Three-beam model for studying dislocations in wave pulses

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Abstract
A model pulsed wavefield is presented that enables the behaviour of the associated wave dislocations to be computed exactly. It consists of three intersecting beams of plane-wave pulses. Because the results depend essentially only on the relative time delays of the three pulses at any given point, the computations have to be done only once, and they are then applicable, by a linear mapping, to any angular arrangement of the three beams. The model produces dislocations showing the most general behaviour: they are curved, with varying edge-screw character, and they glide and climb. The predictions of the theory of Wright and Nye, valid for small bandwidth but not rigorously justified, are shown to be correct for this model. As the bandwidth increases new dislocation behaviour becomes evident: for example, the dislocation trajectories change their connectivity at or close to saddle points for amplitude in the corresponding continuous-wave pattern. At lower bandwidths Lorentzian-shaped pulses give dislocations that travel on looped trajectories beginning and ending on the nulls of the corresponding continuous-wave pattern, while at higher bandwidths the trajectories lie in close pairs, with one member having small arrival times for the dislocations and the other having large arrival times.

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