Maximizing transport in open loop for flashing ratchets

This paper studies open-loop operation of flashing ratchets, which refer to mechanisms that enable motion of particles under diffusion and possibly drag forces along a preferred direction through alternating turning on and off of specifically designed ratchet potentials. Flashing ratchets are used to model certain transport mechanisms of molecular motors and are of special interest to biologists and biophysicists. Mathematically they are are modeled by stochastic hybrid systems. For an open-loop design of on-times and off-times, we derive, under certain practical assumptions, an exact probability density function that reflects the spatial distribution of particles in space after the ratchet has flashed a given number of times, and find an optimal off-time that maximizes the transport velocity for a specific ratchet potential. Validation of the underlying assumptions is also presented. Simulation results show that these open-loop designs achieve as good or better average velocities for particles over certain well known existing feedback strategies in literature.