Gaussian range distribution

Fig. 6.3. Gaussian range distribution for implanted ions with Rp = 2.35ARP and a full width of half-maximum (FWHM) of AXP...

Fig. 7. A shows range distributions for channeled ions implanted along the <100> axis of Si. B shows the Gaussian distribution for incident ions aligned...

This observation is expected from theory, as the observed thickness distributions are exactly the functions by which one-dimensional short-range order is theoretically described in early literature models (Zernike and Prins [116] J. J. Hermans [128]). From the transformed experimental data we can determine, whether the principal thickness distributions are symmetrical or asymmetrical, whether they should be modeled by Gaussians, gamma distributions, truncated exponentials, or other analytical functions. Finally only a model that describes the arrangement of domains is missing - i.e., how the higher thickness distributions are computed from two principal thickness distributions (cf. Sect. 8.7). Experimental data are fitted by means of such models. Unsuitable models are sorted out by insufficient quality of the fit. Fit quality is assessed by means of the tools of nonlinear regression (Chap. 11). 

For the case of D-RADP-20 we have assumed a Gaussian probability distribution of transition temperatures, and therefore used an error function to fit the transition region. For D-RADP-25 the transition temperatures range from 138 K down to 118 K. In this temperature range, it is not possible to separate... 

Range parameters, b (nm), for solvated electrons in various hydrocarbon solvents at room temperature, assuming a gaussian initial distribution of distances from the ionisation site to the thermalisation point... 

All three components showed a very similar patter in their pH-dependent mobility. These patterns were also similar to the one found in previous CE studies (Hosse and Wilkinson, 2001 Schmitt-Kopplin et al., 1998). The SRFA were comparable to the SRNOM in terms of peak shape changes at lower pH. The two humic acids showed Gaussian mobility distributions and highly symmetric peaks over all the pH range. At pH < 3, the humic acids still showed very sharp and nicely shaped signals... 

To more efficiently test ways of constructing population models we have simulated the simulation by using a number of structureless cells. The cells were assigned a mode of cell Increase, and their variation of fission size was accomplished by selecting the next termination size on a random basis and storing It. The range and frequency of fission size was comparable to observed patterns (e.g. 10% coefficient of variation and Gaussian frequency distribution (22, 69). 

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