Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime


Berry, M.V. and Dennis, M.R. (2001) Knotting and unknotting of phase singularities: Helmholtz waves, paraxial waves and waves in 2+1 spacetime Journal of Physics A: Mathematical and General, 34, (42), pp. 8877-8888. (doi:10.1088/0305-4470/34/42/311).

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Description/Abstract

As a parameter a is varied, the topology of nodal lines of complex scalar waves in space (i.e. their dislocations, phase singularities or vortices) can change according to a structurally stable reconnection process involving local hyperbolas whose branches switch. We exhibit families of exact solutions of the Helmholtz equation, representing knots and links that are destroyed by encounter with dislocation lines threading them when a is increased. In the analogous paraxial waves, the paraxial prohibition against dislocations with strength greater than unity introduces additional creation events. We carry out the analysis with polynomial waves, obtained by long-wavelength expansions of the wave equations. The paraxial events can alternatively be interpreted as knotting and linking of worldlines of dislocation points moving in the plane.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1088/0305-4470/34/42/311
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ePrint ID: 29379
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Date Event
2001Published
Date Deposited: 12 May 2006
Last Modified: 16 Apr 2017 22:23
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/29379

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