{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:02:45Z","timestamp":1768744965044,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,6]],"date-time":"2021-03-06T00:00:00Z","timestamp":1614988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11702026, 11532012"],"award-info":[{"award-number":["11702026, 11532012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel\u2019dovich\u2013von Neumann\u2013D\u00f6ring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from \u201cfrozen\u201d to \u201creactive\u201d by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the \u201chot spot\u201d, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.<\/jats:p>","DOI":"10.3390\/e23030314","type":"journal-article","created":{"date-parts":[[2021,3,7]],"date-time":"2021-03-07T20:20:43Z","timestamp":1615148443000},"page":"314","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Onset of the Mach Reflection of Zel\u2019dovich\u2013von Neumann\u2013D\u00f6ring Detonations"],"prefix":"10.3390","volume":"23","author":[{"given":"Tianyu","family":"Jing","sequence":"first","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]},{"given":"Huilan","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0960-9838","authenticated-orcid":false,"given":"Jian","family":"Li","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1360\/03ye0451","article-title":"Fuzzy interface treatment in Eulerian method","volume":"47","author":"Ning","year":"2004","journal-title":"Sci. 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