Conservation principles in solitary impulse propagation through granular chains

An independent-collision model is advanced as a conceptually simple and computationally convenient framework for understanding non-linear impulse propagation in granular chains. In particular, conservation principles are used to show that the independent-collision model supports solitons in uniform granular chains, and exhibits an exponential dispersion of momentum and energy in tapered chains. These results are in qualitative agreement with recent detailed simulations of Hertzian spheres by Sen et al. (Physica A 299 (2001) 551). Near-quantitative agreement is achieved by renormalizing the width of an independent impulse by the solitary wave width. The model is easily extended, as we demonstrate by incorporating the effects of restitution.