Directed transport of a Brownian particle in a periodically tapered tube

The problem of the motion of a Brownian particle in a periodically tapered tube induced by a time-periodic longitudinal force with zero mean is considered. Under the action of this force, the particle is shown to drift in a direction opposite to the constant load force applied to it. Analytical solutions for the drift velocity, the stopping force (the load causing the effect to disappear), and the efficiency of converting the energy introduced by perturbations into directed motion have been obtained at a large amplitude of the driving force, when the effect being discussed is maximal. In the range of its applicability extending from zero to asymptotically large force switching frequencies (proportional to the amplitude of the driving force), these solutions are in good agreement with the results of Brownian dynamics simulations.