Commun. Comput. Phys., 2 (2007), pp. 73-86.


Surface Diffusion on Stressed Solid Surface

Xiaofan Li 1*, Qing Nie 2

1 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.
2 Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875, USA.

Received 18 November 2005; Accepted (in revised version) 6 April 2006
Available online 30 August 2006

Abstract

The surface diffusion of an axi-symmetric solid, a whisker, subject to applied uniaxial stress, is studied numerically based on a new boundary integral formulation for periodic stress configurations. An efficient semi-implicit time-stepping scheme is developed to treat the serve stiffness due to high-order derivatives. When the initial perturbation is small the effect of the stress on the motion of the whisker is found to agree with the linear stability analysis. Numerical simulations of a fully nonlinear case are also presented, and a potential break-up of the whisker is observed.

AMS subject classifications: 74B20, 65N38

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Key words: Surface diffusion, elastic stress, boundary integral method, semi-implicit scheme.

*Corresponding author.
Email: lix@iit.edu (X. Li), qnie@math.uci.edu (Q. Nie)
 

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