Geometric variational problems and discrete geometry with numerical analysis
| Project/Area Number |
26400067
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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 |
Geometry
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| Research Institution | Nagoya University |
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Principal Investigator |
Naito Hisashi 名古屋大学, 多元数理科学研究科, 准教授 (40211411)
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| Project Period (FY) |
2014-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | discrete surfaces / 離散幾何解析 / ラプラシアンの固有値 / 離散曲面 / グラフの固有値 / 離散幾何学 / 微分幾何学 / 曲面論 / 数値解析 / 負曲率炭素構造 |
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| Outline of Final Research Achievements |
We study geometry of trivalent discrete surfaces. In paricular, we define vertex-wise Gauss and mean curvatures for trivalent discrete surfaces in 3-dimensional Euclidean spaces. In our study, we take Carbon nanotubes, Fullerens, and Mackay structures, and we show that the Mackay structure of type P is vertex-wise negatively curved, which is called "a negatively graphene" in material sciences and organic chemistry.
Moreover, we study subdivision of trivalent discrete surfaces. In particular, we show the Hausdorff convergence of the sequence of minimum energies of Mackay structures.
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| Academic Significance and Societal Importance of the Research Achievements |
従来の離散曲面論は，連続曲面の離散化として離散曲面を定義していた． この研究では，分子構造・結晶構造をモデルとした，本質的に離散な曲面を対象とし，その幾何学を展開したことに重要な意義がある． しかも，単純に曲率を定義するだけではなく，離散曲面の細分を定義することにより，収束理論への道を開いた． 一般に，分子構造・決s高構造のミクロな解析では離散的なオブジェクトとしてそれらを扱うが，収束理論を通じて，マクロな連続的なオブジェクトを扱うことができる可能性を示した．
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Report
(7 results)
Research Products
(31 results)
