Renormalization-group study of the Nagel-Schreckenberg model

• Main Authors: Teoh, Han Kheng, Yong, Ee Hou
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2018
• Subjects: Nagel-Schreckenberg Model; Renormalization Group
• Online Access: https://hdl.handle.net/10356/85085; http://hdl.handle.net/10220/45142
• Institution: Nanyang Technological University

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.