Grain boundary motion arising from the gradient flow of the Aviles-Giga functional

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper considers the singular limit of the equation Θt=-εΔ2Θ+ε-1∇·([|∇Θ|2-1] ∇Θ). Grain boundaries (limiting discontinuities in ∇Θ) form networks that coarsen over time. A matched asymptotic analysis is used to derive a free boundary problem consisting of curve motion coupled along hyperbolic characteristics and junction conditions. An intermediate boundary layer near extrema junctions is discovered, along with the relevant nonlocal junction conditions. The limiting dynamics can be viewed in the context of a gradient flow of the sharp interface energy on an attracting manifold. Dynamic scaling of the long-time coarsening process can be explained by dimensional analysis of the reduced problem.

Original languageEnglish (US)
Pages (from-to)80-98
Number of pages19
JournalPhysica D: Nonlinear Phenomena
Volume215
Issue number1
DOIs
StatePublished - Mar 1 2006

Fingerprint

Gradient Flow
Grain Boundary
Grain boundaries
grain boundaries
Limiting
Matched Asymptotics
Dynamic Scaling
gradients
Singular Limit
Asymptotic analysis
Motion
Dimensional Analysis
Coarsening
Free Boundary Problem
Extremum
Asymptotic Analysis
Boundary Layer
Discontinuity
Boundary layers
free boundaries

Keywords

  • Gradient flows
  • Grain boundaries
  • Matched asymptotic expansion

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Grain boundary motion arising from the gradient flow of the Aviles-Giga functional. / Glasner, Karl B.

In: Physica D: Nonlinear Phenomena, Vol. 215, No. 1, 01.03.2006, p. 80-98.

Research output: Contribution to journalArticle

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