Pulse Propagation in Granular Chains

We study pulse propagation in one-dimensional granular chains of spherical granules. Our goal is to develop an analytic approach that makes it possible to predict pulse properties as a function of time. Our method is based on a binary collision approximation that reduces the problem to collisions involving only two granules at a time. We illustrate the procedure and show quantitative agreement with exact numerical simulations for chains with smoothly varying granular profiles. For some more complex configurations (specifically, for decorated chains) we first replace the actual chain with a chain of smooth profile with renormalized masses and intergranular interactions. The binary collision approximation is then applied to this effective chain. Quantitative agreement with numerical simulations of the original chain is again shown. Further applications of the approach are briefly mentioned.