A MEMS brownian ratchet

Abstract

Brownian ratchet is a device that can rectify the random Brownian motion of particles to yield a directed steady-state flow. We can imagine a thermofluid field of particles, which interact with the ratchet. The laws of thermodynamics imply that the ratchet must use energy from some other source.

The dynamics of continuous-time Brownian ratchets are determined by a stochastic partial differential equation. We have used a simplified discrete-time model of a Brownian ratchet called ‘Parrondo's games’, which are governed by a difference equation. In their original form, Parrondo's games are a finite set of simple games of chance. An indefinite pure sequence of any single game is neutral or even losing. A periodic or randomised sequence of mixed games can be winning. There is a steady state flow of probability in the preferred direction.

We have been able to design a feasible and consistent device, by mapping the conservation law of total probability onto the law of conservation of charge. This device can absorb energy from a mechanical field to produce a directed flow of charge. The fundamental architecture is based on a ‘bucket-brigade’ device. The capacitors are 2-port MEMS devices. We use CMOS transmission gates to connect the capacitors in the required topology.

We present an analysis and simulation of the MEMS Brownian ratchet and suggest some possible applications.