2019 Fiscal Year Final Research Report

Mathematical modeling of collectiove motion of self-propelled systems and its analysis

Research Project

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Project/Area Number	16H03949
Research Category	Grant-in-Aid for Scientific Research (B)
Allocation Type	Single-year Grants
Section	一般
Research Field	Foundations of mathematics/Applied mathematics
Research Institution	Hokkaido University
Principal Investigator	NAGAYAMA MASAHARU 北海道大学, 電子科学研究所, 教授 (20314289)
Co-Investigator(Kenkyū-buntansha)	小俣正朗金沢大学, 数物科学系, 教授 (20214223) 北畑裕之千葉大学, 大学院理学研究院, 准教授 (20378532) Ginder Elliott 明治大学, 総合数理学部, 専任准教授 (30648217) 中村健一金沢大学, 数物科学系, 准教授 (40293120) 田中晋平広島大学, 総合科学研究科, 准教授 (40379897) 中田聡広島大学, 理学研究科, 教授 (50217741) 末松信彦明治大学, 総合数理学部, 専任准教授 (80542274)
Project Period (FY)	2016-04-01 – 2020-03-31
Keywords	数理モデリング / 数値シミュレーション / 分機解析 / 集団運動 / 自己組織化
Outline of Final Research Achievements	We carried out mathematical modeling of the self-propelled system and performed mathematical analysis of the mathematical model. In this research, together with the experimental group, we solved the mechanism of oscillation phenomena about the self-propelled material by mathematical modeling. Moreover, it was clarified that the mechanism of collective motion that occurs when multiple self-propelled materials float on the water is not caused by the capillarity phenomenon but is caused by the concentration gradient of the chemical substances contained in the aqueous solution near the water surface. In addition, we have clarified the mechanism of the interaction motion between the string-shaped self-propelled materials and the shape-dependent interaction motion between the self-propelled materials by mathematical modeling and theoretical analysis.
Free Research Field	応用数学
Academic Significance and Societal Importance of the Research Achievements	自己駆動系と呼ばれる化学的または物理的環境に応答しながら駆動する無生物実験系は，生物の群れの運動や細胞運動等の生命現象を理論的に理解する道具として重要な系となっている．この系に現れる現象の理論解析を行うためには，現象を記述する数理モデリングが必須である．この研究では，液滴の集団運動や自律的に周期運動する実験系に注目して，その運動を再現する数理モデリングを行い，その解析から運動が生じるメカニズムの解明を行った．