ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), School of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia.
Institut für Theoretische Physik, Universität zu Köln, 50937 Cologne, Germany.
Phys Rev E. 2019 Nov;100(5-1):052111. doi: 10.1103/PhysRevE.100.052111.
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 v_{max}=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 v_{max}>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.
动力普适类以其动力指数 z 和独特的标度函数来区分，这些函数编码了时空非对称性，例如，慢松弛模式或时间积分电流的分布。到目前为止，Nagel-Schreckenberg（NaSch）模型的普适类还不知道，该模型是高速公路交通流的典范模型。仅当模型对应的最大速度 v_{max}=1 时，该模型才属于具有 z=3/2 的超扩散 Kardar-Parisi-Zhang（KPZ）类。在本文中，我们表明，对于一般的最大速度 v_{max}>1，NaSch 模型也属于 KPZ 类。我们使用非线性涨落流体力学理论计算了非普适系数，确定了动力结构函数和时间积分电流分布的精确渐近解。大尺度蒙特卡罗模拟的结果与没有任何拟合参数的精确渐近 KPZ 解匹配。此外，我们发现非普适的早期效应或初始条件的选择可能会对动力指数的数值确定产生强烈影响，从而导致不确定的结果。我们还表明，通过将模型扩展到具有变道规则的双车道 NaSch 模型，普适类不会改变。
