Crystallization kinetics and self-induced pinning in cellular patterns

Within the framework of the Swift-Hohenberg model it is shown numerically and analytically that the front propagation between cellular and uniform states is determined by periodic nucleation events triggered by the explosive growth of the localized zero-eigenvalue mode of the corresponding linear problem. We derive an 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 find the velocity exponent of "thermally activated" front propagation (creep) beyond the pinning threshold.