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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Astronomy Reports</journal-id><journal-title-group><journal-title xml:lang="en">Astronomy Reports</journal-title><trans-title-group xml:lang="ru"><trans-title>Астрономический журнал</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0004-6299</issn><issn publication-format="electronic">3034-5170</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">647589</article-id><article-id pub-id-type="doi">10.31857/S0004629924010044</article-id><article-id pub-id-type="edn">LFUCTV</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Articles</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>СТАТЬИ</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">MHD modeling of the molecular filament evolution</article-title><trans-title-group xml:lang="ru"><trans-title>МГД-моделирование эволюции молекулярных волокон</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Sultanov</surname><given-names>I. M.</given-names></name><name xml:lang="ru"><surname>Султанов</surname><given-names>И. М.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>syltahof@yandex.ru</email><xref ref-type="aff" rid="aff1"/></contrib><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Khaibrakhmanov</surname><given-names>S. A.</given-names></name><name xml:lang="ru"><surname>Хайбрахманов</surname><given-names>С. А.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>syltahof@yandex.ru</email><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff3"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Chelyabinsk State University</institution></aff><aff><institution xml:lang="ru">Челябинский государственный университет</institution></aff></aff-alternatives><aff-alternatives id="aff2"><aff><institution xml:lang="en">Saint Petersburg State University</institution></aff><aff><institution xml:lang="ru">Санкт-Петербургский государственный университет</institution></aff></aff-alternatives><aff-alternatives id="aff3"><aff><institution xml:lang="en">Ural Federal University</institution></aff><aff><institution xml:lang="ru">Уральский федеральный университет</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2024-01-15" publication-format="electronic"><day>15</day><month>01</month><year>2024</year></pub-date><volume>101</volume><issue>1</issue><issue-title xml:lang="ru"/><fpage>34</fpage><lpage>41</lpage><history><date date-type="received" iso-8601-date="2025-01-28"><day>28</day><month>01</month><year>2025</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2024, The Russian Academy of Sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2024, Российская академия наук</copyright-statement><copyright-year>2024</copyright-year><copyright-holder xml:lang="en">The Russian Academy of Sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0004-6299/article/view/647589">https://journals.eco-vector.com/0004-6299/article/view/647589</self-uri><abstract xml:lang="en"><p>We perform numerical magnetohydrodynamic (MHD) simulations of the gravitational collapse and fragmentation of a cylindrical molecular cloud with the help of the FLASH code. The cloud collapses rapidly along it’s radius without any signs of fragmentation in the simulations without magnetic field. The radial collapse of the cloud is stopped by the magnetic pressure gradient in the simulations with parallel magnetic field. Cores with high density form at the cloud’s edges during further evolution. The core densities are <italic>n</italic> ≈ 1.7×10<sup>8</sup> and 2×10<sup>-</sup><sup>7</sup> cm<sup>–3</sup> in the cases with initial magnetic field strengths <italic>B</italic> = 1.9×10<sup>-</sup><sup>4</sup> and 6×10<sup>-</sup><sup>4</sup> G, respectively. The cores move toward the cloud’s centre with supersonic speeds |<italic>v</italic><italic><sub>z</sub></italic>| = 3.6 and 5.3 km/s. The sizes of the cores along the cloud’s radius and cloud’s main axis are <italic>d</italic><italic><sub>r</sub></italic> = 0.0075 pc and <italic>d</italic><italic><sub>z</sub></italic> = 0.025 pc, <italic>d</italic><italic><sub>r</sub></italic> = 0.03 pc and <italic>d</italic><italic><sub>z</sub></italic> = 0.025 pc, respectively. The masses of the cores increase during the filament evolution and lie in range of ≈(10-20)<italic>M</italic><sub>e</sub>. According to our results, the cores observed at the edges of molecular filaments can be a result of the filament evolution with parallel magnetic field.</p></abstract><trans-abstract xml:lang="ru"><p>В работе с помощью кода FLASH выполнено численное магнитогазодинамическое (МГД) моделирование гравитационного коллапса и фрагментации цилиндрического молекулярного облака. В расчетах без магнитного поля облако быстро сжимается вдоль радиуса, и фрагментации не происходит. В расчетах с продольным магнитным полем коллапс волокна вдоль радиуса останавливается градиентом магнитного давления. В процессе дальнейшей эволюции на концах волокна образуются ядра с повышенной плотностью. В случаях с начальной интенсивностью магнитного поля <italic>B</italic> = 1.9×10<sup>-</sup><sup>4</sup> и 6×10<sup>-</sup><sup>4</sup> Гс концентрации газа в ядрах составляют <italic>n</italic> ≈ 1.7×10<sup>8</sup> и 2×10<sup>7</sup> см⁻³соответственно. Ядра передвигаются к центру со сверхзвуковыми скоростями |<italic>v</italic><italic><sub>z</sub></italic>| = 3.6 и 5.3 км/с, их размеры вдоль радиуса и оси волокна составляют соответственно <italic>d</italic><italic><sub>r</sub></italic> = 0.0075 пк и <italic>d</italic><italic><sub>z</sub></italic> = 0.025 пк, <italic>d</italic><italic><sub>r</sub></italic> = 0.03 пк и <italic>d</italic><italic><sub>z</sub></italic> = 0.025 пк. Масса ядер увеличивается в процессе эволюции волокна и лежит в диапазоне ≈(10-20)<italic>M</italic><sub>e</sub>. Согласно полученным результатам, ядра, наблюдаемые на концах молекулярных волокон, могут быть естественным результатом эволюции волокон с продольным магнитным полем.</p></trans-abstract><kwd-group xml:lang="en"><kwd>magnetic fields</kwd><kwd>magnetohydrodynamics (MHD)</kwd><kwd>methods: numerical</kwd><kwd>ISM: clouds</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>магнитные поля</kwd><kwd>магнитная газодинамика (МГД)</kwd><kwd>численное моделирование</kwd><kwd>межзвездные молекулярные облака</kwd></kwd-group><funding-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Фонд перспективных научных исследований ЧелГУ (проект)</institution></institution-wrap><institution-wrap><institution xml:lang="en">Chelyabinsk State University Advanced Scientific Research Foundation (project)</institution></institution-wrap></funding-source><award-id>2023/7</award-id></award-group><award-group><funding-source><institution-wrap><institution xml:lang="ru">Челябинский государственный университет госзадание(проект)</institution></institution-wrap><institution-wrap><institution xml:lang="en">Chelyabinsk State University state assignment (project)</institution></institution-wrap></funding-source><award-id>FEUz-2020-0038</award-id></award-group></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>P. 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