Journal Article

FZJ-2019-06853

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model

de Gier, J. (Corresponding author) ; Schadschneider, A. ; Schmidt, J. ; Schütz, G. M.FZJ*

2019
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/23751  doi:10.1103/PhysRevE.100.052111

Abstract: Dynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case vmax=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z=3/2. In this paper, we show that the NaSch model also belongs to the KPZ class for general maximum velocities vmax>1. Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. The results of large-scale Monte Carlo simulations match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with lane-changing rules.

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Contributing Institute(s):

1. Theorie der Weichen Materie und Biophysik (ICS-2)

Research Program(s):

1. 551 - Functional Macromolecules and Complexes (POF3-551) (POF3-551)

Appears in the scientific report 2019

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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