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Title: Wavefield singularities : a caustic tale of dislocation and catastrophe
Author: Wright, Francis J.
ISNI:       0000 0004 2734 5922
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 1977
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Thi~ dissertation discusses some aspects of the two principal types of singularity which can arise in wavefields: wavefront dislocations and caustics. After a general introduction in the prologue, chapter 1 develops the concept of wavefront dislocations in continuous and pulsed waves, building on the original work of Nye & Berry. Local models of scalar dislocations, and one example of a dislocation in an electromagnetic wave, are analysed. Chapter 2 examines the dislocations produced by a realistic model of an acoustic radiator by deriving an exact formula for the pulsed wavefield, and evaluating it numerically. An attempt is made in chapter 3 to derive the behaviour of the dislocations in a pulsed wavefield from the continuous wavefield. Chapter 4 introduces the concept of caustics and the diffraction patterns which surround them. Catastrophe theory is presented in the context of caustics to show how it classifies the caustic diffraction patterns. A general method for evaluating the canonical diffraction integrals is presented, and applied in subsequent chapters. Chapter 5 summarizes the cusp diffraction pattern and draws attention to its dislocations. An ultrasonic cusp diffraction pattern is analysed, and the effect of pulsing the wave field is considered. An appendix discusses the focussing of pulses. Chapters 6 and 7 present the three dimensional diffraction patterns associated with the swallowtail and elliptic umbilic catastrophes, with particular emphasis on their dislocation structure. Finally chapter 8 shows that wavefront dislocations themselves are catastrophes.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available