Crystallization kinetics and self-induced pinning in cellular patterns

The aspect of pattern formation in nonequilibrium media such as self-induced pinning and stick-and-slip motion of the interphase boundary, as a particular kind of crystallization or melting is modelled by the Swift-Hohenberg (SH) equation. Within the SH model, the front propagation between cellular and uniform states can be evaluated by periodic nucleation events initiated by a violent growth of the localized zero-eigenvalue mode of the corresponding linear problem. An evolution equation for this mode is estimated using asymptotic analysis wherein the time interval between nucleation events and the front speed are estimated. The creep velocity exponent of `thermally activated' front propagation beyond the pinning threshold is derived.