The flashing ratchet and unidirectional transport of matter

TL;DR

This paper investigates the flashing ratchet model of a Brownian motor, demonstrating that it can achieve unidirectional mass transport through analysis of its attractors and stationary states.

Contribution

It provides a rigorous analysis confirming unidirectional transport in the flashing ratchet model using attractor and Markov chain stationary state analysis.

Findings

The model performs unidirectional transport with proper parameters.

Analysis of attractors confirms the directionality of transport.

Stationary vector analysis supports the unidirectional movement.

Abstract

We study the flashing ratchet model of a Brownian motor, which consists in cyclical switching between the Fokker-Planck equation with an asymmetric ratchet-like potential and the pure diffusion equation. We show that the motor really performs unidirectional transport of mass, for proper parameters of the model, by analyzing the attractor of the problem and the stationary vector of a related Markov chain.