Feedback Control of Singularities in Models of Directional Solidification

Tuesday, October 26, 2004 - 1:30pm - 2:20pm
EE/CS 3-180
Alexander Nepomnyashchy (Technion-Israel Institute of Technology)
Joint work with V. Gubareva (Technion), A.A. Golovin (Northwestern University), and V. Panfilov (University of Nevada, Reno)

The nonlinear evolution of the long-wave morphological instability in a directional solidification front characterized by a small segregation coefficient in some cases does not saturate, leading to the formation of deep cells. In the framework of the Sivashinsky equation, this effect manifests itself through a subcritical instability of a plane solidification front and the development of a singularity in a finite time (blow-up). We investigate the possibility of the suppression of the subcritical instability and the blow-up behavior by means of a feedback adjustment of the pulling speed or temperature gradient. We show that the feedback control eliminates the appearance of deep cells and leads to the formation of localized structures at the crystal-melt interface.

Also, we investigate the possibility of the elimination of singularities in the nonlinear development of a subcritical pulsatile instability which may appear in the rapid solidification. In the framework of the subcritical complex Ginzburg-Landau equation, we find that the feedback control may lead to the formation of solitary waves and multipulse waves.