Nanotechnology was named one of the key enabling technologies by the European Commission and its tremendous impact was envisioned early by 20th century physicist R.Feynman in his now oft-quoted talk "Plenty of Room at the bottom". Nanotechnology and nanoscience deal with structures barely visible with an optical microscope, yet much bigger than simple molecules. Matter at this mesoscale is often awkward to explore as it contains too many atoms to be easily understood by straightforward application of quantum mechanics (although the fundamental laws still apply). Yet, these systems are not so large as to be completely free of quantum effects; thus, they do not simply obey the classical physics governing the macroworld. It is precisely in this intermediate regime, the mesoworld, that unforeseen properties of collective systems emerge. To fully exploit the potential of nanotechnology, a thorough understanding of these properties is paramount. The objective of the present thesis is to investigate and to control the dynamics of an optically levitated particle in high vacuum, a system which belongs to the broader class of nanomechanical oscillators. Nanomechanical oscillators exhibit high resonance frequencies, diminished active masses, low power consumption and high quality factors - significantly higher than those of electrical circuits. These attributes make them suitable for sensing, transduction and signal processing. Furthermore, nanomechanical systems are expected to open up investigations of the quantum behavior of mesoscopic systems. Testing the predictions of quantum theory on macroscopic scales is one of today's outstanding challenges of modern physics and addresses fundamental questions on our understanding of the world. The state-of-the-art in nanomechanics itself has exploded in recent years, driven by a combination of interesting new systems and vastly improved fabrication capabilities. Despite major break-throughs, including ground state cooling, observation of radiation pressure shot noise, squeezing and demonstrated ultra-high force and mass sensitivity, difficulties in reaching ultra-high mechanical quality (Q) factors still pose a major limitation for many of the envisioned applications and significant improvements in mechanical quality (Q) factors are generally needed to facilitate quantum coherent manipulation. This is difficult given that many mechanical systems are approaching fundamental limits of dissipation. To overcome the limitations set by dissipation, I developed an experiment to trap and cool nanoparticles in high vacuum. The combination of nanoparticles and vacuum trapping results in a very light and ultra-high-Q mechanical oscillator. In fact, the Q-factor achieved with this setup is the highest observed so far in any nano- or micromechanical system. The scope of the thesis ranges from a detailed description of the experimental apparatus and proof-of-principle experiments (parametric feedback cooling) to the first observation of phenomena owing to the unique parameters of this novel optomechanical system (thermal nonlinearities). Aside from optomechanics and optical trapping, the topics covered include the dynamics of complex (nonlinear) systems and the study of fluctuation theorems, the latter playing a pivotal role in statistical physics. Optically trapped nanoparticles are just beginning to emerge as a new class of optomechanical systems. Owing to their unique mechanical properties, there is clearly a vast and untapped potential for further research. Primary examples of how levitated particles in high vacuum can impact other fields and inspire new research avenues have been the first observation of thermal nonlinearities in a mechanical oscillator and the study of fluctuation relations with a high-Q nanomechanical resonator. Based on recent progress in the field, a plethora of fundamental research opportunities and novel applications are expected to emerge as this still young field matures.

No description available.

Debris flows can be highly destructive and pose a significant threat to both life and property in those areas in which they naturally occur. Such flows can be especially hazardous when large amplitude surges form, which cause more damage than continuous flows of the same mass flux. It is therefore important to understand how these surges form and subsequently behave. The most likely explanation for their formation is the spontaneous development of roll waves - small shock-like disturbances typically observed in thin liquid films - which merge and coarsen as they travel downslope, in turn growing in amplitude and wavespeed. There have also been observations of naturally occurring debris flows which develop surges with regions of completely stationary material between them. The terminology of 'erosion-deposition' waves is introduced to describe these waves, according to the process by which they propagate steadily through a flow by eroding at the static layer ahead of the wave front and depositing a stationary layer behind it. This behaviour is particularly novel and the pulses can be even more destructive than their roll wave counterparts. A combination of experimental observations, travelling-wave solutions and numerical simulations are used here to study the behaviour of both roll waves and erosion-deposition waves in granular flows.

