Pattern Selection in a Phase Field Model for Directional Solidification
Statistical Mechanics
2009-11-11 v1 Disordered Systems and Neural Networks
Abstract
A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable configuration of the system, which we identify with the selected stationary state. The minimization is constrained by the stationary solutions of stochastic evolution equations and is done numerically. Secondly, additional support for this selected state is obtained from straightforward simulations of the dynamics from a variety of initial states.
Cite
@article{arxiv.cond-mat/0503224,
title = {Pattern Selection in a Phase Field Model for Directional Solidification},
author = {R. N. Costa Filho and J. M. Kosterlitz and Enzo Granato},
journal= {arXiv preprint arXiv:cond-mat/0503224},
year = {2009}
}
Comments
7 pages, 6 figures, to appear in Physica A