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

Rober V. Kohn, Felix Otto

Research output: Contribution to journalArticlepeer-review


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
Issue number2-4
StatePublished - 1997


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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