Universal behaviors in granular flows and traffic flows

TL;DR

This paper reviews universal behaviors in granular and traffic flows, analyzing models through nonlinear techniques and simulations, revealing consistent patterns and spectral properties across these systems.

Contribution

It introduces a weakly nonlinear analysis of traffic flow models and a noise-augmented granular flow model that reproduces specific spectral behaviors.

Findings

Confirmed the validity of the nonlinear analysis through simulations.

Identified the propagating velocity, amplitude, and interface width in traffic flow models.

Reproduced the power spectrum scaling in granular pipe flow with added white noise.

Abstract

We review the current understanding on universal behaviors in granular flows through a vertical pipe and traffic flows. We carry out weakly nonlinear analysis of a model for traffic flows based on the technique of soliton perturbations, and determine the selected propagating velocity, the amplitude, the width of interfaces connecting between jam phase and non-jam phase. From the direct simulation of the model, we have confirmed the validity of our theoretical analysis. We also introduce a model for granular pipe flow supplemented by the white noise, which reproduces $P(f)\sim f^{-4/3}$, where $P(f)$ is the power spectrum in the frequency $f$.