Steady state properties of a driven granular medium

TL;DR

This study investigates a driven two-dimensional granular system reaching a critical steady state with scale-invariant correlations, power-law distributions, and anomalous diffusion, revealing complex non-equilibrium behavior.

Contribution

It demonstrates that a driven granular medium attains a critical state characterized by scale-free correlations and power-law energy dissipation, with novel insights into particle dynamics.

Findings

Velocity distribution is Maxwellian in steady state

Correlation functions follow power-law scaling

Energy dissipation obeys a power-law distribution

Abstract

We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic collision between particles. The velocities of the particles in the steady state satisfy the Maxwellian distribution. We measure the density-density correlation and the velocity-velocity correlation functions in the steady state and find that they are of power-law scaling forms. The locations of collision events are observed to be time-correlated and such a correlation is described by another power-law form. We also find that the dissipated energy obeys a power-law distribution. These results indicate that the system evolves into a critical state where there are neither characteristic spatial nor temporal scales in the correlation functions. A test particle exhibits an anomalous diffusion which is apparently similar to the Richardson law in a three-dimensional turbulent flow.