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 initi ally uniform state evolves to one whose ground state is spatially peri odic. We confirmed previous results which showed that dynamical scalin g occurs at medium quench (epsilon=0.25) with scaling exponents 1/5 an d 1/4 under zero noise and finite noise, respectively. We find logarit hmic scaling behavior for a deep quench (epsilon=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 behavi or with the same exponent. For epsilon=0.25, the scaling exponents are 1/4 and 0.3 at zero and finite noise, respectively.