Depinning transitions in discrete reaction-diffusion equations
Materials Science
2007-05-23 v1 Statistical Mechanics
Abstract
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of traveling waves to steady solutions near threshold and give conditions for front pinning (propagation failure). The critical parameter values are characterized at the depinning transition and an approximation for the front speed just beyond threshold is given.
Cite
@article{arxiv.cond-mat/0208405,
title = {Depinning transitions in discrete reaction-diffusion equations},
author = {A. Carpio and L. L. Bonilla},
journal= {arXiv preprint arXiv:cond-mat/0208405},
year = {2007}
}
Comments
27 pages, 12 figures, to appear in SIAM J. Appl. Math