| Project/Area Number |
21340023
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hokkaido University (2012)
Kanazawa University (2009-2011) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Ken-ichi 金沢大学, 数物科学系, 准教授 (40293120)
SAITO Norikazu 東京大学, 数理科学研究科, 准教授 (00334706)
NAKATA Satoshi 広島大学, 理学研究科, 教授 (50217741)
KITAHATA Hiroyuki 千葉大学, 理学研究科, 准教授 (20378532)
SUMINO Yutaka 愛知教育大学, 教育学部, 助教 (00518384)
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| Co-Investigator(Renkei-kenkyūsha) |
OMATA Seiro 金沢大学, 数物科学系, 教授 (20214223)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥17,160,000 (Direct Cost: ¥13,200,000、Indirect Cost: ¥3,960,000)
Fiscal Year 2012: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
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| Keywords | 応用数学 / 数理モデル / 表面張力 / 自走運動 / 反応拡散系 / スポットパターン / 樟脳粒 / ブレビング運動 / 振動運動 / スポットパターンダイナミクス / 体積保存条件付き反応拡散系 / 液滴のブレビング運動 / 樟脳船 / 粒子運動 / 化学反応 / 間欠運助 / Hopf分岐 / 液滴運動 |
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| Research Abstract |
Through collaborative research with experimental groups, the mathematical modeling and analysis of mechanisms for the self-propelled motion of droplets and particles under chemical reactions were investigated. The target experimental systems regard the motion of surfactant particles with stabilizing and destabilizing reactions driving their motions. By means of mathematical modeling, we clarified that the reaction order plays a central role in the oscillating phenomenon of the stabilizing system, and that the chemical product generated within the destabilizing system strongly influences the oscillation mechanism through chemical reaction. Moreover, by introducing a mathematical model for determining the mechanisms governing the motion of self-propelled grains, which oscillate spontaneously, we were able to explain the corresponding oscillation mechanism. Additionally, we analyzed the case where the particle’s geometry, here taken to be an elliptically shaped camphor disk, influences its motion.
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