Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in Solids

@article{Zhang2008MathematicalAN,
title={Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in Solids},
author={Lei Zhang and Long-Qing Chen and Qiang Du},
journal={J. Sci. Comput.},
year={2008},
volume={37},
pages={89-102}
}

We investigate a phase-field model for homogeneous nucleation and critical nucleus morphology in solids. We analyze the mathematical properties of a free energy functional that includes the long-range, anisotropic elastic interactions. We describe the numerical algorithms used to search for the saddle points of such a free energy functional based on a minimax technique and the Fourier spectral implementation. It is demonstrated that the phase-field model is mathematically well defined and is… CONTINUE READING