https://www.db-thueringen.de/receive/dbt_mods_00055091https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00058374/crystals-12-01657-v2.pdfhttps://www.db-thueringen.de/rsc/thumbnail/dbt_mods_00055091.png text article Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics article Titova, Ekaterina A. Titova Ekaterina A. Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia aut Author 0000-0002-9118-2027 Alexandrov, Dmitri V. Alexandrov Dmitri V. Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia aut Author 0000-0002-6628-745X Toropova, Liubov V. Toropova Liubov V. Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität-Jena aut Author 0000-0003-4587-2630 1279003006 urn:nbn:de:gbv:27-dbt-20221207-143021-005 Angelov, Borislav Angelov Borislav edt Editor 10.3390/cryst12111657 2022-11-17 12 11 1657 text continuingjournal Crystals open access journal journal 2011 Basel MDPI 2021-03-23 en 540 2073-4352 http://uri.gbv.de/document/gvk:ppn:718303067 2661516-2 his Host institution In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion problem of binary melt crystallization with convection. Analyzing this equation coupled with the selection criterion for a stationary dendritic growth in the form of a parabolic cylinder, we show that nonlinear effects stemming from the liquidus equation and atomic kinetics play a decisive role. Namely, the dendrite tip velocity and diameter, respectively, become greater and lower with the increasing deviation of the liquidus equation from a linear form. In addition, the dendrite tip velocity can substantially change with variations in the power exponent of the atomic kinetics. In general, the theory under consideration describes the evolution of a curvilinear crystallization front, as well as the growth of solid phase perturbations and patterns in undercooled binary melts at local equilibrium conditions (for low and moderate Péclet numbers). In addition, our theory, combined with the unsteady selection criterion, determines the non-stationary growth rate of dendritic crystals and the diameter of their vertices. boundary integral equation phase transitions curved solid–liquid interface undercooled melt en 12 Seiten 530 his Host institution Zweitveröffentlichung dbt_mods_00055091https://www.db-thueringen.de/receive/dbt_mods_00055091