Models of granular ratchets

TL;DR

This paper models a granular Brownian ratchet with an asymmetric object in a granular gas, deriving equations to predict its drift and fluctuations, validated by numerical simulations.

Contribution

It introduces a comprehensive model of a granular ratchet, deriving Boltzmann equations and moment equations, and compares theoretical predictions with simulations.

Findings

Predicted net ratchet drift matches simulations

Variance of velocity fluctuations aligns with numerical results

Transition rates in the Markovian limit are accurately estimated

Abstract

We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement is observed.