| Project/Area Number |
15K13448
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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 analysis
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| Research Institution | Osaka University |
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Principal Investigator |
Suzuki Takashi 大阪大学, 基礎工学研究科, 教授 (40114516)
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| Co-Investigator(Kenkyū-buntansha) |
坪田 誠 大阪市立大学, 大学院理学研究科, 教授 (10197759)
中西 賢次 大阪大学, 情報科学研究科, 教授 (40322200)
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| Project Period (FY) |
2015-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 点渦 / ボルツマン・ポアソン方程式 / 爆発機構の量子化 / 循環的階層 / 非局所項 / 平均場理論 / 準平衡 / 緩和方程式 / 非線形解析学 / 非平衡統計力学 / 量子渦 / 量子化する爆発機構 / モース指数 / 緩和時間 |
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| Outline of Final Research Achievements |
Ordered structures are widely observed for long term in turbulence, e.g., the great red spot on Jupiter. It has been known that in the two dimensional flow, this phenomena is due to the quasi-equilibria and equilibria arising in the mean field of many point vortices, while there is a recursive hierarchy through the particles and their mean field. This project is a fusion of nonlinear analysis and non- equilibrium statistical mechanics. We have rigorously proven the recursive hierarchy in the dynamical level, and also derived a mathematical model for the point vortex mean field in the relaxation time compatible to the patch and equilibrium models.
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