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京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第22863号 / 情博第742号 / 新制||情||127(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)教授 矢ヶ崎 一幸, 教授 中村 佳正, 准教授 柴山 允瑠, 教授 國府 寛司 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

The study of waves and instabilities in quantum plasmas is of fundamental importance for understanding collective interactions in superdense astrophysical objects, in high intense laser-plasma/solid-matter interactions, in microelectronic devices and metallic nanostructures. In dense quantum plasmas, there are new pressure laws associated with the Fermi-Dirac distribution functions and new quantum forces associated with the quantum Bohm potential and the Bohr magnetization involving electron ½ spin. These forces significantly alter the collective behavior of dense quantum plasmas. This thesis contains six papers, considering several novel collective modes and instabilities at quantum scales. In Paper I, we have used the quantum hydrodynamical (QHD) model for studying the one-dimensional dust-acoustic (DA) waves incorporating the Fermi pressure law and the quantum Bohm potential. The latter modifies the DA wave dispersion relation in a collisional plasma. In Paper II, we have calculated the electrostatic potential of a test charge in an unmagnetized electron-ion quantum plasma. It is found that the Debye-Hückel and oscillatory wake potentials strongly depend upon the Fermi energy at quantum scales. The results can be of interest for explaining the charged particle attraction and repulsion in degenerate quantum plasmas, such as those in semiconductor and microelectronic devices. Paper III presents the parametric study of nonlinear electrostatic waves in two-dimensional collisionless quantum dusty plasmas. A reductive perturbation method has been employed to the QHD equations together with the Poisson equation, obtaining the cylindrical Kadomtsev-Petviashvili (CKP) equations and their stationary localized solutions. We have numerically examined the quantum mechanical and geometrical effects on the profiles of nonplanar quantum dust-ion-acoustic (DIA) and DA solitary waves. The role of static as well as mobile (negatively or positively charged) dust particles on the low-frequency electrostatic waves has also been highlighted for metallic nanostructures. Paper IV introduces the nonlinear properties of the ion-sound waves in a dense electron-ion Fermi magnetoplasma. The computational analysis of the nonlinear system reveals that the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number at quantum scales. Paper V considers the nonlinear interactions of electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfvén waves in a quantum magnetoplasma. The nonlinear dispersion relations have been analyzed analytically to obtain the growth rates for both the decay and modulational instabilities involving the dispersive IC, LH, and Alfvén waves. In Paper VI, we have identified a new drift-like dissipative instability in a collisional quantum plasma. The modified unstable drift-like mode can cause cross-field anomalous ion-diffusion at quantum scales.

In this thesis, the two-dimensional initial and boundary value problems (IBVPs) and the one-dimensional Cauchy problems defined by the nonlinear reaction- diffusion and wave equations are numerically solved. The dual reciprocity boundary element method (DRBEM) is used to discretize the IBVPs defined by single and system of nonlinear reaction-diffusion equations and nonlinear wave equation, spatially. The advantage of DRBEM for the exterior regions is made use of for the latter problem. The differential quadrature method (DQM) is used for the spatial discretization of IBVPs and Cauchy problems defined by the nonlinear reaction-diffusion and wave equations. The DRBEM and DQM applications result in first and second order system of ordinary differential equations in time. These systems are solved with three different time integration methods, the finite difference method (FDM), the least squares method (LSM) and the finite element method (FEM) and comparisons among the methods are made. In the FDM a relaxation parameter is used to smooth the solution between the consecutive time levels. It is found that DRBEM+FEM procedure gives better accuracy for the IBVPs defined by nonlinear reaction-diffusion equation. The DRBEM+LSM procedure with exponential and rational radial basis functions is found suitable for exterior wave problem. The same result is also valid when DQM is used for space discretization instead of DRBEM for Cauchy and IBVPs defined by nonlinear reaction-diffusion and wave equations.

