Dawson integral

Equations (6.75) and (6.76) are simplified (on using the asymptotic expansion of the Dawson integral, namely... 

In multiple nucleation conditions, the current density may be expressed as a convolution of the growth current of individual nuclei and their birth rate on the surface. In the very initial stages, nuclei are small in both size and number, and they grow independently of each other. The current transient is then given by i(t) = 7tzF(2Dc)y (Mt/p)y No s/At) [9], where (- /At) is the Dawson integral,... 

A convenient way to see how S depends on T is to choose a value for m, and using tabulated values of the Dawson integral or, these days, rather a computer, one can find S from (3.29). Now knowing the pair m and S and using the definition of m from (3.27), we get the corresponding temperature. 

To evaluate f, one can choose a value for m, find the value of Dawson integral for that value m, then calculate S from this, and finally find F in the units of Nk T. 

This may be reduced to an elementary function and error functions for b > o and an elementary function and Dawson s Integral for b < o (13,15). Calculations are easily performed since... 

Dawson, V. L. (1995). Nitric oxide Role in neurotoxicity. Clin. Exp. Pharmacol. Physiol. 22, 305-308. Dirnagl, U., Iadecola, C., and Moskowitz, M. A. (1999). Pathobiology of ischaemic stroke An integrated view. Trends Neurosci. 22, 391—397. 

Robison V. D., Liro L. M., Robison C. R., Dawson W. C., and Russo J. W. (1996) Integrated geochemistry, organic petrology, and sequence stratigraphy of the Triassic Shublik Formation, Tenneco Phoenix weh, North Slope, Alaska, USA. Org. Geochem. 24(2), 257-272. 

We note that both the effective relaxation times and the zero-frequency susceptibilities may be written in terms of Dawson s integral. The detailed expressions are given in Ref. 55. 

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