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Extra resources for Brownian Motion - Fluctuations, Dynamics and Applns
We finally obtain ap(x,t)/at = ~. ax D(x). [~ ax + _1_ (au)] P(x t) kBT ax ,. (7) The diffusion tensor D(x) measures the mean square displacements per unit time, starting from the initial position x. Equation (7) can also be written as: ap(X,t)/ at = !. D(x) P(x). P(xtl P(x,t). (8) This procedure puts clearly into evidence the fact that the diffusion equation is appropriate only for processes in which any fmite change in the x space of the system occurs through a random sequence of small coordinate displacements.
The calculated ratio J/J2 does not differ significantly from 2. In the limiting case of complete alignment « D ~o > -1), the diffusional model predicts a value of 4 for this ratio [4a,21]. Since in some cases the experimental values of J/J2 appear to be close to unity, a strong collision model for the reorientations about the long molecular axis has been invoked . In fact, such a model predicts the same correlation time for all the functions describing uniaxial rotations, irrespective of the rank [3a].
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