Coupled Leidenfrost States as a Monodisperse Granular Clock

TL;DR

This paper demonstrates that monodisperse granular beads in coupled columns can oscillate as a granular clock due to density-inverted states, with a minimal model explaining the mechanism as a Hopf bifurcation.

Contribution

It introduces a new type of granular oscillation driven by Leidenfrost-like effects and provides a minimal theoretical model for understanding the phenomenon.

Findings

Oscillations occur only within an intermediate coupling strength range.

The phase diagram is characterized by the height of the density-inverted structure.

The minimal two-phase model reproduces the oscillatory behavior observed in simulations.

Abstract

Using an event-driven molecular dynamics simulation, we show that simple monodisperse granular beads confined in coupled columns may oscillate as a new type of granular clock. To trigger this oscillation, the system needs to be driven against gravity into a density-inverted state, with a high-density clustering phase supported from below by a gas-like low-density phase (Leidenfrost effect) in each column. Our analysis reveals that the density-inverted structure and the relaxation dynamics between the phases can amplify any small asymmetry between the columns, and lead to a giant oscillation. The oscillation occurs only for an intermediate range of the coupling strength, and the corresponding phase diagram can be universally described with a characteristic height of the density-inverted structure. A minimal two-phase model is proposed and linear stability analysis shows that the triggering mechanism of the oscillation can be explained as a switchable two-parameter Hopf bifurcation. Numerical solutions of the model also reproduce similar oscillatory dynamics to the simulation results.