The Phases of a Discrete Flow of Particles on Graphs

H. Ekstrom

2020, v.26, Issue 2, 343-364

ABSTRACT

We study in detail the linear flow of particles on a graph with one vertex and $k+1$ infinite edges. This has a rich environment with many different emergent behaviours depending on the system parameters. The abrupt change in the behaviour of the system along a continuous change of the parameters manifests multiple phase transitions.
We discuss the physical interpretation of the considered simple model of particle flows and find that it adheres to the fundamental laws of electricity discovered by Ohm and Kirchhoff.
This study paves the way for further analysis of discrete flows on more complicated graphs.

Keywords: dynamics classification, state space partitioning, limit sets, repulsion modelling