{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T05:19:51Z","timestamp":1788153591351,"version":"build-2803163510"},"reference-count":22,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T00:00:00Z","timestamp":1787961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Interfacial anisotropy and undercooling control dendritic growth, but numerical artifacts often distort their apparent effects. To address this, we reimplemented the nondimensional Kobayashi model using isotropic nine-point operators, full-interface sub-grid tip tracking, and a grid-independent seed. Our balanced 4 \u00d7 4 study explored undercooling (\u0394 = 0.4\u20131.0) and sixfold anisotropy (\u03b4 = 0\u20130.025) across 160 simulations at \u0394x = 0.01333 and \u0394t = 2.5 \u00d7 10\u22125. Because extended runs continuously decelerated, we reported common-time late-window kinetics (t = 0.054\u20130.090). Undercooling accounted for 88.7% of the growth rate variance, whereas anisotropy explained 6.9% and their interaction 4.4%. Relative to isotropic growth (\u03b4 = 0), maximum anisotropy (\u03b4 = 0.025) increased rates by 8.9\u2013141.1% depending on \u0394. The marginal gain from \u03b4 = 0.02 to 0.025 was only 0.5\u20132.8%, indicating diminishing sensitivity. Additionally, the \u03b4 \u00d7 \u0394 interaction explained 17.6\u201328.7% of morphological shape variance. Numerical reliability was confirmed via a spatial convergence order of 2.14 and a fine-grid Grid Convergence Index (GCI95) of 2.45%. Furthermore, MATLAB\u2013COMSOL cross-verification reproduced solid-fraction histories within a 2.42\u20133.08% mean relative error. By strictly limiting main claims to positive-stiffness amplitudes, this study delivers a rigorously verified transient numerical interpretation rather than material-specific physical validation.<\/jats:p>","DOI":"10.3390\/ma19173676","type":"journal-article","created":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T04:24:03Z","timestamp":1788150243000},"page":"3676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Transient Anisotropy\u2013Undercooling Coupling in Dendritic Solidification: Grid-Qualified Phase-Field Ensembles and Finite Element Cross Verification"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4100-5170","authenticated-orcid":false,"given":"Mustafa Berkay","family":"Demir","sequence":"first","affiliation":[{"name":"Department of Materials Science and Nanotechnology Engineering, Faculty of Engineering and Natural Sciences, Yeditepe University, 26 A\u011fustos Campus, \u0130n\u00f6n\u00fc Mah., Kay\u0131\u015fda\u011f\u0131 Cad. 326A, Ata\u015fehir, 34755 \u0130stanbul, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5610-7507","authenticated-orcid":false,"given":"Halil \u0130brahim","family":"Yavuz","sequence":"additional","affiliation":[{"name":"Department of Materials Science and Nanotechnology Engineering, Faculty of Engineering and Natural Sciences, Yeditepe University, 26 A\u011fustos Campus, \u0130n\u00f6n\u00fc Mah., Kay\u0131\u015fda\u011f\u0131 Cad. 326A, Ata\u015fehir, 34755 \u0130stanbul, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"visualization","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,29]]},"reference":[{"key":"ref_1","unstructured":"Dantzig, J.A., and Rappaz, M. 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