Structurization of the instability zone and crystallization

E. A. Lukashov   ; E. V. Radkevich   ; N. N. Yakovlev

Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 28 (2011) no. 28, pp. 229-265

Bibliographie

[2] Avetisov V. A., “$p$-Adic description of characteristic relaxation in complex system”, Phys. A.: Math. Gen., 36 (2003), 4239 | DOI | MR | Zbl

[3] Avetisov V. A., Bikulov A. Kh., Zubarev A. P., “O raspredelenii vremeni pervogo vozvrascheniya dlya ultrametricheskogo sluchainogo bluzhdaniya”, Vestn. Samarskogo gos. un-ta, 8:1(67) (2008), 8–22

[4] Volynskii A. L., Bakeev N. F., Strukturnaya samoorganizatsiya amorfnykh polimerov, Fizmatlit, M., 2005

[5] Kablov E. N., Litye lopatki gazoturbinnykh dvigatelei (splavy, tekhnologiya, pokrytiya), MISIS, M., 2001

[6] Kolmogorov A. N., “K statisticheskoi teorii kristallizatsii metallov”, Izv. AN SSSR. Ser. mat., 1937, no. 3, 355–359

[7] Radkevich E. V., “On structures in instability zones”, J. Math. Sci., 165:1 (2010) | DOI | MR

[8] Danilov V. G., Omel'yanov G. A., Radkevich E. V., “Hugoniot-type conditions and weak solutions to the phase field system”, Europ. J. Appl. Math., 10 (1999), 55–77 | DOI | MR | Zbl

[9] Visintin V., Models of Phase Transitions, Birkhäuser, Boston, 1996 | MR | Zbl

[10] Matthews J. W., Blacslee A. E., “Defects in epitaxial multilayers. I. Misfit dislocations”, J. Crystal Growth., 27:1 (1974), 118–125

[11] Lyakishev N. P., Burkhanov G. S., Metallicheskie monokristally, Eliz, M., 2002

[12] Danilov V. G., Omel'yanov G. A., Radkevich E. V., “Asymptotic solution of the conserved phase field system in the fast relaxation case”, Europ. J. Appl. Math., 9 (1998), 1–21 | DOI | MR | Zbl

[13] Radkevich E. V., “The Gibbs–Thomson effect and existence conditions of classical solution for the modified Stefan problem”, Free Boundary-Problems Involving Solids, eds. J. M. Chadam, R. Henning, Longman Scientific Technical, Harlow, 1993, 135–142 | MR | Zbl

[14] Lacey A. A., Tayler A. B., “A mushy region in a Stefan problem”, IMA J. Appl. Math., 30:3 (1983), 303–313 | DOI | MR | Zbl

[15] Oleynik O. A., Radkevich E. V., Second-Order Equations with Nonnegative Characteristic Form, Amer. Math. Soc., Providence, 1973

[16] Radkevich E. V., Matematicheskie voprosy neravnovesnykh protsessov, Belaya kniga, 4, Tamara Rozhkovskaya, Novosibirsk, 2007

[17] Yakovlev N. N., Lukashov E. A., Radkevich E. V., “Problemy rekonstruktsii protsessa napravlennoi kristallizatsii”, Dokl. RAN, 421:5 (2008), 625–629 | MR | Zbl

[18] Biot M. A., “Mechanics of deformation and acoustic propogation in porous media”, J. Appl. Phys., 33:4 (1962), 1482–1498 | DOI | MR | Zbl

[19] Golovin A. A., Davis S. H., Nepomnyashchy A. A., “A convective Cahn–Hillard model for the formation of facets and carners in crystal growth”, Phys. D., 118 (1998), 202–230 | DOI | MR

[20] Watson S. J., Otto F., Rubinstein B. Y., Davis S. H., Coarsening dynamics for the Convective Cahn–Hilliard equation: Preprint, Univ. Bonn, 2003 | MR | Zbl

[21] Zaitsev N. A., Rykov Yu. G., Chislennyi raschet odnoi modeli, opisyvayuschei kristallizatsiyu metallov I. Odnomernyi sluchai, No 72, IPM im. M. V.Keldysha, 2007

[22] Nikitin N. V., Nikitin S. A., Polezhaev V. I., “Konvektivnye neustoichivosti v gidrodinamicheskoi modeli Chokhralskogo”, Uspekhi mekhaniki, 2003, no. 4, 3–45

[23] Shalin R. E., Svetlov I. L., Kachanov E. B., Toloraiya V. N., Gavrilin O. S., Monokristally nikelevykh zharoprochnykh splavov, Mashinostroenie, M., 1997

[24] Vigdorovich V. N., Volpyan A. E., Kurdyumov G. M., Napravlennaya kristallizatsiya i fiziko-khimicheskii analiz, Khimiya, M., 1976

[25] Yakovlev N. N., Radkevich E. V., Lukashov E. A., “Postanovka zadachi modelirovaniya tverdo-zhidkoi oblasti pri kristallizatsii dvoinogo evtekticheskogo splava”, Tez. dokl. mezhdunar. nauchno-tekhnicheskoi konf. “Aktualnye voprosy aviatsionnogo materialovedeniya”, FGUP VIAM, M., 2006, 26