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 language | English |
|---|---|
| Title of host publication | Applied Mathematical Sciences (Switzerland) |
| Publisher | Springer |
| Pages | 503-546 |
| Number of pages | 44 |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
Publication series
| Name | Applied Mathematical Sciences (Switzerland) |
|---|---|
| Volume | 149 |
| 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