Pattern Formation in a 2D Elastic Solid

Details Pattern Formation in a 2D Elastic Solid Pattern Formation in a 2D Elastic Solid

1997-04-29

arxiv.org/abs/cond-mat/9704239v1

Physics

Condensed Matter

LaTeX, 14 pages with four post-script figures included by psfig. Three of these are colour, but viewable in black-and-white. P

Scientific paper

We present a dynamical theory of a two-dimensional martensitic transition in an elastic solid, connecting a high-temperature phase which is nondegenerate and has triangular symmetry, and a low-temperature phase which is triply degenerate and has oblique symmetry. A global mode-based Galerkin method is employed to integrate the deterministic equation of motion, the latter of which is derived by the variational principle from a nonlinear, nonlocal Ginzburg-Landau theory which includes the sound-wave viscosity. Our results display (i) the phenomenon of surface nucleation, and (ii) the dynamical selection of a length scale of the resultant patterns.

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