Microscopic correlation

Furtlier details can be found elsewhere [20, 78, 82 and 84]. An approach to tire dynamics of nematics based on analysis of microscopic correlation fimctions has also been presented [85]. Various combinations of elements of tire viscosity tensor of a nematic define tire so-called Leslie coefficients [20, 84]. 

Sobol et al.8 have measured proton SLR time (7 ) in Rb1 x(NH4)xH2As04 systems in the range 100-4.2 K. Magnetization recovery was found to be non-exponential in the entire range of temperature. The MR data fit to a stretched exponential recovery and the exponent a was found to be temperature dependent implying broadening of the distribution of microscopic correlation times p(r ) with decreasing temperature. 

The contributions to the microscopic correlation function C (t) for an arbitrary reference molecule ( ) may be split into an autocorrelation and a crosscorrelation part as follows ... 

Disturbed outflow the microscopic correlate is centrilobular hyperaemia macroscopically, the liver is enlarged and has a dark red colour. 

Alpert LC, Truong LD, Bossart MI, Spjut HJ. Microcystic adenoma (serous cystadenoma) of the pancreas. A smdy of 14 cases with immunohistochemical and electron-microscopic correlation. Am J Surg Pathol. 1988 12 251-263. 

An equation with the form of the macroscopic law in (2.16) can be obtained from the singlet field kinetic equation by projecting out the velocity dependence of the phase-space correlation functions. A comparison of the resulting equation with this macroscopic law can then yield a microscopic correlation function expression for the rate kernel. 

To present a summary of the most important exact expressions giving e in terms of microscopic correlation functions. 

A = and M.22 z) is the matrix element (2 M(z) 2). All the other matrix elements ot the memory operator are zero [63]. The appearance ot the tactor i corresponds to the Hermitian definition ot the Liouvillian which is not universal. Equation (98) is an exact z-dependent expression. This z-dependence can be eliminated by approximating M22(z) by a positive constant r (Markovian approximation). This approximation is justified since the microscopic correlation time is much shorter than the regression time ot the fluctuation. Then Eq. (98) transtorms into the z-independent effective Liouvillian... 

For water this relaxation (relaxation from the intramolecular interaction in the water) time is 4.78 s. The above equation shows that even though the time observed in NMR experiments could be in the second or millisecond range, the microscopic correlation time can be in the picosecond range. 

Electron Microscopy. The electron microscope provides a direct method for determining dimensions of colloidal particles (Figure 4.7). With improved equipment, individual particles as small as only 1-2 nm can be discerned, but measuring the diameter of particles smaller than 5 nm is difficult. Alexander and Her (142) first demonstrated that the particle size of colloidal silica measured by the electron microscope correlated well with particle size determined by light scattering in solution, and also with the size calculated from the specific surface area of the dried silica powder. 

Figure 8. Microscopic correlation times and and ratios liquid OCS. from dielectric...

BARTHEL - Unfortunately, there is no general theory linking macroscopic and microscopic correlation functions and relaxation times. Some approximations are useful for special cases, such as the Powles Glarum equation for the rotational movements of dipole species. An estimation of the accuracy of the approximations is hardly possible. The Powles Glarum equation has the advantage of simplicity, I agree. 

Incorporating quantum mechanics into neuromolecular computational studies is a difficult, but potentially solveable, problem in experimental design. The microscopic correlates of molecular ensemble behavior cannot be directly observed in laboratory preparations, nor can they (as yet) be realistically... 

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