Crystallization Kinetics in the Swift--Hohenberg Model

It is shown numerically and analytically that the front propagation process in the framework of the Swift-Hohenberg model is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive the evolution equation for this mode using asymptotic analysis, and evaluate the time interval between nucleation events, and hence the front speed. In the presence of noise, we derive the velocity exponent of ``thermally activated'' front propagation (creep) beyond the pinning threshold.