Driven lattice gas with nearest-neighbor exclusion: shear-like drive

We study the lattice gas with nearest-neighbor exclusion on the square lattice and Kawasaki (hopping) dynamics, under the influence of a nonuniform drive, via Monte Carlo simulation. The drive, which favors motion along the +x direction and inhibits motion in the opposite direction, varies linearly with y. (The boundaries along the drive direction are periodic, so that the system is not described by an equilibrium Gibbs distribution.) As in the uniformly driven case [R. Dickman, Phys. Rev. E 64, 16124 (2001)], the onset of sublattice ordering occurs at a lower density than in equilibrium, but here an unexpected feature appears: particles migrate out of the high-drive region. For intermediate system sizes (L ≃100), the accumulation of particles is sufficient for the low-drive region to become ordered at a global density of about 0.3. Above this density we observe a surprising reversal in the density profile, with particles accumulating to the high-drive region, due to jamming. For larger systems (L≥200) particles quickly jam in the high-drive region, as occurs under uniform drive, and the accumulation of particles in the low-field region is severely reduced.     

Dynamical diversity and metastability in a hindered granular column near jamming

Granular media jam into a panoply of metastable states. The way in which these states are achieved depends on the nature of local and global constraints on grains; here we investigate this issue by means of a non-equilibrium stochastic model of a hindered granular column near its jamming limit. Grains feel the constraints of grains above and below them differently, depending on their position. A rich phase diagram with four dynamical phases (ballistic, activated, logarithmic and glassy) is revealed. The statistics of the jamming time and of the metastable states reached as attractors of the zero-temperature dynamics is investigated in each of these phases. Of particular interest is the glassy phase, where intermittency and a strong deviation from Edwards' flatness are manifest.     

Volatile jam and flow fluctuation in counter flow of slender particles

We study the counter flow of slender particles on square lattice under periodic boundaries. Two types of particles going to the right and to the left are taken into account, where the size of right particles is larger than that of left particles. The counter flow of slender particles with different sizes is compared with that of slender particles with the same size. The jamming transition occurs at a critical density. Near the transition point, the volatile jam appears with a period, disappears in time, is formed again, and the process occurs repeatedly. The flow fluctuates highly by forming the volatile jam. The volatile jam moves slowly to the left direction, while the jam is stationary when the size of right particles equals that of left particles.     

Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference

A modified two-dimensional lattice hydrodynamic traffic flow model is proposed by incorporating the optimal current difference effect of leading vehicles. Phase transitions and critical phenomenon are investigated near the critical point both analytically and numerically. Based on the configuration of vehicles, it is shown that two distinct jamming transitions occur: conventional jamming transition to the kink jam and jamming transition to the chaotic jam. It is shown that consideration of optimal current difference effect stabilizes the traffic flow and suppresses the traffic jam efficiently for all possible configurations of vehicles on a square lattice.     

Violation of finite-size scaling in three dimensions

We reexamine the range of validity of finite-size scaling in the lattice model and the field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the lattice model and the field theory in the region . The non-scaling effects in the field theory and in the lattice model differ significantly from each other. Received 5 February 1999     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

The “backward looking” effect in the lattice hydrodynamic model

The novel lattice hydrodynamic model is presented by incorporating the “backward looking” effect. The stability condition for the the model is obtained using the linear stability theory. The result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model. The Korteweg-de Vries (KdV, for short) equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by KdV soliton solution obtained from the KdV equation. The simulation result is consistent with the nonlinear analysis.     

Transition to plastic motion as a critical phenomenon and anomalous interface layer of a 2D driven vortex lattice

The dynamic transition between ordered flow and plastic flow is studied for a two-dimensional driven vortex lattice, in the presence of sharp and dense pinning centers, from numerical simulations. For this system, which does not show smectic ordering, the lattice exhibits a first order transition from a crystal to a liquid, shortly followed by the dynamical transition to plastic flow. The resistivity provides a critical order parameter for the latter, and critical exponents are determined in analogy with a percolation transition. At the boundary between a pinned region and an unpinned one, an anomalous layer is observed, where the vortices are more strongly pinned than in the bulk. Received 22 September 2001     

The Korteweg-de Vries soliton in the lattice hydrodynamic model

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.     

