Grain-boundary motion in layered phases

Denis Boyer, Jorge Viñals

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

We study the motion of a grain boundary that separates two sets of mutually perpendicular rolls in Rayleigh-Bénard convection above onset. The problem is treated either analytically from the corresponding amplitude equations, or numerically by solving the Swift-Hohenberg equation. We find that if the rolls are curved by a slow transversal modulation, a net translation of the boundary follows. We show analytically that although this motion is a nonlinear effect, it occurs in a time scale much shorter than that of the linear relaxation of the curved rolls. The total distance traveled by the boundary scales as [formula presented] where [formula presented] is the reduced Rayleigh number. We obtain analytical expressions for the relaxation rate of the modulation and for the time-dependent traveling velocity of the boundary, and especially their dependence on wave number. The results agree well with direct numerical solutions of the Swift-Hohenberg equation. We finally discuss the implications of our results on the coarsening rate of an ensemble of differently oriented domains in which grain-boundary motion through curved rolls is the dominant coarsening mechanism.

Original languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume63
Issue number6
DOIs
StatePublished - Jan 1 2001
Externally publishedYes

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Grain Boundary
grain boundaries
Swift-Hohenberg Equation
Motion
Coarsening
Modulation
modulation
Linear Relaxation
Amplitude Equations
Rayleigh number
Nonlinear Effects
Rayleigh
Perpendicular
Convection
Time Scales
Ensemble
convection
Numerical Solution

Cite this

Grain-boundary motion in layered phases. / Boyer, Denis; Viñals, Jorge.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 63, No. 6, 01.01.2001.

Research output: Contribution to journalArticle

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