Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials

TL;DR

This paper studies active Brownian particles capable of self-propulsion in linear and ratchet potentials, identifying critical energy conditions for uphill motion and analyzing how potential asymmetry influences net current direction.

Contribution

It introduces a model for active particles with internal energy depot and derives analytical conditions for uphill motion and directed current in ratchet potentials.

Findings

Critical energy conversion rates for uphill motion identified.

Analytical expressions for average velocity and critical parameters derived.

Asymmetry of ratchet potential determines the direction of net current.

Abstract

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a ``high velocity'' or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current.