Mathematical and computational aspects of solidification of pure substances.

[1]  A. A. Wheeler,et al.  Thermodynamically-consistent phase-field models for solidification , 1992 .

[2]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[3]  Disorder, Dynamical Chaos and Structures , 1990 .

[4]  Müller-Krumbhaar,et al.  Dendritic crystallization: Numerical study of the one-sided model. , 1987, Physical review letters.

[5]  J. S. Rowlinson,et al.  Translation of J. D. van der Waals' “The thermodynamik theory of capillarity under the hypothesis of a continuous variation of density” , 1979 .

[6]  Paul C. Fife,et al.  Thermodynamically consistent models of phase-field type for the kinetics of phase transitions , 1990 .

[7]  W. Kurz,et al.  Fundamentals of Solidification , 1990 .

[8]  J. E. Hilliard,et al.  Free Energy of a Nonuniform System. I. Interfacial Free Energy , 1958 .

[9]  R. Kobayashi.  Modeling and numerical simulations of dendritic crystal growth , 1993 .

[10]  G. Meyer.  Multidimensional Stefan Problems , 1973 .

[11]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[12]  Morton E. Gurtin,et al.  On the two-phase Stefan problem with interfacial energy and entropy , 1985 .

[13]  Karol Mikula,et al.  Simulation of anisotropic motion by mean curvature -- comparison of phase field and sharp interface approaches. , 1998 .

[14]  D. Tarzia.  A bibliography on moving-free boundary problems for the heat-diffusion equation. The stefan and related problems , 2000 .

[15]  L. Bronsard,et al.  Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics , 1991 .

[16]  R. Almgren.  Variational algorithms and pattern formation in dendritic solidification , 1993 .

[17]  D. Kinderlehrer,et al.  Morphological Stability of a Particle Growing by Diffusion or Heat Flow , 1963 .

[18]  J. Langer.  Instabilities and pattern formation in crystal growth , 1980 .

[19]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[20]  J. A. Spittle,et al.  A cellular automaton model of the steady-state free'' growth of a non-isothermal dendrite , 1994 .

[21]  G. Caginalp.  An analysis of a phase field model of a free boundary , 1986 .