Geodesic
Isothermal crystal growth in undercooleel binary alloys
Matematičeskoe modelirovanie, Tome 12 (2000) no. 11, pp. 17-37.

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A model is given for local nonequilibrium solidification the mathematical description of isothermal structure formation of crystals in undercooled binary alloy. The model equations describe the kinetics of the liquid-solid interface motion and diffusion mass transport in the liquid phase. Also, the solute trapping at the interface and deviation of the liquidus line from its equilibrium value are taken into account. A main feature of the model equations is the including of crystal growth velocities which have the some order as the diffusion speed. It allows one to describe rapid solidification in undercooled alloy. The results of modelling testify that this model of local nonequilibrium solidification describes the structure formation adequately of natural experiments both at small and at high velocities of solidification. 
@article{MM_2000_12_11_a1,
     author = {P. K. Galenko and M. D. Krivilev},
     title = {Isothermal crystal growth in undercooleel binary alloys},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {17--37},
     publisher = {mathdoc},
     volume = {12},
     number = {11},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2000_12_11_a1/}
}
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P. K. Galenko; M. D. Krivilev. Isothermal crystal growth in undercooleel binary alloys. Matematičeskoe modelirovanie, Tome 12 (2000) no. 11, pp. 17-37. http://geodesic.mathdoc.fr/item/MM_2000_12_11_a1/