On the singularity index and the unfolding of the diffraction catastrophes
type: Item
instance of: scholarly article
title: On the singularity index and the unfolding of the diffraction catastrophes
zbMATH Open document ID: 0603.73027
DOI: 10.1016/0165-2125(87)90043-6
author: Michael G. Brown
published in: Wave Motion
publication date: 1987-01-01T00:00:00Z
review text: The caustics of high-frequency wave propagation may be classified using catastrophe theory. The wavefield in the vicinity of any caustic is described by the corresponding diffraction catastrophe. The singularity index, \(\beta\), is a measure of the rate at which such a wavefield diverges as \(\omega\to \infty\) at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point \(\beta\) also describes a balance between two different measures of the unfolding of the wavefield in each control direction. \(\beta \sigma_ n\rho_ n\). The indices \(\sigma_ n\) and \(\rho_ n\) describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.
Mathematics Subject Classification ID: 74J20
Mathematics Subject Classification ID: 58K35
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 3974412
zbMATH Keywords: caustics
zbMATH Keywords: high-frequency wave propagation
zbMATH Keywords: wavefield
zbMATH Keywords: diffraction catastrophe
zbMATH Keywords: singularity index
zbMATH Keywords: unfolding
MaRDI profile type: Publication
full work available at URL: 0165-2125(87)90043-6
OpenAlex ID: W2026127221
cites work: Q3962198
cites work: Wave propagation and Thom's theorem
cites work: CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
cites work: Focusing and twinkling: critical exponents from catastrophes in non-Gaussian random short waves
description: scientific article; zbMATH DE number 3974412