Automodel Solutions of Biberman-Holstein Equation for Stark Broadening of Spectral Lines

Abstract

Abstract:The accuracy of approximate automodel solutions for the Green's function of the Biberman-Holstein equation for the Stark broadening of spectral lines is analyzed using the distributed computing. The high accuracy of automodel solutions in a wide range of parameters of the problem is shown.

Automodel solutions for superdiffusive transport by Lévy walks

“…The results of the modification of the simplest automodel solution via modification of the propagation front in the framework of optimizing the parameters of interpolation between the known asymptotics of the exact solution show that there is a much freedom for such modifications to achieve the main goal of approximate automodel solutions for the Lévy flights-based transport and of various extensions of the principles [18], namely the construction of approximate solutions of superdiffusive transport problems with high enough accuracy with essential savings of computation time. Indeed, as shown in [22] and [23] for the case of Lévy flights transport, obtaining automodel (self-similar) solutions in the entire space of independent variables requires mass numerical simulations (distributed computing), however, their total volume is significantly reduced due to the self-similarity of the solution.…”

“…For the time-dependent superdiffusive transport by the Lévy flights, recently a wide class of the transport on a uniform background was shown [18][19][20][21][22][23] to possess an approximate automodel solution. The solutions for the Green's function were constructed using the scaling laws for the propagation front (i.e.…”

Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases

“…Note that N(0) = 1 (this follows from the definition of the source in the Equation ( 35) for the Green's function); therefore, N(t) is the fraction of excited particles in the total number of particles in the medium or the fraction of migrants at rest in the total number of migrants. The result (45) means that the number of excited particles (or migrants at rest) can tend to either zero or nonzero constant, highly depending on γ of the model step-length PDF (37), (26). For γ = 0.5, Equation ( 45) coincides within a constant with the scaling law obtained in [6] (see (18) therein for β = 1/4).…”

“…It appears that the use of the propagation front (7) in the case of the spectral line shape, which is a convolution of two substantially different line shapes (e.g., for the Voigt line shape), leads to a noticeable decrease in accuracy [45]. Therefore, an alternative definition of the propagation front was proposed, which provides good accuracy for a wider class of spectral line shapes:…”

“…In the present paper, we provide a survey of the progress in the theory of nonstationary radiative transfer in spectral lines in plasmas and gases, achieved due to the elaboration of a method of deriving an approximate analytic self-similar solution for a wide class of nonstationary superdiffusive transport on a uniform background in the framework of integral equation formalism [41][42][43][44][45][46][47][48][49][50]. The method allows obtaining an approximate self-similar solution that is based on the following three building blocks, namely, scaling law for the propagation front, defined in a way relevant to superdiffusion, and asymptotics of the Green's function far beyond and far in advance of the propagation front.…”