A MEMS implementation of a Brownian Ratchet

Abstract

Brownian Ratchet is a device that can rectify the random Brownianmotion of particles to yield a directed steady-state flow.We can imagine a thermo-fluid field of particles whichinteract with the ratchet. The laws of thermodynamics imply that theratchet must use energy from some other source.The dynamics of continuous-time Brownian ratchets are determined by astochastic partial differential equation. We have used a simplifieddiscrete-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. Anindefinite pure sequence of any single game is neutral or evenlosing. A periodic or randomised sequence of mixed games can bewinning. There is a steady state flow of probability in the preferreddirection.We have been able to design a feasible and consistent device, bymapping the conservation law of total probability onto the law ofconservation of charge. This device can absorb energy from amechanical field to produce a directed flow of charge. The fundamentalarchitecture is based on a ``bucket-brigade'' device. The capacitorsare 2-port MEMS devices. We use CMOS transmission gates to connect thecapacitors in the required topology.We present an analysis and simulation of the MEMS Brownian ratchet andsuggest some possible applications.