References |
Alexandrov, D.V., Solidification with a quasiequilibrium two-phase zone (2001) Acta Mater., 49, pp. 759-764; 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) Int. J. Heat and Mass Transfer, 50, pp. 3616-3623; Alexandrov, D.V., Nonlinear dynamics of solidification in three-component systems (2008) Doklady Physics, 53 (9), pp. 471-475; Ang, W.-T., A numerical method based on integro-differential formulation for solving a one-dimensional Stefan problem (2008) Numerical Methods for Partial Differential Equations, 24, pp. 939-949; De Boor, C., (2001) A Practical Guide to Splines, , Revised Edition, Springer-Verlag, New York; De Boor, C., Convergence of cubic spline interpolation with the not-a-knot condition (1985) MRC, 2876. , University of Wisconsin at Madison; Borisov, V.T., (1987) Theory of the Two-Phase Zone of A Metal Ingot, , Moscow, Metallurgiya Publishing House; Boyd, J.P., (2001) Chebyshev and Fourier-Spectral Methods, , Second Edition, Dover, Mineola, New York; Buyevich, Y.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , Begell House, New York-Wallingford; Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., (2006) Spectral Methods, Fundamentals in Single Domains, , Springer, New York; Crank, J., (1984) Free and Moving Boundary Problems, , Clarendon Press, Oxford, England; Fowler, A.C., The formation of freckles in binary alloys (1985) IMA J. Appl. Math., 35, pp. 159-174; Hills, R.N., Loper, D.E., Roberts, P.H., A thermodynamically consistent model of a mushy zone (1983) Quarterly Jnl. of Mechanics and App. Maths., 36, pp. 505-540; Huppert, E.H., Worster, M.G., Dynamic solidification of a binary melt (1985) Nature, 314, pp. 703-707; Ivantsov, G.P., Diffusive supercooling in binary alloy solidification (1951) Dokl. Akad. Nauk SSSR, 81, pp. 179-182; Javierre, E., Vuik, C., Vermolen, F.J., Van Der Zwaag, S., A comparison of numerical models for one-dimensional Stefan problem (2006) JCAM, 192, pp. 445-459; Morison, J., McPhee, M., Muench, R., The lead ex experiment (1993) EOS. Trans. AGU, 74, pp. 393-397; Mullins, W.W., Sekerka, R.F., Stability of a planar interface during solidification of a dilute binary alloy (1964) J. Appl. Phys., 35, p. 444451; Osher, S., Fedkiw, R., (2003) Level Set Methods and Dynamic Implicit Surfaces, , Springer, New York; Saad, Y., (2003) Iterative Methods for Sparse Linear System, Second Edition, , SIAM, Philadelphia, USA; Sethian, J.A., (1999) Level Set Methods and Fast Marching Methods, , Cambridge University Press, New York; Shen, J., Tang, T., (2006) Spectral and High-Order Methods with Applications, , Science Press, Beijing, P.R. China; Stefan, I., Übereinige probleme der theorie der warmeleitung (1898) Sitzber. Kais. Akad. Wiss. Wien, Math.-Naturw. Kl., 98, p. 437438. , No. IIa; Tang, T., Xu, J., (2007) Adaptive Computations: Theory with Algorithms, , Science Press, Beijing, P.R. China; Vuik, C., Some historical notes about the Stefan problem (1993) Nieuw Archief voor Wiskunde, 157. , 4e, Serie 11; Wettlaufer, J.S., Worster, M.G., Huppert, H.E., Solidification of leads: Theory, experiment and field observations (2000) J. Geophys. Res., 105, pp. 1123-1134; Worster, M.G., Solidification of an alloy from a cooled boundary (1988) J. Fluid Mech., 167, pp. 481-501 |