Special Topics:Modeling and Simulation

An example of one phenomenon being studied is the effect of noise of various types on crystal growth. Shown here are patterns which can arise when the tips of growing dendrites are periodically subjected to short small pulses of heat, such as might be introduced by a laser. Each pulse appears to momentarily slow the growth of the tip and encourage the development of side branches. When the frequency is too high, surface tension prevents any growth of side branches (in the absence of additional noise). At lower frequencies, natural instabilities in the growth are triggered, as shown, and at much lower frequencies, as shown, the growth looks very unnatural as the growth laws cope with this (highly nonlinear) perturbation.

How to make it: The mathematical and computational model developed to make these simulations was developed by team member Andrew Roosen, working with senior team member Jean Taylor. A related model has been developed by Robert Almgren, working with senior team member Fred Almgren; Roosen in fact used part of the code written by R. Almgren.

Image created: 1991

Copyright © 1991 by The Geometry Center, University of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.umn.edu.

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Created: Thu Jun 25 15:09:38 CDT 1998 --- Last modified: Thu Jun 25 15:09:38 CDT 1998