ABSTRACT Under stationary atmosphere and on uniform depth, this paper treats the standing waves in real fluids formed by two progressive waves possessing same properties but in opposite direction. Being different from the preceding scholars who usually treated the waves in real fluids with boundary layer theory, the author uses complete Navior-Stokes Equ. to analyze the entire flow field. When dealing with the free surface dynamical boundary condition, under the equilibrium of forces, the author takes account of atmosphere pressure, shear stress and surface tension. As for the bottom condition, at first consider the perfect smooth, then no-sliding and sliding condition. After constructing the boundary conditions and the governing equation, perturbation method is used to get those of second order, and the second order solution can be derived. In addition to relative depth , the bottom-adherence affects the bottom boundary effect. No matter in progressive or standing wave fields, we can see the variation of over-shot height, the asymmetric diagrams of fluid particle¡¦s horizontal velocity with phases, the phase difference between the second and first order bottom shear. Besides, in standing wave field, the existence of second-order interaction term not only affects the flow field in the boundary layer but also the field outside it.

Within a wave energy converter's operational bandwidth, device operation tends to be optimal in converting mechanical energy into a more useful form at an incident wave period that is proximal to that of a power-producing mode of motion. Point absorbers, a particular classification of wave energy converters, tend to have a relative narrow optimal bandwidth. When not operating within the narrow optimal bandwidth, a point absorber's response and efficiency is attenuated. Given the wide range of sea-states that can be expected during a point absorber's operational life, these devices require a means to adjust, or control, their natural response to maximize the amount of energy absorbed in the large population of non-optimal conditions. In the field of wave energy research, there is considerable interest in the use of non-linear control techniques to this end. Non-linear control techniques introduce time-varying and state dependent control parameters into the point absorber motion equations, which usually motivates a computationally expensive numerical integration to determine the response of the device - important metrics such as gross converted power and relative travels of the device's pieces are extracted through post processing of the time series data. As an alternative, the work presented in this thesis was based on a closed form perturbation based approach for analysis of the response of a device with periodically-varying control parameters, subject to regular wave forcing, in the frequency domain. The proposed perturbation based method provides significant savings in computational time and enables the device's response to be represented in a closed form manner with a relatively small number of solution components - each component is comprised of a complex amplitude and oscillation frequency. This representation of the solution was found to be very concise and descriptive, and to lend itself to the calculation of gross absorbed power and travel constraint violations, making it extremely useful in the automated design optimization process; the methodology allows large number of design iterations, including both physical design and control variables, to be evaluated and conclusively compared. In the development of the perturbation method, it was discovered that the device's motion response can be calculated from an in nite series of second order ordinary differential equations that can be truncated without destroying the solution accuracy. It was found that the response amplitude operator for the generic form of a solution component provides a means to gauge the device's response to a given wave input and control parameter variation, including a gauge of the solution process stability. It is unclear as of yet if this is physical, a result of the solution process, or both. However, for a given control parameter set resulting in an unstable solution, the instability was shown to be, at least in part, a result of the device's dynamics. If the stability concerns can be addressed through additional constraints and updates to the wave energy converter hydrodynamic parameters, the methodology will expand on the commonly accepted boundaries for wave energy converter frequency domain analysis methods and be of much practical importance in the evaluation of control techniques in the field of wave energy converter technology. / Graduate

Yes / This article presents the homotopy perturbation method (HPM) employed to investigate the effects of inclination on the thermal behavior of a porous fin heat sink. The study aims to review the thermal characterization of heat sink with the inclined porous fin of rectangular geometry. The study establishes that heat sink of an inclined porous fin shows a higher thermal performance compared to a heat sink of equal dimension with a vertical porous fin. In addition, the study also shows that the performance of inclined or tilted fin increases with decrease in length–thickness aspect ratio. The study further reveals that increase in the internal heat generation variable decreases the fin temperature gradient, which invariably decreases the heat transfer of the fin. The obtained results using HPM highlights the accuracy of the present method for the analysis of nonlinear heat transfer problems, as it agrees well with the established results of Runge–Kutta. / Supported in part by the Tertiary Education Trust Fund of Federal Government of Nigeria, and the European Union’s Horizon 2020 research and innovation programme under grant agreement H2020-MSCA-ITN-2016SECRET-722424.

Standard statistical decision-making tools, such as inference, confidence intervals and forecasting, are contingent on the assumption that the statistical model used in the analysis is the true model. In linear mixed-effect models, ignoring model uncertainty results in an underestimation of the residual variance, contributing to hypothesis tests that demonstrate larger than nominal Type-I errors and confidence intervals with smaller than nominal coverage probabilities. A novel utilization of the generalized degrees of freedom developed by Zhang et al. (2012) is used to adjust the estimate of the residual variance for model uncertainty. Additionally, the general global linear approximation is extended to linear mixed-effect models to adjust the standard errors of the parameter estimates for model uncertainty. Both of these methods use a perturbation method for estimation, where random noise is added to the response variable and, conditional on the observed responses, the corresponding estimate is calculated. A simulation study demonstrates that when the proposed methodologies are utilized, both the variance and standard errors are inflated for model uncertainty. However, when a data-driven strategy is employed, the proposed methodologies show limited usefulness. These methods are evaluated with a trial assessing the performance of cervical traction in the treatment of cervical radiculopathy.

