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

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.

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
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