扇形定理的严格证明和微游泳器的有限质量效应
A rigorous proof of the scallop theorem and a finite mass effect of a microswimmer
摘要：
我们重新考虑了在Stokes流中自推进游泳者的流体动力学。在给出游泳运动员变形的精确定义的基础上，给出了包含身体转动的Purcell扇形定理的证明。利用微扰展开方法讨论了有限Stokes数下定理的失效，发现失效一般发生在Stokes数的一阶.此外，采用Purcell的“扇贝”模型，我们证明了定理成立，以更高的顺序，如果中风的游泳运动员有一定的对称性。
英文摘要：
We reconsider fluid dynamics for a self-propulsive swimmer in Stokes flow. With an exact definition of deformation of a swimmer, a proof is given to Purcell's scallop theorem including the body rotation. The breakdown of the theorem due to a finite Stokes number is discussed by using a perturbation expansion method and it is found that the breakdown generally occurs at the first order of the Stokes number. In addition, employing the Purcell's "scallop" model, we show that the theorem holds up to a higher order if the strokes of the swimmer has some symmetry.
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