Renormalization-group study of the Nagel-Schreckenberg model

Physical Review. E
Han Kheng Teoh, Ee Hou Yong

Abstract

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/(v_{max}+1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various v_{max}. 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.

References

Jun 15, 1992·Physical Review. a·D ben-Avraham, J Köhler
Mar 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A VespignaniL Pietronero
Apr 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·K Nagel, M Paczuski
Apr 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M SchreckenbergN Ito
Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S KraussC Gawron
Sep 30, 1991·Physical Review Letters·J Krug
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S CheybaniM Schreckenberg
Apr 17, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·S CheybaniM Schreckenberg
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·X LiR Jiang
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J de Gier, B Nienhuis
Mar 24, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Najem Moussa
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A M C Souza, L C Q Vilar
Feb 2, 2013·Physical Review Letters·A S de WijnP Schall
Mar 17, 2017·Physical Review. E·M L L Iannini, Ronald Dickman

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.

Related Papers

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
C CastellanoL Pietronero
Physical Review Letters
M E Fisher, M Randeria
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
C Itoi, H Mukaida
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Jian-Xin Le, Z R Yang
© 2022 Meta ULC. All rights reserved