Type of Document Dissertation Author Kim, Jeong Hoon URN etd-10202005-102830 Title Stochastic turning point problem Degree PhD Department Mathematics Advisory Committee

Advisor Name Title Kohler, Werner E. Committee Chair Besieris, Ioannis M. Committee Member Day, Martin V. Committee Member Kim, Jong Uhn Committee Member Renardy, Yuriko Y. Committee Member Keywords

- Sound-waves Scattering Mathematical models.
- Sound-waves Mathematical models.
Date of Defense 1993-09-05 Availability restricted AbstractA one-dimensional refractive, randomly-layered medium is considered in an acoustic context. A time harmonic plane wave emitted by a source is incident upon it and generates totally reflected fields which consist of "signal" and "noise". The statistical properties, i.e., mean and correlation functions, of these fields are to be obtained. The variations of the medium structure are assumed to have two spatial scales; microscopic random fluctuations are superposed upon slowly varying macroscopic variations. With an intermediate scale of the wavelength, the interplay of total internal reflection (geometrical acoustics) and random multiple scattering (localization phenomena) is analyzed for the turning point problem. The problem, in particular, above the turning point is formulated in terms of a transition scale. Two limit theorems for stochastic differential equations with multiple spatial scales, called Theorem 1 and Theorem 2, are derived. They are applied to the stochastic initial value problems for reflection coefficients in the regions above and below the turning point, respectively. Theorem 1 is an extension of a limit theorem on O( 1) scaled interval to infinite scale and provides uniformly-valid approximate statistics for random multiple scattering in the region above the turning point (transition as well as outer regions). Theorem 2 deals with stochastic problems with a rapidly varying deterministic component and approximates the reflection process in the region below the turning point which is characterized by the random noise. Finally, the evolution of the reflection coefficient statistics in the whole region is described by combining the two results as a product of a transformation at the turning point and two evolution operators corresponding to the two regions.

Files

Filename Size Approximate Download Time (Hours:Minutes:Seconds)

28.8 Modem 56K Modem ISDN (64 Kb) ISDN (128 Kb) Higher-speed Access LD5655.V856_1993.K566.pdf3.21 Mb 00:14:51 00:07:38 00:06:41 00:03:20 00:00:17 next to an author's name indicates that all files or directories associated with their ETD are accessible from the Virginia Tech campus network only.

Browse All Available ETDs by
( Author |
Department )

If you have questions or technical problems, please Contact DLA.