Paper Info
Title
A Boundary Integral Method for Computing the Dynamics of an Epitaxial Island
Abstract
In this paper, we present a boundary integral method for computing the quasi-steady evolution of an epitaxial island. The problem consists of an adatom diffusion equation (with desorption) on terrace and a kinetic boundary condition at the step (island boundary). The normal velocity for step motion is determined by a two-sided flux. The integral formulation of the problem involves both double- and single-layer potentials due to the kinetic boundary condition. Numerical tests on a growing/shrinking circular or a slightly perturbed circular island are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient, and spectrally accurate in space. Nonlinear simulations for the growth of perturbed circular islands show that sharp tips and flat edges will form during growth instead of the usual dense branching morphology seen throughout physical and biological systems driven out of equilibrium. In particular, Bales-Zangwill instability is manifested in the form of wave-like fronts (meandering instability) around the tip regions. The numerical techniques presented here can be applied generally to a class of free/moving boundary problems in physical and biological science.
Year
DOI
Venue
2011
10.1137/100814871
SIAM J. Scientific Computing
Keywords
Field
DocType
boundary integral method,bales-zangwill instability,boundary problem,epitaxial island,circular island,island boundary,biological system,biological science,integral formulation,kinetic boundary condition,potential theory,integral equation
Boundary value problem,Potential theory,Mathematical optimization,Nonlinear system,Mathematical analysis,Instability,Integral equation,Free boundary problem,Flux,Geometry,Mathematics,Diffusion equation
Journal
Volume
Issue
ISSN
33
6
1064-8275
Citations 
PageRank 
References 
4
0.50
11
Authors
2
Name
Order
Citations
PageRank
Shuwang Li1242.73
Xiaofan Li2412.45