Geodesic
Effective motion of a curvature-sensitive interface through a heterogeneous medium
Bogdan Craciun1 ; Kaushik Bhattacharya2
1Synopsys, Inc., Mountain View, USA
2California Institute of Technology, Pasadena, USA
Interfaces and free boundaries, Tome 6 (2004) no. 2, pp. 151-173

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DOI

This paper deals with the evolution of fronts or interfaces propagating with normal velocity vn​=f−cκ where f is a spatially periodic function, c a constant and κ the mean curvature. This study is motivated by the propagation of phase boundaries and dislocation loops through heterogeneous media. We establish a homogenization result when the scale of oscillation of f is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law vn​=fˉ​(n). We illustrate the results using examples. We also provide an explicit characterization of fˉ​ in the limit c→∞.
DOI : 10.4171/ifb/95
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Front propagation, phase boundaries, heterogeneous media

Bogdan Craciun  1   ; Kaushik Bhattacharya  2

1 Synopsys, Inc., Mountain View, USA
2 California Institute of Technology, Pasadena, USA 
Bogdan Craciun; Kaushik Bhattacharya. Effective motion of a curvature-sensitive interface through a heterogeneous medium. Interfaces and free boundaries, Tome 6 (2004) no. 2, pp. 151-173. doi: 10.4171/ifb/95
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