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000868303 0247_ $$2doi$$a10.1103/PhysRevE.100.052111
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000868303 0247_ $$2ISSN$$a1550-2376
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000868303 1001_ $$00000-0001-5415-3318$$ade Gier, Jan$$b0$$eCorresponding author
000868303 245__ $$aKardar-Parisi-Zhang universality of the Nagel-Schreckenberg model
000868303 260__ $$aWoodbury, NY$$bInst.$$c2019
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000868303 520__ $$aDynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case vmax=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z=3/2. In this paper, we show that the NaSch model also belongs to the KPZ class for general maximum velocities vmax>1. Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. The results of large-scale Monte Carlo simulations match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with lane-changing rules.
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000868303 7001_ $$0P:(DE-Juel1)130966$$aSchütz, Gunter M.$$b3
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