Ihor Lubashevsky

Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model.

The present paper proposes an interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerners hypothesis about the existence of a multitude of metastable states in the fundamental diagram. Using single-vehicle data collected at the German highway A1, temporal velocity patterns have been analyzed to show a collection of certain fragments with approximately constant velocities and sharp jumps between them. The particular velocity values in these fragments vary in a wide range. In contrast, the flow rate is more or less constant because its fluctuations are mainly due to the discreteness of traffic flow. Subsequently, we develop a model for synchronized traffic that can explain these characteristics. Following previous work [I. A. Lubashevsky and R. Mahnke, Phys. Rev. E 62, 6082 (2000)] the vehicle flow is specified by car density, mean velocity, and additional order parameters h and a that are due to the many-particle effects of the vehicle interaction. The parameter h describes the multilane correlations in the vehicle motion. Together with the car density it determines directly the mean velocity. The parameter a, in contrast, controls the evolution of h only. The model assumes that a fluctuates randomly around the value corresponding to the car configuration optimal for lane changing. When it deviates from this value the lane change is depressed for all cars forming a local cluster. Since exactly the overtaking maneuvers of these cars cause the order parameter a to vary, the evolution of the car arrangement becomes frozen for a certain time. In other words, the evolution equations form certain dynamical traps responsible for the long-time correlations in the synchronized mode.

Probabilistic Description of Traffic Breakdowns

We analyze the characteristic features of traffic breakdown. To describe this phenomenon we apply the probabilistic model regarding the jam emergence as the formation of a large car cluster on a highway. In these terms, the breakdown occurs through the formation of a certain critical nucleus in the metastable vehicle flow, which enables us to confine ourselves to one cluster model. We assume that, first, the growth of the car cluster is governed by attachment of cars to the cluster whose rate is mainly determined by the mean headway distance between the car in the vehicle flow and, maybe, also by the headway distance in the cluster. Second, the cluster dissolution is determined by the car escape from the cluster whose rate depends on the cluster size directly. The latter is justified using the available experimental data for the correlation properties of the synchronized mode. We write the appropriate master equation converted then into the Fokker-Planck equation for the cluster distribution function and analyze the formation of the critical car cluster due to the climb over a certain potential barrier. The further cluster growth irreversibly causes jam formation. Numerical estimates of the obtained characteristics and the experimental data of the traffic breakdown are compared. In particular, we draw a conclusion that the characteristic intrinsic time scale of the breakdown phenomenon should be about 1 min and explain the case why the traffic volume interval inside which traffic breakdown is observed is sufficiently wide.

Noised induced phase transition in an oscillatory system with dynamical traps

Abstract.A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular “forces” are depressed substantially. By way of an example, a simple oscillatory system

Long-lived states of oscillator chains with dynamical traps

\{x,v = \dot{x}\}

Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics

with additive white noise is considered and its dynamics is analyzed numerically. The dynamical trap region is assumed to be located near the x-axis where the “velocity” v of the system becomes sufficiently low. The meaning of this assumption is discussed. The observed phase transition is caused by the asymmetry in the residence time distribution in the vicinity of zero value “velocity”. This asymmetry is due to a cooperative effect of the random Langevin “force” in the trap region and the regular “force” not changing the direction of action when crossing the trap region.

Continuous-time multidimensional Markovian description of Lévy walks

Abstract.An oscillator chain with dynamical traps and additive white noise is considered. Its dynamics are studied numerically. New type nonequilibrium phase transitions are shown to arise in the case when the trap effect is pronounced. Locally they manifest themselves in distortion of the symmetry of particle arrangement. Depending on the system parameters, the particle arrangement is characterized by the corresponding distributions taking either a bimodal form, or a twoscale one, or a unimodal onescale form that, however, deviates substantially from the Gaussian distribution. The particle velocities also exhibit a number of anomalies, in particular, their distribution can be extremely wide or take a quasi-cusp form. A large number of various cooperative structures and superstructures are found in the visualized time patterns. In a certain sense their evolution is independent of the individual particle dynamics, enabling us to regard them as dynamical phases.

Boundary-reaction-diffusion model for oscillatory zoning in binary crystals grown from solution

A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equation governing the system dynamics is obtained. The agents are considered to interact with one another implicitly via the reward of one agent depending on the choice of the other agents. The pairwise interaction model is adopted to describe this effect. As a specific example of systems with non-transitive interactions, a two agent and three agent systems of the rock-paper-scissors type are analyzed in detail, including the stability analysis and numerical simulation. Scale-free memory is demonstrated to cause complex dynamics of the systems at hand. In particular, it is shown that there can be simultaneously two modes of the system instability undergoing subcritical and supercritical bifurcation, with the latter one exhibiting anomalous oscillations with the amplitude and period growing with time. Besides, the instability onset via this supercritical mode may be regarded as “altruism self-organization”. For the three agent system the instability dynamics is found to be rather irregular and can be composed of alternate fragments of oscillations different in their properties.

Order Parameter as an Additional State Variable of Unstable Traffic Flow

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to treat Lévy flights or Lévy random walks in inhomogeneous media or systems with boundaries in the future. The proposed model assumes the velocity of a wandering particle to be affected by a linear friction and a nonlinear Langevin force whose intensity is proportional to the magnitude of the velocity for its large values. Based on the singular perturbation technique, the corresponding Fokker-Planck equation is analyzed and the relationship between the system parameters and the Lévy exponent is found. Following actually the previous paper we demonstrate also that anomalously long displacements of the wandering particle are caused by extremely large fluctuations in the particle velocity whose duration is determined by the system parameters rather than the duration of the observation interval. In this way we overcome the problem of ascribing to Lévy random-walk non-Markov properties.

Physics of systems with motivation as an interdisciplinary field of science

Oscillatory Zoning (OZ) is a phenomenon exhibited by many geologically formed crystals. It is characterized by quasiperiodic oscillations in the composition of a solid solution, caused by self-organization. We present a model for OZ. The growth mechanism applied includes species diffusion through the solution bulk, particle adsorption, surface diffusion, and subsequently desorption or incorporation into the crystal. This mechanism, in particular, can provide the synchronization effects necessary to reproduce the layered structure of experimentally obtained crystals, lacking in other models. We conduct a linear stability analysis combined with numerical simulations. Our results reproduce the experimental findings with respect to the patterns formed and a critical supersaturation necessary for OZ to occur.

Complex Fundamental Diagram of Traffic Flow in the Deep Lefortovo Tunnel (Moscow)

We discuss a phenomenological approach to the description of unstable vehicle motion on multilane highways that could explain in a simple way such observed self-organizing phenomena as the sequence of the phase transitions“free flow → synchronized motion → jam” and the hysteresis in them. We introduce a new variable called order parameter that accounts for possible correlations in the vehicle motion at different lanes. So, it is principally due to “many-body” effects in the car interaction in contrast to such variables as the mean car density and velocity being actually the zeroth and first moments of the “one-particle” distribution function. Therefore, we regard the order parameter as an additional independent state variable of traffic flow and formulate the corresponding evolution equation governing the lane changing rate. In this context we analyze the instability of homogeneous traffic flow manifesting itself in both of these phase transitions and endowing them with the hysteresis. Besides, the jam state is characterized by the vehicle flows at different lanes being independent of one another.