by Tam Chi Yung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 66-67). / by Tam Chi Yung. / Contents --- p.i / List of Figures --- p.iii / Acknowledgement --- p.iv / Abstract --- p.v / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Open systems and quasinormal modes --- p.1 / Chapter 1.2 --- Gravitational waves --- p.3 / Chapter Chapter 2. --- Green's Function Formalism --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Constructing the Green's function --- p.7 / Chapter 2.3 --- The norm --- p.9 / Chapter 2.4 --- Completeness --- p.11 / Chapter Chapter 3. --- Potentials With No Tail --- p.13 / Chapter 3.1 --- Introduction --- p.13 / Chapter 3.2 --- Completeness --- p.14 / Chapter 3.2.1 --- Proof --- p.14 / Chapter 3.2.2 --- Examples --- p.16 / Chapter 3.3 --- The two-component approach --- p.20 / Chapter 3.3.1 --- Formalism --- p.21 / Chapter 3.3.2 --- Comparison of different expansion schemes --- p.23 / Chapter 3.3.3 --- Linear Space --- p.29 / Chapter 3.4 --- Perturbation theory --- p.31 / Chapter 3.4.1 --- Formalism --- p.31 / Chapter 3.4.2 --- Examples --- p.33 / Chapter 3.5 --- Conclusion --- p.35 / Chapter Chapter 4. --- Potentials With Exponential Tails --- p.36 / Chapter 4.1 --- Introduction --- p.36 / Chapter 4.2 --- Single exponential tail --- p.37 / Chapter 4.3 --- Asymptotics of QNM's --- p.40 / Chapter 4.4 --- The Born series --- p.43 / Chapter 4.5 --- Poschl-Teller potential --- p.44 / Chapter 4.5.1 --- Analytic solutions --- p.44 / Chapter 4.5.2 --- The norm --- p.46 / Chapter 4.6 --- The problem of cut-off --- p.48 / Chapter 4.7 --- An effective numerical scheme --- p.49 / Chapter 4.8 --- Conclusion --- p.53 / Chapter Chapter 5. --- Logarithmic Perturbation --- p.54 / Chapter 5.1 --- Introduction --- p.54 / Chapter 5.2 --- Formalism --- p.54 / Chapter 5.3 --- Examples --- p.57 / Chapter 5.4 --- Conclusion --- p.59 / Chapter Chapter 6. --- Conclusion --- p.60 / Appendix A. Asymptotic behaviour of the Green's function --- p.61 / Appendix B. Derivation of the equation (4.16) --- p.63 / Appendix C. Different definitions of the norm --- p.64 / Bibliography --- p.66

Huang, Xiaobo. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 108-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

We prove two results; first, we show that a boundary value problem for the semilinear wave equation with smooth, asymptotically linear nonlinearity and sinusoidal smooth forcing along a characteristic cannot have a continuous solution. Thereafter, we show that if the sinusoidal forcing is not isolated to a characteristic of the wave equation, then the problem has a continuous solution.

