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.


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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