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

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Title: Existence and non-existence of asymmetrically rotating solutions to a mathematical model of self-propelled motion
Authors: Mamoru, Okamoto Browse this author
Takeshi, Gotoda Browse this author
Masaharu, Nagayama Browse this author →KAKEN DB
Keywords: Camphor model
Asymmetrically rotating solution
Reaction-diffusion system
Issue Date: Sep-2020
Publisher: Springer
Journal Title: Japan Journal of Industrial and Applied Mathematics
Volume: 37
Issue: 3
Start Page: 883
End Page: 912
Publisher DOI: 10.1007/s13160-020-00427-x
Abstract: 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.
Rights: https://creativecommons.org/licenses/by/4.0/
Type: article
URI: http://hdl.handle.net/2115/79204
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

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