Dynamical scaling behavior of the Swift-Hohenberg equation following a quench to the modulated state

We study the kinetics of phase transitions in a Rayleigh-Benard system after onset of convection using 2D Swift-Hohenberg equation. An initially uniform state evolves to one whose ground state is spatially periodic. We confirmed previous results which showed that dynamical scaling occurs at medium quench (ε = 0.25) with scaling exponents 1/5 and 1/4 under zero noise and finite noise, respectively. We find logarithmic scaling behavior for a deep quench (ε = 0.75) at zero noise. A simple method is devised to measure the proxy of domain wall length. We find that the energy and domain wall length exhibit scaling behavior with the same exponent. For ε = 0.25, the scaling exponents are 1/4 and 0.3 at zero and finite noise, respectively.