A NONLINEAR STABILITY ANALYSIS OF A MODEL EQUATION FOR ALLOY SOLIDIFICATION .2.

The authors begin by formulating a plane-front model equation for solidification. They introduce fixed- interface variables and briefly describe a Stuart-Watson-type weakly nonlinear stability analysis of this reformulated model equation, cataloguing the solution so obtained as well as discussing the direct versus adjoint operator methods of solvability. A sketch of the equivalence of the solutions to these two coordinate-system models and a discussion of the result are provided. They investigate the multiple scales approach to this problem and then use it as a vehicle for deducing the basic difference in the asymptotic solutions yielded by either the Malkus-Veronis or two-time methods when compared with the results of the Stuart-Watson method. In order to make this investigation more transparent they explicitly consider the asymptotic solutions which result upon the application of these various methods to our simplified interfacial model equation. The authors conclude with a comparison to other work. 38 Refs.