Pinning and de-pinning phenomena in front propagation in heterogeneous media

Reference:

Dirr, N. and Yip, N. K., 2006. Pinning and de-pinning phenomena in front propagation in heterogeneous media. Interfaces and Free Boundaries, 8 (1), pp. 79-109.

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Abstract

This paper investigates the pinning and de-pinning phenomena of some evolutionary partial differential equations which arise in the modelling of the propagation of phase boundaries in materials under the combined effects of an external driving force F and an underlying heterogeneous environment. The phenomenology is the existence of pinning states - stationary solutions - for small values of F, and the appearance of genuine motion when F is above some threshold value. In the case of a periodic medium, we characterise quantitatively, near the transition regime, the scaling behaviour of the interface velocity as a function of F. The results are proved for a class of semilinear and reaction-diffusion equations.

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