Abstract
AbstractMathematical 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.
Funder
Japan Society for the Promotion of Science
Core Research for Evolutional Science and Technology
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Engineering
Reference50 articles.
1. Ballerini, M., Cabibbo, N., Candelier, R., Cavagna, A., Cisbani, E., Giardina, I., et al.: Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study. Proc. Natl. Acad. Sci. USA 105, 1232–1237 (2008)
2. Bánsági Jr., T., Wrobe, M.M., Scott, S.K., Taylor, A.F.: Motion and interaction of aspirin crystals at aqueous-air interfaces. J. Phys. Chem. B 117, 13572–13577 (2013)
3. Boniface, D., Cottin-Bizonne, C., Kervil, R., Ybert, C., Detcheverry, F.: Self-propulsion of symmetric chemically active particles: point-source model and experiments on camphor disks. Phys. Rev. E 99, 062605 (2019)
4. C̆ejková, J., Novák, M., S̆tĕpánek, F., Hanczyc, M.M.: Dynamics of chemotactic droplets in salt concentration gradients. Langmuir 30, 11937–11944 (2014)
5. Chen, X., Ei, S.-I., Mimura, M.: Self-motion of camphor discs. Model and analysis. Netw. Heterog. Media 3, 1–18 (2009)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献