by Li Kam Shun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 76). / 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.

In this thesis, we shall give a concise account for the classification of the structure of positive radial solutions of the semilinear elliptic equation$$Delta u+K(|x|)u^{p}=0 .$$ It is known that a radial solution $u$ is crossing if $u$ has a zero in $(0, infty)$; $u$ is slowly decaying if $u$ is positive but $displaystylelim_{r ightarrow{infty}}r^{n-2}u=infty$; u is rapidly decaying if $u$ is positive, $displaystylelim_{r ightarrow{infty}}r^{n-2}u$ exists and is positive. Using some Pohozaev identities, we show that under certain condition on $K$, by comparing some parameters $r_{G}$ and $r_{H}$, the structure of positive radial solutions for various initial conditions can be classified as Type Z ($u(r; alpha)$ is crossing for all $r>0$ ), Type S ($u(r; alpha)$ is slowly decaying for all $r>0$), and Type M (there is some $alpha_{f}$ such that $u(r; alpha)$ is crossing for $alphain(alpha_{f}, infty)$, $u(r; alpha)$ is slowly decaying for $alpha=alpha_{f}$, and $u(r; alpha)$ is rapidly decaying for $alphain(0, alpha_{f})$). The above work is due to Yanagida and Yotsutani.

As we know, the theory about the linear equation AX−XB=C has already been well developed in the finite-dimensional cases. In this paper, we will try to extend it to infinite-dimensional cases by using a similar technique developed recently in the finite-dimensional case.

Many waveguide components in the integrated optics are built with bending structures, such as Y-branches, couplers, tapered waveguides, etc. The bending angles are getting larger and larger in order to fill into a smaller integrated optical circuit. The influences of wide bending angles are no longer ignorable. Commercially available beam-propagation method (BPM) design tools are inadequate for simulating and optimizing the problem we consider. These include tightly curved waveguide sections, reflection/transmission from slanted end facets and U-turn reflectors. In this thesis, we applied the coupled transverse-mode integral-equation (CTMIE) formulation and mode matching method to study the field distribution in a 2-dimentional rectangular waveguide structure with perfect boundary conditions. The problem is first separated into parts and then converted into a block-diagonal matrix equation. By considering the symmetry of the bending structures, the original problem is broken down to two smaller problems each with it¡¦s own boundary conditions. The combined solutions provide the desired results.

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Rapid development of wireless communications has led to the excessive use of wireless equipments. The purpose of communication is achieved through the transmission and reception of electromagnetic waves by the wireless equipments. Living in the environment of massive electromagnetic exposure coming from these wireless equipments, the health issue is a growing concern among the people who use the equipments and also the general public. The GSM communication system is the most widely used segment of wireless communications currently in Taiwan. The user of the mobile terminal (handset) is in close proximity to the radiating antenna. Most of the EM radiation emitting from the antenna will pass through the body of the user and be absorbed by the human tissue. It is therefore important to consider possible health hazards due to this type of EM exposure. Among all the possible biological effects caused by EM exposure, the heating effect is the most significant and its influence on biological tissues is proven. Currently most countries require the handsets to be tested for SAR values before the handsets are ready for purchasing on the markets. SAR tests require the utilization of expensive measurement facilities. Moreover, even though the phantom used for SAR measurement is prepared according to standards, theoretically the phantom is still not identical to the anatomical constituents of the human head. Henceforth, it is necessary to investigate the field distribution inside the human head, using an anatomical model, due to the exposure of radiation coming from the handset antennas from the theoretical point of view. The whole human body is an inhomogeneous lossy dielectrics as far as EM wave propagation is concerned. This feature renders the problem easy to tackle using the FDTD numerical method. This thesis presents a method to build up a numerical human head model suitable for the FDTD analysis using data set from the ¡§visible human¡¨ project readily available from the internet. The thesis then investigates the field distribution inside the human head, under the exposure of the quarter-wavelength monopole antenna on a dielectric covered metal box. Temperature increases due to the absorption of EM energy by the human head will then be deducted from the bioheat equation.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 72-80). Also available in print.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

High frequency wave propagation is well described even at caustics by Gaussian beams and the complex eikonal equation. In contrast to the real eikonal equation, the complex eikonal equation is elliptic and not well posed as an initial value problem. We develop a new model that approximates the 2D complex eikonal equation but is well posed as an initial value problem. This model consists of a coupled system of partial and ordinary differential equations. We prove that there exists a local solution to this new system by a Picard iteration method and show uniqueness under certain constraints. Different numerical approximations are then developed based on direct finite difference approximations or the method of characteristics. Numerical simulations with a variety of velocity profiles are presented and compared with solutions to the corresponding Helmholtz equation. / text

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