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Thesis (Ph.D.)--McMaster University, 2002. / Advisors: Dr. John Litva, Dr. Ke-Li Wu. Includes bibliographical references (leaves 106-115). Also available via World Wide Web.

Thesis (Ph.D.)--McMaster University, 2002. / Advisors: Dr. John Litva, Dr. Ke-Li Wu. Includes bibliographical references (leaves 106-115). Also available via World Wide Web.

The problem of electromagnetic wave propagation across the junction of two similar planar dielectric waveguides is analysed, within the Kirchhoff approximation, by expanding the field into transverse variations of all possible modes. It is proven that the expansion can represent any solution for any planar dielectric waveguide. The spectral function is introduced into the representation, and this helps resolve some of the theoretical problems in passing from the limit of closed waveguides to open waveguides. Using the spectral function and the Gel'fand-Levitan integral equation some new exact solutions to novel dielectric planar waveguides can be found. Examples of waveguiding by total internal reflection or by Bragg reflection (which are physically very different processes) can be generated by changing a single parameter in the formulation. Usually the representation for an open dielectric waveguide requires the matrix spectral function. However the Gel'fand-Levitan reconstruction is defined for scalar spectral functions. A technique for constructing the spectral matrix and the scattering solutions from two spectral functions is demonstrated. This technique uses a variational formulation of a scattering experiment. The connection between a dielectric structure and the characteristics of propagation on it is obscure. However the connection between these characteristics and the spectral function is much clearer. It is sometimes possible to make predictions about the properties of the waveguide by looking at its spectral function only. Since the connection between the spectral function and the dielectric structure is well established by inverse spectral theory, introducing the spectral function has been of help in establishing the desired connection between the dielectric structure and the characteristics of propagation on it. Such considerations suggest one of the above waveguides is sensitive to small perturbations and could be used as an electro-optic modulator. Detailed calculations confirm the hypothesis. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

It is intended that this paper present an acceptable proof of the existence of a solution for the wave equation.

This master thesis is done within the Energy Systems Engineering program at Uppsala University and performed for CorPower Ocean. Wave energy converters (WECs) are devices that utilize ocean waves for generation of electricity. The WEC developed by CorPower Ocean is small and intended to be deployed in an array. Placed in an array the different WECs will interact hydrodynamically and the combined power output is altered. The aim of this thesis is to model and investigate how the array configuration affects the electric power output. The goal is to target an optimal array layout for CorPower Ocean WECs, considering both average power and power smoothness in the optimization.   In this thesis multiple buoys have been implemented in the time-domain model at CorPower Ocean. The hydrodynamic interactions are computed using an analytical interactions theory together with a recently developed calibration method able of handling WEC bodies of complicated shapes. The array behavior in regular waves is analyzed and it is identified how the beneficial separation distances vary with wave length. It is observed that the best separation distances for high average power does not exactly correspond to the best for minimizing the peak-to-average power. Simulation results show that it is possible to obtain both high average array power as well as increased power smoothening in a regular wave. A genetic algorithm for optimizing the array configuration is designed and tested for two different array patterns. Initial simulations are conducted in realistic multi-directional irregular waves. The power smoothening capacity of the array remains even in these conditions but the exact extent of it is still uncertain.   This thesis delivers a WEC array simulation model as well as an initial view on the array characteristics of the phase controlled CorPower Ocean WEC. Additionally, it demonstrates an optimization algorithm taking both average power and power smoothness into account.

It is well known that second order effects may in many cases be important for the nonlinear hydrodynamic problems arising in ocean engineering. Despite considerable efforts having been made in the past in calculating second order unsteady forces, similar studies are rare for the actual second order velocity potential itself, which is important for the understanding of wave kinematics. A mathematical model has been developed for the calculation of the second order sum frequency diffraction potential for fixed bodies in waves. It is believed that a first step towards the solution of the second order problem is the accurate evaluation of the first order quantities. By the use of Green's second identity, the first order problem can be cast into the form of a Fredholm integral equation and then solved by the Boundary Element Method. Some new developments based on this technique have been undertaken in this work, and as a result, there is a major improvement in the accuracy of the first order analysis. For the second order problem, the solution procedures are similar to those used for the first order problem except that special techniques have been developed to calculate efficiently the additional free surface integral which decays slowly to infinity in a highly oscillatory manner. In addition, an effective method has also been implemented to calculate the second derivative term in the free surface integral. From the numerical results presented, a number of interesting findings are illustrated. A closed form expression for a vertical circular cylinder has also been developed which not only furnishes a valuable check on the general numerical model but also provides some physical explanation for the second order phenomena. Moreover, it has been used to investigate some theoretical problems which (in the past) have caused confusion and error in the second order analysis. They are mainly associated with the troublesome nonhomogeneity presented in the free surface boundary condition.

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published_or_final_version / Physics / Doctoral / Doctor of Philosophy