Pattern Selection in a Phase Field Model for Directional Solidification

Details Pattern Selection in a Phase Field Model for Directional Solidification Pattern Selection in a Phase Field Model for Directional Solidification

2005-03-09

arxiv.org/abs/cond-mat/0503224v1

Physica A 354, 333 (2005)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 6 figures, to appear in Physica A

Scientific paper

10.1016/j.physa.2005.03.010

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.

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