Yu, Rongfeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 57-63). / Abstracts in English and Chinese. / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.11 / Chapter 1.1 --- Notations and function spaces --- p.11 / Chapter 1.2 --- Some useful inequalities --- p.12 / Chapter 1.3 --- Fundamental lemmas --- p.15 / Chapter 2 --- Compressible Navier-Stokes Equations for Quantum Fluids --- p.16 / Chapter 2.1 --- Background --- p.17 / Chapter 2.2 --- Derivation of model --- p.17 / Chapter 3 --- Global Weak Solutions to Barotropic Navier-Stokes Equations for Quantum Fluids --- p.22 / Chapter 3.1 --- Reformulation and main results --- p.23 / Chapter 3.2 --- Construction of approximate solutions --- p.27 / Chapter 3.3 --- A priori estimates --- p.39 / Chapter 3.4 --- Proof of Theorem 3.1.6 --- p.40 / Chapter 4 --- Global Existence and Large Time Behavior of Weak Solutions to Quantum Navier-Stokes-Poisson Equa-tions --- p.46 / Chapter 4.1 --- Global existence of weak solutions --- p.47 / Chapter 4.2 --- Large time behavior --- p.50 / Chapter 5 --- Discussions and Future Work --- p.55 / Bibliography --- p.56

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This thesis examines the flow of very viscous Newtonian fluids driven by gravity. It is written with concern for specific applications in the optics industry, with emphasis on the slumping of molten glass into a mould, as in the manufacture of optical components, which are in turn used to manufacture ophthalmic lenses. This process is known as thermal replication. However, the work has more general applicability, and disc viscometry, used to determine the viscosity of very viscous fluids, is also considered. In addition, one chapter of the thesis is devoted to the flow of dripping honey, as another example of a very viscous flow to which the model can be applied. The Stokes creeping-flow equations are used to model the very viscous flows of interest. The main solution method is finite elements, and a purpose-written computer program has been developed to solve the creeping-flow equations by this method. The present program is restricted to solving for either two-dimensional or axisymmetric flows but is extendible to three dimensions. In addition, semi-analytic series and asymptotic methods are used for some small portions of the work. The optical applications of this work demand consideration of the topic of computing surface curvature, and therefore second derivatives, from inexact and discrete numerical and experimental data. For this purpose, fitting of B-splines by a least-squares method to coordinate data defining the surface has been used. Much of the work assumes isothermal conditions, but in the context of the accuracy required in optical component manufacture it is also possible that non-isothermal effects will be important. Consequently, this restriction is eventually relaxed and some consideration given to non-isothermal conditions. In order to validate the creeping-flow model and finite-element program, comparisons of numerical simulations with experimental results are performed. A preliminary assessment of the importance of non-isothermal conditions to the thermal-replication process is also made by comparing isothermal and non-isothermal simulations with experimental results. The isothermal model is found to best match the experimental data. / Thesis (Ph.D.)--School of Applied Mathematics, 1998.

Microscale fluid processes are an increasingly important subgroup of fluid mechanics. Applications for heat transfer and micro-electro-mechanical devices use flows on the scale of less than one hundred microns. This study is part of a larger work in which a multiphase, high shear environment is studied in a microchannel that has a depth of approximately 130 μm. Velocities are obtained using non-invasive imaging schemes. Laser induced fluorescent Particle Image Velocimetry (PIV) is used to analyze the velocity distribution in the microchannel. Multiple image processing techniques are used to optimize the images for correlation calculations. Velocity profiles for three flow rates and three void fractions (one of which is zero) are developed experimentally. The effect of the microbubbles on the PIV analysis is shown to flatten the profile through one primary mechanism and possibly a secondary, less dominant mechanism. / Graduation date: 2006

In the continuum modeling of traffic networks, a macroscopic cost-flow function (MCF) and macroscopic fundamental diagram (MFD) can be used to represent the fundamental relationships between traffic quantities such as speed, flow, and density. The MCF governs the steady-state cost-flow relationship, whereas the MFD represents the instantaneous inter-relationship between speed, flow, and density of traffic streams. This thesis explores the influence of network topologies on the MCF and MFD. The Hong Kong road system is divided into unit-sized road networks with various physical characteristics for which the network structure and signal timings are reserved. By universally scaling the origin-destination (OD) matrices of the morning peak, traffic conditions ranging from free-flow to congestion are created for microscopic simulation. From the simulation results, an MCF that relates the average journey time and the number of vehicles traveling through the network in one hour and an MFD that relates space to the mean speed and average density aggregated across 300s intervals are derived. The MCF and MFD are calibrated with mathematical models for each network. The density of roads, junctions, and signal junctions all influence the value of the macroscopic parameters in the MCF and MFD, and predictive equations are constructed that relate the macroscopic parameters to the network topological characteristics. Based on the fitting performance of the mathematical models, recommendations are made for selecting MCF and MFD models for continuum modeling. / published_or_final_version / Civil Engineering / Master / Master of Philosophy

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