Phase field computations of single-needle crystals, crystal growth, and motion by mean curvature. (English) Zbl 0793.65099

Caginalp, G.; Socolovsky, E.

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)

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