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On the role of kinetic and interfacial anisotropy in the crystal growth theory
| Title: | On the role of kinetic and interfacial anisotropy in the crystal growth theory |
| Authors: | Giga, Mi-Ho Browse this author | | Giga, Yoshikazu Browse this author |
| Keywords: | Facet | | curvature flow equation | | crystalline flow | | viscosity solution. |
| Issue Date: | 3-Oct-2012 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1019 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | A planar anisotropic curvature flow equation with constant driving force term is considered when the interfacial energy is crystalline. The driving force term is given so that a closed convex set grows if it is sufficiently large. If initial shape is convex, it is shown that a flat part called a facet (with admissible orientation) is instantaneously formed. Moreover, if the initial shape is convex and slightly bigger than the critical size, the shape becomes fully faceted in a finite time provided that the Frank diagram of interfacial energy density is a regular polygon centered at the origin. The proofs of these statements are based on approximation by crystalline algorithm whose foundation was established a decade ago. Our results indicate that the anisotropy of intefacial energy plays a key role when crystal is small in the theory of crystal growth. In particular, our theorems explain a reason why snow crystal forms a hexagonal prism when it is very small. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69824 |
| 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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