| Project/Area Number |
18K03416
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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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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Yamaguchi University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2018: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Keywords | 力学系 / キラル液晶 / ブルー相 / ベルトラミ流 / 不変トーラス / 磁気群 / 液晶 / 結晶群 |
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| Outline of Final Research Achievements |
Magnetic groups were shown to be useful for determining the parameters in the dynamical system whose set of all integral curves was required to have the symmetry of a space group specified. This was demonstrated in the case of chiral hexagonal symmetry. Then the arrangement of invariant tori numerically obtained were shown to be similar to the arrangement that had been previously proposed for double twist cylinders in a blue phase of a chiral smectic liquid crystals. Moreover, which cubic magnetic group should be applied to a dynamical system was made clear when the set of invariant tori was required to have a similar arrangement to each of the six cubic rod packings (two of which are the same as the arrangements of double twist cylinders in blue phases of cholesteric liquid crystals).
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| Academic Significance and Societal Importance of the Research Achievements |
結晶学的対称性をもつ力学系の研究は過去にも存在したが，欲しい結晶学対称性や欲しい不変トーラスの配置を実現させるため，磁気群を力学系に適用する方法は，従来には無かった新しいものである．そのアプローチで力学系の積分曲線を用いてキラル液晶中の分子配向をモデル化することについては課題も残ったが，電磁場中の電気力線や磁力線について本研究の手法が適用可能とみられ，今後も研究の価値があると思われる．
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