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
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References

Publications referenced by this paper.
Showing 1-10 of 41 references

Minimax Methods in Critical Point Theory with Applications to Differential Equations

  • P. Rabinowitz
  • Am. Math. Soc., Providence
  • 1986
Highly Influential
4 Excerpts

Theory of Structural Transformations in Solids

  • A. Khachaturyan
  • Wiley, New York
  • 1983
Highly Influential
3 Excerpts

Diffuse-interface description of strain-dominated morphology of critical nuclei in phase transformations

  • L. Zhang, L. Chen, Q. Du
  • Acta Mater.
  • 2008
1 Excerpt

A sharp-interface limit for a two-well problem in geometrically linear elasticity

  • S. Conti, B. Schweizer
  • Arch. Ration Mech. Anal. 179, 413–452
  • 2006
1 Excerpt

On asymptotic limits of Cahn-Hilliard systems with elastic misfit

  • H. Garcke, D. Kwak
  • Analysis, Modeling and Simulation of Multiscale…
  • 2006
2 Excerpts

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