Ko, Tze Cheung = 均勻湍流對流殼模型內的熱傳送及雷諾數標度律 / 高子翔. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 76-78). / Abstracts in English and Chinese. / Ko, Tze Cheung = Jun yun tuan liu dui liu ke mo xing nei de re chuan song ji Leinuo shu biao du lü / Gao Zixiang. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Description of Rayleigh-Benard convection --- p.2 / Chapter 1.2 --- Interesting issues in turbulent Rayleigh-Benard convection --- p.3 / Chapter 2 --- Earlier studies of heat transport in Rayleigh-Benard convection --- p.6 / Chapter 2.1 --- Marginal stability arguments --- p.7 / Chapter 2.2 --- The Chicago mixing zone model --- p.8 / Chapter 2.3 --- Shraiman and Siggia theory --- p.10 / Chapter 2.4 --- Grossmann and Lohse theory --- p.12 / Chapter 2.4.1 --- Estimating the kinetic dissipation rates due to boundary layer and bulk --- p.13 / Chapter 2.4.2 --- Estimating the thermal dissipation rates due to boundary layer and bulk --- p.13 / Chapter 2.4.3 --- The four regimes --- p.15 / Chapter 2.5 --- The asymptotic limit of very high Ra --- p.17 / Chapter 3 --- The shell model used --- p.20 / Chapter 3.1 --- Background of shell models of turbulence --- p.20 / Chapter 3.2 --- The model used --- p.22 / Chapter 3.2.1 --- The Brandenburg model --- p.22 / Chapter 3.2.2 --- The requirement of a large scale drag term --- p.23 / Chapter 3.3 --- Previous work on the Brandenburg model --- p.24 / Chapter 4 --- "Definitions of Ra, Nu, and Re and two exact results" --- p.26 / Chapter 4.1 --- Heat transport study using shell model --- p.26 / Chapter 4.2 --- Two exact results --- p.28 / Chapter 5 --- Results and discussions --- p.29 / Chapter 5.1 --- Parameters used --- p.29 / Chapter 5.2 --- "Nu(Ra,Pr) and Re(Ra,Pr) scaling results" --- p.29 / Chapter 5.3 --- "Scaling results of ε, εdrag and x" --- p.32 / Chapter 5.4 --- Physical meaning of the drag term --- p.35 / Chapter 5.5 --- Understanding the dependence of ε on Re --- p.36 / Chapter 5.6 --- Understanding the dependence of x and εdrag on Re and Pr --- p.40 / Chapter 5.7 --- The form of the added drag term --- p.41 / Chapter 6 --- Possible changes of Nu and Re due to non-Boussinesq effects --- p.43 / Chapter 6.1 --- Background --- p.43 / Chapter 6.2 --- Method of study --- p.44 / Chapter 6.3 --- Effects due to the temperature dependence of kinematic viscosity --- p.45 / Chapter 6.4 --- Effects due to the temperature dependence of thermal diffusivity --- p.50 / Chapter 6.5 --- Effects due to the temperature dependence of volume expansion coefficient --- p.55 / Chapter 6.6 --- Understanding the scaling behavior under non-Boussinesq effects --- p.61 / Chapter 6.6.1 --- Scaling behavior of x on Re --- p.61 / Chapter 6.6.2 --- Scaling behavior of εtotai on Re --- p.65 / Chapter 6.6.3 --- Scaling behavior of Nu and Re on Ra --- p.66 / Chapter 6.7 --- Summary and future work --- p.68 / Chapter 7 --- Conclusion --- p.69 / Chapter A --- Height independence of Nu for homogeneous turbulent convection with periodic boundary conditions --- p.73 / Chapter B --- "Height independence of (uz)A,t for homogeneous turbulent convection with periodic boundary conditions" --- p.75 / Bibliography --- p.76

Typescript. / Digitized by Kansas Correctional Industries

Tese de mestrado integrado. Engenharia Química. Faculdade de Engenharia. Universidade do Porto. 2010

This papers is divided into numbered sections. The equations are numbered anew in each section, and equation numbers are always enclosed in parentheses. Merely the equation number is given when referring to an equation in the same section as the references; otherwise the section number is prefixed. Thus equation (4) refers to the fourth equation of the same section as the reference, and equation (2.2) refers to the second equation of the second section.

