No description available.

No description available.

After introducing the nonlinear evolution equations of interest: the finite depth fluid (FDF), the Kadomtsev-Petviashvili (KP), the Classical and the ordinary Boussinesq equations, formal asymptotic derivations of the KP and the FDF equations are given for the description of surface and interfacial waves. The N-soliton solution of the FDF equation is reconstructed as a finite sum of Wronskian type determinants. This solution is then shown to reduce to the solutions of the KdV and the Benjamin - Ono equations under specific limiting conditions. Interactions between two solitons of the FDF equation are studied and their interaction properties are shown to reduce to those of the KdV and the Benjamin - Ono equations. Computer plots of the interactions of two-soliton solutions of the FDF and the Benjamin - Ono equations are given. Resonance phenomena in solitons are studied with reference to the KP equation. After discussion of the basic concepts of these phenomena, the N-soliton solution is shown to reduce to the Wronskian of N/2 functions (N-even), each of which represents a triad of solitons when the solitons resonate in pairs. Asymptotic behaviour of the interactions between a triad and a soliton and between two triads are examined and the phase shifts of the triads are obtained directly from the Wronskian representation. The interactions are analysed in detail with reference to numerical computations of the full solutions. After showing that the Classical Boussinesq equations are obtained from Whitham's shallow water wave equations, the basic concept of Hirota's pq=c reduction of the first modified KP hierarchy is outlined. The Classical Boussinesq equations are shown as the pq=O reduction of the same hierarchy. The solution of the hierarchy is manipulated to incorporate the pq=O reduction. As a result of these limiting procedures applied to the problem, Wronskian solutions of the Classical Boussinesq equations in terms of rational functions are produced. Finally the pq=c reduction of the KP hierarchy is applied to the ordinary Boussinesq equation. Using this, the N-soliton solution is expressed as a finite sum of Wronskian type determinants. Analytic verification made for the two-soliton solution shows that a number of Wronskian identities are needed for this purpose. The reason for this behaviour is examined.

No description available.

No description available.

Graduation date: 1997

Surface gravity waves in the world’s oceans contain a renewable source of free power on the order of terawatts that has to this date not been commercially utilized. The division of Electricity at Uppsala University is developing a technology to harvest this energy. The technology is a point absorber type wave energy converter based on a direct-driven linear generator placed on the sea bed connected via a line to a buoy on the surface. The work in this thesis is focused mainly on the energy transport of ocean waves and on increasing the transfer of energy from the waves to the generator and load. Potential linear wave theory is used to describe the ocean waves and to derive the hydrodynamic forces that are exerted on the buoy. Expressions for the energy transport in polychromatic waves travelling over waters of finite depth are derived and extracted from measured time series of wave elevation collected at the Lysekil test site. The results are compared to existing solutions that uses the simpler deep water approximation. A Two-Body system wave energy converter model tuned to resonance in Swedish west coast sea states is developed based on the Lysekil project concept. The first indicative results are derived by using a linear resistive load. The concept is further extended by a coupled hydrodynamic and electromagnetic model with two more realistic non-linear load conditions. Results show that the use of the deep water approximation gives a too low energy transport in the time averaged as well as in the total instantaneous energy transport. Around the resonance frequency, a Two-Body System gives a power capture ratio of up to 80 percent. For more energetic sea states the power capture ratio decreases rapidly, indicating a smoother power output. The currents in the generator when using the Two-Body system is shown to be more evenly distributed compared to the conventional system, indicating a better utilization of the electrical equipment. Although the resonant nature of the system makes it sensitive to the shape of the wave spectrum, results indicate a threefold increase in annual power production compared to the conventional system.

This thesis describes the theoretical and practical implementation of a long-range high-resolution millimetre wave imaging radar system to aid with the navigation and guidance of both airborne and ground-based autonomous vehicles. To achieve true autonomy, a vehicle must be able to sense its environment, comprehensively, over a broad range of scales. Objects in the immediate vicinity of the vehicle must be classified at high resolution to ensure that the vehicle can traverse the terrain. At slightly longer ranges, individual features such as trees and low branches must be resolved to allow for short-range path planning. At long range, general terrain characteristics must be known so that the vehicle can plan around difficult or impassable obstructions. Finally, at the largest scale, the vehicle must be aware of the direction to its objective. In the past, short-range sensors based on radar and laser technology have been capable of producing high-resolution maps in the immediate vicinity of the vehicle extending out to a few hundred metres at most. For path planning, and navigation applications where a vehicle must traverse many kilometres of unstructured terrain, a sensor capable of imaging out to at least 3km is required to permit mid and long-range motion planning. This thesis addresses this need by describing the development a high-resolution interrupted frequency modulated continuous wave (FMICW) radar operating at 94GHz. The contributions of this thesis include a comprehensive analysis of both FMCW and FMICW processes leading to an effective implementation of a radar prototype which is capable of producing high-resolution reflectivity images of the ground at low grazing angles. A number of techniques are described that use these images and some a priori knowledge of the area, for both feature and image based navigation. It is shown that sub-pixel registration accuracies can be achieved to achieve navigation accuracies from a single image that are superior to those available from GPS. For a ground vehicle to traverse unknown terrain effectively, it must select an appropriate path from as long a range as possible. This thesis describes a technique to use the reflectivity maps generated by the radar to plan a path up to 3km long over rough terrain. It makes the assumption that any change in the reflectivity characteristics of the terrain being traversed should be avoided if possible, and so, uses a modified form of the gradient-descent algorithm to plan a path to achieve this. The millimetre wave radar described here will improve the performance of autonomous vehicles by extending the range of their high-resolution sensing capability by an order of magnitude to 3km. This will in turn enable significantly enhanced capability and wider future application for these systems.

Thesis (M.S.) -- Worcester Polytechnic Institute. / Keywords: CROW; PBG; PhC; coupled resonator optical waveguide; metamaterials; photonic crystal; Bloch wave; photonic band gap;dynamic waveguide; Brillouin zone; thermal spreading. Includes bibliographical references (p. 84-87).

Thesis (Ph. D.)--University of Oregon, 2007. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 231-242). Also available for download via the World Wide Web; free to University of Oregon users.