Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion

• Mamoru Okamoto

• Takeshi Gotoda

• Masaharu Nagayama

抄録

Mathematical models for self-propelled motions are often utilized for understanding the mechanism of collective motions observed in biological systems. Indeed, several patterns of collective motions of camphor disks have been reported in experimental systems. In this paper, we show the existence of asymmetrically rotating solutions of a two-camphor model and give necessary conditions for their existence and non-existence. The main theorem insists that the function describing the surface tension should have a concave part so that asymmetric motions of two camphor disks appear. Our result provides a clue for the dependence between the surfactant concentration and the surface tension in the mathematical model, which is difficult to be measured in experiments.

収録刊行物

• Japan Journal of Industrial and Applied Mathematics

  Japan Journal of Industrial and Applied Mathematics 37 (3), 883-912, 2020-06-22

  Springer Science and Business Media LLC

キーワード

• Applied Mathematics
• General Engineering

詳細情報

• CRID: 1362260173466927744
• NII論文ID: 210000187062
• DOI: 10.1007/s13160-020-00427-x
• ISSN: 1868937X
• ISSN: 09167005
• Web Site: https://link.springer.com/content/pdf/10.1007/s13160-020-00427-x.pdf
• Web Site: https://link.springer.com/article/10.1007/s13160-020-00427-x/fulltext.html
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