Expanding selfsimilar solutions of a crystalline flow with applications to contour figure analysis

Hidekata Hontani, Mi Ho Giga, Yoshikazu Giga, Koichiro Deguchi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

A numerical method for obtaining a crystalline flow starting from a general polygon is presented. A crystalline flow is a polygonal flow and can be regarded as a discrete version of a classical curvature flow. In some cases, new facets may be created instantaneously and their facet lengths are governed by a system of singular ordinary differential equations (ODEs). The proposed method solves the system of the ODEs numerically by using expanding selfsimilar solutions for newly created facets. The computation method is applied to a multi-scale analysis of a contour figure.

Original languageEnglish
Pages (from-to)265-285
Number of pages21
JournalDiscrete Applied Mathematics
Volume147
Issue number2-3
DOIs
Publication statusPublished - 2005 Apr 15

Keywords

  • Crystalline flow
  • Evolving polygon
  • Multi-scale analysis
  • Selfsimilar solutions

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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