APPLICATIONS OF SELF-DEFINED ARRAYS FOR PATTERN-FORMING ALLOY SOLIDIFICATION

In this paper, we consider a pattern-forming solidification problem in volving self-defined arrays (SDAs). These SDAs originate from an itera ted function system (IFS) and are imposed on the moving boundary so th at microstructures' evolve as prescribed shape attractors during itera ted advance of a phase boundary. SDAs are generated from iterated appl ication of a geometric rule requiring the pth iterate of a given array to be defined in terms of the (p - 1)th iterate. In this study, we us e a geometric rule based on the Canter middle-third fractal set to gen erate an SDA for an isolated dendrite microstructure. We apply this no tion of an SDA to a phase change problem where fractal mass-flow creat es the SDA geometry and results in a solidification microstructure. (C ) 1998 Elsevier Science B.V.