The construction of approximate grids for quasicrystals using control points

2015 Fiscal Year Final Research Report

• Project/Area Number: 23540141
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kochi University
• Principal Investigator: Komatsu Kazushi 高知大学, 教育研究部自然科学系理学部門, 准教授 (00253336)
• Co-Investigator(Kenkyū-buntansha): AKIYAMA Shigeki 筑波大学, 数理物質科学研究科(系), 教授 (60212445) ; GOTO Satoru 東京理科大学, 薬学部, 教授 (50253232) ; EI Hiromi 弘前大学, 理工学研究科, 助教 (60333051)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Keywords: タイル貼り / 数理モデル

Outline of Final Research Achievements

We construct a family of uncountable many non-periodic 3-Archimedean tilings with 6-fold rotational symmetry, that admit three type of vertex configurations by regular triangles and squares. As a limit of the patch sequence, we obtain a tiling or an unbounded configuration. In Danzer tilings, we cover all singular vertex configurations and all wedge-shaped unbounded configurations by up-down generation. We construct non-periodic tilings by gathering wedge-shaped unbounded configurations around a point.
We provide a mathematical model of n-membered hydrocarbon molecules. The configuration space of the model straight-chain hydrocarbon molecules is parametrized by chain lengths. We determine the topological types of fibers of the configuration space of the model by chain lengths when n = 5.

Free Research Field

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