Renormalization-group study of the Nagel-Schreckenberg model
Teoh, Han Kheng
Yong, Ee Hou
Date of Issue2018
School of Physical and Mathematical Sciences
We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p=0, the dynamics remain invariant in each renormalization-group (RG) transformation. Two fully attractive fixed points, ρ∗c=0 and 1, and one unstable fixed point, ρ∗c=1/(vmax+1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various vmax. The critical exponent appears to decrease weakly with v max from ν=1.62 to the asymptotical value of 1.00. For the random case p>0, the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p→0 is studied with simulation, and the RG flow in the ρ−p plane is obtained. The fixed points p=0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.
Physical Review E
© 2018 American Physical Society. This paper was published in Physical Review E and is made available as an electronic reprint (preprint) with permission of American Physical Society. The published version is available at: [http://dx.doi.org/10.1103/PhysRevE.97.032314]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.