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Phase transition in binary systems and the binary alloy problem
Author(s) -
Xie Weiqing
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150306
Subject(s) - binary number , mathematics , binary alloy , alloy , phase transition , boundary value problem , regularization (linguistics) , mass transfer , thermodynamics , dimension (graph theory) , kinetic energy , statistical physics , mathematical analysis , materials science , physics , pure mathematics , classical mechanics , metallurgy , computer science , arithmetic , artificial intelligence
In this paper we consider a phase transition in binary systems describing the solidification of a dilute alloy in one space dimension, in which the equations of heat and mass transfer are coupled through the conditions at the free boundary. A kinetic condition is introduced to suggest a regularization of the model, which admits a unique solution, and to obtain the generalized solution of the dilute‐alloy problem under an additional assumption.