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- Title
スパイラル成長の等高線法とその応用.
- Authors
大塚 岳
- Abstract
A level set approach for evolving spirals is introduced to handle merging spiral steps. For this purpose, the level set method is extended to describe curves by an auxiliary surface and a surface defined by a pre-determined multivalued function, like as a Riemann surface. Since the level set equation is a degenerate parabolic type, its solution is considered in the viscosity sense. The comparison principle or the existence and uniqueness of viscosity solution globally-in-time are explained as the results of the mathematical analysis. This method can be applied to compute the growth rate of a crystal surface that is evolving via spiral steps. As an application of this, the growth rate of a crystal surface with several screw dislocations is investigated numerically. We improved the estimate of the surface growth rate compared to that reported by Burton et al.
- Subjects
LEVEL set methods; VISCOSITY solutions; CRYSTAL surfaces; MATHEMATICAL analysis; SCREW dislocations; RIEMANN surfaces; DEGENERATE parabolic equations
- Publication
Bulletin of the Japan Society for Industrial & Applied Mathematics, 2023, Vol 33, Issue 3, p9
- ISSN
0917-2270
- Publication type
Article