Travelling with/against the flow. Deterministic diffusive driven systems

TL;DR

This paper introduces a deterministic lattice model for oppositely charged particles under a constant electric field, analyzing traffic flow dynamics, phase transitions, and velocity-density relationships.

Contribution

It presents a novel deterministic model for bidirectional traffic flow and characterizes its phase diagram and fundamental diagram.

Findings

Identification of free, jammed, and hysteresis phases.

Analysis of how particle velocities depend on densities.

Characterization of phase transitions in the system.

Abstract

We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars moving in opposite directions along a narrow road. Our main results concern the Fundamental diagram of the system describing the dependence of average particle velocities on their densities and the Phase diagram describing the partition of the space of particle configurations into regions having different qualitative properties, which we identify with free, jammed and hysteresis phases.