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Hokkaido University Preprint Series in Mathematics >
Stability of facets of crystals growing from vapor
| Title: | Stability of facets of crystals growing from vapor |
| Authors: | Giga, Yoshikazu Browse this author | | Rybka, Piotr Browse this author |
| Issue Date: | 14-Dec-2004 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 679 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | Consider a Stefan-like problem with Gibbs-Thomson and kinetic effects as a model of crystal growth from vapor. The equilibrium shape is assumed to be a regular circular cylinder. Our main concern is a problem whether or not a surface of cylindrical crystals (called a facet) is stable under evolution in the sense that its normal velocity is constant over the facet. If a facet is unstable, then it breaks or bends. A typical result we establish is that all facets are stable if the evolving crystal is near the equilibrium. The stability criterion we use is a variational principle for selecting the correct Cahn-Hoffman vector. The analysis of the phase plane of an evolving cylinder (identi ed with points in the plane) near the unique equilibrium provides a bound for ratio of velocities of top and lateral facets of the cylinders. 1 |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69484 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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