TY - JOUR

T1 - On the singularity index and the unfolding of the diffraction catastrophes

AU - Brown, Michael G.

N1 - Funding Information:
An anonymous reviewer suggested the scaling argument used in Section 2. This argument is more general than the one used originally by the author and its incorporation into this paper resulted in a significant improvement over the original manuscript. This work was supported by the Office of Naval Research.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1987/1

Y1 - 1987/1

N2 - 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, β, is a measure of the rate at which such a wavefield diverges as ω→∞ at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point β also describes a balance between two different measures of the unfolding of the wavefield in each control direction, β = σnρ{variant}n. The indices σn and ρ{variant}n describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.

AB - 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, β, is a measure of the rate at which such a wavefield diverges as ω→∞ at the point where all control parameters and moduli are set equal to zero. It is shown that away from this point β also describes a balance between two different measures of the unfolding of the wavefield in each control direction, β = σnρ{variant}n. The indices σn and ρ{variant}n describe, respectively, the rate at which individual ray arrivals separate in time and decay as a function of control parameter.

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U2 - 10.1016/0165-2125(87)90043-6

DO - 10.1016/0165-2125(87)90043-6

M3 - Article

AN - SCOPUS:0023163951

VL - 9

SP - 107

EP - 110

JO - Wave Motion

JF - Wave Motion

SN - 0165-2125

IS - 1

ER -