Comment on “Critical behavior of a traffic flow model”

Chowdhury, Debashish; Kertész, János; Nagel, Kai; Santen, Ludger; Schadschneider, Andreas

doi:10.1103/physreve.61.3270

Cited by 373 publications

(549 citation statements)

References 13 publications

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“…Finally, from these ratios, we can estimate the value of the critical exponent ν || . We found the values 1.8(1) for the linear chain, 1.21 (8) for the square lattice and 1.13(8) for the cubic lattice. In Fig.…”

Section: Dynamic Monte Carlo Simulationsmentioning

confidence: 83%

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Catalysis with competitive reactions: static and dynamical critical behavior

Costa

Figueiredo²

2003

Braz. J. Phys.

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We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A → A2 and A + B → AB, where A and B are two monomers that arrive at the surface with probabilities y A and y B , respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter y A is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents β, ν ⊥ and the dynamical critical exponents ν || , δ, η and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class. I IntroductionIn the course of the last decade the statistical mechanics community has made great progress in the study of nonequilibrium phenomena. Until now, we do not have a complete theory accounting for the nonequilibrium systems. The fundamental concept of a Gibbsian distribution of states in equilibrium has no counterpart in the nonequilibrium situation. This happens because many of these systems do not present even an hamiltonian function and, if it is possible to define an hamiltonian, the detailed balance would be violated.Examples of recent problems on nonequilibrium processes include markets [1, 2], rain precipitation [3], sandpiles [4] and conserved contact process [5]. There is also a great interest in modeling interface growth [6,7], traffic flow [8], temperature dependent catalytic reactions [9], etc. Nonequilibrium magnetic systems, with a well defined hamiltonian, have been also studied in the context of nonequilibrium processes [10,11] as well.For the equilibrium systems we can induce phase transitions by changing some external parameters. Usually, the temperature is the selected control parameter to study phase transitions between equilibrium states. In the case of continuous phase transitions, at the critical point, long range correlations are established inside the system and a set of critical exponents can be defined to describe the critical behavior of some thermodynamic properties. The renormalization group theory [12] is a well known theory that allows the calculation of these critical exponents.We can also consider external constraints for the nonequilibrium systems that can drive the dynamical behavior of the system. The nature of the external parameter depends on the nature of the system. For instance, in an epidemic mode...

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Section: Dynamic Monte Carlo Simulationsmentioning

confidence: 83%

“…There is also a great interest in modeling interface growth [6,7], traffic flow [8], temperature dependent catalytic reactions [9], etc. Nonequilibrium magnetic systems, with a well defined hamiltonian, have been also studied in the context of nonequilibrium processes [10,11] as well.…”

Section: Introductionmentioning

confidence: 99%

Catalysis with competitive reactions: static and dynamical critical behavior

Costa

Figueiredo²

2003

Braz. J. Phys.

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“…The paradigmatic model of driven lattice gases is the one-dimensional totally asymmetric simple exclusion process (TASEP) [4,5], which exhibits boundary induced phase transitions [6] and the steady state of which is exactly known [7,8]. Beside theoretical interest, this model and its numerous variants have found a wide range of applications, such as the description of vehicular traffic [9] or modeling of transport processes in biological systems [10]. Inspired by the traffic of cytoskeletal motors [11], such models were introduced where a totally asymmetric exclusion process is coupled to a finite compartment where the motion of particles is diffusive [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

Juhász

2007

Phys. Rev. E

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We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system. Stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit, by solving the differential equations describing the steady state of the system, analytically for vanishing total current and numerically for nonzero total current. The system possesses phases with a localized shock in the density profile in one of the lanes, similarly to exclusion processes endowed with nonconserving kinetics in the bulk. Besides, the system undergoes a discontinuous phase transition, where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk. This phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process, however, as a consequence of the interaction between lanes, the density profiles are deformed and in the case of asymmetric lane change, the motion of the shocks is confined to a limited domain.

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“…Because the distribution of spacing reflects the unmeasurable interaction forces or potentials between vehicles that governs their motions, increasing investigation are put into this field to reveal the complex dynamics of vehicle traffic flow and explain some important phenomena, i.e. phrase transition [1], [2], [3], [4].…”

Section: Introductionmentioning

confidence: 99%

Modeling of spacing distribution of queuing vehicles at signalized junctions using random-matrix theory

Jin

Zhang

et al. 2009

Tinshhua Sci. Technol.

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Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to explain the spacing distribution of queuing vehicles in front of a signalized junction based on random-matrix theory. We show that the recently measured spacing distribution data well fit the spacing distribution of a Gaussian symplectic ensemble (GSE). These results are also compared with the spacing distribution observed for car parking problem. Why vehicle-stationary-queuing and vehicle-parking have different spacing distributions (GSE vs GUE) seems to lie in the difference of driving patterns.

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Comment on “Critical behavior of a traffic flow model”

Cited by 373 publications

References 13 publications

Catalysis with competitive reactions: static and dynamical critical behavior

Catalysis with competitive reactions: static and dynamical critical behavior

Weakly coupled, antiparallel, totally asymmetric simple exclusion processes

Modeling of spacing distribution of queuing vehicles at signalized junctions using random-matrix theory

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