by Tan Wai Pin. / Thesis (M.Phil)--Chinese University of Hong Kong, 1993. / Includes bibliographical references. / DEDICATION --- p.ii / ABSTRACT --- p.iii / ACKNOWLEDGMENTS --- p.ix / Chapter CHAPTER 1 --- p.10 / Chapter 1 --- INTRODUCTIONS --- p.10 / Chapter 2. --- REFERENCE --- p.15 / Chapter CHAPTER 2 --- COMPUTATION OF CYLINDER FUNCTIONS --- p.17 / Chapter 1. --- INTRODUCTION --- p.17 / Chapter 2. --- NEED OF COMPUTING CYLINDER FUNCTION OF COMPLEX ARGUMENTS --- p.18 / Chapter 3. --- NEED OF COMPUTING HANKEL FUNCTIONS --- p.19 / Chapter 4. --- OUTLINE OF APPROACH --- p.22 / Chapter 5. --- ALGORITHMS --- p.24 / Chapter 5.1. --- REGION 1: IM(Z) < 5 AND RE(Z)<16 : --- p.25 / Chapter 5.1.1. --- Computation of Jn(z) : --- p.25 / Chapter 5.1.2. --- Determination of Starting Index M: --- p.26 / Chapter 5.1.3. --- Determination of Normalization Constant : --- p.26 / Chapter 5.1.4. --- "Computation of Yn(z),Hn(1)(z) and Hn(2) (z)" --- p.29 / Chapter 5.2. --- REGION 2 : --- p.30 / Chapter 5.3. --- REGION 3 : --- p.32 / Chapter 5.3.1 --- Computation of Jn(z) : --- p.52 / Chapter 5.3.2 --- "Computation of Hn(1) (z),H(n2)(z) and Yn(z) :" --- p.40 / Chapter 5.3.3 --- Determination of Point of Starting Exponential Scaling : --- p.42 / Chapter 5.4. --- REGION 4 : --- p.42 / Chapter 5.5. --- REGION 5 : --- p.42 / Chapter 6. --- VERIFICATION --- p.43 / Chapter 7. --- REFERENCE --- p.46 / Chapter CHAPTER 3 --- INPUT IMPEDANCE OF CYLINDRICAL-RECTANGULAR MICROSTRIP ANTENNA --- p.48 / Chapter 1. --- INTRODUCTION --- p.48 / Chapter 2. --- FORMULATION --- p.49 / Chapter 3. --- DISCUSSION --- p.62 / Chapter 4. --- REFERENCES --- p.68 / Chapter CHAPTER 4 --- MUTUAL IMPEDANCE OF CYLINDRICAL-RECTANGULAR MICROSTRIP PATCH ANTENNAS --- p.70 / Chapter 1. --- INTRODUCTION --- p.70 / Chapter 2. --- FORMULATION --- p.70 / Chapter 3. --- DISCUSSION --- p.77 / Chapter 4. --- REFERENCES --- p.83 / Chapter CHAPTER 5 --- RESONANCE OF RECTANGULAR MICROSTRIP ANTENNA INSIDE A METALLIC CYLINDER --- p.84 / Chapter 1. --- INTRODUCTION --- p.84 / Chapter 2. --- FORMULATION --- p.85 / Chapter 3. --- NUMERICAL RESULTS --- p.96 / Chapter 4. --- CONCLUSION --- p.98 / Chapter 5. --- REFERENCES --- p.102 / Chapter CHAPTER 6 --- INPUT IMPEDANCE OF RECTANGULAR MICROSTRIP ANTENNA INSIDE A METALLIC CYLINDER --- p.104 / Chapter 1. --- INTRODUCTION --- p.104 / Chapter 2. --- FORMULATION --- p.104 / Chapter 3. --- NUMERICAL RESULTS --- p.106 / Chapter 4. --- CONCLUSION --- p.111 / Chapter 5. --- REFERENCES --- p.112 / Chapter CHAPTER 7 --- SUMMARY --- p.113 / APPENDIX A --- p.117 / APPENDIX B --- p.119 / PUBLICATION LIST : --- p.121

Chu Shun Yin. / "August 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 55-60). / 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.

Boundary variation method and material distribution method are distinct approaches for structural optimization. In the early days, due to the fact that boundary variation methods were generally not able to handle topological changes, it was applied only in shape optimization problems where the topology of initial design is fixed during optimization process. To enable topological changes that are essential to deliver major performance improvements, material distribution method was introduced in the work of Bendsoe and Kikuchi, and thereafter widely adopted in nearly all aspects of topology optimization. Recently a novel boundary variation method for topology optimization was developed based on level set method, in which topological changes is allowed for. In the thesis, we study the level set based boundary variation method and material distribution method for structure optimization problem. / Finally, we studied the semi-Lagrange scheme to solve the Hamilton-Jacobi equation in level set based boundary variation method. In level set method, the free boundary of a structure is optimized via solution of a Hamilton-Jacobi equation. The numerical stability condition in explicit schemes for discrete Hamilton-Jacobi equation severely restricts the time step. To improve the numerical efficiency, we employ a semi-Lagrange scheme to solve Hamilton-Jacobi equation. Therefore, much larger time steps can be obtained and the number of iterations before convergence is greatly reduced. / Firstly, we studied the minimum compliance optimization problem of thermoelastic structures. In this optimization problem, we find that the optimal structures given by the state-of-art material distribution method, SIMP i method, generally have large area of intermediate density values that are not feasible in practical engineering applications because of their poor manufacturability and high costs. Therefore, we apply level set based boundary variation method in the optimization problem. As numerical results show, the optimal structures obtained are well suited to engineering applications. / To sum up, we explore in this thesis the boundary variation method and material distribution method for structure optimization problem. Several meaningful results and conclusions are obtained. / We secondly studied the stress minimization problem. In practical applications the most important requirement on a structure is often the strength of structure which characterizes the resistance to failure. In stress minimization problem, the objective is to minimize the distribution of von Mises stress in a structure. Here, level set method gives a significant convenience for stress optimization, in particular, we need not to incorporate any stress amplification factor of material microstructure which would be an important issue in material distribution method. Moreover, in order to derive more control of maximum stress, we utilize the Kreisselmeier-Steinhauser function to aggregate stresses at each point in a structure into a single global function. / Xia, Qi. / "October 2007." / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 69-08, Section: B, page: 4993. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 102-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

