Abstract
The rectification of thermal motion can give rise to a steady state flow of particles. This process is believed to occur in nature and to be of central importance for intra-cellular transport. Ajdari and Prost have proposed an "on-off" or "flashing" ratchet and Magnasco has proposed a similar "tilting" or "rocking" ratchet mechanism. These developments led to new and active fields of research in statistical physics and physical chemistry. Recent work by Gillespie and Eisenberg suggests that the effectiveness of the natural transport process, in biological ion channels, depends strongly on how we model the effect of ion to ion interactions. At high local ion concentrations the effect of the crowding of charge is significant. It is necessary to include this effect in the models. If we are interested in average ion currents then we can replace the complicated many-body problem with a time-average mean-field for the distribution of charge. To date, all analyses of artificial, human-made, ratchets require us to neglect the effect of distributed charge. This means that the analysis is only strictly valid for dilute solutions. The purpose of our present paper is to include the effect of distributed charge in the analysis of artificial Brownian ratchets. We formulate the Brownian ratchet problem for the case where distributed charge is significant. We investigate methods of solution and find that the finite difference approach is not adequate because the governing equations are very "stiff." We propose an alternative approach based on Fourier series.
Published Version
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