Characteristics of weak chaos in view of large deviation analysis and infinite ergodicity
| Project/Area Number |
25400411
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Waseda University |
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Principal Investigator |
Aizawa Yoji 早稲田大学, 理工学術院, 名誉教授 (70088855)
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| Co-Investigator(Kenkyū-buntansha) |
原山 卓久 早稲田大学, 理工学術院, 教授 (70247229)
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| Co-Investigator(Renkei-kenkyūsha) |
TSUGAWA Satoru 早稲田大学, 理工学術院, 助手 (20607600)
NAKAGAWA Masaki 早稲田大学, 理工学術院, 助手 (80649202)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | 非線形力学系 / カオス理論 / 近可積分ハミルトン系 / 無限エルゴード性 / 非カオス的ストレンジアトラクター / 光乱流現象 / 生物の群れの集団運動 / 地震統計法則 / 弱いカオス現象 / 非定常カオス / 地震統計則 / ワイブル分布 / マルチアフィン特性 / 位相鋭敏性 / 群れの自己駆動系モデル / 群れの統計則 / 非平衡・非線形物理学 / エルゴード性 / 大偏差特性 / 劣拡散 / 対数拡散 / Lyapunov解析 / 量子ビリヤード系 / ハミルトン系カオス / 無限測度エルゴード性 / 異常拡散 / アーノルド拡散 / リアプノフ解析 / 1/fスペクトルゆらぎ / 対数ワイブル則 |
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| Outline of Final Research Achievements |
There still remain many unsolved problems in the nonstationary regime of chaotic or turbulent phenomena; for instance, anomalous diffusion in hamiltonian systems, intermittency, and infinite ergodicity, et cetera. In this research, we studied several nonlinear dynamical models, such as the hamiltonian dynamics of lattice vibrations, mushroom billiards with clear boundaries between chaos and torus, antlion models with dissipative infinite measure ergodicity, nonchaotic strange attractors in periodically driven systems, wave turbulence in Bloch equation, etc., and succeeded to elucidate the diversity of the nonstationary chaos and its universal aspects in statistical behaviors. Furthermore, we studied a new method for the numerical analysis of chaotic intermittent time series by using the real data of interoccurrence time statistics of earthquakes, and succeeded to obtain some new statistical laws of magnitude correlations in the shock sequences.
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Report
(5 results)
Research Products
(29 results)