朱寶盈. / "2006年8月" / 論文(哲學碩士)--香港中文大學, 2006. / 參考文獻(leaves 164-169). / "2006 nian 8 yue" / Abstracts in Chinese and English. / Zhu Baoying. / Lun wen (zhe xue shuo shi)--Xianggang Zhong wen da xue, 2006. / Can kao wen xian (leaves 164-169). / 目錄 --- p.V / Chapter 第一章 --- 緒論 --- p.1 / Chapter 第一節 --- 引言 --- p.1 / Chapter 第二節 --- 《昭明太子集》 --- p.4 / Chapter 第三節 --- 前人研究述評 --- p.5 / Chapter 一、 --- 主要硏究觀點 --- p.5 / Chapter 二、 --- 蕭統詩作硏究商榷 --- p.8 / Chapter 第四節 --- 硏究目的及方向 --- p.12 / Chapter 第二章 --- 蕭統詩作析論（一）：從意象論其典麗風格 --- p.14 / Chapter 第一節 --- 引言 --- p.14 / Chapter 第二節 --- 駢句的運用´ؤ´ؤ意象的突顯 --- p.15 / Chapter 一、 --- 蕭詩駢句的應用情形 --- p.16 / Chapter 1) --- 詩作的基本結構單位 --- p.16 / Chapter 2) --- 屬對工整嚴密，具元嘉味道 --- p.17 / Chapter 二、 --- 駢句與意象的突顯 --- p.23 / Chapter 1) --- 相關理論 --- p.23 / Chapter 2) --- 駢句在蕭統詩中的情形 --- p.25 / Chapter 第三節 --- 蕭統詩基調的形成´ؤ´ؤ辭藻的修飾與意象的性質傾向 --- p.31 / Chapter 一、 --- 意象的性質傾向 --- p.31 / Chapter 1) --- 色彩華麗的意象 --- p.32 / Chapter 2) --- 典正雍容的意象 --- p.35 / Chapter 二、 --- 冷靜客觀的景物描寫 --- p.38 / Chapter 第四節 --- 結語 --- p.42 / Chapter 第三章 --- 蕭統詩作析論（二）：論蕭詩的典故運用 --- p.44 / Chapter 第一節 --- 引言 --- p.44 / Chapter 第二節 --- 用典的準則一一風格與內容的配合 --- p.45 / Chapter 一、 --- 體式 --- p.46 / Chapter 二、 --- 題材內容 --- p.47 / Chapter 第三節 --- 典故的構成形式與詩歌密度的提升 --- p.51 / Chapter 一、 --- 典故的構成形式 --- p.52 / Chapter 1) --- 截取具代表性的詞語 --- p.55 / Chapter 2) --- 壓縮原典句子 --- p.56 / Chapter 3) --- 改變原典次序和結構 --- p.57 / Chapter 二、 --- 用典方法對詩歌效果的影響 --- p.58 / Chapter 第四節 --- 以典故達意的具體情形 --- p.62 / Chapter 一、 --- 以典詠物 --- p.62 / Chapter 二、 --- 以典詠人 --- p.67 / Chapter 三、 --- 以典抒情 --- p.70 / Chapter 第五節 --- 結語 --- p.73 / Chapter 第四章 --- 蕭統詩與齊梁新變詩風之比較 --- p.75 / Chapter 第一節 --- 引言 --- p.75 / Chapter 第二節 --- 齊梁新變詩風 --- p.76 / Chapter 一、 --- 齊梁文學的新變思潮 --- p.76 / Chapter 二、 --- 「永明體」 --- p.79 / Chapter 三、 --- 「宮體」 --- p.80 / Chapter 第三節 --- 蕭統詩與「永明體」及「宮體」之比較 --- p.82 / Chapter 一、 --- 體式 --- p.83 / Chapter 二、 --- 題材 --- p.90 / Chapter 1) --- 與「永明體」的比較 --- p.90 / Chapter 2) --- 與「宮體」的比較 --- p.92 / Chapter 3) --- 佛教眾會 --- p.97 / Chapter 4) --- 小結 --- p.100 / Chapter 三、 --- 聲律 --- p.101 / Chapter 四、 --- 語言 --- p.108 / Chapter 第四節 --- 結語 --- p.113 / Chapter 第五章 --- 蕭統與梁朝詩壇 --- p.115 / Chapter 第一節 --- 引言 --- p.115 / Chapter 第二節 --- 蕭統與東宮文人 --- p.116 / Chapter 一、 --- 東宮文人的主要成員簡介 --- p.116 / Chapter 二、 --- 蕭統及東宮文人之關係 --- p.122 / Chapter 第三節 --- 東宮文人的文學主張及創作傾向 --- p.126 / Chapter 一、 --- 文學主張 --- p.127 / Chapter 1) --- 劉孝綽 --- p.127 / Chapter 2) --- 王筠 --- p.130 / Chapter 二、 --- 創作傾向 --- p.132 / Chapter 1) --- 劉孝綽 --- p.133 / Chapter 2) --- 王筠 --- p.138 / Chapter 3) --- 小結 --- p.141 / Chapter 第四節 --- 蕭統與梁朝中期詩壇 --- p.145 / Chapter 一、 --- 關於「蕭統文學集團」說 --- p.146 / Chapter 二、 --- 關於「梁朝中期復古思潮」說 --- p.151 / Chapter 第五節 --- 關於《文選》編纂者的爭議 --- p.157 / Chapter 第六節 --- 結語 --- p.159 / Chapter 第六章 --- 總結 --- p.161 / 主要參考書目 --- p.164 / 附錄一：劉孝綽短篇詩作中的入律句子 --- p.170 / 附錄二：王筠短篇詩作中的入律句子 --- p.175

We give an alternate description of the usual shell equation that does not depend on the special mid surface coordinates, but uses differential operators defined on the mid surface.:1 Introduction 2 Basic differential geometry 3 The strain tensor and its simplifications 4 The resulting shell energy 5 Introducing the Kirchhoff-Hypothesis towards Koiter-shell

This thesis explores the use of stabilized finite element formulations for the incompressible Navier-Stokes equations to simulate turbulent flow problems. Turbulence is a challenging problem due to its complex and dynamic nature and its simulation if further complicated by the fact that it involves fluid motions at vastly different length and time scales, requiring fine meshes and long simulation times. A solution to this issue is turbulence modeling, in which only the large scale part of the solution is retained and the effect of smaller turbulent motions is represented by a model, which is generally dissipative in nature. In the context of finite element simulations for