Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
Abstract
We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field during materials processing. Our numerical approach uses the systematic renormalization-group formulation of the phase field crystal model 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 is 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 domain formation in two dimensions.
Keywords
Cite
@article{arxiv.cond-mat/0702173,
title = {Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model},
author = {Badrinarayan P. Athreya and Nigel Goldenfeld and Jonathan A. Dantzig and Michael Greenwood and Nikolas Provatas},
journal= {arXiv preprint arXiv:cond-mat/0702173},
year = {2009}
}
Comments
37 pages, 15 figures. Submitted to Phys. Rev. E