This master’s thesis deals with analytical and numerical description of surface gravity waves. Wave theories and their influence on water particle movement is described in the theoretical part of the thesis. Water particle moves in the same direction as wave propagation and this phenomenon is called Stokes drift. It has a significant influence on sediment transport and floating particle movement at water free surface. The experimental part consists of wave profile monitoring and water particle tracking in a wave flume with wave generator and beach model. The experimental results are compared with numerical simulation performed in the ANSYS Fluent software. Finally, the wave profiles obtained from simulation are compared with experimental wave profiles extracted by digital image processing.

Sensitive nonlinear acoustic methods are suitable for material characterization. This thesis describes three nonlinear acoustic methods that are proven useful for detection of defects like cracks and delaminations in solids. They offer the possibility to use relatively low frequencies which is advantageous because attenuation and diffraction effects are smaller for low frequencies. Therefore large and multi-layered complete objects can be investigated in about one second. Sometimes the position of the damage is required. But it is in general difficult to limit the geometrical extent of low-frequency acoustic waves. A technique is presented that constrains the wave field to a localized trapped mode so that damage can be located.

In dieser Arbeit entwickeln und untersuchen wir ein numerisches Schema für die eindimensionale Wellengleichung mit Hysterese für unterschiedliche Arten von Randbedingungen. Diese Gleichung ist ein Modell für die Longitudinal- oder Torsionsschwingungen eines homogenen Stabes unter dem Einfluß einer uniaxialen äußeren Kraftdichte, wobei wir ein elastoplastisches Materialgesetz annehmen. Hysterese-Operatoren sind ratenunabhängige Volterra-Operatoren, die Zeitfunktionen in Zeitfunktionen abbilden. Mit ihnen lassen sich Gedächtniseffekte modellieren, wie sie zum Beispiel in der Elastoplastizität oder im Ferromagnetismus auftauchen. Zunächst führen wir Hysterese-Operatoren allgemein ein und analysieren dann eine spezielle Klasse von Hysterese-Operatoren, die Prandtl-Ishlinskii-Operatoren. Wir untersuchen ihre Gedächtnisstruktur und erklären, wie sich die Operatoren numerisch auswerten lassen. Dazu stellen wir zwei verschiedene Approximationsansätze vor. Wir führen aus, wie sich die approximierenden Operatoren implementieren lassen und leiten lineare und quadratische Fehlerabschätzungen her. Zur numerischen Lösung des gekoppelten Systems aus der Wellengleichung mit einem Hysterese-Operator führen wir ein implizites Differenzenschema mit Gedächtnis ein. Für eine Klasse von Hysterese-Operatoren zeigen wir die Existenz und Eindeutigkeit der Lösung des numerischen Schemas, beweisen mit Hilfe von Kompaktheitsschlüssen und einem Monotonieargument die Konvergenz des Verfahrens und leiten eine Fehlerabschätzung der Ordnung 1/2 her. Wir diskutieren, wie das vorgestellte Verfahren auf die Prandtl-Ishlinskii-Operatoren angewendet werden kann. / In this thesis we develop and investigate a numerical scheme for the one-dimensional wave equation with hysteresis for different kinds of boundary conditions. This equation can be regarded as a model for the longitudinal or torsional oscillations of a homogeneous bar under the influence of an uniaxial external force density assuming an elastoplastic material law. Hysteresis operators are rate-independent Volterra operators mapping time functions to time functions. This kind of operator can be used to model memory effects as they appear in elastoplasticity or ferromagnetism, for example. We first give an introduction to the general concept of hysteresis operators before we analyze a special class of hysteresis operators called Prandtl-Ishlinskii operators. We investigate their memory structure and explain how the operators can be evaluated numerically. To that end we present two different kinds of approximation schemes. We point out how the approximating operators can be implemented and we derive linear and quadratic error estimates. For the numerical solution of the coupled system of the wave equation with a hysteresis operator we introduce an implicit difference scheme with memory. For a class of hysteresis operators we show the existence and uniqueness of the numerical solution. We prove the convergence of the scheme by compactness and monotonicity arguments. We derive an error estimate of order 1/2. We discuss the application of the method presented to Prandtl-Ishlinskii operators.

