Caginalp, G.; Socolovsky, E. Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature. (English) Zbl 0793.65099 SIAM J. Sci. Comput. 15, No. 1, 106-126 (1994). The authors commence by discussing possible model representations for moving boundary problems; and indicate the advantages of the phase field model where the system is represented by a parameter \(\varphi\) which is approximately 1 in the liquid state and –1 in the solid state. They discuss the problems which can arise when two growing solid seeds merge. They indicate how single-needle dendrites can emerge and consider a number of other problems associated with surface instability and crystal growth.The paper is descriptive rather than mathematical. There are over 40 references. Reviewer: Ll.G.Chambers (Bangor) Cited in 22 Documents MSC: 65Z05 Applications to the sciences 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 82B24 Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics 35R35 Free boundary problems for PDEs 35Q72 Other PDE from mechanics (MSC2000) 82D25 Statistical mechanics of crystals Keywords:single-needle crystals; moving boundary problems; phase field model; surface instability; crystal growth PDF BibTeX XML Cite \textit{G. Caginalp} and \textit{E. Socolovsky}, SIAM J. Sci. Comput. 15, No. 1, 106--126 (1994; Zbl 0793.65099) Full Text: DOI Link OpenURL