Mathematical and numerical aspects of a phase-field approach to critical nuclei morphology in solids

Lei Zhang, Long Qing Chen, Qiang Du

Research output: Contribution to journalArticle

15 Scopus citations

Abstract

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 able to efficiently predict the critical nucleus morphology in elastically anisotropic solids without making a priori assumptions.

Original languageEnglish (US)
Pages (from-to)89-102
Number of pages14
JournalJournal of Scientific Computing
Volume37
Issue number1
DOIs
StatePublished - Oct 1 2008

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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