京都大学 / 0048 / 新制・課程博士 / 博士(エネルギー科学) / 甲第18384号 / エネ博第296号 / 新制||エネ||61(附属図書館) / 31242 / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 岸本 泰明, 教授 中村 祐司, 教授 松田 一成 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

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在這篇論文中，我們探討了在任何正參數之下，范德波爾方程的極限環結果。藉由改良後的同倫擾動方法，我們求得了一些極限環的近似結果。 相對於傳統的擾動方法，這種同倫方法在方程中並不受限於小的參數。除此之外，我們也設計了一個演算法來計算極限環的近似振幅及頻率。 / In this thesis, we study the limit cycle of van der Pol equation for parameter ε>0. We give some approximate results to the limit cycle by using the modified homotopy perturbation technique. In constract to the traditional perturbation methods, this homotopy method does not require a small parameter in the equation. Besides, we also devise a new algorithm to find the approximate amplitude and frequency of the limit cycle.

Dans le cadre de la présente thèse, on a procédé à l’étude du comportement dynamique d’un système d’engrenage comportant des paramètres incertains. Une des principales hypothèses faite dans l’utilisation des méthodes de prise en compte des incertitudes, est que le modèle est déterministe, c’est-à-dire que les paramètres utilisés dans le modèle ont une valeur définie et invariante. Par ailleurs, la connaissance du domaine de variation de la réponse dynamique du système dues aux incertitudes qui découle des coefficients d’amortissement, des raideurs d’engrènement, la présence de frottement entre les pièces, les défauts de montage et de fabrication ou l’inertie des pales dans le cas d’éolienne est essentielle. Pour cela, dans la première partie, on s’applique à décrire la réponse dynamique d’une transmission par engrenage comportant des paramètres modélisés par des variables aléatoires. Pour ce faire, nous utilisons la simulation de Monte Carlo, la méthode de perturbation et la méthode de projection sur un chaos polynomial. Dans la seconde partie,deux approches sont utilisées pour analyser le comportement dynamique d’un système d’engrenage d’éolienne : l’approche probabiliste et l’approche ensembliste basée sur la méthode d’analyse par intervalles. L'objectif consiste à comparer les deux approches pour connaitre leurs avantages et inconvénients en termes de précision et temps de calcul. / In the present work, the dynamic behavior of a gear system with uncertain parameters is studied. One of the principal hypotheses in the use of methods for taking into account uncertainties is that the model is deterministic, that is to say that parameters used in the model have a defined and fixed value. Furthermore, the knowledge of variation response of a gear system involving damping coefficients, mesh stiffness, friction coefficient, assembly defect, manufacturing defect or the input blades in the case of wind turbine is essential. In the first part, we investigate the dynamic response of a gear system with uncertain parameters modeled as random variables. A Monte Carlo simulation, a perturbation method and a polynomial chaos method are carried out. In the second part, two approaches are used to analyze the dynamic behavior of a wind turbine gear system : the probabilistic approach and the interval analysis method. The objective is to compare the two approaches to define their advantages and disadvantages in terms of precision and computation time.

A theoretical investigation of acoustic wave interactions with turbulent premixed flames was performed. Such interactions affect the characteristic unsteadiness of combustion processes, e.g., combustion instabilities. The small perturbation method (SPM) was utilized to evaluate the scattered fields as a result of the flame-wave interaction at the instantaneous wrinkling surface of a randomly moving turbulent flame. Stochastic analysis of ensemble-averaged net acoustic energy was conducted to examine coherent and incoherent acoustic energy amplification /damping by the interaction. Net acoustic energy flux out of the flame is due to two factors: the acoustic velocity jump due to unsteady heat release from flame. The other is the flames unsteady motion. Five(5) dimensionless parameters that govern this net acoustic energy were determined: rms height and correlation length of flame front, incident wave frequency, the ratio of flames diffusion time to flame fronts correlation time, and incidence angle. The dependence of net acoustic energy upon these dimensionless parameters was illustrated and discussed by numerical simulations in case of Gaussian statistics of flame front. The laminar flame response to equivalence ratio perturbations was also examined, showing that the overall heat release response is controlled by the superposition of three disturbances: heat of reaction, flame speed, and flame area. Heat of reaction disturbances dominate the flame response at low Strouhal numbers, roughly defined as (frequency x flame length)/(axial flow velocity). All three disturbances play equal roles at Strouhal numbers of O(1). In addition, the mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio.