Phase Transitions in the Time Synchronization Model

摘要

There are two types i=1,2 of particles on the line {f 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}lpha _{ij}. We find phase transitions in the clusterization (synchronization) behavior of this system of particles on different time scales t=t(N) relative to N=N_{1}+N_{2}.