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

Source: [Dynamical Scaling Behavior of the Swift-Hohenberg Equation Following a Quench to the Modulated State](<https://www.sota2.com/research/paper/68fa31e21e209131ce882f3d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T19:08:34.534Z

Authors: Qing Hou, Shin-ichi Sasa, Nigel Goldenfeld

Published: 1998-08-03T05:03:32.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/patt-sol/9808001>)

[PDF](<https://arxiv.org/pdf/patt-sol/9808001.pdf>)