| References |
Ivantsov, G.P., Diffusive supercooling in binary alloy solidification (1951) Dokl. Akad. Nauk SSSR, 81, pp. 179-182. , in Russian; Mullins, W.W., Sekerka, R.F., Stability of a planar interface during solidification of a dilute binary alloy (1964) J. Appl. Phys., 35, pp. 444-451; Wollkind, D.J., Segel, L.A., A nonlinear stability analysis of the freezing of a dilute binary alloy (1970) Phil. Trans. Roy. Soc. A, 268, pp. 351-380; Worster, M.G., Solidification of an alloy from a cooled boundary (1986) J. Fluid Mech., 167, pp. 481-501; Hunt, J.D., Steady state columnar and equiaxed growth of dendrites and eutectic (1984) Materials science and engineering, 65 (1), pp. 75-83. , DOI 10.1016/0025-5416(84)90201-5; Buyevich, Yu.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , Begell House New York-Wallingford; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) International Journal of Heat and Mass Transfer, 49 (25-26), pp. 4903-4909. , DOI 10.1016/j.ijheatmasstransfer.2006.05.046, PII S001793100600411X; Aleksandrov, D.V., Theory of Solidification with a Quasi-Equilibrium Two-Phase Zone (2000) Doklady Physics, 45 (11), pp. 569-573. , DOI 10.1134/1.1333856; Alexandrov, D.V., Solidification with a quasiequilibrium mushy region: Exact analytical solution of nonlinear model (2001) Journal of Crystal Growth, 222 (4), pp. 816-821. , DOI 10.1016/S0022-0248(00)00960-X; Alexandrov, D.V., Solidification with a quasiequilibrium two-phase zone (2001) Acta Materialia, 49 (5), pp. 759-764. , DOI 10.1016/S1359-6454(00)00388-8, PII S1359645400003888; Alexandrov, D.V., Aseev, D.L., One-dimensional solidification of an alloy with a mushy zone: Thermodiffusion and temperature-dependent diffusivity (2005) J. Fluid Mech., 527, pp. 57-66; Alexandrov, D.V., Aseev, D.L., Directional solidification with a two-phase zone: Thermodiffusion and temperature-dependent diffusivity (2006) Computational Materials Science, 37 (1-2), pp. 1-6. , DOI 10.1016/j.commatsci.2005.12.019, PII S0927025605003472; Aseev, D.L., Alexandrov, D.V., Unidirectional solidification with a mushy layer. The influence of weak convection (2006) Acta Mater., 54, pp. 2401-2406; Alexandrov, D.V., Rakhmatullina, I.V., Malygin, A.P., On the theory of solidification with a two-phase concentration supercooling zone (2010) Russian Metall. (Metally), 8, pp. 745-750; Alexandrov, D.V., Ivanov, A.A., Malygin, A.P., Self-similar solidification of binary alloys (2009) Acta Phys. Polonica A, 115, pp. 795-799; Alexandrov, D.V., Malygin, A.P., Self-similar solidification of an alloy from a cooled boundary (2006) International Journal of Heat and Mass Transfer, 49 (3-4), pp. 763-769. , DOI 10.1016/j.ijheatmasstransfer.2005.07.047, PII S0017931005005296; Alexandrov, D.V., Malygin, A.P., Analytical description of seawater crystallization in ice fissures and their influence on heat exchange between the ocean and the atmosphere (2006) Doklady Earth Sciences, 411 (9), pp. 1407-1411. , DOI 10.1134/S1028334X06090169; Alexandrov, D.V., Malygin, A.P., Alexandrova, I.V., Solidification of leads: Approximate solutions of non-linear problem (2006) Annals of Glaciology, 44, pp. 118-122. , DOI 10.3189/172756406781811213; Huppert, H.E., Sparks, R.S.J., Double-diffusive convection due to crystallization in magmas (1984) Anuu. Rev. Earth Planet Sci., 12, pp. 11-37; Kurz, W., Fisher, D.J., (1986) Fundamentals of Solidification, , Trans. Tech. Publications Aedermannsdorf; Hurle, D.J.T., (1993) Handbook of Crystal Growth, , North-Holland Amsterdam; Worster, M.G., Solidification of Fluids (2000) Perspectives in Fluid Dynamics, pp. 393-446. , G.K. Batchelor, H.K. Moffatt, M.G. Worster, Cambridge University Press; Thompson, A.F., Huppert, H.E., Worster, M.G., Aitta, A., Solidification and compositional convection of a ternary alloy (2003) Journal of Fluid Mechanics, 497, pp. 167-199. , DOI 10.1017/S002211200300661X; Alexandrov, D.V., Ivanov, A.A., Nonlinear dynamics of directional solidification of ternary solutions with mushy layers (2009) Heat Mass Trans., 45, pp. 1467-1472; Aitta, A., Huppert, H.E., Gray Worster, M., Diffusion-controlled solidification of a ternary melt from a cooled boundary (2001) Journal of Fluid Mechanics, 432, pp. 201-217; Bloomfield, L.J., Huppert, H.E., Solidification and convection of a ternary solution cooled from the side (2003) Journal of Fluid Mechanics, 489, pp. 269-299. , DOI 10.1017/S0022112003005172; Anderson, D.M., A model for diffusion-controlled solidification of ternary alloys in mushy layers (2003) Journal of Fluid Mechanics, 483, pp. 165-197. , DOI 10.1017/S0022112003004129; Alexandrov, D.V., Nonlinear dynamics of solidification in three-component systems (2008) Dokl. Phys., 53, pp. 471-475; Alexandrov, D.V., Ivanov, A.A., Solidification of a ternary melt from a cooled boundary, or nonlinear dynamics of mushy layers (2009) Int. J. Heat Mass Transfer, 52, pp. 4807-4811; Alexandrov, D.V., Ivanov, A.A., The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions (2009) J. Exp. Theoretical Phys., 108, pp. 821-829; Alexandrov, D.V., Solidification with a quasiequilibrium mushy zone: Exact analytical solution (2000) Int. J. Fluid Mech. Res., 27, pp. 213-222; Deguen, R., Alboussiere, T., Brito, D., On the existence and structure of a mush at the inner core boundary of the Earth (2007) Physics of the Earth and Planetary Interiors, 164 (1-2), pp. 36-49. , DOI 10.1016/j.pepi.2007.05.003, PII S0031920107001021; Alexandrov, D.V., Malygin, A.P., Coupled convective and morphological instability of the inner core boundary of the Earth (2011) Phys. Earth Planet. Inter., 189, pp. 134-141; Buffett, B.A., Earth's core and the geodynamo (2007) Science, 288, pp. 2007-2012; Fedotov, S., Bashkirtseva, I., Ryashko, L., Stochastic dynamo model for subcritical transition (2006) Phys. Rev. e, 73, pp. 066307-066311 |