Physics
Scientific paper
Sep 1930
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1930phrv...36..823u&link_type=abstract
Physical Review, vol. 36, Issue 5, pp. 823-841
Physics
559
Scientific paper
With a method first indicated by Ornstein the mean values of all the powers of the velocity u and the displacement s of a free particle in Brownian motion are calculated. It is shown that u-u0exp(-βt) and s-u0β[1-exp(-βt)] where u0 is the initial velocity and β the friction coefficient divided by the mass of the particle, follow the normal Gaussian distribution law. For s this gives the exact frequency distribution corresponding to the exact formula for s2 of Ornstein and Fürth. Discussion is given of the connection with the Fokker-Planck partial differential equation. By the same method exact expressions are obtained for the square of the deviation of a harmonically bound particle in Brownian motion as a function of the time and the initial deviation. Here the periodic, aperiodic and overdamped cases have to be treated separately. In the last case, when β is much larger than the frequency and for values of t>>β-1, the formula takes the form of that previously given by Smoluchowski.
Ornstein L. S.
Uhlenbeck G. E.
No associations
LandOfFree
On the Theory of the Brownian Motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the Theory of the Brownian Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Theory of the Brownian Motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1263456