fluids, a second problem is the apparition of numerical instabilities. These can be avoided by the use of stabilized formulations, in which the problem is modified to ensure that it has a stable solution. Since stabilization methods typically introduce numerical dissipation, the relation between numerical and physical dissipation plays a crucial role in the accuracy of turbulent flow simulations. We investigate this issue by studying the behavior of stabilized finite element formulations based on the Variational Multiscale framework and on Finite Calculus, analyzing the results they provide for well-known reference problems, with the final goal of obtaining a method that both ensures numerical stability and introduces physically correct turbulent dissipation. Given that, even with the use of turbulence models, turbulent flow problems require significant computational resources, we also focused on programming and implementation aspects of finite element codes, specially in ensuring that our solver can perform efficiently on distributed memory architectures and high-performance computing clusters. Finally, we have developed an adaptive mesh refinement technique to improve and optimize unstructured tetrahedral meshes, again with the goal of enabling the simulation of large turbulent flow problems. This technique combines an error estimator based on Variational Multiscale principles with a simple refinement procedure designed to work in a distributed memory context and we have applied it to the simulation of both turbulent and non-Newtonian flow problems. / Aquesta tesi estudia la possibilitat d'utilitzar formulacions estabilitzades d'elements finits de les equacions de Navier-Stokes incompressibles per a la simulació de problemes de flux turbulent. La descripció de la turbulència és un repte, ja que es tracta d'un problema altament dinàmic i complex i la seva simulació numèrica es veu complicada pel fet que hi intervenen moviments de masses fluides amb dimensions i temps característics molt diferents i per tant requereix malles de càlcul molt fines i temps de simulació llargs. Això s'ha provat de resoldre mitjançant l'ús de models de turbulència, mantenint únicament la part de la solució de més gran escala i introduint un model de l'efecte dels moviments de petita escala, que acostuma a tenir un efecte dissipatiu. En el context de la simulació de fluids amb elements finits es planteja un segon problema amb l'aparició d'inestabilitats numèriques. Aquestes es poden evitar amb l'ús de formulacions estabilitzades, en les quals el problema es modifica per assegurar que tingui una solució estable. Ja que els mètodes d'estabilització típicament introdueixen dissipació addicional, la relació entre la dissipació numèrica i la dissipació física té un paper fonamental en la qualitat de la solució. Per investigar aquest fenomen hem estudiat el comportament de diferents formulacions d'elements finits basades en mètodes variacionals de subescala (VMS) i en el càlcul finit (FIC) en termes del seu comportament en la simulació de problemes turbulents de referència, amb l'objectiu final de trobar un mètode que a la vegada garanteixi l'estabilitat de la solució i introdueixi la dissipació turbulenta físicament necessària. Tenint en compte que, fins i tot quan s'utilitzen models de turbulència, la simulació de problemes de flux turbulent requereix molts recursos de càlcul, també hem estudiat aspectes de la implementació paral·lela de programes d'elements finits per tal de garantir que el nostre codi pot treure partit d'arquitectures de memòria distribuïda i servidors de càlcul d'alt rendiment. Finalment, hem desenvolupat una tècnica de refinament adaptatiu de malla que permeti millorar la qualitat de malles de càlcul tetraèdriques, novament amb la intenció de facilitar la simulació de grans problemes de flux turbulent. Aquesta tècnica combina un estimador d'error basat en els principis de la formulació variacional de subescala amb un procediment de refinament dissenyat per funcionar fàcilment en un context de memòria distribuïda i s'ha utilitzat per simular problemes de flux turbulent i no-Newtonià.

