Abstract
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 language | English (US) |
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Pages | 359-383 |
Number of pages | 25 |
State | Published - 2006 |
Event | 25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain Duration: Aug 22 2006 → Aug 30 2006 |
Other
Other | 25th International Congress of Mathematicians, ICM 2006 |
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Country/Territory | Spain |
City | Madrid |
Period | 8/22/06 → 8/30/06 |
Keywords
- Action minimization
- Aviles-giga problem
- Calculus of variations
- Cross-tie wall
- Martensitic transformation
- Micromagnetics
- Microstructure
ASJC Scopus subject areas
- General Mathematics