This thesis investigates questions of uniqueness in the theory of Compressible flow. First, various uniqueness theorems for compressible flow are reviewed in an expository manner. Roughly, these theorems state that fluid motion in a bounded region Ω = Ω(t) is uniquely determined by its initial data together along with certain boundary conditions. Next, this analysis is extended to magnetohydrodynamic flows and uniqueness theorems are given for a variety of possible cases. The basic question in all these theorems is the determination of appropriate boundary conditions. The proofs are by energy estimates. / Science, Faculty of / Mathematics, Department of / Graduate

This thesis presents the numerical solution for two-dimensional incompressible viscous flow over a rigid bluff body which is elastically supported or alternately undergoing a specified harmonic oscillations. Solutions for the related associate flow in which the body is at rest in a two-dimensional incompressible time-dependent viscous flow have also been -obtained. This work is an extension of the work by Pattani [19] to include the effect of a steady far field flow on an oscillating body. The numerical model utilizes the finite element method based on a velocity-pressure primitive variable representation of the complete Navier-Stokes equations. Curved isoparametric elements with quadratic interpolation for velocities and bilinear interpolation for pressure are used. Nonlinear boundary conditions on the moving body are represented to the first order in the body amplitude parameter. The method of averaging is used to obtain the resulting periodic motion of the fluid. Three non-dimensional parameters are used to completely characterise the flow problem: the frequency Reynolds number Rω , the Reynolds number of steady flow Rℯ₁ and the Reynolds number for time-dependent flow Rℯ₂. Numerical results are obtained for a circular body, a square body and an equilateral triangular body. A parametric study is conducted for different values of the Reynolds numbers in the viscous flow regime. In all cases, results are obtained for streamlines, streaklines, added mass, added damping, added force and the drag coefficients. The limiting cases of steady flow over a fixed body and an oscillating body in a stationary fluid are checked with known results. Results for the associated flow are also obtained. The transformations derived, between the two associated flows are checked. Good agreement is obtained between the present results and other known results. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

No description available.

Ahuna Mons is a 4 km tall mountain on Ceres interpreted as a geologically young cryovolcanic dome. Other possible cryovolcanic features are more ambiguous, implying that cryovolcanism is only a recent phenomenon or that other cryovolcanic structures have been modified beyond easy identification. We test the hypothesis that Cerean cryovolcanic domes viscously relax, precluding ancient domes from recognition. We use numerical models to predict flow velocities of Ahuna Mons to be 10-500 m/Myr, depending upon assumptions about ice content, rheology, grain size, and thermal parameters. Slower flow rates in this range are sufficiently fast to induce extensive relaxation of cryovolcanic structures over 10(8)-10(9) years, but gradual enough for Ahuna Mons to remain identifiable today. Positive topographic features, including a tholus underlying Ahuna Mons, may represent relaxed cryovolcanic structures. A composition for Ahuna Mons of >40% ice explains the observed distribution of cryovolcanic structures because viscous relaxation renders old cryovolcanoes unrecognizable.

In South Africa mineral processing is a very important activity and ""lith declining om grades and increased need for foreign' revenue it is necessarv to develop methods which wUl keep are processing'~osts as low as possible. (( Milling is an example of a capital intensive unit operation 'which has much scope for more efficient Operation. Better control of the viscosity of the slurry discharged from a rotary 9rir~ding mill will result in improved milling efficiency and hence a saving 1'1electricity ~nd steel costs will be experienced. More effective and conslstent grinding in the mil! will also result in em lmproved mineral recovery. Slurry rheology is the variable of interest in monitoring and controlling a wet grinding mill rather than other rneascres of slurry composition presently used (eg percent solids). Up to this point in time however this variable has not been successfully used due to the fact that a sufficiently reliable and robust device for measuring the viscosities of slurries on an on-line basis has riot been available, This project was undertaken to develop just such a device (which is in the process of being patented bV Professor M H Mays). The flow rate of a fluid down a vertical tube is a function if its viscosity as well as ether quantifiable variables. This is the basis of the operation of the measurement device. Useful features of this device Include the fact tl'tat it has no movin~ paris, is inexpensive and robust and is subject tli) little wear. ''rha measurement can b --------------------------------------.--~~-----~------ performed directly on the stream in question and it is unlikely to be blocked up by fibres/particles. A self cleaning facility may also be Included. Ba$ed On the experimental results the technique shows much promise and it is anticipate:ted that the basic design could easily evolve into a useful, practical devi~e for th~ measurement of the apparent viscosity of settling slurries as well as other fluids. If a differential pressure tell" Is also connected to the device it may be used to obtain the density of the fluid being sampled. A model based on the. principles of conservation of momentum was developed and solved numerically using MATLAB {which uses 5th order Runge Kuttal as well as a Turbo pascal program using 4th order Runge i<utta. The model was also' simp.lified slightly by neglecting acceleration of th~ flui¢ (a simplificatlcbn which was shown ~xperimentally to hold) and solved analytically. The results predict~d by the model ~3~ffar only slightly from the experimentally determined i' results. The devil~e has been tested on pilot mills at MINTEK's research facility as wall as the Anglo American Research labs, with varying degrees of success.

by Xin-liang Qiu. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (p. 98-103). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / by Xin-liang Qiu.

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

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.

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 222-229). Available also in a digital version from Dissertation Abstracts.

Thesis--M. Phil., University of Hong Kong, 1984.