La propagation des ondes élastiques dans les structures périodiques infinies est décrite par la théorie de Floquet-Bloch. Les contraintes expérimentales conduisant nécessairement à des cristaux phononiques de taille finie, des écarts à la théorie sont donc envisageables. Par ailleurs, le comportement expérimental des ondes élastiques au sein de ces milieux périodiques est mal décrit à ce jour, car déduit du signal transmis. Ainsi, un grand nombre de phénomènes, n'existant qu'au sein des cristaux, ne peuvent être mis en évidence. La première partie de ce travail expérimental vise à mieux appréhender la dispersion des ondes élastiques se propageant au sein de cristaux phononiques bidimensionnels. Ces derniers sont composés d'inclusions d'air obtenues par photolithographie et attaque chimique de plaques minces de silicium. Un montage "ultrasons-laser", permettant la génération et la détection d'ondes élastiques en tout point de la surface de l'échantillon, a été mis au point. L'analyse des champs de déplacements de surface a permis la mise en évidence de la décomposition des vecteurs d'onde telle que prédite par la théorie de Floquet-Bloch. Une observation des modes à vitesse de groupe nulle en bord de gap a également été réalisée. Enfin, l'influence de la dissymétrie des inclusions sur l'ouverture de gap intra-bande a été étudiée. La seconde partie de ce travail est consacrée à l'observation expérimentale de la réfraction négative d'ondes élastiques, de Lamb et de Rayleigh, par des cristaux phononiques à deux dimensions et à matrices solides (silicium et silice). Le lien entre la propagation des ondes au sein du cristal phononique et leur réfraction à l'interface avec le milieu homogène est établi.

Le contexte général dans lequel s'inscrivent les travaux développés dans ce mémoire est le contrôle des processus industriels complexes. Ces travaux proposent des nouvelles techniques d'amélioration du contrôle statistique des processus non gaussiens : la carte de contrôle avec des paramètres variables et la carte de contrôle théorique pour la loi de distribution de Rayleigh. Un modèle d'intégration des outils des domaines de l'APC ( Automatic Process Control ) et de la MSP est proposée et ensuite analysée par le biais des deux modèles de processus réel.

The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions. We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes. The algorithms developed can be applied to other fields where a variational form of the problem exists and where such tensor product B-spline functions can be specified as potential solutions.

Esta investigación está conducida a la resolución del problema de encontrar soluciones rentables para el despliegue de redes de fibra hasta el hogar (Fibre to the Home - FTTH). En una red de FTTH, el equipo transmisor-receptor de usuario así como el despliegue de la fibra en la llamada 'última milla' son las barreras principales. Una topología que consiste en hacer llegar una única fibra para dirigirse a cada usuario reduce la cantidad de fibra requerida. Por otro lado, los componentes ópticos pasivos alivian los requisitos de mantenimiento de la red de acceso. El efecto del backscattering de Rayleigh se ha identificado como la interferencia más crítica de este tipo de transmisión, el efecto sobre el funcionamiento del sistema y las investigaciones de posibles soluciones al mencionado problema son centro de estudio de esta tesis. Los experimentos realizados, revelan que, a pesar de la interferencia causada por del effecto Rayleigh no se puede eliminar totalmente, hay diferentes técnicas capaces de atenuar dicho efecto. El uso de los amplificadores ópticos semiconductores para implementar las funciones de transmisión-recepción agrega simplicidad al diseño de red en términos de transparencia de la longitud de onda y gracias a las capacidades de la amplificación de esta familia de dispositivos.Los resultados experimentales presentaron en este trabajo demuestran con éxito la modulación y la detección a 1Gbit/s y 2.5Gbit/s con los dispositivos basados en semiconductores, en enlaces de hasta 30km e incluso de hasta 50km de longitud. Nuevos prototipos son potencialmente capaces de transmitir a 10Gbit/s. Estructuras reflectoras basadas en amplificadores ópticos semiconductores reflectores son los candidatos mas adecuados.Éstos, realizan funciones de transmisión eficientemente y proporcionan la amplificación adecuada. Sin embargo, es necesario el diseño de nuevos diseños capaces de transmitir datos a una velocidad mayor. Una estrategia de comunicación bidireccional mediante una única fibra es la arquitectura más interesante los términos de reducción de costes por usuario (CAPEX). Por estos motivos, la ONU se convierte en un elemento clave en redes de acceso y un área muy interesante de investigación. Para una evolución exitosa de FTTH el diseño de la unidad de red debe ser simple, robusto, flexible y bajo coste para el cliente final. La traducción de los requisitos anteriormente mencionados en especificaciones técnicas establece las pautas siguientes para el diseño del FTTH ONU- Una única fibra por cada usuario para reducir tamaño de la red de acceso- Independencia de la longitud de onda para permitir una operación transparente en redes WDM- Que no haya fuente de luz activa en las dependencias de usuario para prevenir el mantenimiento en el lado del usuario- Con amplificación y así poder aumentar el número de usuarios y alcanzar mayores distanciasDe esta manera, el objetivo principal de esta tesis es la investigación de unidades ópticas de red reflectoras, especialmente las basadas en amplificadores ópticos de semiconductor, así como su funcionamiento en redes de FTTH, basadas en tecnología de acceso WDM-PON. Esto implica fundamentalmente- Identificar arquitecturas y dispositivos propuestos por medio de la investigación del trabajo publicado relacionado y destacar limitaciones y requisitos de los sistemas actuales- evaluar las diversos alternativas para la ONU y para proponer soluciones mejoradas, demostradas con simulaciones y experimentos - investigar limitaciones posibles de los sistemas transmisión bidireccionales y desarrollar soluciones para la mejora de la transmisión- desarrollar descripciones analíticas de las señales implicadas en la transmisión / This research was conducted to deal with the problem of finding cost-effective solutions for Fibre-to-the-Home (FTTH) network deployment. In the FTTH network, the transceiver at the user premises and the deployment of fibre at the last mile are the major barriers. A single-fibre topology to address each user reduces the amount of fibre required; passive optical components alleviate maintenance requirements in the access network.The Rayleigh backscattering effect is identified as the most critical crosstalk in such transmission, the effect on the system performance and the investigations of possible solutions are presented in this thesis. The studies reveal that despite the Rayleigh backscattering crosstalk can not be totally eliminated, several techniques can mitigate the effect.The use of the semiconductor optical amplifiers to feature transceiver tasks at the user premises adds simplicity to the network design in terms of wavelength transparency and amplification capabilities. We propose implementations with semiconductor amplifiers and test modulation and detection potentials inside the optical network. The experimental results successfully demonstrate modulation and detection at 1Gbit/s and 2.5Gbit/s with semiconductor-based devices, in links of 30km and even though of 50km length; bit rate of 10Gbit/s is feasible with novel prototypes as well. Reflective structures based on reflective semiconductor optical amplifiers are potential candidates, as they perform transmission functions efficiently and provide adequate amplification however, it is necessary the design of further structures capable of transmitting at a higher bit rates.

