Interdisciplinary Seminar in Nonlinear Science

Title: Steps, Kinetic Anisotropy, and Long--Wave Instabilities in Directional Solidification
Speaker: Dr. H.P. Grimm
Speaker Info: Northwestern U.
Brief Description:
Special Note:

We consider the effect of anisotropic interface kinetics on long--wave instabilities during the directional solidification of a binary alloy having a vicinal interface. Linear theory predicts that a planar solidification front is stabilized under the effect of anisotropy as long as the segregation coefficient is small enough, whereas a novel instability appears at high rates of solidification. We identify conditions for which linear stability theory predicts the instability of the planar interface to long--wavelength traveling waves. A number of distinguished limits provide evolution equations that describe the resulting dynamical behavior of the crystal-melt interface and generalize previous work by Sivashinsky, Brattkus and Davis, and Riley and Davis. Bifurcation analysis and numerical computations for the derived evolution equations show that the anisotropy is able to promote the tendency to supercritical bifurcation, and also leads to the development of strongly-preferred interface orientations for finite-amplitude deformations.
Date: Friday, October 2, 1998
Time: 2:00pm
Where: Tech M416
Contact Person: Prof. Riecke
Contact email: h-riecke@nwu.edu
Contact Phone: 847-491-8316
Copyright © 1997-2024 Department of Mathematics, Northwestern University.