A Granular Brownian Ratchet Model

TL;DR

This paper demonstrates through simulations and theory that a fixed, non-rotating asymmetric body can exhibit directed motion when interacting with a gas, due to inelastic collisions breaking time-reversal symmetry.

Contribution

It introduces a granular Brownian ratchet model explaining how inelastic collisions induce steady drift, supported by theoretical derivation and numerical simulations.

Findings

Directed motion observed in simulations of the ratchet system.

Effective Langevin equation derived with parameters linked to microscopic properties.

Quantitative agreement between theory and simulations for mobility, diffusivity, and velocity.

Abstract

We show by numerical simulations that a non rotationally symmetric body, whose orientation is fixed and whose center of mass can only slide along a rectilinear guide, under the effect of inelastic collisions with a surrounding gas of particles, displays directed motion. We present a theory which explains how the lack of time reversal induced by the inelasticity of collisions can be exploited to generate a steady average drift. In the limit of an heavy ratchet, we derive an effective Langevin equation whose parameters depend on the microscopic properties of the system and obtain a fairly good quantitative agreement between the theoretical predictions and simulations concerning mobility, diffusivity and average velocity.