Highly Nonlinear Solitary Waves in Heterogeneous Periodic Granular Media

I have finally realized one of my life-long dreams: I now have a published paper that starts on page 666. (Who could ask for anything more?) And it's especially appropriate in this case, too, as the revisions for this particular paper were painful and entirely author-inflicted. Basically, the two referees (both of whom told us who they were during the process) asked only for trivial changes that took up about 0.25 % or less of the revision effort. We, on the other hand, had to deal with the fact that (among other things) the Caltech machine shop labeled "brass" as "bronze", which required us to rerun all of the numerical simulations with new (and correct!) parameter values. There were other issues as well, such as quadruple-checking the analytics and an extremely annoying factor of \sqrt{2}. So this paper really deserves to start on page 666, given all of the self-inflicted pain. It now has volume, issue, and page numbers, which means we're officially done, done, DONE with it! On to the next papers (which includes several follow-up papers to this article)!

Oh, and here are the title, authors, and abstract.

Title: Highly nonlinear solitary waves in heterogeneous periodic granular media

Authors: Mason A. Porter, Chiara Daraio, Ivan Szelengowicz, Eric B. Herbold, and P.G. Kevrekidis

Abstract: We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, brass, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find good agreement between experiments and numerical simulations. We also find good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system.