| References |
Kent, G.M., Harding, A.J., Orcutt, J.A., Evidence for a smaller magma chamber beneath the East Pacific Rise at 9°30' N (1990) Nature, 344, pp. 650-653; Marsh, B.D., Magma chambers (1989) Ann. Rev. Earth Planet. Sci., 17, pp. 439-472; 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. , D.A. Yuen (ed.) New-York, Springer-Verlag; Lopes, R.M.C., Kamp, L.W., Smythe, W.D., Mouginis-Mark, P., Kargel, J., Radebaugh, J., Turtle, E.P., Doute, S., Lava lakes on Io: Observations of Io's volcanic activity from Galileo NIMS during the 2001 fly-bys (2004) Icarus, 169 (1), pp. 140-174. , DOI 10.1016/j.icarus.2003.11.013; Hansen, V.L., Geologic constraints on crustal plateau surface histories, Venus: The lava pond and bolide impact hypotheses (2006) Journal of Geophysical Research E: Planets, 111 (11), pp. E11010. , DOI 10.1029/2006JE002714; Rubinshtein, L.I., (1971) The Stefan Problem, , AMS, Providence; Meirmanov, A.M., (1992) The Stefan Problem, , De Gruyter, Berlin; Stefan, J., Warmeleitung, U.E.P.D.T.D., Sitzungsberichte de Mathematisch-Naturawissenschaftlichen Classe der Kaiserlichen (1889) Akademie der Wissenschaften, 98 (2 A), pp. 473-484; Stefan, J., (1889) Uber Die Theorie der Eisbildung, Insbesondere Über Die Eisbildung im Polarmeere, Sitzungsberichte de Mathematisch-Naturawissenschaftlichen Classe der Kaiserlichen, Akademie der Wissenschaften, 98 (2 A), pp. 965-983; 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., Morphological Stability (1973) Crystal Growth: An Introduction, pp. 403-442. , P. Hartman (ed.) North-Holland; Ivantsov, G.P., Diffusive supercooling in binary alloy solidification (1951) Dokl. Akad. Nauk SSSR, 81, pp. 179-182. , (in Russian); Worster, M.G., Solidification of an alloy from a cooled boundary (1986) J. Fluid Mech., 167, pp. 481-501; Wollkind, D.J., Segel, L.A., A nonlinear stability analysis of the freezing of a dilute binary alloy (1970) Philos. Trans. Roy. Soc. A, 268, pp. 351-380; Stuart, J.T., Nonlinear stability theory (1971) Ann. Rev. Fluid Mech., 3, pp. 347-370; Hills, R.N., Loper, D.E., Roberts, P.H., Thermodynamically consistent model of a mushy zone (1983) Quarterly Journal of Mechanics and Applied Mathematics, 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) 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., 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. Exper. Theor. Phys., 108, pp. 821-829; 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; 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) Dokl. Earth Sci., 411 A, pp. 1407-1410; Alexandrov, D.V., Aseev, D.L., Nizovtseva, I.G., Huang, H.-N., Lee, D., Nonlinear dynamics of directional solidification with a mushy layer. Analytic solutions of the problem (2007) International Journal of Heat and Mass Transfer, 50 (17-18), pp. 3616-3623. , DOI 10.1016/j.ijheatmasstransfer.2007.02.006, PII S0017931007001512; Kurz, W., Fisher, D.J., (1986) Fundamentals of Solidification, , Trans. Tech. Publications Aedermannsdorf; Buyevich, Yu.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Cristallization, , Begell House, New-York, Wallingford; Aseev, D.L., Alexandrov, D.V., Nonlinear dynamics for the solidification of binary melt with a nonequilibrium two-phase zone (2006) Doklady Physics, 51 (6), pp. 291-295. , DOI 10.1134/S1028335806060024; 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; Alexandrov, D.V., Churbanov, A.G., Vabishchevich, P.N., Emergence of a mushy region in processes of binary melt solidification (1999) International Journal of Fluid Mechanics Research, 26 (2), pp. 248-264; 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. Polonica A, 115, pp. 791-794; Worster, M.G., Huppert, H.E., Sparks, R.S., Convection and crystallization in magma cooled from above (1990) Earth Planet. Sci. Lett., 101, pp. 78-89; Worster, M.G., Huppert, H.E., Sparks, R.S., The crystallization of lava lakes (1993) J. Geophys. Res., 98 (9 B), pp. 15891-15901; Turner, J.S., Huppert, H.E., Sparks, R.S.J., Komatiites II: Experimental and theoretical