Koyano Yuki, Kitahata Hiroyuki, Nakata Satoshi, Gorecki Jerzy
Department of Physics, Graduate School of Science, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai 980-8578, Japan.
Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan.
Chaos. 2020 Feb;30(2):023105. doi: 10.1063/1.5140626.
We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release-operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.
我们提出了一个简单的数学模型，该模型使用诸如物体位置、活性分子的表面浓度和流体动力表面流等变量来描述自推进物体在液体表面上的时间演化。该模型被应用于模拟由一个在其角落处装有樟脑丸的多边形板组成的转子的时间演化。我们定性地重现了实验结果，在这些实验中研究了在周期性停止和释放操作下旋转方向的反转。该模型正确地将反转概率描述为转子停止阶段持续时间的函数。此外，该模型允许引入实际实验中不可避免的转子不对称性，并研究其对所研究现象的影响。我们的数值模拟表明，旋转方向反转的概率由流对樟脑分子的输运、转子的固有不对称性和噪声幅度之间的竞争决定。
