Brownian ratchet ratchet will not rotate continuously in one direction but will move randomly back and forth, and therefore will not produce any useful work. The reason is that since the pawl is at the same temperature as the paddle, it will also undergo Brownian motion, "bouncing" up and down. It therefore will intermittently fail by allowing a ratchet tooth to slip backward under the pawl while it is up. Another issue is that when the pawl rests on the sloping face of the tooth, the spring which returns the pawl exerts a sideways force on the tooth which tends to rotate
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