Phase transitions in the time synchronization model

Details Phase transitions in the time synchronization model Phase transitions in the time synchronization model

2012-01-17

arxiv.org/abs/1201.3550v1

Theory Probab. Appl. 50, pp. 134-141 (2006)

Physics

Mathematical Physics

10 pages; first published in Theory Probab. Appl. 50, pp. 134-141 (2006); small corrections in text of the paper; bibliography

Scientific paper

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 $N=N_{1}+N_{2}$.

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