Fluid-like behavior of a one-dimensional granular gas

TL;DR

This paper investigates the fluid-like behavior of a one-dimensional inelastic granular gas, revealing clustering, non-Gaussian velocity distributions, and sub-diffusive transport properties through molecular dynamics simulations.

Contribution

It provides a detailed analysis of the average properties, fluctuations, clustering, and transport phenomena in a 1D granular gas with inelastic collisions, supported by simulations.

Findings

Velocity distributions are slightly non-Gaussian.

Density field exhibits clustering with a peak in the structure factor.

Transport is sub-diffusive with <|x(t)-x(0)|^2> ~ t^{1/2}.

Abstract

We study the properties of a one-dimensional (1D) granular gas consisting of $N$ hard rods on a line of length $L$ (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature $T_b$ and viscosity $\gamma$. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature $T_g=m< v^2>$, kinetic pressure and density $\rho=N/L$. Thereafter, we consider the fluctuations around the average behavior obtaining a slightly non-Gaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the $k \sim 0$ region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical sub-diffusive behavior of 1D stochastically driven systems, i.e. $<|x(t)-x(0)|^2 > \sim Dt^{1/2}$ where $D$ for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave-vectors.