Small surface energy, coarse-graining, and selection of microstructure

Robert Kohn, Felix Otto

Research output: Contribution to journalArticle

Abstract

We discuss some static and dynamic problems involving a competition between "bulk" and "surface" energy. In each case the bulk energy prefers microstructure, and the surface energy is a singular perturbation. It is natural to treat the surface energy density as a small parameter. In our static examples - involving branching of twins and magnetic domains - this leads to scaling laws for the energy and the length scale of microstructure. In our dynamic example - involving the fracture of a ferrofluid thin film by an applied magnetic field - it provides a novel approach to coarse-graining.

Original languageEnglish (US)
Pages (from-to)272-289
Number of pages18
JournalPhysica D: Nonlinear Phenomena
Volume107
Issue number2-4
StatePublished - 1997

Fingerprint

Coarse-graining
Surface Energy
Interfacial energy
surface energy
Microstructure
microstructure
Ferrofluid
Magnetic domains
Magnetic fluids
ferrofluids
Scaling laws
Scaling Laws
Singular Perturbation
Dynamic Problem
magnetic domains
Energy
Energy Density
Small Parameter
Length Scale
scaling laws

Keywords

  • Calculus of variations
  • Magnetic domain structure
  • Magnetic fluids
  • Martensitic transformation
  • Surface energy

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Small surface energy, coarse-graining, and selection of microstructure. / Kohn, Robert; Otto, Felix.

In: Physica D: Nonlinear Phenomena, Vol. 107, No. 2-4, 1997, p. 272-289.

Research output: Contribution to journalArticle

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