Pulse Velocity in a Granular Chain

TL;DR

This paper compares continuum and binary collision models to analyze pulse propagation in granular chains, highlighting their respective strengths depending on particle interaction softness.

Contribution

It evaluates the applicability of two distinct analytical approaches to pulse propagation in granular chains, providing insights into their accuracy for different potential types.

Findings

Continuum model is more accurate for softer potentials.

Binary collision approximation works better for harder potentials.

Both methods capture qualitative features of pulse propagation.

Abstract

We discuss the applicability of two very different analytic approaches to the study of pulse propagation in a chain of particles interacting via a Hertz potential, namely, a continuum model and a binary collision approximation. While both methods capture some qualitative features equally well, the first is quantitatively good for softer potentials and the latter is better for harder potentials.