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Phase singularities in isotropic random waves

Phase singularities in isotropic random waves
Phase singularities in isotropic random waves
The singularities of complex scalar waves are their zeros; these are dislocation lines in space, or points in the plane. For waves in space, and waves in the plane (propagating in two dimensions, or sections of waves propagating in three), we calculate some statistics associated with dislocations for isotropically random Gaussian ensembles, that is, superpositions of plane waves equidistributed in direction but with random phases. The statistics are: mean length of dislocation line per unit volume, and the associated mean density of dislocation points in the plane; eccentricity of the ellipse describing the anisotropic squeezing of phase lines close to dislocation cores; distribution of curvature of dislocation lines in space; distribution of transverse speeds of moving dislocations; and position correlations of pairs of dislocations in the plane, with and without their strength (topological charge) -1. The statistics depend on the frequency spectrum of the waves. We derive results for general spectra, and specialize to monochromatic waves in space and the plane, and black-body radiation.
phase dislocations, Gaussian waves, randomness, singularities
1364-5021
2059-2079
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61
Berry, M.V.
ab44fe7c-0c8c-4c7a-981f-50fe4a5bc6ad
Dennis, M.R.
ff55cf66-eb8b-4eb9-83eb-230c2f223d61

Berry, M.V. and Dennis, M.R. (2000) Phase singularities in isotropic random waves. Proceedings of the Royal Society of London A, 456 (2001), 2059-2079. (doi:10.1098/rspa.2000.0602).

Record type: Article

Abstract

The singularities of complex scalar waves are their zeros; these are dislocation lines in space, or points in the plane. For waves in space, and waves in the plane (propagating in two dimensions, or sections of waves propagating in three), we calculate some statistics associated with dislocations for isotropically random Gaussian ensembles, that is, superpositions of plane waves equidistributed in direction but with random phases. The statistics are: mean length of dislocation line per unit volume, and the associated mean density of dislocation points in the plane; eccentricity of the ellipse describing the anisotropic squeezing of phase lines close to dislocation cores; distribution of curvature of dislocation lines in space; distribution of transverse speeds of moving dislocations; and position correlations of pairs of dislocations in the plane, with and without their strength (topological charge) -1. The statistics depend on the frequency spectrum of the waves. We derive results for general spectra, and specialize to monochromatic waves in space and the plane, and black-body radiation.

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Published date: 2000
Keywords: phase dislocations, Gaussian waves, randomness, singularities

Identifiers

Local EPrints ID: 29374
URI: https://eprints.soton.ac.uk/id/eprint/29374
ISSN: 1364-5021
PURE UUID: efa5b470-3563-4e5f-8aa2-d321f18e574b

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Date deposited: 19 Jul 2006
Last modified: 17 Jul 2017 15:58

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