Wavefront singularities associated with the conical point in elastic solids with cubic symmetry

Details Wavefront singularities associated with the conical point in elastic solids with cubic symmetry Wavefront singularities associated with the conical point in elastic solids with cubic symmetry

2007-02-06

arxiv.org/abs/cond-mat/0702124v1

Wave Motion 44(6), 513-527, 2007.

Physics

Condensed Matter

Materials Science

21 pages, 5 figures

Scientific paper

10.1016/j.wavemoti.2007.02.007

The wavefronts from a point source in a solid with cubic symmetry are examined with particular attention paid to the contribution from the conical points of the slowness surface. An asymptotic solution is developed that is uniform across the edge of the cone in real space, the interior of which contains the plane lid wavefront analyzed by Burridge \cite{Burridge67}. The uniform solution also contains the regular wavefronts away from the cone edge, a delta pulse on one side and its Hilbert transform on the other. In the direction of the cone edge the three wavefronts merge to produce a singularity of the form $H(t) t^{-3/4}$.

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