The flow of a reversible ratchet

A reversible ratchet by which Brownian particles can be transported might be attained through the periodic change of a potential in space and time. Since the integrated flow of particles in the ratchet along a certain process can be expressed as a contour integral in the space of potential parameters, it is possible, therefore, to investigate what kind of process has a better net flow of particles in a reversible ratchet system. In a certain process, we study the behavior of the particle flow in two potential parameters and then find that structures exist in the net flow of particles in different potentials or processes. Our findings can be useful in the design of Brownian motors.