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), 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
ISSNs: 0305-4470 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 29379
Date Deposited: 12 May 2006
Last Modified: 27 Mar 2014 18:17
URI: http://eprints.soton.ac.uk/id/eprint/29379

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