Satoshi Yukawa

Coupled-Map Modeling of One-Dimensional Traffic Flow

We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle properly, and the maps are coupled to each other through the headway distance. By simulating the model, we obtain a plot of the flow against the concentration similar to the observed data in real traffic flows. Realistic traffic jam regions are observed in space-time trajectories.

Coupled Map Traffic Flow Simulator Based on Optimal Velocity Functions

A coupled map traffic flow model is introduced, based on optimal velocity functions. The model is simulated under open boundary conditions. Effects of noises in velocity are investigated. The average car density increases with the noise level. The high throughput flow is realized when the noise level is sufficiently large, and power law behavior appears in temporal spectra of density fluctuations at the same time. By introducing traffic bottlenecks, a hysteresis loop, which indicates the emergence of traffic jams, is observed in the headway-velocity plane. Temporal spectra of density fluctuations also obey a power law in this case, whose exponent is independent of the noise level.

Metastability in the formation of an experimental traffic jam

We show detailed data about the process of jam formation in a traffic experiment on a circuit without any bottlenecks. The experiment was carried out using a circular road on a flat ground. At the initial stage, vehicles are running homogeneously distributed on the circuit with the same velocity, but roughly 10 min later a traffic jam emerges spontaneously on the circuit. In the process of the jam formation, we found a homogeneous flow with large velocity is temporarily realized before a jam cluster appears. The instability of such a homogeneous flow is the key to understanding jam formation.

Density Fluctuations in Traffic flow

Density fluctuations in traffic current are studied by computer simulations using the deterministic coupled map lattice model on a closed single-lane circuit. By calculating the power spectral density of temporal density fluctuations at a local section, we find that it exhibits a power law, being proportional to 1/ f 1.8 where f is the frequency, in the noncongested flow phase. The distribution of the headway distance h also follows a power law, being proportional to 1/ h 3.0 . The power-law fluctuations are destroyed by the occurrence of a traffic jam.

Phase transition in traffic jam experiment on a circuit

The emergence of a traffic jam is considered to be a dynamical phase transition in a physics point of view; traffic flow becomes unstable and changes phase into a traffic jam when the car density exceeds a critical value. In order to verify this view, we have been performing a series of circuit experiments. In our previous work (2008 New J. Phys. 10 033001), we demonstrated that a traffic jam emerges even in the absence of bottlenecks at a certain high density. In this study, we performed a larger indoor circuit experiment in the Nagoya Dome in which the positions of cars were observed using a high-resolution laser scanner. Over a series of sessions at various values of density, we found that jammed flow occurred at high densities, whereas free flow was conserved at low densities. We also found indications of metastability at an intermediate density. The critical density is estimated by analyzing the fluctuations in speed and the density–flow relation. The value of this critical density is consistent with that observed on real expressways. This experiment provides strong support for physical interpretations of the emergence of traffic jams as a dynamical phase transition.

A Quantum Analogue of the Jarzynski Equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well.

Simulational study on dimensionality dependence of heat conduction

Heat conduction phenomena are studied theoretically using computer simulation. The systems are crystal with nonlinear interaction, and fluid of hard-core particles. Quasi-one-dimensional systems of the size L x × L y × L z ( L z ≫ L x , L y ) are simulated. Heat baths are put in both ends: one has a higher temperature than the other. In the case of the crystal, the interaction potential V has a fourth-order nonlinear term in addition to the harmonic term, and the Nose-Hoover method is used for the heat baths. In the case of the fluid, the stochastic boundary condition is charged, which performs the function of the heat baths. Fourier-type heat conduction is reproduced in both crystal and fluid models in a three-dimensional system, but it is not observed in lower-dimensional systems. The autocorrelation function of heat flux is also observed and long-time tails of the form ∼ t - d /2 , where d denotes the dimensionality of the system, are confirmed.

Noise Induced Congested Traffic Flow in Coupled Map Optimal Velocity Model

The optimal velocity traffic flow model is one of the car-following models which describe the behavior of cars by differential equations. In that model, each car controls its speed toward an optimal (safety) velocity, which depends only on the headway. We constructed a new car-following type simulation model for traffic flow in a coupled map form based on the optimal velocity model. We can easily simulate open road systems with the model. The emergence of weakly congested flow induced by noise is investigated. We observe the enhancement of the car density induced by noise. The strong traffic jam hardly occurs in open road systems. We discuss the problems of unrealistic acceleration in the optimal velocity model and the possibility of spontaneous formation of strong traffic jams.

Power-Law Fluctuation in Expressway Traffic Flow: Detrended Fluctuation Analysis

The temporal behavior of expressway traffic flow is a complex mixture of various time scales. The fundamental response time of drivers is on the order of 1 s, and the periodic appearances of traffi...

Analysis of congested flow at the upper stream of a tunnel

We analyze the traffic data observed at the upper stream of a tunnel (Nihonzaka Tunnel) on Tomei Expressway linking Nagoya with Tokyo. We observe the fundamental properties of the traffic flow including temporal sequences and statistical properties. We also observe the reverse-lane usage in which the flow on the fast lane exceeds the one on the slow lane.