turkmath.org

In this talk, we consider a model of granular chains interacting only with the nearest neighbour through a Hertzian force (physically, one should think about an infinite line of tightly packed metal beads). This is a highly non-linear model, for which we show that travelling waves exist. In addition, we show such waves are bell-shaped and in some cases, they are compactons (i.e. have an unusual double exponential rate of decay). We also consider the same issues for more sophisticated models (with pre-compressed beads), as well as the mass-in-mass system (in which each bead has an internal mass embedded into it). Our approach is through calculus of variations for the corresponding non-standard functionals, but some simple Fourier analysis comes into play as well. This is based on a series of papers with Panos Kevrekidis (University of Massachusetts).