Fronts in lattices

Abstract

Simple models of defect motion in lattices identify dislocations [1] and cracks [8,9] with discrete traveling waves [4,10]. In overdamped limits, such lattice models often become discrete bistable equations [3,5], similar to the ones encountered in biology (to describe nerve propagation [7], for instance). In this talk, we will review recent results on front propagation in spatially discrete models, discussing existence of stationary and travelling wave fronts [2,5,6] together with strategies to predict their speeds and the thresholds for propagation failure [3].