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Additional info for Constrained Dynamics - With Applns to Yang-Mills Theory...

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6 (c) as calculated by numerical integration (continuous lines) and from the approximate analytic expansion equation (75) (dashed lines) [29]. 2. An Example. In [49] we have determined, through deuterium NMR, the ordering matrix for perylene dissolved in various nematic solvents. The results for the second rank order parameters in four nematics at different temperatures are shown in figure 10. The molecular coordinate system assumed has the z axis perpendicular to the perylene plane and the x axis in the direction of the peri bond.

And Torruella, A. 1. (1972) 1. chern. , 56, 303. Lynden-Bell, R M. (1980) Chern. Phys. , 70, 477. Pick, R. M. and Yvinec, M. (1983) in Symmetries and Properties of Non-Rigid Molecules, 1. ), Elsevier, 439. Abramowitz, M. and Segun, I. A. ) (1964) Handbook of Mathematical Functions, Dover. Janes, E. T. (1957) Phys. , 106, 620. 40 [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] Levine, R D. and Tribus, M. ) (1979) The Maximum Entropy Formalism, MIT Press.

In fact, the average value of any function F(Q) is defmed as (F) I I dZ = dn F(Q) P(Z,Q) (21) and therefore the integration over the angular variables leads in general to a function depending on Z. Equation (21) can be recast as the translational mean value of an orientational averageF(Z) having an explicit position dependence F{Z) = PT(Z)-t I dn F(Q) P(Z,Q). (22) The same is obviously true for any function F(Z,Q). As a consequence, the translations along Z in a smectic phase modulate orientational properties, giving rise to new contributions in the spectral densities superimposed on those provided by the rotational diffusion.

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