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On the role of kinetic and interfacial anisotropy in the crystal growth theory

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84165

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
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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