Asymmetry of the shape of surroundings as a mechanism for generating directed motion

A mechanism for generating a directed motion of a Brownian particle in an asymmetric channel under the action of a varying force field is considered. The setup implementing such a mechanism resembles typical Brownian motors using asymmetry of the energy potential (ratchet effect). It is shown that under certain conditions, the asymmetry of the shape may ensure the maximal level of rectification for a large intensity of the external field drawing the system from equilibrium. The main question formulated here is the dependence of the rectifying ability of such a mechanism on the external action parameters and, above all, on the form of the time dependence. The results obtained here for a sine signal and an aperiodic train of pulses are compared with the previous results obtained by the authors for bipolar rectangular pulses. General estimates obtained for pulses of an arbitrary shape determine its influence on the velocity of directed motion. Analysis of the proposed mechanism is based of the combination of analytic calculations for a strong external field with simulation by the method of Brownian dynamics for arbitrary parameters.