The dynamical evolution away from an unstable steady state is studied for the two-sided symmetric model in two dimensions by means of numerically solving the interface equations of motion. Evidence is presented for the appearance of a regime of self-similar growth in which the pattern is characterized by a single length scale R(t). The asymptotic time dependence of such a length is R(t)∼t. The results also show that the local deviation of the interface from planarity, the local normal growth velocity, and the power spectrum of the interface satisfy scaling relations. In addition, by assuming the existence of such a scaling regime, we are able to derive from dimensional and heuristic arguments a power-law growth with exponents in accord with those found in the numerical solution.

• Received 10 April 1989

DOI:https://doi.org/10.1103/PhysRevA.40.3864