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Kolomgorov","year":"1991","journal-title":"A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem"},{"key":"nyjy-xjp3Cc44R2","first-page":"26","type":"journal-article","volume":"1","author":"A.\u2009N. Kolomgorov","year":"1937","journal-title":"Mosk. Gos. Univ. Ser. A Mat. Mekh."},{"key":"nyjy-xjp3Cc45R1","unstructured":"Teboul et\u00a0al. [24] follow a similar approach to derive the quasi-relaxed distribution in angular momentum when strong scatterings are dominant, but the equation has no simple analytic solution. This suggests the possibility of a simple, combined treatment of weak and strong scatterings.","type":"other"},{"key":"nyjy-xjp3Cc46R1","unstructured":"The maximum value of R must be large enough that the solution inside the loss cone is insensitive to it, since f is set to be uniform in \u03c4 here. See the Appendix for our estimate Rmax.","type":"other"},{"key":"nyjy-xjp3Cc47R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stab3387","type":"journal-article"},{"key":"nyjy-xjp3Cc48R1","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/adace7","type":"journal-article"},{"key":"nyjy-xjp3Cc50R1","unstructured":"The approximant for R=Rrlx is worse at predicting the R distribution at disruption than the average distribution. In fact, the numerical solution shows that at any value of q the distribution at RLC is not uniform in \u03c4 (see the Appendix).","type":"other"},{"key":"nyjy-xjp3Cc51R1","doi-asserted-by":"publisher","DOI":"10.1088\/0004-637X\/774\/1\/87","type":"journal-article"},{"key":"nyjy-xjp3Cc52R1","doi-asserted-by":"publisher","DOI":"10.1093\/mnras\/stac2255","type":"journal-article"},{"key":"nyjy-xjp3Cc53R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/acafe1","type":"journal-article"},{"key":"nyjy-xjp3Cc54R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/ad89bd","type":"journal-article"},{"key":"nyjy-xjp3Cc55R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/ada8a8","type":"journal-article"},{"key":"nyjy-xjp3Cc56R1","doi-asserted-by":"publisher","DOI":"10.1086\/155534","type":"journal-article"},{"key":"nyjy-xjp3Cc57R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/ac9bfd","type":"journal-article"},{"key":"nyjy-xjp3Cc58R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/acd54f","type":"journal-article"},{"key":"nyjy-xjp3Cc59R1","doi-asserted-by":"publisher","DOI":"10.3847\/1538-4357\/aa8cc8","type":"journal-article"},{"key":"nyjy-xjp3Cc61R1","doi-asserted-by":"publisher","DOI":"10.3847\/0004-637X\/831\/1\/84","type":"journal-article"},{"key":"nyjy-xjp3Cc62R1","doi-asserted-by":"publisher","DOI":"10.3847\/2041-8213\/adeca7","type":"journal-article"},{"key":"nyjy-xjp3Cc63R1","doi-asserted-by":"publisher","DOI":"10.1088\/0264-9381\/31\/24\/244002","type":"journal-article"},{"key":"nyjy-xjp3Cc64R1","doi-asserted-by":"publisher","DOI":"10.1137\/141000671","type":"journal-article"},{"key":"nyjy-xjp3Cc65R1","doi-asserted-by":"publisher","DOI":"10.21105\/joss.03349","type":"journal-article"},{"key":"nyjy-xjp3Cc66R1","unstructured":"M. Kittisopikul and T.\u2009E. Holy, juliamath\/interpolations.jl, (2023).","type":"other"},{"key":"nyjy-xjp3Cc67R1","doi-asserted-by":"publisher","DOI":"10.1086\/378086","type":"journal-article"},{"key":"nyjy-xjp3Cc68R1","unstructured":"L. Broggi, Dynamics of Tidal Disruptions and Extreme Mass Ratio Inspirals in Galactic Nuclei, (2024), https:\/\/boa.unimib.it\/handle\/10281\/459238.","type":"other"},{"key":"nyjy-xjp3Cc69R1","unstructured":"The partial derivative \u2202R in Eq.\u00a0(a1) is at fixed r, and the term should transform when changing variable to \u03c4CK since r(R,\u03c4CK)\u2260r(R+dR,\u03c4CK). We maintain \u03c4CK instead of changing variable to \u03c4 to keep the same level of approximation.","type":"other"},{"key":"nyjy-xjp3Cc70R1","unstructured":"The solution was originally derived by Milosavljevic following a related derivation of Milosavljevi\u0107 and Merritt [67], later presented in Strubbe\u2019s [71], and published in Merritt [35]. See Chap.\u00a03 of Broggi [68] for a detailed derivation based on the separation of variables.","type":"other"},{"key":"nyjy-xjp3Cc71R1","unstructured":"L. Strubbe, Ph.D. thesis, University California, 2011.","type":"other"},{"key":"nyjy-xjp3Cc72R1","unstructured":"The 1D Fokker-Planck code phaseflow uses \u03b7P [59].","type":"other"}],"container-title":["Physical Review Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/nyjy-xjp3","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/nyjy-xjp3\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T17:10:28Z","timestamp":1764609028000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/nyjy-xjp3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,1]]},"references-count":66,"journal-issue":{"issue":"23","published-print":{"date-parts":[[2025,12]]}},"URL":"https:\/\/doi.org\/10.1103\/nyjy-xjp3","relation":{},"ISSN":["0031-9007","1079-7114"],"issn-type":[{"value":"0031-9007","type":"print"},{"value":"1079-7114","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,1]]},"assertion":[{"value":"2024-11-06","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"\u00a9 2025 American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2025","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"231201"}}