Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State

Details Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State

1998-08-03

arxiv.org/abs/patt-sol/9808001v1

Physica A 239, 219-226 (1997)

Physics

Condensed Matter

Soft Condensed Matter

8 pages, 9 figures, CPIP'96 conference in London, Canada

Scientific paper

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 ($\epsilon = 0.25$) with scaling exponents 1/5 and 1/4 under zero noise and finite noise respectively. We find logarithmic scaling behavior for a deep quench ($\epsilon = 0.75$) 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 behavior with the same exponent. For $\epsilon = 0.25$, the scaling exponents are 1/4 and 0.3 at zero and finite noise respectively.

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