JournalsifbVol. 6, No. 2pp. 151–173

Effective motion of a curvature-sensitive interface through a heterogeneous medium

  • Bogdan Craciun

    Synopsys, Inc., Mountain View, USA
  • Kaushik Bhattacharya

    California Institute of Technology, Pasadena, USA
Effective motion of a curvature-sensitive interface through a heterogeneous medium cover
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Abstract

This paper deals with the evolution of fronts or interfaces propagating with normal velocity vn=fcκv_n = f - c \kappa where ff is a spatially periodic function, cc a constant and κ\kappa 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 ff is small compared to the macroscopic dimensions, and show that the overall front is governed by a geometric law vn=fˉ(n)v_n = \bar{f}(n). We illustrate the results using examples. We also provide an explicit characterization of fˉ\bar{f} in the limit cc \rightarrow \infty.

Cite this article

Bogdan Craciun, Kaushik Bhattacharya, Effective motion of a curvature-sensitive interface through a heterogeneous medium. Interfaces Free Bound. 6 (2004), no. 2, pp. 151–173

DOI 10.4171/IFB/95