This thesis is about the stabilization of the numerical solution of the Euler and Navier- Stokes equations of compressible flow. When simulating numerically the flow equations, if no stabilization is added, the solution presents non-physical (but numerical) oscillations. For this reason the stabilization of partial differential equations and of the fluid dynamics equations is of great importance. In the framework of the so-called variational multiscale stabilization, we present here a stabilization method for compressible flow. The method assessment is done first of all on a batch of academical examples for different Mach numbers, for viscous and inviscid, steady and transient flow. Afterwards the method is applied to atmospheric flow simulations. To this end we solve the Euler equations for dry and moist atmospheric flow. In the presence of moisture a set of transport equations for water species should be solved as well. This domain of application is a real challenge from the stabilization point of view because the correct amount of stabilization must be added in order to preserve the physical properties of the atmospheric flow. At this point, in order to even improve our method, we turn towards local preconditioning. Local preconditiong permits to reduce the stiffness problems that present the flow equations and cause a bad and slow convergence to the solution. With this purpose in mind we combine our stabilization method with local preconditioning and present a stabilization method for the preconditioned Navier-Stokes equations of compressible flow, that we call P-VMS. This method is tested over several examples at different Mach numbers and proves a significant improvement not only in the convergence to the solution but also in the accuracy and robustness of the method. Finally, the benefits of P-VMS are theoretically assessed using Fourier stability analysis. As a result of this analysis a modification on the computation of the time step is done even improving the convergence of the method. / Aquesta tesi tracta sobre l'estabilització de la solució numèrica de les equacions d'Euler i Navier-Stokes de flux compressible. Quan es simulen numèricament les equacions que governen els fluids, si no s'afegeix cap estabilització, la solució presenta oscil·lacions no físiques sinó numèriques. Per aquest motiu l'estabilització de les equacions en derivades parcials i de les equacions de la mecànica de fluids és de gran importància. Dins del marc de l'anomenada estabilització de multiescales variacionals, presentem aquí un mètode d'estabilització per flux compressible. L'evaluació del mètode es realitza primer en varis exemples acadèmics per diferents nombres de Mach, per flux viscós, inviscid, estacionari i transitori. Després el mètode s'aplica a simulacions de flux atmosfèric. Per això, resolem les equacions d'Euler per flux atmosfèric sec i humit. En presència d'humitat, també s'ha de resoldre un grup d'equacions de transport d'espècies d'aigua. Aquest domini d'aplicació representa un desafiament des del punt de vista de l'estabilització, donat que s'ha d'afegir la quantitat adequada d'estabilització per tal de preservar les propietats físiques del flux atmosfèric. Arribat aquest punt, per tal de millorar el nostre mètode, ens interessem pels precondicionadors locals. Els precondicionadors locals permeten reduir els problemes de rigidesa que presenten les equacions dels fluids i que són causa d'una pitjor i més lenta convergència cap a la solució. Amb aquest propòsit en ment, combinem el nostre mètode d'estabilització amb els precondicionadors locals i presentem un mètode d'estabilització per les equacions de Navier-Stokes de flux compressible, anomenem aquest màtode P-VMS. Aquest mètode es evaluat per mitjà de varis exemples per diferents nombres de Mach i demostra una millora sustancial no només pel que fa la convergència cap a la solució, sinó també en la precisió i robusteza del mètode. Finalment els beneficis del P-VMS es demostren teòricament a través de l'anàlisi d'estabilitat de Fourier. Com a resultat d'aquest anàlisi, sorgeix una modificació en el càlcul del pas de temps que millora un cop més la convergència del mètode

