Ordering dynamics in the two-dimensional stochastic swift-hohenberg equation

Numerical and analytic techniques are used to study the roll patterns which appear following a convective instability as modeled by the Swift-Hohenberg equation. The results of this work reveal the presence of a disordered state and a quasiordered state at large and small noise strengths, respectively. The dynamical approach to these states is shown to be rapid in the former case and slow in the later. Both numerical and analytic calculations indicate that the slow dynamics can be characterized by a simple scaling relationship.