PATTERN-FORMATION IN A 2D ELASTIC SOLID

We present a dynamical theory of a two-dimensional martensitic transit ion 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-ba sed Galerkin method is employed to integrate the deterministic equatio n of motion, the latter of which is derived by the variational princip le from a nonlinear, nonlocal Ginzburg-Landau theory which includes th e sound-wave viscosity. Our results display (i) the phenomenon of surf ace nucleation, and (ii) the dynamical selection of a length scale of the resultant patterns.