Le secteur de l’énergie houlomotrice s’appuie fortement sur la modélisation mathématique et la simulation d’expériences physiques mettant en jeu les interactions entre les ondes et les corps. Dans ce travail, nous avons développé un modèle d’interaction de fidélité moyenne vague-corps pour la simulation de structures tronquées flottantes fonctionnant en mouvement vertical. Ce travail concerne l’ingénierie de l’énergie marine, pour des applications telles que les convertisseurs d’énergie de vague (WEC) à absorption ponctuelle, même si ses applications peuvent aussi être utilisées en ingénierie maritime et navale. Les motivations de ce travail reposent sur les méthodes standard actuelles pour décrire l’interaction corps-vague. Cellesci sont basées sur des modèles résolvant le flux de potentiel linéaire (LPF), du fait de leur grande efficacité. Cependant, les modèles LPF sont basés sur l’hypothèse de faible amplitude et ne peuvent pas répresenter les effets hydrodynamiques non linéaires, importants pour le WEC opérant dans la région de résonance ou dans les régions proches du rivage. En effet, il a été démontré que les modèles LFP prédisent de manière excessive la production de puissance, sauf si des coefficients de traînée sont calibrés. Plus récemment, des simulations Reynolds Averaged Navier-Stokes (RANS) ont été utilisées pour les WEC. RANS est un modèle complet et précis, mais très coûteux en calcul. Il n’est ni adapté à l’optimisation d’appareils uniques ni aux parcs énergétiques. Nous avons donc proposé un modèle de fidélité moyenne basé sur des équations de type Boussinesq, afin d’améliorer le compromis entre précision et efficacité. Les équations de type Boussinesq sont des modèles d’ondes intégrées en profondeur et ont été un outil d’ingénierie standard pour la simulation numérique de la propagation d’ondes non linéaires dans les eaux peu profondes et les zones côtières. Grâce à l’élimination de la dimension verticale, le modèle résultant est très efficace et évite la description temporelle de la limite entre la surface libre et l’air. Jiang (2001) a proposé un modèle de Boussinesq unifié, décomposant le problème en deux domaines : surface libre et corps. Dans cette méthode, le domaine du corps est également modélisé par une approche intégrée en profondeur - d’où le terme unifié. Récemment, Lannes (2016) avait analysé de manière rigoureuse une configuration similaire dans une équation non linéaire en eaux peu profondes, en déduisant une solution exacte et semi-analitique pour des corps en mouvement. Suivant la même approche, Godlewski et al. (2018) a élaboré un modèle de flux d’eau peu profonde encombrée. [...] Dans cette thèse, nous développons les résultats présentés par Eskilsson et al. (2016) et Bosi et al. (2019). Le modèle est étendu à deux dimensions horizontales. Le modèle 1D est vérifié à l’aide de solutions fabriquées et validé par rapport aux résultats publiés sur l’interaction vague-corps en 1D pour les pontons fixes et corps en mouvement de soulèvement forcé et libre. Les résultats des preuves de concept de la simulation de plusieurs corps sont présentés. Nous validons et vérifions le modèle 2D en suivant des étapes similaires. Enfin, nous mettons en oeuvre la technique de verrouillage, une méthode de contrôle de mouvement du corps pour améliorer la réponse au mouvement des vagues. Il est démontré que le modèle possède une excellente précision, qu’il est pertinent pour les applications d’ondes en interaction avec des dispositifs à énergie houlomotrice et qu’il peut être étendu pour simuler des cas plus complexes. / The wave energy sector relies heavily on mathematical modelling and simulation of the interactions between waves and floating bodies. In this work, we have developed a medium-fidelity wave-body interaction model for the simulation of truncated surface piercing structures operating in heave motion, such as point absorbers wave energy converters (WECs). The motivation of the work lies in the present approach to wave-body interaction. The standard approach is to use models based on linear potential flow (LPF). LPF models are based on the small amplitude/ small motion assumption and, while highly computational efficient, cannot account for nonlinear hydrodynamic effects (except for Morison-type drag). Nonlinear effects are particularly important for WEC operating in resonance, or in nearshore regions where wave transformations are expected. More recently, Reynolds Averaged Navier-Stokes (RANS) simulations