Evolution of a spiral-shaped polygonal curve by the crystalline curvature flow with a pinned tip

Tetsuya Ishiwata, Takeshi Ohtsuka

研究成果: Article

抄録

We present a new ODE approach for an evolving polygonal spiral by the crystalline eikonal-curvature flow with a fixed center. In this approach, we introduce a mechanism of new facet generation at the center of the growing spiral, which is based on the theory of two-dimensional nucleation. We prove the existence, uniqueness and intersection free of solution to our formulation globally-in-time. In the proof of the existence we also prove that new facets are generated repeatedly in time. The comparison result of the normal velocity between inner and outer facets with the same normal direction leads intersection-free result. The normal velocities are positive after the next new facet is generated, so that the center is always behind of the moving facets.

元の言語English
ページ(範囲)5261-5295
ページ数35
ジャーナルDiscrete and Continuous Dynamical Systems - Series B
24
発行部数10
DOI
出版物ステータスPublished - 2019 10 1

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Crystalline materials
Nucleation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

これを引用

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AU - Ohtsuka, Takeshi

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N2 - We present a new ODE approach for an evolving polygonal spiral by the crystalline eikonal-curvature flow with a fixed center. In this approach, we introduce a mechanism of new facet generation at the center of the growing spiral, which is based on the theory of two-dimensional nucleation. We prove the existence, uniqueness and intersection free of solution to our formulation globally-in-time. In the proof of the existence we also prove that new facets are generated repeatedly in time. The comparison result of the normal velocity between inner and outer facets with the same normal direction leads intersection-free result. The normal velocities are positive after the next new facet is generated, so that the center is always behind of the moving facets.

AB - We present a new ODE approach for an evolving polygonal spiral by the crystalline eikonal-curvature flow with a fixed center. In this approach, we introduce a mechanism of new facet generation at the center of the growing spiral, which is based on the theory of two-dimensional nucleation. We prove the existence, uniqueness and intersection free of solution to our formulation globally-in-time. In the proof of the existence we also prove that new facets are generated repeatedly in time. The comparison result of the normal velocity between inner and outer facets with the same normal direction leads intersection-free result. The normal velocities are positive after the next new facet is generated, so that the center is always behind of the moving facets.

KW - Crystalline curvature flow

KW - Evolution of convex polygonal spiral

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