Macroscopic correlation

Most studies of overall cell density have reported no significant change in schizophrenia (Dwork, 1997 Harrison, 1999 Arnold, 2000). Two studies provided estimates of total hippocampal cell number and found no changes in any of the four sectors of the cornu ammonis in schizophrenia (Heckers et al., 1991 Walker et al., 2002). The finding of normal total cell number is important for the interpretation of decreased hippocampal volume reported by neuroimaging studies of patients with schizophrenia. In contrast to neuropsychiatric disorder such as temporal lobe epilepsy and dementia, smaller hippocampal volume is not the macroscopic correlate of pyramidal cell loss in schizophrenia. 

The macroscopic correlation function can be expressed as a product of the relaxation functions g z/zj) at all stages of self-similarity of the fractal system considered [47,154] ... 

Figure 31. Semilog plot of the macroscopic correlation function of the 20-pm sample ( ) and the 30-pm sample (A) at the temperature corresponding to percolation. The solid lines correspond to the htting of the experimental data by the KWW relaxation function. (Reproduced with permission from Ref. 2. Copyright 2002, Elsevier Science B.V.)...

Equations (4.4) and (4.S) are reminiscent of each other in the sense that the diffusional behavior of water in the long-time region results from different, randomly explored, environments, each one being characterized by well-defined diffusion coefficients. Therefore, the corresponding macroscopic correlation function turns out to be an average over several molecular environments, the permanence time in each environment and the transition rate from one to another being determined by a well-defined statistical process. 

Interphase momentum transfer is the focus of this section. Macroscopic correlations are based on dynamic forces due to momentum flux that act across the fluid-solid interface, similar to terms of type 2, 3, and 4 in the equation of motion. Gravity enters into this discussion via the hydrostatic contribution to fluid pressure, because volumetric body forces are not operative across an interface. The outward-directed unit normal vector from the solid surface into the fluid is n. As discussed earlier, forces due to total momentum flux, transmitted in the —n direction from the flnid to the solid across the interface at r = / , are (i.e., see equation 8-20) ... 

Lecuna, J., Johnson, J., Ortoleva, P. and Sporleder, R., Development of Macroscopic Correlation in Precipitating Systems, J. Chem. Phys. (submitted for publication)... 

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