Energy-driven pattern formation

Robert V. Kohn

Research output: Contribution to conferencePaperpeer-review


Many physical systems can be modelled by nonconvex variational problems regularized by higher-order terms. Examples include martensitic phase transformation, micromagnetics, and the Ginzburg-Landau model of nucleation. We are interested in the singular limit, when the coefficient of the higher-order term tends to zero. Our attention is on the internal structure of walls, and the character of microstructure when it forms. We also study the pathways of thermally-activated transitions, modeled via the minimization of action rather than energy. Our viewpoint is variational, focusing on matching upper and lower bounds.

Original languageEnglish (US)
Number of pages25
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006


Other25th International Congress of Mathematicians, ICM 2006


  • Action minimization
  • Aviles-giga problem
  • Calculus of variations
  • Cross-tie wall
  • Martensitic transformation
  • Micromagnetics
  • Microstructure

ASJC Scopus subject areas

  • General Mathematics


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