In pursuit of negatively associated measures, this thesis focuses on certain negative correlation properties in matroids. In particular, the results presented contribute to the search for matroids which satisfy $$P(\{X:e,f\in X\}) \leq P(\{X:e\in X\})P(\{X:f\in X\})$$ for certain measures, $P$, on the ground set. Let $\mathcal M$ be a matroid. Let $(y_g:g\in E)$ be a weighting of the ground set and let $${Z = \sum_{X}\left( \prod_{x\in X} y_x\right) }$$ be the polynomial which generates Z-sets, were Z $\in \{$ B,I,S $\}$. For each of these, the sum is over bases, independent sets and spanning sets, respectively. Let $e$ and $f$ be distinct elements of $E$ and let $Z_e$ indicate partial derivative. Then $\mathcal M$ is Z-Rayleigh if $Z_eZ_f-ZZ_{ef}\geq 0$ for every positive evaluation of the $y_g$s. The known elementary results for the B, I and S-Rayleigh properties and two special cases called negative correlation and balance are proved. Furthermore, several new results are discussed. In particular, if a matroid is binary on at most nine elements or paving or rank three, then it is I-Rayleigh if it is B-Rayleigh. Sparse paving matroids are B-Rayleigh. The I-Rayleigh difference for graphs on at most seven vertices is a sum of monomials times squares of polynomials and this same special form holds for all series parallel graphs.

This research investigates the effects of beam diffraction from a source of finite width on nonlinear Rayleigh wave propagation in an elastic half space. Previous work has shown that nonlinear ultrasonic Rayleigh waves can be used to evaluate material damage due to plastic deformation and fatigue. In this measurement, a relatively small wedge transducer is employed to launch Rayleigh surface waves in the specimen and the first and second harmonic amplitudes are measured in the far field as a function of propagation distance. In order to obtain a reliable set of measurement data, one needs to make numerous points in a wide range of distance, which can be impractical in many cases. This research investigates model is employed and the computation results are compared with experiment ones. This research will make measurements on 7075-T651 aluminum as a specimen, compensate the diffraction effects and then, will compare the feasibility of the method proposed in this research in the results of normalized second harmonic amplitude vs propagation distance.