have been employed for modelling WECs. RANS is a complete and accurate model but computationally very costly. At present RANS models are therefore unsuited for the optimization of single devices, not to mention energy farms. Thus, we propose a numerical model based built on Boussinesq-type equations to include wave-wave interaction as well as finite body motion in a computationally efficient formulation. Boussinesq-type equations are depth-integrated wave models and are standard engineering tool for numerical simulation of propagation of nonlinear wave in shallow water and coastal areas. Thanks to the elimination of the vertical dimension and the avoidance of a time-dependent computational the resulting model is very computational efficient. Jiang (Jiang, 2001) proposed a unified Boussinesq model, decomposing the problem into free surface and body domains. Notably, in Jiang’s methodology also the body domain is modeled by a depth-integrated approach –hence the term unified. As all models based on Boussinesq-type equations, the model is limited to shallow and intermediate depth regimes. We consider the Madsen and Sørensen model, an enhanced Boussinesq model, for the propagation of waves. We employ a spectral/hp finite element method (SEM) to discretize the governing equations. The continuous SEM is used inside each domain and flux-based coupling conditions are derived from the discontinuous Galerkin method. The use of SEM give support for the use of adaptive meshes for geometric flexibility and high-order accurate approximations makes the scheme computationally efficient. In this thesis, we present 1D results for the propagation and interaction of waves with floating structures. The 1D model is verified using manufactured solutions. The model is then validated against published results for wave-body interaction. The hydrostatic cases (forced motion and decay test) are compared to analytical and semi-analytical solutions (Lannes, 2017), while the non-hydrostatic tests (fixed pontoon and freely heaving bodies) are compared to RANS reference solutions. The model is easily extended to handle multiple bodies and a proof-of-concept result is presented. Finally, we implement the latching technique, a method to control the movement of the body such that the response to the wave movement is improved. The model is extended to two horizontal dimensions and verified and validated against manufactured solutions and RANS simulations. The model is found to have a good accuracy both in one and two dimensions and is relevant for applications of waves interacting with wave energy devices. The model can be extended to simulate more complex cases such as WEC farms/arrays or include power generation systems to the device.

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No. of bitstreams: 2 Dissertação - Douglas Xavier de Andrade - 2016.pdf: 8750687 bytes, checksum: b47edd6565843d8ae15e173adda15ab2 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-10-13 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Among the main problems faced by Physics teachers in the Brazilian Basic Education system are: the distance of the contents studied from the daily lives of students and the lack of materials and methodologies suitable to work topics of Modern and Contemporary Physics in the classroom. Given the need to give referrals, at least in part, the problems mentioned above, the authors of this paper sought basically to work in three fundamental points: 1) Curriculum - expand undulating physics content to cover non-linear aspects of physical systems known such as the mass-spring system, the simple pendulum, waves on a string and shallow water in order to introduce the concept of soliton and some of its applications. 2) adaptable and accessible material for topics of Physics Nonlinear - talk about the educational potential of creating a website using the tools provided by "google sites"and present disclosure page (Solitons and phenomena nonlinear) and 3) methodology - report the experiences of the discussion of topics in nonlinear physics for high school students verifying the challenges and prospects of use of a website in the classroom context of a school public high school in the state of Goiás. Thus, it is _rst introduced the subject of study by presenting the research objectives and the dissertation of the structure and then we present topics of nonlinear physics based on systems which are usually treated only in a linear fashion in high school