Call number: LD2668 .T4 1936 G51

Exact and distance-independent expressions for beam-shape coefficients (BSC's) in various cases are obtained. For a weakly focused beam in the two-dimensional (three-dimensional) case, the expression is shown equal (linearly related) to the value of the beam field at the distance of m/k ( ll+1 /k) from the origin, where m( l) is the azimuthal (principal) angular momentum number and k is the wavenumber. This provides a rigorous foundation for and a better understanding of the localization principle of van de Hulst. Furthermore, it gives corrections to the principle if the beam is more focused. With the knowledge of the asymptotic behavior of the positions and widths (or quality value) for the morphology-dependent resonances (MDR's) in Mie's scattering, the results are applied to discuss and answer questions regarding the excitation of high-Q MDR's by good collimated wave beams focused at positions essentially off the surface of the sphere. / Fu, Pengpeng = 波東形狀係數、局域化原理及米氏散射中的共振激發 / 傅芃芃. / Adviser: Hon Meng Lai. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 75-81). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Fu, Pengpeng = Bo dong xing zhuang xi shu, ju yu hua yuan li ji Mi shi san she zhong de gong zhen ji fa / Fu Pengpeng.

No description available.

Typescript (photocopy) / vii, 192 leaves : ill. ; 30 cm / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1983

Not available / text

A weakly nonlinear system under simultaneous sinusoidal external and parametric excitations is investigated. Quadratic and cubic nonlinearities are present in the governing equations. A general perturbation analysis, the Method of Multiple Scales (MMS), is performed for numerous resonance frequencies. Emphasis is initially placed on the response of the system under parametric excitation alone. The nonresonant external and parametric excitations are then considered. Finally, responses involving both parametric and external excitations are considered. The excitation frequencies are assumed to be from the same source. . When the frequency of the_parametric and external excitations are different (λ≠Ω), many of the different resonances investigated have solvability conditions similar to those found in two preliminary works performed by Mook, Plaut and HaQuang. When the frequencies are nearly equal, numerous steady-state response curves are shown. Unlike the linear analysis, the frequency-response curves show many multi-valued responses. In some instances, as many as five amplitudes exist for a given frequency. Three are stable and two are unstable. In addition, multi-modal responses were found to exist under a single-mode excitation. This result is unique since no internal resonance was considered. For certain values of the coefficient of the nonlinear restoring forces, stable bimodal steady states were observed. In order to verify some of the theoretical results obtained by MMS, a sixth-order Runge Kutta procedure was performed on the original governing equation. The numerically integrated results and the approximate solution of MMS show excellent agreement when the parameter ε is sufficiently small. However, when ε is sufficiently large, the MMS approximate solution breaks down. Interesting phenomena, such as periodic doubling and chaos, are observed. / Ph. D. / incomplete_metadata