The phase diagram and the pathway of phase transitions for traffic flow in a circular one-lane roadway

This paper demonstrates that patient driving habits lead to homogenous congested flow while impatient driving habits lead to wide-moving jam flow in the high density region based on the numerical simulation of the intelligent driver model proposed by M.Treiber [M. Treiber, A.Hennecke, D. Helbing, Phys. Rev. E 62 (2) (2000), 1805-1824]. In a circular one lane traffic system which includes homogeneous drivers, we obtain the stable condition of homogenous flow and the phase diagram of traffic flow based on the linearization analysis. The phase diagram shows three possible pathways of phase transition along with the increase of global density: from the homogenous free flow to the homogenous congested flow directly, from the homogenous free flow to the synchronized flow then to the homogenous congested flow, or from the homogenous free flow to synchronized flow then to the wide-moving jam flow. The paper also analyzes the traffic flow including heterogenous drivers, and the results indicate that homogenous congested flow will lose its stability when the proportion of impatient drivers reaches a critical value and some new kinds of traffic flow emerge: wide-moving jam flow or a mixture of synchronized flow and wide-moving jam flow.     

Coexistence of liquid and solid phases in flowing soft-glassy materials

Magnetic-resonance-imaging rheometrical experiments show that concentrated suspensions or emulsions cannot flow steadily at a uniform rate smaller than a critical value (gamma(c)). As a result, a "liquid" region (sheared rapidly, i.e., at a rate larger than gamma(c)) and a "solid" region (static) coexist. The behavior of the fluid in the liquid region follows a simple power-law model, while the extent of the solid region increases with the degree of jamming of the material.     

Edge of chaos in a parallel shear flow

We study the transition between laminar and turbulent states in a Galerkin representation of a parallel shear flow, where a stable laminar flow and a transient turbulent flow state coexist. The regions of initial conditions where the lifetimes show strong fluctuations and a sensitive dependence on initial conditions are separated from the ones with a smooth variation of lifetimes by an object in phase space which we call the "edge of chaos." We describe techniques to identify and follow the edge, and our results indicate that the edge is a surface. For low Reynolds numbers we find that the surface coincides with the stable manifold of a periodic orbit, whereas at higher Reynolds numbers it is the stable set of a higher-dimensional chaotic object.     

Transition from homogeneous to inhomogeneous flows in a lattice-gas binary mixture of slender particles

We study the unidirectional flow of a binary mixture of biased-random walkers on a square lattice under a periodic boundary. The lattice-gas mixture consists of two types of slender particles (walkers) which have different biases (drift coefficients). When the density is higher than a critical value, a dynamical transition occurs from the homogeneous flow to the inhomogeneous flow and clogging appears. The inhomogeneous state returns to the homogeneous congested flow with further increasing density. The clogging does not appear in the unidirectional flow of the conventional lattice-gas binary mixture of single-site particles. The jamming (clogging) transition is clarified for various sizes of slender particles.     

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.     

Flow overshooting in crossing flow of lattice gas

We study the lattice gas flow of two components of biased-random walkers at a crossing under a periodic boundary. The lattice gas mixture consists of two components of particles (walkers) in which one component of particles moves north and the other component of particles moves east. The current (flow) increases with ρ_x (density of the east-bound particles) at low density and displays overshooting at an intermediate density. The flow overshooting occurs only for a certain range of ρ_y (density of the north-bound particles). Then clogging occurs and the current saturates. Furthermore, when the density is high, the current decreases with increasing density. The overshooting shown in the current-density (fundamental) diagram is due to the formation of an unstable oscillating jam just before clogging occurs. It is shown that flow overshooting does not occur in unidirectional flow through a porous medium but occurs in unidirectional flow through a group of Brownian particles.     

A New Lattice Model of Two-Lane Traffic Flow with the Consideration of the Honk Effect

In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries (KdV) equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coefficient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.     

A New Lattice Model of Two-Lane Trafc Flow with the Consideration of the Honk Efect

In this paper,a new lattice model of two-lane trafc flow with the honk efect term is proposed to study the influence of the honk efect on wide moving jams under lane changing.The linear stability condition on two-lane highway is obtained by applying the linear stability theory.The modified Korteweg-de Vries(KdV)equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described,which shows that the critical point,the coexisting curve and the neutral stability line decrease with increasing the honk efect coefcient.A wide moving jam can be conceivably described approximately in the unstable region.Numerical simulation is performed to verify the analytic results.The results show that the honk efect could suppress efectively the congested trafc patterns about wide moving jam propagation in lattice model of two-lane trafc flow.     

Commensurability effects for fermionic atoms trapped in 1D optical lattices

Fermionic atoms in two different hyperfine states confined in optical lattices show strong commensurability effects due to the interplay between the atomic density wave ordering and the lattice potential. We show that spatially separated regions of commensurable and incommensurable phases can coexist. The commensurability between the harmonic trap and the lattice sites can be used to control the amplitude of the atomic density waves in the central region of the trap.     

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani's model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink--antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.