January 15 2003

Fit average curvatures with Gaussian distributions (2624 atoms)

The sum of three Gaussian distributions have been used to fit the average ( (smaller+larger)/2 ) curvature distributions. The fitting Gaussian distribution function is given as:

f = a0 / sigma * exp( - ( x - <x> )^2 / 2 / sigma^2 )

Because the integral of the density function is 1 (here with a factor of 1/sqrt(2*PI)), a0 is the fraction of the peak, which is propotional to number of particles.

The peak value

p = f ( <x> ) = a0 / sigma

For each Gaussian peak, there are three independent parameters: (p, sigma, <x>) or (a0, sigma, $lt;x>).