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Extra resources for Brownian Motion - Fluctuations, Dynamics and Applns

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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 [22]. In fact, such a model predicts the same correlation time for all the functions describing uniaxial rotations, irrespective of the rank [3a].

And Zannoni, C. (1988) Molec. , 65, 1505. , van der Meer, B. W. and Ameloot, M. (1986) Chern. Phys. 102, 37. Zanno~ C. (1979) Molec. Crystals liq. , 49, 247. Saupe, A (1968) Angew. Chern. (Int. ), 7,97. Michl, J. and Thulstrup, E. W. (1987) in Spectroscopy with Polarised Light, VCH. Luckhurst, G. L. and Segre; U. (1975) Molec. , 30, 1345. Shilstone, G. , Zannoni, C. and Veracini, C. A (1989) Liq. Crystals, in press. , Verac~ C. A and Zannoni, C. (1983) Israel 1. , 23, 283. Zanno~ C. (1979) Molec.

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