Long-scale deformations of resonant three-dimensional patterns and the structure of confined dislocations

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Abstract
It is shown that three-dimensional patterns dominated by triplet interactions in the vicinity of a symmetry-breaking bifurcation point acquire rigidity owing to resonant interactions between constituent modes. Phase equations determining the response of octahedral, tetrahedral, and icosahedral structures to long-scale perturbations are derived and analyzed. The nonisotropic long-scale response spectrum is universal, being dependent on the crystalline structure only. It is shown that the resonance condition causes confinement of dislocations in a number of constituent modes to a common dislocation line. The phase equations are applied to compute the far field structure of the dislocations.

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