In most cases of seismic processing and interpretation, elastic isotropy is assumed. However, velocity anisotropy is found to exist in most subsurface media. Hence, there exists a fundamental inconsistency between theory on the one hand, and practice on the other. If not recognised, this can invalidate interpretation of seismic data. In this thesis, inversion methods for elastic parameters are developed to quantify the degree of velocity anisotropy of multi-layered transversely isotropic media. This primarily involves examining the velocity fields of layered media using anisotropic elastic wave propagation theory, and developing inversion programs to recover elastic parameters from those velocity fields. The resolved elastic parameter information is used in carrying out further studies on the effects of seismic anisotropy on normal moveout (NMO). Mathematical analyses, numerical simulations, and physical modelling experiments are used in this research for verification purposes before application to field survey data. Numerical studies show the transmission velocity field through layered media appears to be equivalent to that through a single-layered medium, within the practical offset limits in field surveys. The elastic parameters, which describe the property of such equivalent single-layered media, can be used as apparent elastic parameters to describe the collective mechanical property of the layered media. During this research, Snell's law was used in ray tracing to determine ray paths through the interface between any two component layers. By analyzing the signals recorded by any receiver in a walkaway VSP survey, the apparent transmission velocity field for the layered media above this receiver depth was inverted. / Software was developed to recover the apparent elastic parameters for the layered media above this receiver depth using the transmission velocity field as input. Based on a two-layered model, another method was developed to recover the interval elastic parameters for an individual layer of interest, using the signals recorded by receivers on the upper and lower surfaces of this layer. The recovered elastic parameters may be considerably different from the real values if a transversely isotropic medium with a tilted symmetry axis (TTI) is treated as a transversely isotropic medium with a vertical symmetry axis (VTI). A large angle of tilt of the symmetry axis significantly influences the recorded velocity field through the medium. An inversion program was written to recover the value of the tilt angle of a TTI medium, and the elastic parameters of the medium. Programs were also developed to combine information from P, SV, and SH-waves in an inversion procedure. This capability in inversion programs enables us to use the additional information provided by a multi-component VSP survey to obtain accurate estimates of the elastic parameters of geological formations. Software testing and development was carried out on numerically generated input data. Up to 10 milliseconds of random noise in travel time was added to the input to confirm the stability of the inversion software. Further testing was carried out on physical model data where the parameters of the model were known from direct measurements. Finally the inversion software was applied to actual field data and found to give plausible results. / In software testing in the physical modelling laboratory, other practical problems were encountered. System errors caused by the disproportionately large size of the transducers used affected the accuracy of the inversion results obtained. Transducer performance was studied, and it was found that reducing the size of transducers or making offset corrections would decrease the errors caused by the disproportionately large transducer dimensions. In using the elastic parameters recovered, it was found that the elastic parameter δ significantly influences the seismic records from a horizontal reflector. The normal moveout velocity was found to show variations from the zero-offset normal moveout velocity depending on the value and sign of elastic parameter δ. New approximate expressions for anisotropic normal moveout, phase and ray velocity functions at short offsets were developed. The value of anisotropic parameter δ was found to be the major factor controlling these relations. If the recovered parameter δ has a large negative value, analytical and numerical studies demonstrated that the new expression for moveout velocity developed herein should be used instead of Thomsen's normal moveout equation.

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.

No description available.

<p>At the Division for Electricity at Uppsala University a new marine substation for waveenergy is being built. The marine substation is required to connect the wave energyconverters to the grid. In this thesis a part of the main circuit for the marinesubstation is assembled and tested. Furthermore, a part of the measurement system isdesigned and a prototype is built and evaluated. The test results from the set-up ofthe main circuit agree well with simulations done in MATLAB Simulink. A detailed listof components combined with a finished CAM-model for a measurement card arepresented along with interface cards and shielding solutions.</p>

We exhibit long-lived resonances in scattering from two-dimensional soft cage potentials comprised of three and four Gaussian peaks. Specific low-energy resonances with very narrow width are shown to correspond to classical multiple-reflection events. These states have much larger probability densities inside the cage than outside and mimic bound states in the sense that the symmetry-breaking effect of the incident wave is relatively small. As a result we have found that isolated states display the simple symmetry characteristics of bound states. Overlapping resonances exhibit a mixing of symmetry classes leading to wave functions of lower symmetry, like those of wider resonances at higher energy. We demonstrate that at energies below the lowest resonances of two-dimensional cages, where the distance across the entrance of the cage corresponds to less than half a wavelength, the wave function may still gain access to the interior region by squeezing its wavelength in the necessary direction at the expense of the kinetic energy in the direction normal to the opening. The resulting curvature of the wave function in the donor dimension corresponds to an imaginary wavenumber, curving away from the plane defined by zero amplitude. This mechanism for passing between obstacles may be relevant for electronic and optical devices having spatial structures with dimensions comparable to the wavelengths of the energy carriers. / Graduation date: 2005

Graduation date: 1997

Thèse -- Université de Paris.