Highly Nonlinear Solitary Waves in Phononic Crystal Dimers

My paper, Highly Nonlinear Solitary Waves in Phononic Crystal Dimers, was just published as a "rapid communication" in Physical Review E. (For those of you who don't know the lingo, that means we almost pushed it into PRL but couldn't quite get it in there.)

My coauthors on the paper are theorist Panos Kevrekidis and experimentalists Chiara Daraio, Eric Herbold, and Ivan Szelengowicz (Chiara's grad student).

Here is the project in English: We have a chain of beads in which soft particles alternate with harder ones. We hit the thing and look at the properties of the pulse that goes through the system---basically, how its width and propagation speed depend on the properties of the beads and on having two different types of them (and the ensuing periodic structure) in the first place. We do analytics, numerics, and experiments and have some nice agreement between the three. (In fact, the analytics even got pretty technical in this paper.)

Here is the official abstract, which many of you will probably find much less understandable than what I just wrote (if you look closely, however, you can see that it basically says the same thing as what I just wrote---just without the technical terms that make things more precise): We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (
stainless steel) are alternated with softer and lighter ones
(polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and also provides key insights into the influence of the dimer lattice on the properties
width and propagation speed of the highly nonlinear wave solutions.