References |
Thompson, D.W., (1952) On Growth and Form, , Cambridge University Press; Langer, J.S., Instabilities and pattern formation in crystal growth (1980) Rev. Mod. Phys., 52, pp. 1-28; Pelce, P., (1988) Dynamics of Curved Fronts, , Academic Press Boston; Buyevich, Yu.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , Begell House, New York-Wallingford; Chalmers, B., (1964) Principles of Solidification, , John Wiley & Sons New York; Ravi, V.K., (1981) Imperfections and Impurities in Semiconductor Silicon, , John Wiley & Sons New York; Kurz, W., Fisher, D.J., (1986) Fundamentals of Solidification, , Trans. Tech. Publications Aedermannsdorf; Eicken, H., Structure of under-ice melt ponds in the central Arctic and their effect on the sea-ice cover (1994) Limnol. Oceanogr., 39, pp. 682-694; Eicken, H., Krouse, H.R., Kadko, D., Perovich, D.K., Tracer studies of pathways and rates of meltwater transport through Arctic summer sea ice (2002) J. Geophys. Res., 107, pp. 1-20; 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; Sekerka, R.F., A stability function for explicit evaluation of the Mullins-Sekerka interface stability criterion (1965) J. Appl. Phys., 36, pp. 264-268; Sekerka, R.F., Morphological Stability (1968) J. Crystal Growth, 3-4, pp. 71-81; Sekerka, R.F., (1973) Morphological Stability, in Crystal Growth: An Introduction, pp. 403-442. , P. Hartman (Ed.), North-Holland; Cserti, J., Tichy, G., Stability of anisotropic liquid-solid interfaces (1968) Acta Metall., 34, pp. 1029-1034; Wilson, L.O., The effect of fluctuating growth rates on segregation in crystals grown from the melt (1980) J. Cryst. Growth, 48, pp. 435-458; Wheeler, A., The effect of a periodic growth rate on the morphological stability of a freezing binary alloy (1984) J. Cryst. Growth, 67, pp. 8-26; Wollhover, K., Scheiwe, M., Hartmann, U., Korber, Ch., On morphological stability of planar phase boundaries during unidirectional transient solidification of binary aqueous solutions (1985) Int. J. Heat Mass Trans., 28, pp. 897-902; Laxmanan, V., Morphological transitions in the rapid solidification regime: A re-examination of the fundamental validity of the absolute stability concept of Mullins and Sekerka (1989) Acta Metall., 37, pp. 1109-1119; Alexandrov, D.V., Mansurov, V.V., Dynamic stability of a solidification process of a binary melt in the presence of a broad quasiequilibrium mushy region (1996) Scripta Mater., 35, pp. 787-790; Alexandrov, D.V., Mansurov, V.V., Dynamical instability of quasi-steady solidification in a binary melt with a narrow pseudoequilibrium two-phase zone (1996) Crystallogr. Rep., 41, pp. 357-359; Alexandrov, D.V., Mansurov, V.V., Galenko, P.K., Morphological stability of the plane phase boundary in a binary melt for processes of high-rate crystallization (1996) Phys. Dokl., 41, pp. 511-513; Alexandrov, D.V., Ivanov, A.O., Dynamic stability analysis of the solidification of binary melts in the presence of a mushy region: Changeover of instability (2000) J. Crystal Growth, 210, pp. 797-810; Alexandrov, D.V., Self-similar solidification: Morphological stability of the regime (2004) Int. J. Heat Mass Trans., 47, pp. 1383-1389; Alexandrov, D.V., Malygin, A.P., Convective instability of directional crystallization in a forced flow: The role of brine channels in a mushy layer on nonlinear dynamics of binary systems (2011) Int. J. Heat Mass Trans., 54, pp. 1144-1149; Delves, R.T., Theory of stability of a solid-liquid interface during growth from stirred melts (1968) J. Crystal Growth, 3-4, pp. 562-568; Coriell, S.R., Hurle, D.T.J., Sekerka, R.F., (1976) Interface Stability during Crystal Growth: The Effect of Stirring, 32, pp. 1-7; Favier, J.J., Rouzaud, A., Morphological stability of the solidification interface under convective conditions (1983) J. Crystal Growth, 64, pp. 367-379; Forth, S.A., Wheeler, A.A., Coupled convective and morphological instability in a simple-model of the solidification of a binary alloy (1992) J. Fluid Mech., 236, pp. 61-94; Chen, Y.