Universität zu Köln

de Gier, Jan, Schadschneider, Andreas ORCID: 0000-0002-2054-7973, Schmidt, Johannes and Schuetz, Gunter M. (2019). Kardar-Parisi-Zhang universality of the Nagel-Schreckenberg model. Phys. Rev. E, 100 (5). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2470-0053

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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 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code de Gier, Jan UNSPECIFIED UNSPECIFIED UNSPECIFIED Schadschneider, Andreas UNSPECIFIED orcid.org/0000-0002-2054-7973 UNSPECIFIED Schmidt, Johannes UNSPECIFIED UNSPECIFIED UNSPECIFIED Schuetz, Gunter M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-127811
DOI:	10.1103/PhysRevE.100.052111
Journal or Publication Title:	Phys. Rev. E
Volume:	100
Number:	5
Date:	2019
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2470-0053
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CELLULAR-AUTOMATA MODELS; SCALING FUNCTIONS; RANDOM MATRICES; GROWTH-MODELS; HYDRODYNAMICS; DISTRIBUTIONS; FLUCTUATIONS; SYSTEM; LIMIT Multiple languages Physics, Fluids & Plasmas; Physics, Mathematical Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12781