| Project/Area Number |
16K13846
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | The University of Tokyo (2018)
Tokyo Institute of Technology (2016-2017) |
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Principal Investigator |
Takeuchi Kazumasa 東京大学, 大学院理学系研究科(理学部), 准教授 (50622304)
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| Research Collaborator |
Shimizu Taro P.
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | 非線形科学 / カオス / 大自由度力学系 / 時系列解析 / 不安定性 / 電子回路 |
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| Outline of Final Research Achievements |
Whereas chaos abounds in a wide variety of nonlinear phenomena, it had been basically impossible to measure its instability in large experimental systems. Here, as a first step, we developed a method for systems with a simple form of coupling. By using symmetry of the systems, our method allows us to fully quantify the chaos instability, out of a time series of a local signal. We confirmed the validity of our method numerically and proposed a few techniques to improve the accuracy. Experimentally we made a chaotic circuit and obtained some hints on conditions to use our method. Moreover, we also developed a method to extract weak instability modes with a potentially lower computational cost. Our result suggested the validity of the method, while it also revealed some issues to resolve in future studies.
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| Academic Significance and Societal Importance of the Research Achievements |
大自由度のカオス現象は、気象をはじめとする乱流現象、ある種の振動性媒質中の位相伝播や、諸説あるが心室細動など、様々な実例がある。しかしながら、カオス最大の特徴である不安定性を大自由度系で計測する実験手法が存在しないため、そうした現象のカオスとしての性質が理解されているとは言い難い。我々の成果は、単純な種類の大自由度カオス系で不安定性計測を実現するための1つの基礎となりうる手法の開発であり、将来、より現実的な系へ拡張するための端緒を開くものである。不安定性は、カオス系の予測や制御のため重要な性質であり、そのような研究が大自由度系で行われるための準備段階の研究成果という位置付けでもある。
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