Distribution of differences plot

It is generally understood that the reactive intermediates are generated in a random distribution of different microenvironments, each with its own energy barrier. The complex decay of this dispersion of rates leads to the nonexponential kinetics. Thus, disappearance plots are dominated at early times by reaction of those species in fast sites , which have lower energy barriers. As these sites are cleared, the distribution of rates over time becomes more reflective of sites with higher barriers. Finally, at longer times, the decay curves are dominated by the slowest sites. It is often observed that plots of In [intensity] versus or are approximately linear. It... 

Maximum likelihood estimates for the parameters of the normal distributions of differences between log(median CDio) estimates in different species shown in Figures 27.4-27.6 are shown in Table 27.1. The same comparisons are shown graphically in Figure 27.8, plotted against the logarithm of body weight ratio for the... 

Figure 2.5 shows the distribution of different sizes of pores thus calculated. Figure 2.5a-d correspond to 20,30,40, and 50% of total porosity, respectively for a hypothetical CL. In these plots, one can observe the pore size variation by normalizing (total porosity percentage assigned). From Figure 2.5 it can be seen that when 4> decreases, the frequency of the 50 nm pore size (left... 

FIGURE 18.2 (See color insert following page 300.) Chemical space plot of the phase distribution of different chemicals in a dry snow pack as a function of the snow surface/air sorption coefficient (log ATiA/m) and the humic acid/air partition coefficient (log / ha/a)- IA and Kha/A values were determined based on Roth et al. (2004) and Niedeier et al. (2006). 

Plot the number distribution of segments in loops and trains against segment number s from Eqs. XI-21 and 22. How do these profiles differ ... 

The curve for core size distribution—Foster s plot of 6 j6r against r —is also shown, as Curve D, in Fig. 3.18. It differs markedly from the pore size distribution curves, clearly showing that the corrections for the film thinning effect which have become possible since Foster s day, are of first-order importance. 

When an analyst performs a single analysis on a sample, the difference between the experimentally determined value and the expected value is influenced by three sources of error random error, systematic errors inherent to the method, and systematic errors unique to the analyst. If enough replicate analyses are performed, a distribution of results can be plotted (Figure 14.16a). The width of this distribution is described by the standard deviation and can be used to determine the effect of random error on the analysis. The position of the distribution relative to the sample s true value, p, is determined both by systematic errors inherent to the method and those systematic errors unique to the analyst. For a single analyst there is no way to separate the total systematic error into its component parts. 

This expression is plotted in Fig. 6.7 for several large values of p. Although it shows a number distribution of polymers terminated by combination, the distribution looks quite different from Fig. 5.5, which describes the number distribution for termination by disproportionation. In the latter Nj,/N decreases monotonically with increasing n. With combination, however, the curves go through a maximum which reflects the fact that the combination of two very small or two very large radicals is a less probable event than a more random combination. 

Figure 8.5 illustrates the sort of separation this approach predicts. Curve A in Fig. 8.5 shows the weight fraction of various n-mers plotted as a function of n. Comparison with Fig. 6.7 shows that the distribution is typical of those obtained in random polymerization. Curve B shows the distribution of molecular weights in the more dilute phase-the coacervate extract-calculated for the volumes of the two phases in the proportion 100 1. The distribution in the concentrated phase is shown as curve C it is given by the difference between curves A and B. 

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