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,
Fractional Brownian motion Friedrich Gauss. Prior to the introduction of the fractional Brownian motion, used the Riemann–Liouville fractional integral to define the process where integration is with respect to the white noise measure "dB"("s"). This integral turns out to be ill-suited to applications of fractional Brownian motion because of its over-emphasis of the origin . The idea instead is to use a different fractional integral of white noise to define the process: the Weyl integral for "t" > 0 (and similarly for "t" < 0). The main difference between fractional Brownian motion and regular Brownian motion is that while the increments in Brownian