investigations of post-emplacement cooling and crystallization (1986) J. Petrol., 27, pp. 397-437; 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; Turner, J.S., (1979) Buoyancy Effects in Fluids, , Cambridge University Press Cambridge; Denton, R.A., Wood, I.R., Turbulent convection between two horizontal plates (1979) International Journal of Heat and Mass Transfer, 22 (10), pp. 1339-1346. , DOI 10.1016/0017-9310(79)90196-0; McPhee, M.G., A time-dependent model for turbulent transfer in a stratified oceanic boundary layer (1987) J. Geophys. Res., 92, pp. 6977-6986; Notz, D., McPhee, M., Worster, M.G., Maykut, G.A., Schlünzen, H., Eiken, H., Impact of underwater-ice evolution on Arctic summer sea ice (2003) J. Geophys. Res., 108, p. 3223; Worster, M.G., Kerr, R.C., The transient behaviour of alloys solidified from below prior to the formation of chimneys (1994) Journal of Fluid Mechanics, 269, pp. 23-44; Alexandrov, D.V., Nizovtseva, I.G., Malygin, A.P., Huang, H.-N., Lee, D., Unidirectional solidification of binary melts from a cooled boundary: Analytical solutions of a nonlinear diffusion-limited problem (2008) J. Phys. Condens. Matter, 20, p. 114105; Lee, D., Alexandrov, D.V., Numerical modeling of one-dimensional binary solidification - The classical two-phase Stefan problem (2010) Int. J. Pure Appl. Math., 58 (4), pp. 381-416; 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; Alexandrov, D.V., Nonlinear dynamics of solidification in three-component systems (2008) Dokl. Phys., 53 (9), pp. 471-475; Alexandrov, D.V., Ivanov, A.A., Analytical solution for a problem of directional solidification in a ternary system (2009) Acta Phys. Polonica A, 115, pp. 786-790; 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; Batchelor, G.K., Transport properties of two-phase materials with random structure (1974) Ann. Rev. Fluid Mech., 6, pp. 227-255; Huppert, H.E., Worster, M.G., Dynamic solidification of a binary melt (1985) Nature, 314, pp. 703-707; Kerr, R.C., Woods, A.W., Worster, M.G., Huppert, H.E., Solidification of an alloy cooled from above. Part 2. Non-equilibrium interfacial kinetics (1990) J. Fluid Mech., 217, pp. 331-348; Kirkpatrick, R.J., Robinson, G.R., Hays, J.F., Kinetics of crystal growth from silicate melts: Anorthite and diopside (1976) J. Geophys. Res., 81, pp. 5715-5720; MacDonald, K.C., Anatomy of the magma reservoir (1989) Nature, 339, pp. 178-179; Burnett, M.S., Caress, D.W., Orcutt, J.A., Tomographic image of the magma chamber at 12°50′N on the East Pacific Rise (1989) Nature, 339 (6221), pp. 206-208. , DOI 10.1038/339206a0; Hussenoeder, S.A., Seismic analysis of the magma chamber reflector along the southern East Pacific Rise from conventional reflection profiling (1996) J. Geophys. Res., 101, pp. 22087-22105; Kent, G.M., Harding, A.J., Orcutt, J.A., Distribution of magma beneath the East Pacific Rise near the 9°03' N overlapping spreading center from forward modeling of CDP data (1993) J. Geophys. Res., 98, pp. 13971-13995; Day, A.J., Peirce, C., Sinha, M.C., Three-dimensional crustal structure and magma chamber geometry at the intermediate-spreading, back-arc Valu Fa Ridge, Lau Basin- results of a wide-angle seismic tomographic inversion (2001) Geophysical Journal International, 146 (1), pp. 31-52. , DOI 10.1046/j.0956-540X.2001.01446.x; Ginibre, C., Worner, G., Kronz, A., Structure and dynamics of the Laacher See magma chamber (Eifel, Germany) from major and trace element zoning in sanidine: A cathodoluminescence and electron microprobe study (2004) Journal of Petrology, 45 (11), pp. 2197-2223. , DOI 10.1093/petrology/egh053; Neill, D.F., Hon, R., Navrotsky, A., The igneous system CaMgSi2 O6-CaAl 2Si2O3-NaAlSi3O8: Variations on a classic theme by Bowen (1980) Physics of Magmatic Processes, , Hargraves (ed.) Princeton Univ. Press, New Jersy; Kirckpatrick, R.J., Crystal growth from the melt: A review (1975) Am. Mineralogist, 60, pp. 798-814; Carslaw, H.S., Jaeger, J.S., (1959) Conduction of Heat in Solids, , Cambridge Univ. Press Cambridge |