2018 Fiscal Year Final Research Report
The Interfacial and Free-Boundary Dynamics of Active Matter
| Project/Area Number |
15KT0099
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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 | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Meiji University (2017-2018)
Hokkaido University (2015-2016) |
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Principal Investigator |
Ginder Elliott 明治大学, 総合数理学部, 専任准教授 (30648217)
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| Co-Investigator(Kenkyū-buntansha) |
中田 聡 広島大学, 理学研究科, 教授 (50217741)
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| Project Period (FY) |
2015-07-10 – 2019-03-31
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| Keywords | active matter / free boundary problems / interfacial dynamics / physical chemistry / mathematical modeling |
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| Outline of Final Research Achievements |
We researched the mathematical modeling of interfacial active matter. A chemical system of surfactant filaments was designed and experimentally investigated. The system was modeled using free boundary problems, where line mass delta functions (Hausdorff measures) were used to express the location of surfactant filaments. A mathematical analysis of the model equations was performed, where the existence and stability of stationary and traveling pulse solutions was addressed. Numerical methods for performing simulations of the model equations were designed and implemented. Here, finite element methods and immersed boundary techniques were used. Simulations were used to compare the mathematical model with experimental observations of the chemical system. Overall, we showed that the proposed model is able to capture the main properties of the chemical system. We also showed that line masses are an effective in describing interfacial active matter.
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| Free Research Field |
応用数学
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| Academic Significance and Societal Importance of the Research Achievements |
界面運動は，科学的および工業的の応用において，社会の発展には欠かせない重要なテーマです．界面の動きを数理的な特性から理解することは，応用範囲を広げる基盤をつくることに繋がります．このような研究で使われる通常のデルタ関数は，点質量(point mass)の設定でよく利用されていますが，本研究では界面型アクティブマターの応用のため，線質量（line mass, ハウスドルフ測度）の数理科学および計算手法を開発しました．これにより，様々な分野での問題点や開発において，詳細な視点から合理的に分析が可能となることを期待しています．
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