Models of granular ratchets

Abstract

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