Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model

Badrinarayan P. Athreya, Nigel Goldenfeld, Jonathan A. Dantzig, Michael Greenwood, Nikolas Provatas

Research output: Contribution to journalArticlepeer-review

Abstract

We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes. Our numerical approach uses the systematic renormalization-group formulation of a phase-field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field-a quantity that is spatially uniform except near topological defects, grain boundaries, and other lattice imperfections. Our algorithm employs a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions.

Original languageEnglish (US)
Article number056706
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume76
Issue number5
DOIs
StatePublished - Nov 16 2007

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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