Modelling vibroacoustic problems in the field of building design is a challenging problem due to the large size of the domains and the wide frequency range required by regulations. Standard numerical techniques, for instance finite element methods (FEM), fail when trying to reach the highest frequencies. The required element size is too small compared to the problem dimensions and the computational cost becomes unaffordable for such an everyday calculation. Statistical energy analysis (SEA) is a framework of analysis for vibroacoustic problems, based on the wave behaviour at high frequencies. It works directly with averaged magnitudes, which is in fact what regulations require, and its computational cost is very low. However, this simplified approach presents several limitations when dealing with real-life structures. Experiments or other complementary data are often required to complete the definition of the SEA model. This thesis deals with the modelling of building acoustic problems with a reasonable computational cost. In this sense, two main research lines have been followed. In the first part of the thesis, the potential of numerical simulations for extending the SEA applicability is analysed. In particular, three main points are addressed: first, a systematic methodology for the estimation of coupling loss factors from numerical simulations is developed. These factors are estimated from small deterministic simulations, and then applied for solving larger problems with SEA. Then, an SEA-like model for non-conservative couplings is presented, and a strategy for obtaining conservative and non-conservative coupling loss factors from numerical simulations is developed. Finally, a methodology for identifying SEA subsystems with modal analysis is proposed. This technique consists in performing a cluster analysis based on the problem eigenmodes. It allows detecting optimal SEA subdivisions for complex domains, even when two subsystems coexist in the same region of the geometry. In the second part of the thesis, the sound transmission through double walls is analysed from different points of view, as a representative example of the complexities of vibroacoustic simulations. First, a compilation of classical approaches to this problem is presented. Then, the finite layer method is proposed as a new way of discretising the pressure field in the cavity inside double walls, especially when it is partially filled with an absorbing material. This method combines a FEM-like discretisation in the direction perpendicular to the wall with trigonometric functions in the two in-plane directions. This approach has less computational cost than FEM but allows the enforcement of continuity and equilibrium between fluid layers. It is compared with experimental data and also with other prediction models in order to check the influence of commonly assumed simplifications. Finally, a combination of deterministic and statistical methods is presented as a possible solution for dealing with vibroacoustic problems consisting of double walls and other elements. The global analysis is performed with SEA, and numerical simulations of small parts of the problem are used to obtain the required parameters. Combining these techniques, a realistic simulation of the vibroacoustic problem can be performed with a reasonable computational cost.

