The construction of approximate grids for quasicrystals using control points
| Project/Area Number |
23540141
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kochi University |
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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)
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| 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)
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | タイル貼り / 数理モデル / 回転対称性 / 準周期タイリング / grid / 準周期性 / タイリング |
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| 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.
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Report
(6 results)
Research Products
(15 results)
