Graphs plotted curve attributes

Plot the net count rates in Data Table 10.1 on a semilog graph for In net count rate vv.time (linear) in days. Draw a straight line of best fit through the points. If the last few points curve upward, try to fit 2 straight lines to the points, one for the last few points and the other to the initial points minus the count rate attributed to the lower line. Calculate the negative slope (i.e., the decay constant) for the line (or both lines). Does the line confirm the half life of 131I Estimate the uncertainty of the slope. 

Therefore a plot of — log s2 vs. T should be a straight line if the original equation was valid. Lacey has plotted this graph, as shown in Fig. 30. The initial portion in all cases is curved, which Lacey attributes to initial... 

At very long times, the solute s mean-square displacement is proportional to the time t. This proportionality is commonly used to determine the diffusion coefficients by fitting a straight line, either in an vs t plot or a log vs log t graph. At short times, however, the mean-square displacement may obey a different power law, oc t" with n < 1. In most of the calculations of diffusion coefficients by MD it has tacitly been assumed that the long-time limit has been reached in the calculation. In most cases in the literature only the diffusion coefficients have been reported and not the mean-square displacement curves upon closer inspection of the displacements, where reported [27,28,60, 65,66], one often notes that the mean-square displacement is a wobbly line that can be interpreted as straight only if the nonlinearity is attributed to statistical uncertainties for insufficient simulation lengths. 

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