Phase transitions in the time synchronization model

TL;DR

This paper investigates phase transitions in a two-type particle synchronization model on the real line, analyzing how cluster formation depends on system size and time scales, extending previous work on time synchronization dynamics.

Contribution

It identifies phase transitions in clusterization behavior of a two-type particle system, revealing how synchronization patterns change with different time scales and system sizes.

Findings

Discovered phase transitions in clusterization behavior.

Analyzed synchronization on various time scales.

Extended understanding of particle synchronization dynamics.

Abstract

We continue the study of the time synchronization model from arXiv:1201.2141 . There are two types $i=1,2$ of particles on the line $R$, with $N_{i}$ particles of type $i$. Each particle of type $i$ moves with constant velocity $v_{i}$. Moreover, any particle of type $i=1,2$ jumps to any particle of type $j=1,2$ with rates $N_{j}^{-1}\alpha_{ij}$. We find phase transitions in the clusterization (synchronization) behaviour of this system of particles on different time scales $t=t(N)$ relative to $N=N_{1}+N_{2}$.