Active Brownian Motion Models and Applications to Ratchets

TL;DR

This paper reviews Active Brownian Motion models, focusing on their application to ratchet systems with various potentials, analyzing stochastic effects and potential uses in molecular motors.

Contribution

It provides a comprehensive overview of ABM applications to ratchets, including analytical and numerical evaluations, and explores stochastic influences on particle flux directionality.

Findings

Stochastic noise influences the directionality of particle flux.

Different potential forms affect the ratchet's efficiency.

Nonmonotonic behavior observed in particle trajectory statistics.

Abstract

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircase-like and Mateos ratchet potentials, also with the additional loads modeled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This \textit{stochastically driven directionality} effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed