2012 Fiscal Year Final Research Report
Mathematical analysis of the droplet motion and the particle motion with the chemical reaction.
| 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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| Keywords | 応用数学 |
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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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