A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions

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

doi:10.1007/978-3-540-39966-7_44

A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions

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

INF - System Information Sciences

Research output: Chapter in Book/Report/Conference proceeding › Chapter

3 Citations (Scopus)

Abstract

A numerical method for obtaining a crystalline flow from a given polygon is presented. A crystalline flow is a discrete version of a classical curvature flow. In a crystalline flow, a given polygon evolves, and it remains polygonal through the evolving process. Each facet moves keeping its normal direction, and the normal velocity is determined by the length of the facet. In some cases, a set of new facets sprout out at the very beginning of the evolving process. The facet length is governed by a system of singular ordinary differential equations. The proposed method solves the system of ODEs, and obtain the length of each new facet, systematically. Experimental results show that the method obtains a crystalline flow from a given polygon successfully.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Ingela Nystrom, Gabriella Sanniti di Baja, Stina Svensson
Publisher	Springer Verlag
Pages	465-474
Number of pages	10
ISBN (Electronic)	3540204997, 9783540204992
DOIs	https://doi.org/10.1007/978-3-540-39966-7_44
Publication status	Published - 2003

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2886
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

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10.1007/978-3-540-39966-7_44

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Hontani, H., Giga, M. H., Giga, Y., & Deguchi, K. (2003). A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions. In I. Nystrom, G. S. di Baja, & S. Svensson (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 465-474). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2886). Springer Verlag. https://doi.org/10.1007/978-3-540-39966-7_44

A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions. / Hontani, Hidekata; Giga, Mi Ho; Giga, Yoshikazu; Deguchi, Koichiro.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Ingela Nystrom; Gabriella Sanniti di Baja; Stina Svensson. Springer Verlag, 2003. p. 465-474 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2886).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Hontani, H, Giga, MH, Giga, Y & Deguchi, K 2003, A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions. in I Nystrom, GS di Baja & S Svensson (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2886, Springer Verlag, pp. 465-474. https://doi.org/10.1007/978-3-540-39966-7_44

Hontani H, Giga MH, Giga Y, Deguchi K. A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions. In Nystrom I, di Baja GS, Svensson S, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2003. p. 465-474. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-540-39966-7_44

Hontani, Hidekata ; Giga, Mi Ho ; Giga, Yoshikazu ; Deguchi, Koichiro. / A computation of a crystalline flow starting from non-admissible polygon using expanding selfsimilar solutions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Ingela Nystrom ; Gabriella Sanniti di Baja ; Stina Svensson. Springer Verlag, 2003. pp. 465-474 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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