics. For the first time we present a comprehensive picture of different subdiffusive spreading regimes and self-trapping phenomena, explain the underlying mechanisms and derive precise asymptotics of spreading. Moreover, we have successfully generalized the theory to models with spatially inhomogeneous nonlinearity, quasiperiodic potentials, higher lattice dimensions and arbitrary nonlinearity index. Furthermore, we have revealed a remarkable similarity to the evolution of wave packets in the nonlinear diffusion equation. Finally, we have studied the limits of strong disorder and small nonlinearities to discover the probabilistic nature of Anderson localization in nonlinear disordered systems, demonstrating the finite probability of its destruction for arbitrarily small nonlinearity and exponentially small probability of its survival above a certain threshold in energy. Our findings give a new dimension to the theory of wave packet spreading in localizing environments, explain existing experimental results on matter and light waves dynamics in disordered and quasiperiodic lattice potentials, and offer experimentally testable predictions.

A major limitation of silica-based high-Q microcavities is the lack of functionalities such as gain, plasmonic resonance, and second-order nonlinearity. Silica possesses third order nonlinearity but cannot produce second order nonlinearity, plasmonic resonances, or fluorescence emission. The key to overcome this deficiency is to develop versatile methods that can functionalize the surface of a silica microsphere with appropriate nanomaterials. The goal of this thesis is to present and characterize an electrostatic self-assembly based approach that can incorporate a large number of functional materials onto the surface of a silica resonator with nanoscale control. We consider several types of functional materials: polar ionic self-assembled multilayer (ISAM) films that possess second order nonlinearities, Au nanoparticles (NPs) that support plasmonic resonances, and fluorescent materials such as CdSe/ZnS core/shell QDs. A major part of this thesis is to investigate the relationship between cavity Q factors and the amount of nanomaterials deposited onto the silica microspheres. In particular, we fabricate multiple functional microspheres with different ISAM film thickness and Au NPs density. We find that the Q factors of these microspheres are mainly limited by optical absorption in the case of the ISAM film, and a combination of optical absorption and scattering in the case of the Au NPs. By controlling the number of polymer layers or the NPs density, we can adjust the Q factors of these functional microspheres in the range of 106 to 107. An agreement between theoretical prediction and experimental data was obtained. The results may also be generalized to other functional materials including macromolecules, dyes, and non-spherical plasmonic NPs. We also study the adsorption of Au NPs onto spherical silica surface from quiescent particle suspensions. The surfaces consist of microspheres fabricated from optical fibers and were coated with a polycation, enabling irreversible nanosphere adsorption. Our results fit well with theory, which predicts that particle adsorption rates depend strongly on surface geometry. This is particularly important for plasmonic sensors and other devices fabricated by depositing NPs from suspensions onto surfaces with non-trivial geometries. We use two additional examples to illustrate the potential applications of this approach. First, we explored the possibility of achieving quasi-phase-matching (QPM) in a silica fiber taper coated with nonlinear polymers. Next, we carry out a preliminary investigation of lasing in a silica fiber coated with CdSe/ZnS core/shell quantum dots (QDs). / Ph. D.

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In this study, methods for the geometric nonlinear analysis and the material nonlinear analysis of plane frames subjected to elevated temperatures are presented. The method of analysis is based on a Eulerian (co-rotational) formulation, which was developed initially for static loads, and is extended herein to include geometric and material nonlinearities. Local element force-deformation relationships are derived using the beam-column theory, taking into consideration the effect of curvature due to temperature gradient across the element cross-section. The changes in element chord lengths due to thermal axial strain and bowing due to the temperature gradient are also taken into account. This "beam-column" approach, using stability and bowing functions, requires significantly fewer elements per member (i.e. beam/column) for the analysis of a framed structure than the "finite-element" approach. A computational technique, utilizing Newton-Raphson iterations, is developed to determine the nonlinear response of structures. The inclusion of the reduction factors for the coefficient of thermal expansion, modulus of elasticity and yield strength is introduced and implemented with the use of temperature-dependent formulas. A comparison of the AISC reduction factor equations to the Eurocode reduction factor equations were found to be in close agreement. Numerical solutions derived from geometric and material analyses are presented for a number of benchmark structures to demonstrate the feasibility of the proposed method of analysis. The solutions generated for the geometrical analysis of a cantilever beam and an axially restrained column yield results that were close in proximity to the exact, theoretical solution. The geometric nonlinear analysis of the one-story frame exhibited typical behavior that was relatively close to the experimental results, thereby indicating that the proposed method is accurate. The feasibility of extending the method of analysis to include the effects of material nonlinearity is also explored, and some preliminary results are presented for an experimentally tested simply supported beam and the aforementioned one-story frame. The solutions generated for these structures indicate that the present analysis accurately predicts the deflections at lower temperatures but overestimates the failure temperature and final deflection. This may be in part due to a post-buckling reaction after the first plastic hinge is formed. Additional research is, therefore, needed before this method can be used to analyze the materially nonlinear response of structures.

