We present a thermal velocity sampling method for calculating Doppler-broadened atomic spectra, which more efficiently reaches convergence than regular weighted sampling. The uses equal-population of the 1D distribution, “inverse transform” cumulative distribution function, and is broadly applicable to normal distributions. also discuss efficiency by eliminating classes, do not significantly co...

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.