Operation of theoretical Brownian motors based on morphological adaptations

The dynamics of autonomous Brownian motors that achieve rectified motion due to morphological changes is analyzed. These motors are assumed to be deformable, with restitution internal forces, and to be able to adapt their shapes as function of their total elongation. A generic protocol for morphology adaptation is presented which guarantees unidirectional motion at a constant average speed. This protocol is illustrated by diverse particular examples. Motors operating under non-linear internal forces are analyzed. It is shown that non-linear forces produce considerable variations of the average speed and could serve as a control mechanism for the biased dynamics. The effects of hydrodynamic interactions are quantified as function of the morphological asymmetry. Such interactions are found to promote a very slight reduction of the rectification phenomenon, and could be observable only for motors operating at extremely reduced velocities. The theoretical analysis is found to be in very good agreement with the results of Brownian Dynamics simulations.