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Random triangulated surfaces are created by taking an even number, n, of triangles and arbitrarily ”gluing” together pairs of edges until every edge has been paired. The resulting surface can be described in terms of its number of boundary cycles, a random variable denoted by h. Building upon the work of Nicholas Pippenger and Kristin Schleich, and using a recent result from Alex Gamburd, we establish an improved approximation for the expectation of h for certain values of n. We use a computer simulation to exactly determine the distribution of h for small values of n, and present a method for calculating these probabilities. We also conduct an investigation into the related problem of creating one connected component out of n triangles.

Errata pasted onto front end-paper. Bibliography: leaves 101-104. This thesis employs integral equation methods, or boundary element methods (BEMs), for the solution of three kinds of engineering problems associated with inhomogeneous materials or media: a class of elliptical boundary value problems (BVPs), the boundary value problem of static linear elasticity, and the calculation of the solution of the initial-boundary value problem of non-linear heat conduction for anisotropic media.

Typescript (Photocopy) Bibliography: leaf 75.

This thesis is concerned with a mathematical study of several problems involving infiltration from irrigation channels into an unsaturated homogeneous soil. All the problems considered are two dimensional and are solved numerically by employing boundary integral equation techniques. In the first chapter I introduce some of the literature and ideas surrounding my thesis. Some background information is stated followed by an outline of the thesis and a list of author’s published works that support the material in the thesis. Full descriptions of the fundamental equations used throughout the thesis are provided in chapter 2. Chapter 3 contains the first problem considered in this thesis which is infiltration from various shapes of single and periodic irrigation channels. Specifically strip, semi-circular, rectangular and v shaped channels. The solutions are obtained using the boundary element technique. The solutions are then compared with the results obtained by Batu [14] for single and periodic strip sources. In chapter 4 a boundary integral equation method is adopted for the solution of flow from single and periodic semi-circular channels into a soil containing impermeable inclusions. The impermeable inclusions considered are of rectangular, circular and square shapes. The aim is to observe how the various shapes of inclusions can affect the direction of the flow particularly in the region adjacent to the zone where plant roots would be located. Chapter 5 solves the problem of infiltration from single and periodic semicircular irrigation channels into a soil containing impermeable layers. A modification is made to the boundary integral equation in order to include the impermeable layers with the integration over the layers involving Hadamard finite-part integrals. The objective of the work is to investigate how the number and the depth of the impermeable layers affects the flow. Chapter 6 employs a particular Green’s function in the boundary integral equation. The Green’s function is useful for flow from a single channel since it removes the need to evaluate the boundary integral along the soil surface outside the irrigation channel. A time dependent infiltration problem is considered in chapter 7. The Laplace transform is applied to the governing equations and the boundary integral equation technique is used to solve the resulting partial differential equation. The Laplace transform is then inverted numerically to obtain the time dependent values of the matric flux potential. / Thesis (Ph.D.) - University of Adelaide, School of Mathematical Sciences, 2008

Errata pasted onto front end-paper. / Bibliography: leaves 101-104. / xi, 174 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis employs integral equation methods, or boundary element methods (BEMs), for the solution of three kinds of engineering problems associated with inhomogeneous materials or media: a class of elliptical boundary value problems (BVPs), the boundary value problem of static linear elasticity, and the calculation of the solution of the initial-boundary value problem of non-linear heat conduction for anisotropic media. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 2002

A baroclinic, convective mixed-layer was modeled, using water, in a laboratory convection tank identical to that used in the free convection study of Deardorff and Willis (1985). Baroclinicity and mean-flow shearing were achieved by tilting the tank by an angle of 1O⁰. The resulting mechanical-production rate of turbulence kinetic energy was comparable in magnitude to the buoyancy-production rate at mid-levels within the mixed-layer. Velocities were obtained by taking time-lapse photographs of neutrally-buoyant oil droplets suspended in the mixed-layer fluid. Variances and other statistical descriptors of the turbulence obtained from these velocities are presented in comparison to the free convection results of Deardorff and Willis (1985). The deviation of the present results from those of Deardorff and Willis (1985) are assumed to be related to the effects of mean-flow shearing and are explained wherever possible with the aid of an appropriate kinetic energy budget (kinetic energy, here, refers to the kinetic energy of the turbulence and is not to be confused with the kinetic energy of the mean-flow). The results indicate that a maximum in downstream horizontal kinetic energy at mid-levels within the mixed layer was generated by shear-production and, also, by conversion from vertical kinetic energy. In the lower mixed-layer, vertical kinetic energy was amplified by a mechanical-production term associated with the divergence of the mean vertical velocity. Total turbulence kinetic energy, normalized by the square of the convective velocity scale, was much larger at mid-levels than in Deardorff and Willis (1985) due to mechanical-production which is not accounted for by simple mixed-layer scaling. Horizontal turbulence structure was predominately controlled by convection while vertical turbulence structure was significantly altered by mean-flow shearing. / Graduation date: 1989