Granular ratchets

The general model for granular Brownian ratchets is reviewed. It consists of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which is kept in steady state by an external random driving force. In the dilute limit, the two coupled Boltzmann Equations describing the gas and the object are discussed and, with reasonable approximations, a closed system for the main velocity moments is obtained. In the limit of large ratchet mass, a Langevin-like equation for the ratchet velocity is derived, which incorporates an effective force due to dissipation in collision. Fair agreement with simulations under Molecular Chaos assumption is shown.