Pulse propagation in decorated random chains

TL;DR

This paper investigates pulse propagation in one-dimensional chains of spherical granules with random small decorations, extending effective models and binary collision approximations to predict pulse behavior in such complex systems.

Contribution

It extends existing effective descriptions and binary collision approximations to analyze pulse dynamics in randomly decorated granular chains.

Findings

Effective description can predict pulse properties in random chains.

Binary collision approximation provides analytical insights.

Randomly sized decorations influence pulse propagation characteristics.

Abstract

We study pulse propagation in one-dimensional chains of spherical granules decorated with small randomly-sized granules placed between bigger monodisperse ones. Such "designer chains" are of interest in efforts to control the behavior of the pulse so as to optimize its propagation or attenuation, depending on the desired application. We show that a recently proposed effective description of simple decorated chains can be extended to predict pulse properties in chains decorated with small granules of randomly chosen radii. Furthermore, we also show that the binary collision approximation can again be used to provide analytic results for this system.