# Homogeneous dynamics in a vibrated granular monolayer

## TL;DR

This paper models a vibrated granular monolayer using inelastic hard spheres, deriving temperature evolution equations and validating them with molecular dynamics simulations, revealing detailed insights into the system's behavior.

## Contribution

It introduces a kinetic model for a vibrated granular monolayer and derives temperature evolution equations with strong agreement to simulations.

## Key findings

- Theoretical predictions match molecular dynamics results for temperature dynamics.
- Derived equations accurately describe stationary and transient temperature behaviors.
- Model effectively captures the physics of vibrated granular monolayers.

## Abstract

A simple model of a vibrated granular monolayer is studied. It consists of inelastic hard spheres confined between two parallel hard plates separated a distance smaller than twice the diameter of the particles. Both walls are elastic and one of them is vibrating in a sawtooth way. For low densities, a kinetic equation is proposed from which closed evolution equations for the horizontal and vertical temperatures are derived assuming spatial homogeneity and that the system is very thin. An excellent agreement between the theoretical predictions and Molecular Dynamics simulation results is obtained both, for the stationary values and for the dynamics of the temperatures.