Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases
Abstract
:1. Introduction
2. Materials and Methods
2.1. Approximate Self-Similar Solution of the Biberman–Holstein (BH) Equation (BH Step-Length PDF, , 3D Case)
2.1.1. Biberman–Holstein Equation and Its General Solution
2.1.2. Propagation Front and Asymptotics of Biberman–Holstein Equation Green’s Function
2.1.3. Approximate Self-Similar Solution
2.2. A Method of Deriving an Self-similar Green’s Function for Lévy Flights (Simple Step-Length PDF, C = ∞, 1D Case)
2.3. A Method of Deriving a Self-Similar Green’s Function for Lévy Walks (Simple Step-Length PDF, , 1D, 2D and 3D Cases)
2.3.1. General Solution of the Time-Dependent Superdiffusive Transport Equation
2.3.2. Asymptotics of the Green’s Function Far Ahead and Far behind the Perturbation Front
2.3.3. Integral Characteristics of Green’s Function
2.3.4. Approximate Self-Similar Solution and Test of Its Accuracy
2.4. Distributed Computing Parameters and Implementation for Verification for Accuracy of the Approximate Self-Similar Solution
2.4.1. A Test of the Proposed Self-Similar Solution for a Simple Model PDF, 1D Case
2.4.2. A Test of the Self-Similar Solution of Biberman–Holstein Equation
3. Results
3.1. Illustration of Nonlocality by Monte Carlo Calculations of Trajectories
3.2. A Test of the Proposed Self-Similar Solution (Simple Step-Length PDF, , 1D Case)
3.3. Verification for Accuracy of the Approximate Self-Similar Solution for Various Spectral Line Shapes (Biberman–Holstein Step-Length PDF, , 3D Case)
3.3.1. Lorentz Spectral Line Shape
3.3.2. Doppler Spectral Line Shape
3.3.3. Voigt Spectral Line Shape
3.3.4. Holtsmark Spectral Line Shape
3.4. Verification for Accuracy of the Approximate Self-Similar Solution for Lévy Walks (Simple Step-Length PDF, , 1D, 2D and 3D Cases)
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Kukushkin, A.B.; Kulichenko, A.A.; Neverov, V.S.; Sdvizhenskii, P.A.; Sokolov, A.V.; Voloshinov, V.V. Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases. Symmetry 2021, 13, 394. https://doi.org/10.3390/sym13030394
Kukushkin AB, Kulichenko AA, Neverov VS, Sdvizhenskii PA, Sokolov AV, Voloshinov VV. Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases. Symmetry. 2021; 13(3):394. https://doi.org/10.3390/sym13030394
Chicago/Turabian StyleKukushkin, Alexander B., Andrei A. Kulichenko, Vladislav S. Neverov, Petr A. Sdvizhenskii, Alexander V. Sokolov, and Vladimir V. Voloshinov. 2021. "Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases" Symmetry 13, no. 3: 394. https://doi.org/10.3390/sym13030394