such as: the simple pendulum (when built a pendulum corresponding to na arrangement of coupled pendula), the mass-spring system (when we study a chain of particles coupled to each other by means of springs) and linear wave equation. The study of these systems leads respectively to the equation Sine-Gordon, the Toda model, and KdV equation when they are treated in a non-linear fashion. After these equations are discussed presented their solutions 1- and 2-solitons solutions using Hirota method. After analyzing the above systems, we discuss some natural physical phenomena where solitons are present and some of their technological applications. Later we perform a review of the literature, where we use theoretical concepts to support the use of Information and Communication Technologies (ICT) in science education, and presented a website built to introduce the subjects of nonlinear Physics in high school. Then we discuss a teaching sequence designed in order to provide the use of the internet page in the classroom and the results of the didactic sequence implementation are reported in the classroom indicating that the creation and use of a website is a important tool to work subjects of Nonlinear Physics in high school to allow the use of multiple virtual learning objects and motivate the continuity of the learning process outside the classroom context. / Entre os principais problemas enfrentados pelos professores de Física da Educação Básica brasileira se encontram: o distanciamento dos conteúdos estudados com o cotidiano dos estudantes e a falta de material e metodologias adequados para se trabalhar tópicos de Física Moderna e Contemporânea em sala de aula. Diante da necessidade de dar encaminhamentos, ao menos em parte, aos problemas, acima citados, os autores desta dissertação buscaram atuar basicamente em três pontos fundamentais: 1)Currículo - expandir os conteúdos de Física Ondulatória para abranger aspectos não-lineares de sistemas físicos conhecidos como o sistema massa-mola, o pêndulo simples, as ondas numa corda e em águas rasas com o intuito de introduzir o conceito de sóliton e algumas de suas aplicações para que professores da Educação Básica possam discutí-los em sala de aula; 2) Material adaptável e acessível de divulgação de tópicos de Física Não-Linear - discorrer sobre as potencialidades educacionais da criação de uma página na internet usando as ferramentas disponibilizadas pelo "google sites" e apresentar a página de divulgação "Sólitons e fenômenos não-lineares" e 3) Metodologia - relatar as experiências da discussão de tópicos de Física Não-Linear no Ensino Médio veri_cando os desa_os e potencialidades da utilização de uma página na internet no contexto de sala de aula de uma escola pública de Ensino Médio do Estado de Goiás. Dessa forma, inicialmente é introduzido o tema de estudo através da apresentação dos objetivos da pesquisa e da estrutura da dissertação e em seguida são apresentados tópicos de Física não-linear de sistemas físicos conhecidos geralmente tratados apenas em uma forma linear no Ensino Médio a saber: o pêndulo simples, o sistema massa-mola e equação de onda linear. O estudo desses sistemas em uma forma não-linear nos levam respectivamente à equação de Sine-Gordon (quando construímos um arranjo de pêndulos acoplados), ao Modelo de Toda (quando estudamos uma rede com N massa-molas ligados), e a Equação de KdV. Após discutidas essas equações são apresentadas as suas soluções para 1 e 2-sólitons utilizando o método de Hirota. Após a análise dos sistemas supracitados discorremos sobre alguns fenômenos físicos naturais onde os sólitons estão presentes e algumas aplicações tecnológicas dos mesmos. Posteriormente é feita uma revisão de literatura, onde utilizamos concepções teóricas para fundamentar a utilização das Tecnologias de Informação e Comunicação (TIC) no ensino de Ciências, e apresentada uma página na internet construída para introduzir os assuntos de Física Não-Linear no Ensino Médio. Por fim, discorre-se sobre uma sequência didática pensada de forma a propiciar o uso da página da internet em sala de aula e são relatados os resultados da implementação da sequência didática em sala de aula indicando que a criação e utilização de uma página na internet é uma importante ferramenta para se trabalhar assuntos de Física Não-Linear no Ensino Médio ao permitir o uso de diversos objetos virtuais de aprendizagem e motivar a continuidade do processo de aprendizagem fora do contexto de sala de aula.