{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T03:24:36Z","timestamp":1776050676737,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T00:00:00Z","timestamp":1614470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["18-07-01269-\u0430"],"award-info":[{"award-number":["18-07-01269-\u0430"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["19-32-90281"],"award-info":[{"award-number":["19-32-90281"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["20-07-00701-a"],"award-info":[{"award-number":["20-07-00701-a"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Radiative transfer (RT) in spectral lines in plasmas and gases under complete redistribution of the photon frequency in the emission-absorption act is known as a superdiffusion transport characterized by the irreducibility of the integral (in the space coordinates) equation for the atomic excitation density to a diffusion-type differential equation. The dominant role of distant rare flights (L\u00e9vy flights, introduced by Mandelbrot for trajectories generated by the L\u00e9vy stable distribution) is well known and is used to construct approximate analytic solutions in the theory of stationary RT (the escape probability method is the best example). In the theory of nonstationary RT, progress based on similar principles has been made recently. This includes approximate self-similar solutions for the Green\u2019s function (i) at an infinite velocity of carriers (no retardation effects) to cover the Biberman\u2013Holstein equation for various spectral line shapes; (ii) for a finite fixed velocity of carriers to cover a wide class of superdiffusion equations dominated by L\u00e9vy walks with rests; (iii) verification of the accuracy of above solutions by comparison with direct numerical solutions obtained using distributed computing. The article provides an overview of the above results with an emphasis on the role of distant rare flights in the discovery of nonstationary self-similar solutions.<\/jats:p>","DOI":"10.3390\/sym13030394","type":"journal-article","created":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T20:43:32Z","timestamp":1614545012000},"page":"394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Self-Similar Solutions in the Theory of Nonstationary Radiative Transfer in Spectral Lines in Plasmas and Gases"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5780-1584","authenticated-orcid":false,"given":"Alexander B.","family":"Kukushkin","sequence":"first","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"},{"name":"National Research Nuclear University MEPhI Moscow Engineering Physics Institute, 115409 Moscow, Russia"},{"name":"Moscow Institute of Physics and Technology, National Research University, 141700 Dolgoprudny, Moscow Region, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei A.","family":"Kulichenko","sequence":"additional","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladislav S.","family":"Neverov","sequence":"additional","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Petr A.","family":"Sdvizhenskii","sequence":"additional","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0107-2519","authenticated-orcid":false,"given":"Alexander V.","family":"Sokolov","sequence":"additional","affiliation":[{"name":"Institute for Information Transmission Problems of Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir V.","family":"Voloshinov","sequence":"additional","affiliation":[{"name":"Institute for Information Transmission Problems of Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shlesinger, M., Zaslavsky, G.M., and Frisch, U. 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