# Exclusion in Junction Geometries

## TL;DR

This paper studies the complex dynamics of particle flow in junction geometries within the asymmetric exclusion process, revealing rich spatial structures, phase diagrams, and the effects of initial conditions and boundary rates.

## Contribution

It introduces a detailed analysis of exclusion processes at junctions, including phase diagrams and the impact of initial densities and boundary conditions, which advances understanding of transport phenomena in networked systems.

## Key findings

- Rich spatial structures in density profiles at junctions
- Phase diagram characterization of open systems with boundary rates
- Impact of initial conditions on wave dynamics and flow patterns

## Abstract

We investigate the dynamics of the asymmetric exclusion process at a junction. When two input roads are initially fully occupied and a single output road is initially empty, the ensuing rarefaction wave has a rich spatial structure. The density profile also changes dramatically as the initial densities are varied. Related phenomenology arises when one road feeds into two. Finally, we determine the phase diagram of the open system, where particles are fed into two roads at rate $\alpha$ for each road, the two roads merge into one, and particles are extracted from the single output road at rate $\beta$.