Pros and cons of swimming in a noisy environment.

The problem of optimal microscopic swimming in a noisy environment is analyzed. A simplified model in which propulsion is generated by the relative motion of three spheres connected by immaterial links has been considered. We show that an optimized noisy microswimmer requires less power for propulsion (on average) than an optimal noiseless counterpart migrating with identical mean velocity and swimming stroke amplitude. We also show that noise can be used to overcome some of the limitations of the scallop theorem and have a swimmer that is able to propel itself with control over just one degree of freedom.