Extraordinary Caustics in the Phonon Focusing Patterns of Crystals
Catastrophe theory provides a convenient framework for classifying the phonon focusing caustics of crystals [1–4]. There are however many prominent focusing singularities which, because they arise in the vicinity of degeneracy between different branches of the phonon dispersion relation, or because they are consequent upon the special properties of the Christoffel wave equation, are not readily accommodated in elementary catastrophe theory. The “extraordinary” caustics described here have been obtained from computer generated phonon images. The search for such structures is not complete, and a mathematical analysis of the possibilities would be very useful.
KeywordsElastic Constant Conical Point Catastrophe Theory Hexagonal Symmetry Slowness Surface
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