Transient correlation plot

Figure 17. Contour plot of the 360MHz homonuclear spin correlation mpa of 10 (2 mg, CDCL, high-field expansion) with no delay inserted in the pulse sequence shown at the top of the figure. Assignments of cross peaks indicating coupled spins in the E-ring are shown with tljie dotted lines. The corresponding region of the one-dimensional H NMR spectra is provided on the abscissa. The 2-D correlation map is composed of 128 x 512 data point spectra, each composed of 16 transients. A 4-s delay was allowed between each pulse sequence (T ) and t was incremented by 554s. Data was acquired with quadrature phase detection in both dimensions, zero filled in the t dimension, and the final 256 x 256 data was symmetrized. Total time of the experiment was 2.31 h (17).

In order to illustrate how the multi-variate SR model works, we consider a case with constant Re>. = 90 and Schmidt number pair Sc = (1, 1/8). If we assume that the scalar fields are initially uncorrelated (i.e., pup 0) = 0), then the model can be used to predict the transient behavior of the correlation coefficients (e.g., pap(i)). Plots of the correlation coefficients without (cb = 0) and with backscatter (Cb = 1) are shown in Figs. 4.14 and 4.15, respectively. As expected from (3.183), the scalar-gradient correlation coefficient gap(t) approaches l/yap = 0.629 for large t in both figures. On the other hand, the steady-state value of scalar correlation pap depends on the value of Cb. For the case with no backscatter, the effects of differential diffusion are confined to the small scales (i.e., (), / h and s)d) and, because these scales contain a relatively small amount of the scalar energy, the steady-state value of pap is close to unity. In contrast, for the case with backscatter, de-correlation is transported back to the large scales, resulting in a lower steady-state value for p p. 

Studies on the ciearance (pi/h) of modei hydrophilic solutes such as calcein (MW 623) and dextrans FD-4 (MW 4400) and FD-40 (MW 38000) in tritiated water across the skin under the influence of US have revealed a good flux correlation with H20. Unexpectedly, the slopes obtained by linear regression of the plots were consistent for all solutes examined [116]. In other words, the permeability coefficients of the solutes were comparable with those of tritiated water and independent of molecular size up to 40 kDa under the effect of US. This can be ascribed to the above-described asymmetric collapse of transient cavitation bubbles at the liquid-solid interface, which can produce transport routes for hydrophilic solutes in the stratium corneum. 

Fig. 14.11 The reactive flux correlation function, Eq. (14.99) plotted against time. After the initial transient period this function becomes essentially constant on the time scale shown.

Even without an analytical expression to describe the shape of H, it is clear that increasing steepness of H in the transition zone as portrayed in Fig. 12-11 will be accompanied by a compression of the transition from rubberlike to glasslike consistency into a narrower region of logarithmic time scale. Plots of both transient and dynamic moduli and compliances, as exemplified in Chapter 2, rise and fall with steeper slopes. Perhaps the most sensitive index of the sharpness of the transition is the loss tangent, which is plotted in Fig. 12-12 for several prototypes the polyurethane rubber, poly( -octyl methacrylate), poly(vinyl acetate), and Hevea rubber. Here the frequency scale has been arbitrarily selected to make the maxima coincide. The sharpness in the loss maximum correlates with the slope of H in the transition zone. The shape emphasizes the failure of the modified Rouse theory to provide a detailed description of the properties in the transition zone, since it predicts tan 5 = 1 independent of frequency in this region. The drop in tan 5 at high... 

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