Powerlaw

Reactions Reactions R 1 (POWERLAW) Input Data Browser... 

Here t is time in years. This equation provides a perfect fit for the sales figures for EPO as a function of time in years. Once again, t = 0 here indicates the base year, 1992, for which the sales numbers were first available. For practical or predictive purposes Eq. (2) may be better to use than Eq. (3) since it is a power-law type of equation and has some physical basis, even though Eq. (3) provides more accurate estimates than Eq. (2). Second-order polynomial fits can of course be applied to a wide variety of sales curves for different drugs with considerable accuracy. In other words, if one were to attempt to predict future sales of EPO, one should (a) obviously use caution, (b) extrapolate only for a short period (since one cannot predict market forces), and (c) use the powerlaw model as compared to the second-order polynomial model (Eq. 3). 

For simple self-similar fractals /(e) scales like a powerlaw /(e) e", where v is called the uncertainty exponent. In this case the quantities needed in (2.3.8) for calculating the fractal dimension are easily available k = f e) N, m = 1/e. Therefore,... 

Fig. 8.3. Powerlaw decay of the phase-space probability for the kicked hydrogen atom.

In order to corroborate the numerical results with analytical estimates of the onset of the Ericson regime we need estimates of the mean level density p — /D and the average resonance width F. The following analytical arguments are based on the assumption that subsets of classical phase space decay exponentially to the continuum. This assumption may not be true as indicated by the powerlaw results obtained in Chapter 8. Nevertheless, the argument is illustrative, and may be modified eventually to take the true decay mechanism of the hehum phase space into account. 

The aggregates formed during silica gel preparation often tend to exhibit fractal properties. This implies a powerlaw distribution of particle or micropore sizes. Power law kinetics appear to be the consequence of processes where objects grow and/or decompose. The growth rates are typically random and independent of the particle size. 

---