Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber
Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber
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DOI：
10.1039/d2cp02456j
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发表时间：
2022-08-11
影响因子：
3.3
通讯作者：
Gorecki, Jerzy
中科院分区：
文献类型：
--
作者：
Kitahata, Hiroyuki;Koyano, Yuki;Gorecki, Jerzy
我们考虑一个自推进的矩形物体在圆形水腔内的运动。自运动的数学模型包括矩形的方向和位置方程以及活性分子表面浓度随时间变化的带有效扩散系数的反应扩散方程。对不同活性分子供给速率S与蒸发速率a之比进行了运动数值模拟。以S-0 = S/a为控制参数，找到表征轨迹的变量的临界行为，并识别出不同类型的运动。如果S-0值很小，则矩形停留在腔室中心。对于较大的S-0，观察到矩形穿过中心的互反运动。在更高的供给率下，星多边形运动出现，轨迹保持在离腔中心一定距离处。用樟脑-樟烯-聚丙烯塑料制成的矩形在培养皿中运动的实验中，我们观察了从星形多边形运动到倒向运动的时间转变。如果我们假设供给率随着时间的推移而减少，那么这种转变可以在已开发的模型的基础上理解。
We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S-0 = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S-0 is small, the rectangle rests at the chamber center. For larger S-0, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.