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@ARTICLE{deGier:868303,
      author       = {de Gier, Jan and Schadschneider, Andreas and Schmidt,
                      Johannes and Schütz, Gunter M.},
      title        = {{K}ardar-{P}arisi-{Z}hang universality of the
                      {N}agel-{S}chreckenberg model},
      journal      = {Physical review / E},
      volume       = {100},
      number       = {5},
      issn         = {2470-0045},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2019-06853},
      pages        = {052111},
      year         = {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.},
      cin          = {ICS-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)ICS-2-20110106},
      pnm          = {551 - Functional Macromolecules and Complexes (POF3-551)},
      pid          = {G:(DE-HGF)POF3-551},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:31869969},
      UT           = {WOS:000495976600001},
      doi          = {10.1103/PhysRevE.100.052111},
      url          = {https://juser.fz-juelich.de/record/868303},
}