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

Tetsuya Ishiwata, Takeshi Ohtsuka

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)5261-5295
Number of pages35
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume24
Issue number10
DOIs
Publication statusPublished - 2019 Oct 1

Keywords

  • Crystalline curvature flow
  • Evolution of convex polygonal spiral

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Evolution of a spiral-shaped polygonal curve by the crystalline curvature flow with a pinned tip'. Together they form a unique fingerprint.

  • Cite this