Persistent Link:
http://hdl.handle.net/10150/288741
Title:
Pattern formation and wavelets
Author:
Bowman, Christopher, 1969-
Issue Date:
1997
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This thesis is a collection of results associated with pattern formation, and consists of several novel results. A multi-scale analysis is carried out near the lasing bifurcation on equations which model the free carrier semiconductor laser. This analysis produces an amplitude equation which resembles the Swift-Hohenberg equation derived for the simpler two level laser, but with extra terms arising from the more complicated semiconductor system. New results are also presented in the analysis of phase equations for patterns, showing that defects are weak solutions of the phase diffusion equation, and that the Gaussian curvature of the phase surface condenses onto point and line defects. This latter fact allows for considerable simplification of the phase diffusion equation, and this analysis is presented as well. Finally, and most importantly, an algorithm is presented, based on the continuous wavelet transform, for the extraction of local phase and amplitude information from roll patterns. This algorithm allows a precise detection of phase grain boundaries and point defects, as well as the computation of soft modes like the mean flow. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. The algorithm is then applied to actual experimental convection patterns, and conclusions about the nature of the wave director field in such patterns are presented.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Newell, Alan C.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titlePattern formation and waveletsen_US
dc.creatorBowman, Christopher, 1969-en_US
dc.contributor.authorBowman, Christopher, 1969-en_US
dc.date.issued1997en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis thesis is a collection of results associated with pattern formation, and consists of several novel results. A multi-scale analysis is carried out near the lasing bifurcation on equations which model the free carrier semiconductor laser. This analysis produces an amplitude equation which resembles the Swift-Hohenberg equation derived for the simpler two level laser, but with extra terms arising from the more complicated semiconductor system. New results are also presented in the analysis of phase equations for patterns, showing that defects are weak solutions of the phase diffusion equation, and that the Gaussian curvature of the phase surface condenses onto point and line defects. This latter fact allows for considerable simplification of the phase diffusion equation, and this analysis is presented as well. Finally, and most importantly, an algorithm is presented, based on the continuous wavelet transform, for the extraction of local phase and amplitude information from roll patterns. This algorithm allows a precise detection of phase grain boundaries and point defects, as well as the computation of soft modes like the mean flow. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. The algorithm is then applied to actual experimental convection patterns, and conclusions about the nature of the wave director field in such patterns are presented.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNewell, Alan C.en_US
dc.identifier.proquest9814361en_US
dc.identifier.bibrecord.b37741445en_US
All Items in UA Campus Repository are protected by copyright, with all rights reserved, unless otherwise indicated.