The application of robotic manipulators in machining systems has gained a great interest in manufacturing because of their lower prices, higher kinematic flexibility and larger workspace compared to conventional CNC machine tools. However, their performance is limited due to the much lower structural rigidity which makes them more susceptible to excessive and unstable vibrations, known as chatter, during the machining process. Highly effective chatter modeling and avoidance methods that have been developed for CNC machining in the past decades are now being used by the industry to design high-performance chatter-free machining operations. The available methods, however, face major difficulties when applied to robotic machining, mainly due to the high flexibility and pose-dependency of the vibration response in robots. High flexibility leads to high-amplitude vibrations which affect the process dynamics and excite structural nonlinearities. The existing approaches to modeling machining vibrations assume linearity of the structural dynamics of the robotic manipulator. This assumption, considering the inherent nonlinearities in the robot’s revolute joints, may cause considerable inaccuracies in predicting the stability of vibrations during the process. This thesis studies the high flexibility and nonlinearity of the robot’s structural dynamics and their effects on chatter vibrations. The research starts with investigating the effects of high flexibility of robot's structure in the process dyamics by considering the modulation of cutting forces by axial vibrations, which is normally ignored in CNC milling due to high rigidity of the machine in this direction. The results of chatter prediction considering this effect are shown and discussed. The rest of the thesis focuses on the structural nonlinearity. Firstly, an experimental study is presented to investigate the extent of nonlinearity in structural dynamics of the robot. The results confirm that structural nonlinearities in robotic machining systems can be effectively excited in the presence of high-amplitude vibrations due to milling forces, such that they cause remarkable differences in chatter prediction. The following step is modeling the structural nonlinearities. For this purpose, the variation of restoring forces with the dynamic response (displacement and velocity) are observed when the robot is subjected to harmonic excitation. Based on the experimental observations, the nonlinear effects are modeled by cubic stiffness and damping characteristics. Parameters of the nonlinear model are then identified using Higher-order Frequency Response Functions (HFRF) extracted from measurements. The identified model can predict the vibration behavior of the robotic machining system when subjected to periodic loads such as milling forces. The developed model of nonlinear structural dynamics is then coupled with the chatter model. Consequently, the system is described by nonlinear Delay Differential Equations (DDE) with periodic coefficients. Bifurcation diagrams for the forced vibrations in the described system are developed using the numerical continuation method. The effects of cutting parameters such as feedrate as well as the nonlinear parameters are studied. The thesis is concluded by proposing the use of in-process FRF in the linear model of chatter stability for quick prediction of stability limits. In this approach, the exact characteristics of the nonlinear mechanisms are not studied; instead, the measured FRF during the milling process are used, which are assumed to represent the nonlinear structural dynamics that are linearized about the applied operational conditions. Two methods of measuring in-process FRF are proposed and employed in the robotic milling system. The measured FRF are then used in the linear chatter model to develop the Stability Lobes Diagram (SLD) which shows the combination of cutting parameters that lead to stable or unstable vibrations. Experimental chatter tests show that better agreement with predictions can be achieved by using in-process FRF instead of FRF measured at the idle state of the system. The results of this thesis contribute to better characterization of vibrations in robotic machining with high-amplitude forces and selecting suitable strategies to enhance productivity of the operation. / Graduate