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Grain-boundary motion in layered phases
1School of Computational Science and Information Technology, Florida State University, Tallahassee, Florida 32306-4120, USA.
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.
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.