Self-propulsion velocity of N-sphere micro-robot
  The aim of this paper is to derive an analytical expression for the self-propulsion velocity of a micro-swimmer that consists of N spheres moving along a fixed line. The spheres are linked to each other by the rods of the prescribed lengths changing periodically. For the derivation we use the asymptotic procedure containing the two-timing method and a distinguished limit. Our final formula shows that in the main approximation the self-propulsion velocity is determined by the interactions between all possible triplets of spheres. 
Vladimir A.Vladimirov
physics.flu-dyn cond-mat.mes-hall physics.bio-ph