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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.