2007/11/27 by Gianni Pagnini, Pagnini, Gianni, Francesco Mainardi +1
Earth and Planetary Sciences · Environmental Science · Mathematics · Physics and Astronomy · #26A33 #33C60 #45K05 #60G18 #60G55 #60J60 #60J70 #Atmospheric aerosols and clouds #Atmospheric chemistry and aerosols #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Wind and Air Flow Studies #cond-mat.stat-mech #math-ph #math.MP #math.PR #msc:26A33 #msc:33C60 #msc:45K05 #msc:60G18 #msc:60G55 #msc:60J60 #msc:60J70
paper · pdf · doi:10.48550/arxiv.0711.4246
9 pages. 2 Figures Conference ``Special Functions, Information Theory and Mathematical Physics'',Granada, Spain, September 17-19 2007. Journal of Computational and Applied Mathematics, in press (2008)
openalex publication_date 2007/11/27 · arxiv created 2008/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral representation, the Voigt profile can be interpreted as the probability density function of the sum of two independent random variables with Gaussian density (due to the Doppler effect) and Lorentzian density (due to the pressure effect). Since these densities belong to the class of symmetric Lévy stable distributions, a probabilistic generalization is proposed as the convolution of two arbitrary symmetric Lévy densities. We study the case when the widths of the considered distributions depend on a scale-factor τ that is representative of spatial inhomogeneity or temporal non-stationarity. The evolution equations for this probabilistic generalization of the Voigt function are here introduced and interpreted as generalized diffusion equations containing two Riesz space-fractional derivatives, thus classified as space-fractional diffusion equations of double order.