A Langevin Approach to One-Dimensional Granular Media Fluidized by Vibrations

TL;DR

This paper introduces a Langevin-based theoretical model to describe the steady-state behavior of one-dimensional vibrated granular media, providing analytical predictions that match simulation results.

Contribution

It develops a linear Langevin equation framework for granular media fluidized by vibrations, deriving analytical expressions for macroscopic quantities and power spectra.

Findings

Good agreement between theory and molecular dynamics simulations.

Analytical expressions accurately predict the center of mass dynamics.

Power spectrum of the center of mass height is successfully derived.

Abstract

We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this framework, we derive analytical expressions for several macroscopic quantities. We also predict the power spectrum for the height of the center of mass. We find good agreement between our theoretical predictions and extensive event-driven molecular dynamics simulations.