-J., Davis, S.H., Directional solidification of a binary alloy into a cellular convective flow: Localized morphologies (1999) J. Fluid Mech., 395, pp. 253-270; Ivantsov, G.P., Diffusive supercooling in binary alloy solidification (1951) Dokl. Akad. Nauk SSSR, 81, pp. 179-182. , (in Russian); Shimizu, H., Poirier, J.P., Le Mouel, J.L., On crystallization at the inner core boundary (2005) Phys. Earth Planet. Inter., 151, pp. 37-51; Worster, M.G., Solidification of an alloy from a cooled boundary (1986) J. Fluid Mech., 167, pp. 481-501; Aseev, D.L., Alexandrov, D.V., Nonlinear dynamics for the solidification of binary melt with a nonequilibrium two-phase zone (2006) Dokl. Phys., 51, pp. 291-295; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) Int. J. Heat Mass Transfer, 49, pp. 4903-4909; Hills, R.N., Loper, D.E., Roberts, P.H., A thermodynamically consistent model of a mushy zone (1983) Q. J. Appl. Math., 36, pp. 505-539; Fowler, A.C., The formation of freckles in binary alloys (1985) IMA J. Appl. Math., 35, pp. 159-174; Borisov, V.T., (1987) Theory of Two-Phase Zone of Metallic Ingot, Metallurgia, Moscow, , in Russian; Alexandrov, D.V., Theory of solidification with a quasi-equilibrium two-phase zone (2000) Phys. Dokl., 45, pp. 569-573; Alexandrov, D.V., Solidification with a quasiequilibrium mushy region: Exact analytical solution of nonlinear model (2001) J. Crystal Growth, 222, pp. 816-821; Alexandrov, D.V., Solidification with a quasiequilibrium two-phase zone (2001) Acta Mater., 49, pp. 759-764; 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., Rakhmatullina, I.V., Malygin, A.P., On the theory of solidification with a two-phase concentration supercooling zone (2010) Russian Metallurgy (Metally), 8, pp. 745-750; Aseev, D.L., Alexandrov, D.V., Unidirectional solidification with a mushy layer. the influence of weak convection (2006) Acta Mater., 54, pp. 2401-2406; Deguen, R., Alboussire, T., Brito, D., On the existence and structure of a mush at the inner core boundary of the Earth (2007) Phys. Earth Planet. Inter., 164, pp. 36-49; Alexandrov, D.V., Galenko, P.K., Herlach, D.M., Selection criterion for the growing dendritic tip in a non-isothermal binary system under forced convective flow (2010) J. Crystal Growth, 312, pp. 2122-2127; Huppert, H.E., Worster, M.G., Vigorous motions in magma chambers and lava lakes (1992) Chaotic Processes in the Geological Sciences, 41, pp. 141-173. , Ed. D.A. Yuen. New-York, Springer-Verlag; Loper, D.E., A model of the dynamical structure of Earth's outer core (2000) Phys. Earth Planet. Inter., 117, pp. 179-196; Worster, M.G., Natural convection in a mushy layer (1991) J. Fluid Mech., 224, pp. 335-359; Batchelor, G.K., Transport properties of two-phase materials with random structure (1974) Ann. Rev. Fluid Mech., 6, pp. 227-255; Buyevich, Yu.A., Alexandrov, D.V., (2005) Heat Transfer in Dispersions, , Begell House New York; Scheil, E., Bemerkungen zur schichtkiistallbildung (1942) Zeichrift fur Metallkunde, 34, pp. 70-72; Flemings, M.C., (1974) Solidification Processing, , McGraw-Hill Book Company New York; Kerr, R.C., Woods, A.W., Worster, M.G., Huppert, H.E., Solidification of an alloy cooled from above. Part 1. Equilibrium growth (1990) J. Fluid Mech., 216, pp. 323-342; Alexandrov, D.V., Nizovtseva, I.G., To the theory of underwater ice evolution, or nonlinear dynamics of "false bottoms" (2008) Int. J. Heat Mass Transfer, 51, pp. 5204-5208; Zeldovich, Ya.B., On the theory of formation of a new phase (1942) Cavitation, Zh. Eksperiment. Technich. Fiz., 12, pp. 525-536; Frenkel, J., (1955) Theory of Liquids, , Dover New York; Chernov, A.A., Givargizov, Ye.I., Bagdasarov, Kh.S., (1990) Modern Crystallography. Crystallization Processes, 3. , Nauka Publishing House, Moscow; Nayfen, A.H., (1981) Introduction to Perturbation Techniques, , Wiley Interscience Publication New York, Chichester, Brisbane, Toronto; Fedoryuk, M.V., (1987) Asymptotics, , Nauka Publishing House, Moscow Integrals and Series; Alexandrov, D.V., Churbanov, A.G., Vabishchevich, P.N., (1999) Int. J. Fluid Mech. Res., 26, pp. 248-264; Alexandrov, D.V., Incipience of a mushy zone in binary melt solidification processes (2000) Int. J. Fluid Mech. Res., 27, pp. 223-238; Alexandrova, I.V., Alexandrov, D.V., Aseev, D.L., Bulitcheva, S.V., Mushy layer formation during solidification of binary alloys from a cooled wall: The role of boundary conditions (2009) Acta Phys. Pol. A, 115, pp. 791-794 |