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Grain-boundary motion in layered phases.

D Boyer1, J Viñals

  • 1School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306-4120, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 21, 2001
PubMed
Summary

We found that curved rolls in Rayleigh-Bénard convection cause grain boundary motion. This nonlinear effect occurs rapidly and is crucial for understanding domain coarsening.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Pattern Formation

Background:

  • Rayleigh-Bénard convection exhibits complex patterns above onset.
  • Grain boundaries separate domains with different roll orientations.
  • Understanding grain boundary motion is key to pattern evolution.

Purpose of the Study:

  • To investigate the motion of grain boundaries in Rayleigh-Bénard convection.
  • To analyze the effect of curved rolls on grain boundary translation.
  • To determine the scaling laws and time scales of this motion.

Main Methods:

  • Analytical treatment using amplitude equations.
  • Numerical solutions of the Swift-Hohenberg equation.
  • Comparison of analytical predictions with numerical simulations.

Main Results:

  • Curved rolls induce a net translation of the grain boundary.
  • This nonlinear motion occurs on a faster timescale than roll relaxation.
  • Boundary travel distance scales as epsilon^(-1/2), where epsilon is the reduced Rayleigh number.
  • Analytical expressions derived for relaxation rate and velocity dependence on wave number.

Conclusions:

  • The study provides a detailed understanding of grain boundary dynamics in convective patterns.
  • Results offer insights into the dominant coarsening mechanism in multi-domain systems.
  • Findings are validated by agreement between analytical and numerical methods.

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