水面坦克踩踏：珀塞尔环形游泳者的推进
Surface tank-treading: propulsion of Purcell's toroidal swimmer
摘要：
在这项工作中，我们解决的“吸烟环”推进技术，最初提出的E。M.珀塞尔我们首先考虑自我运动的甜甜圈形状的游泳提供动力的表面坦克踩。假设不同的表面运动模式，并确定推进速度和游泳效率。游泳者被逆着其外表面运动的方向推进，内表面几乎没有影响。最简单的游泳模式对应于恒定的角速度，可以实现高达66%的表面坦克踩踏速度和游泳效率高达13%。更高的效率是可能的更复杂的模式，通过旋转的可延伸表面。一个潜在的实际设计的游泳运动员的动机Purcell的想法，提出并证明了数值。最后，显式解的两维游泳者组成的两个反向旋转的磁盘，使用复变量技术。
英文摘要：
In this work we address the "smoking ring" propulsion technique, originally proposed by E. M. Purcell. We first consider self-locomotion of a doughnut-shaped swimmer powered by surface tank-treading. Different modes of surface motion are assumed and propulsion velocity and swimming efficiency are determined. The swimmer is propelled against the direction of its outer surface motion, the inner surface having very little affect. The simplest swimming mode corresponding to constant angular velocity, can achieve propulsion speeds of up to 66% of the surface tank-treading velocity and swimming efficiency of up to 13%. Higher efficiency is possible for more complicated modes powered by twirling of extensible surface. A potential practical design of a swimmer motivated by Purcell's idea is proposed and demonstrated numerically. Lastly, the explicit solution is found for a two-dimensional swimmer composed of two counter-rotating disks, using complex variable techniques.
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