Three-dimensional fundamental diagram of particle system of 5 neighbors with two conserved densities

TL;DR

This paper develops a three-dimensional fundamental diagram for a particle system with five neighbors and two conserved densities, revealing phase transitions and proposing similar systems with unique dependencies.

Contribution

It introduces a novel three-dimensional fundamental diagram for a specific particle system and demonstrates phase transition behavior, also proposing related systems with similar properties.

Findings

Fundamental diagram depends uniquely on two densities.

Phase transition observed in asymptotic behavior.

Proposed systems exhibit similar dependency numerically.

Abstract

We discuss a particle system of 5 neighbors with two independent conserved densities. The mean momentum uniquely depends on a pair of the densities and a three-dimensional fundamental diagram is obtained. It shows the phase transition of behavior of asymptotic solution to the system. Moreover, we propose two other systems which have the similar unique dependency obtained numerically.