Flower patterns on honeycomb structures

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Bifurcation mechanism of honeycomb structures is elucidated by the study of a that is the direct product of O(2) and two reflection group. A flower pattern is theoretically assessed to branch from a triple bifurcation point and is actually found by a numerical analysis of a honeycomb cellular solid. Other bifurcating patterns of interest are found in this study through the analysis of bifurcation points with the multiplicity of six and twelve. Fundamentals of group representation theory in Chap. 7 and group-theoretic bifurcation theory in Chap. 8 are foundations of this chapter.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages503-546
Number of pages44
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume149
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Bifurcation
  • Bifurcation equation
  • Cyclic group
  • Dihedral group
  • Equivariant branching lemma
  • Flower pattern
  • Group-theoretic bifurcation theory
  • Hexagonal lattice
  • Honeycomb structure
  • Symmetry

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Ikeda, K., & Murota, K. (2019). Flower patterns on honeycomb structures. In Applied Mathematical Sciences (Switzerland) (pp. 503-546). (Applied Mathematical Sciences (Switzerland); Vol. 149). Springer. https://doi.org/10.1007/978-3-030-21473-9_17