Diffusion-Mediated Transport¶and the Flashing Ratchet

Diffusion-mediated transport is a phenomenon in which a unidirectional motion of particles is achieved as a result of two opposing tendencies: diffusion, which spreads the particles uniformly through the medium and transport, which concentrates the particles at some special sites. The flashing-ratchet version of the Brownian motor, a simple model for protein motors, where the switching between transport and diffusion is periodic, illustrates diffusion-mediated transport. In this paper we show rigorously that the flashing ratchet can be tuned in such a way that the transport of mass against the gradient of the potential takes place and the concentration of mass during the transport phase occurs at sites located at the wells of an asymmetric potential. This goal is accomplished by comparing the flashing ratchet with an approximating Markov chain. A principle achievement of this work is to establish the connection between the dynamics of the ratchet and the Markov chain in the weak^* topology.