The spontaneous motion of a camphor particle with a slight modification from a circle is investigated. The effect of the shape on the motion is examined by the perturbation method. We introduce a slight $n$-mode modification from a circle, where the profile is described by $r = R(1 + \epsilon \cos n\theta)$ in polar coordinates. The results predict that a camphor particle with an $n=3$ mode modification from a circle, i.e., a triangular modification, moves in the direction of a corner for a small particle, while it moves in the direction of a side for a large particle. The numerical simulation results well reproduce the theoretical prediction. The present study will help understand the effect of the particle shape on spontaneous motion.

中文翻译：

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由圆作三角修正的樟脑粒子自发运动

研究了从圆稍作修改的樟脑粒子的自发运动。形状对运动的影响是通过微扰方法检查的。我们从一个圆中引入了一个轻微的 $n$-mode 修改，其中的轮廓由极坐标中的 $r = R(1 + \epsilon \cos n\theta)$ 描述。结果预测，一个圆的$n=3$模态修改的樟脑颗粒，即三角形修改，小颗粒向角方向移动，大颗粒向边方向移动。粒子。数值模拟结果很好地再现了理论预测。本研究将有助于了解粒子形状对自发运动的影响。