The asymptotic behaviour of an elastically supported infinite string and an elastic isotropic half plane (in frames of specific asymptotic model) under a moving point load are studied. The main results of this work are uniform asymptotic formulae and the asymptotic profile for the string and the exact solution and uniform asymptotic formulae for a half plane. The crucial assumption for both structures is that the acceleration is sufficiently small. In order to describe asymptotically the oscillations of an infinite string auxiliary canonical functions are introduced, asymptotically analyzed and tabulated. Using these functions uniform asymptotic formulae for the string under constant accelerating and decelerating point loads are obtained. Approximate formulae for the displacement in the vicinity of the point load and the singularity area behind the shock wave using the steady speed asymptotic expansion with additional contributions from stationary points where appropriate are derived. It is shown how to generalise uniform asymptotic results to the arbitrary acceleration case. As an example these results are applied for the case of sinusoidal load speed. It is shown that the canonical functions can successfully be used in the arbitrary acceleration case as well. The graphical comparative analysis of numerical solu- tion and approximations is provided for different moving load speed intervals and values of the parameters. Vibrations of an elastic half plane are studied within the framework of the asymp- totic model suggested by J. Kaplunov et al. in 2006. Boundary conditions for the main problem are obtained as a solution for the problem of a string on the surface of a half plane subject to uniformly accelerated moving load. The exact solution over the interior of the half plane is derived with respect to boundary conditions. Steady speed and Rayleigh wave speed asymptotic expansions are obtained. In the neighborhood of the Rayleigh speed the uniform asymptotic formulae are derived. Some of their interesting properties are discovered and briefly studied. The graphical comparative analysis of the exact solution and approximations is provided for different moving load speed intervals and values of the parameters.

Les joints sans contact sont des solutions d’étanchéité optimales pour les systèmes mécaniques fonctionnant à des vitesses relativement élevées. Ils ont une durée de vie importante et ont été proposés pour une utilisation dans les moteurs spatiaux. Une type de joints d'étanchéité sans contact, le joint visqueux, est étudié en détail dans ce travail de thèse au moyen d'une analyse numérique et expérimentale. Ce travail présente un modèle numérique développé pour prédire le comportement du joint visqueux en régime laminaire et turbulent. L’interface liquide-air dans le joint est également étudiée en utilisant une approche CFD basée sur la méthode VOF. La conception et la réalisation d’un dispositif expérimental a permis de confronter les résultats numériques et expérimentaux, l’écart entre les deux approches n’excède pas 10% dans 95% des cas étudiés. / Contactless seals are optimal sealing solution for mechanical systems operating with relatively high speeds. They have an important operation life time, and they were proposed for use in space engines. One sub-category of non-contact seals, the viscoseal, is studied in detail in this work through a numerical and experimental analysis. This work presents a numerical model developed to predict the viscoseal performance in laminar and turbulent regime. Furthermore the sealing performance of the viscoseal is investigated for different geometrical characteristics of the seal. The interface liquid-air in the seal is also studied using a CFD approach based on VOF method. The design and installation of an experimental device allowed the comparison of the numerical and experimental results, the difference between the two does not exceed 10% for 95% of studied cases.