Brownian meander factor for the spatial axis must be square root of the scaling factor for the time axis. The process resulting from this snip-and-scale procedure is a Brownian meander. As the name suggests, it is a piece of Brownian motion that spends all its time away from its starting point formula_5. The transition density formula_12 of Brownian meander is described as follows: For formula_13 and formula_14, and writing we have and In particular, i.e. formula_19 has the Rayleigh distribution with parameter 1, the same distribution as formula_20, where formula_21 is an exponential random variable with parameter 1. Brownian meander In the
Brownian motor bias the motion of a particle (like an ion or polypeptide); the result would essentially be diffusion of a particle whose net motion is strongly biased in one direction. The translocation of the particle would only be loosely coupled to hydrolysis of ATP. The dynamics and activity of Brownian motors are current topics of study in theoretical and experimental biophysics. Brownian motors are sometimes modeled using the Fokker-Planck equation or with Monte Carlo methods. Many researchers are presently engaged in understanding how molecular-scale motors operate in environments with non-negligible thermal noise. The thermodynamics of such motors is constrained by the