Zero-range model of traffic flow

Kaupužs, J.; Mahnke, Reinhard; Rj, Harris

doi:10.1103/physreve.72.056125

Cited by 60 publications

(68 citation statements)

References 23 publications

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“…Examples include shaken granular gasses [1], vehicular traffic [2][3][4], the macroeconomics of wealth distribution [5,6], and others [7,8]. Mechanisms that can lead to the formation of condensates have been studied extensively in recent years, mainly by analyzing prototypical toy models.…”

Section: Introductionmentioning

confidence: 99%

Emergent motion of condensates in mass-transport models

2013

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We examine the effect of spatial correlations on the phenomenon of real-space condensation in driven masstransport systems. We suggest that in a broad class of models with a spatially correlated steady state, the condensate drifts with a nonvanishing velocity. We present a robust mechanism leading to this condensate drift. This is done within the framework of a generalized zero-range process (ZRP) in which, unlike the usual ZRP, the steady state is not a product measure. The validity of the mechanism in other mass-transport models is discussed.

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Section: Introductionmentioning

confidence: 99%

Emergent motion of condensates in mass-transport models

2013

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“…For previous work focusing on the description of jam formation as a nucleation process, see [11,12,13,14]. It is related to phase separation and metastability in low-dimensional driven systems, a topic which has attracted much recent interest [15,16,17,18,19]. Metastability and hysteresis effects have been observed in real traffic, see, e. g., [20,21,22,23,24,25,26] for discussion of empirical data and the various different modelling approaches.…”

Section: Introductionmentioning

confidence: 99%

Application of thermodynamics to driven systems

et al. 2007

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Abstract. Application of thermodynamics to driven systems is discussed. As particular examples, simple traffic flow models are considered. On a microscopic level, traffic flow is described by Bando's optimal velocity model in terms of accelerating and decelerating forces. It allows to introduce kinetic, potential, as well as total energy, which is the internal energy of the car system in view of thermodynamics. The latter is not conserved, although it has certain value in any of two possible stationary states corresponding either to fixed point or to limit cycle in the space of headways and velocities. On a mesoscopic level of description, the size n of car cluster is considered as a stochastic variable in master equation. Here n = 0 corresponds to the fixed-point solution of the microscopic model, whereas the limit cycle is represented by coexistence of a car cluster with n > 0 and free flow phase. The detailed balance holds in a stationary state just like in equilibrium liquid-gas system. It allows to define free energy of the car system and chemical potentials of the coexisting phases, as well as a relaxation to a local or global free energy minimum. In this sense the behaviour of traffic flow can be described by equilibrium thermodynamics. We find, however, that the chemical potential of the cluster phase of traffic flow depends on an outer parameter -the density of cars in the free-flow phase. It allows to distinguish between the traffic flow as a driven system and purely equilibrium systems.

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“…One is interested in the properties of the stationary state generated by the stochastic dynamics, for example the single-site mass distribution which is the probability distribution of the amount of mass at a lattice site. Such models provide both microscopic and effective descriptions of the dynamics of various complex systems, for example traffic flow [3,4], granular clustering [5], phase ordering [6], network rewiring [7,8], force propagation [9], aggregation and fragmentation [10,11] and energy transport [12]. In this paper we study another realisation of stochastic mass transport in a new context: the sampling of polydispersity in simulations of hard-rod systems.…”

Section: Introductionmentioning

confidence: 99%

Condensation transition in polydisperse hard rods

Evans

Majumdar

Pagonabarraga

et al. 2010

The Journal of Chemical Physics

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We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume v, with the constraint of a fixed total volume V = N i=1 vi, N being the total number of particles. The particles, referred to as p-spheres, have a linear size that behaves as v 1/p i and our model thus represents a gas of polydisperse hard rods with variable diameters v 1/p i . We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed N and V . Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for p > 1: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles.

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Zero-range model of traffic flow

Cited by 60 publications

References 23 publications

Emergent motion of condensates in mass-transport models

Emergent motion of condensates in mass-transport models

Application of thermodynamics to driven systems

Condensation transition in polydisperse hard rods

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