Brownian ratchet a heat bath in that they undergo random Brownian motion with a mean kinetic energy that is determined by the temperature. The device is imagined as being small enough that the impulse from a single molecular collision can turn the paddle. Although such collisions would tend to turn the rod in either direction with equal probability, the pawl allows the ratchet to rotate in one direction only. The net effect of many such random collisions would seem to be that the ratchet rotates continuously in that direction. The ratchet's motion then can be used to do work on other systems,
Brownian excursion Brownian excursion process, formula_1, is a Wiener process (or Brownian motion) conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. Another representation of a Brownian excursion formula_1 in terms of a Brownian motion process "W" (due to Paul Lévy and noted by Kiyoshi Itō and Henry P. McKean, Jr.) is in terms of the last time formula_3 that "W" hits zero before time 1 and the first time formula_4 that Brownian motion formula_5 hits zero after time 1: Let formula_7 be the time that a