Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model

Jan de Gier, Andreas Schadschneider, Johannes Schmidt, and Gunter M. Schütz
Phys. Rev. E 100, 052111 – Published 12 November 2019

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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
3 More
  • Received 8 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.052111

©2019 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Jan de Gier1, Andreas Schadschneider2, Johannes Schmidt2,3, and Gunter M. Schütz4

  • 1ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia
  • 2Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany
  • 3Bonacci GmbH, Robert-Koch-Strasse 8, 50937 Cologne, Germany
  • 4Theoretical Soft Matter and Biophysics, Institute of Complex Systems II, Forschungszentrum Jülich, 52425 Jülich, Germany

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 100, Iss. 5 — November 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×