The tilted flashing Brownian ratchet

TL;DR

This paper investigates the tilted flashing Brownian ratchet, a stochastic process combining Brownian motion and ratchet dynamics, analyzing how static forces influence directed motion through numerical and simulation methods.

Contribution

It introduces methods to study the tilted flashing Brownian ratchet numerically, including random walk approximations and Fokker-Planck equation solutions, for the first time.

Findings

Directed motion can be reduced or reversed by static forces.

Numerical methods effectively analyze the process.

Stochastic simulation provides additional insights.

Abstract

The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a periodic asymmetric sawtooth potential. The result is directed motion. In the presence of a static homogeneous force that acts in the direction opposite that of the directed motion, there is a reduction (or even a reversal) of the directed motion effect. Such a process may be called a tilted flashing Brownian ratchet. We show how one can study this process numerically, using a random walk approximation or, equivalently, using numerical solution of the Fokker-Planck equation. Stochastic simulation is another viable method.