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

Rober V. Kohn; Felix Otto

doi:10.1016/S0167-2789(97)00094-8

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

Rober V. Kohn, Felix Otto

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	272-289
Number of pages	18
Journal	Physica D: Nonlinear Phenomena
Volume	107
Issue number	2-4
DOIs	https://doi.org/10.1016/S0167-2789(97)00094-8
State	Published - 1997

Keywords

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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10.1016/S0167-2789(97)00094-8

Cite this

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AU - Kohn, Rober V.

AU - Otto, Felix

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AB - 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.

KW - Calculus of variations

KW - Magnetic domain structure

KW - Magnetic fluids

KW - Martensitic transformation

KW - Surface energy

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JF - Physica D: Nonlinear Phenomena

IS - 2-4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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